Linearity

Problem 301

Line 1: $y=\frac{x}{2} x$
Line 2: $-3 x+2 y=0$
This system of equations is: consistent dependent consistent independent inconsistent This means the system has: a unique solution Solution: $\square$ $\square$ infinitely many solutions no solution
Line 1: $y=x$
Line 2: $y=-\frac{1}{2} x-3$
This system of equations is: consistent dependent consistent independent inconsistent This means the system has: a unique solution Solution: $\square$ $\square$ infinitely many solutions no solution
Line 1: $y=1$
Line 2: $y=-4$
This system of equations is: consistent dependent consistent independent inconsistent This means the system has: a unique solution Solution: $\square$ $\square$ infinitely many solutions no solution

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Problem 302

Задача 1. Коллинеарны ли векторы $\vec{c}$ и $\vec{d}$ , построенные по векторам $\vec{a}$ и $\vec{b}$ ? \begin{tabular}{|c|c|c|c|c|} \hline № & $\vec{a}$ & $\vec{b}$ & $\vec{c}$ & $\vec{d}$ \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|l|} \hline 9 & $(2,4,-6)$ & $(3,6,-2)$ & $2 \vec{a}-3 \vec{b}$ & $6 b-5 \vec{a}$ \\ \hline \end{tabular}

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Problem 303

Line 1: $y=-3 x+4$
Line 2: $3 x+y=4$
This system of equations is: consistent independent consistent dependent inconsistent This means the system has: a unique solution Solution: $\square$ $\square$ infinitely many solutions no solution
Line 1: $y=3 x-3$
Line 2: $y=3 x+2$
This system of equations is: consistent independent consistent dependent inconsistent This means the system has: a unique solution Solution: $\square$ $\square$ infinitely many solutions no solution
Line 1: $y=-2 x+1$ Line 2: $y=-\frac{1}{2} x+1$
This system of equations is: consistent independent consistent dependent inconsistent This means the system has: a unique solution Solution: $\square$ ( $\square$ $\square$ infinitely many solutions no solution

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Problem 304

100\%
After the community clean-up, the ecology club collected all the empty drink containers. There were 40 more $5 申$ deposit containers than 10 \& deposit containers. If the club received $\$ 24.80$ from the recycling center, how many $5 \notin$ deposit containers did they have? A. 112 B. 125 C. 152 D. 165

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Problem 305

Grephy and Fynetion Application problem with a inear function: Finding a coordinate given th... Martavius Espaniol
Suppose that the weight (in pounds) of an airplane is a linear function of the total amount of fuel (in gallons) in its tank. When graphed, the function gives a line with a slope of 6.1. See the figure below.
With 54 gallons of fuel in its tank, the airplane has a weight of 2429.4 pounds. What is the weight of the plane with 25 gallons of fuel in its tank? $\square$ Explanation Check Q 2024 MeGraw Hill LLC. All Rights Reserved. Terms of Use I Privacy Center Accessibility

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Problem 306

A grocery store sells sliced pastrami by weight. The relationship between the amount of pastrami in pounds, $x$ , and the total cost in dollars of the sliced pastrami, $y$ , is represented by the graph below.
Two points, C and A , are labeled. Which statement about the graph is true?
Answer Point A means that the unit rate is $\$ 6.00$ per pound Point A means that the unit rate is 6 pounds per dollar Point C means that the unit rate is 6 pounds per dollar Point $C$ means that the unit rate is $\$ 36.00$ per pound

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Problem 307

Watch Video Show Examples
A small town has two local high schools. High School A currently has 300 students and is projected to grow by 50 students each year. High School B currently has 450 students and is projected to grow by 25 students each year. Let $A$ represent the number of students in High School $A$ in $t$ years, and let $B$ represent the number of students in High School B after $t$ years. Graph each function and determine which high school is projected to have more students in 8 years.

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Problem 308

A company orders boxed lunches from a deli, which all cost the same price. The relationship between the number of boxed lunches ordered, $x$ , and the total cost in dollars of the lunches, $y$ , is represented by the graph below.
What does the ordered pair ( 3,36 ) indicate?
Answer 3 lunches that cost a total of $\$ 36.00$ 3 tunches that cost $\$ 36.00$ each 36 lunches that cost $\$ 3.00$ each 36 lunches that cost a total of $\$ 3.00$

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Problem 309

$9-2 x=35$

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Problem 310

Find the intercepts of the equation. $x+2 y=6$
X-intercept (Blank 1, Blank 2) y-intercept (Blank 3, Blank 4)

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Problem 311

$-5 x-10=10$

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Problem 312

$-8=\frac{x+11}{-2}$

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Problem 313

$-12 x-17=-89$

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Problem 314

$5-x=12$

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Problem 315

8. A car travels 252 miles in 4 hours. Assuming that the distance the car travels varies directly with the time, how far will the car travel in 6 hours?

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Problem 316

$-7+13 x+2 x+8$

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Problem 317

Translate to a system of equations and solve the system.
Three times a number plus three times a second number is fifteen. Four times the first plus twice the second number is fourteen. Find the numbers.

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Problem 318

$4 x-6 \geq 6 x-20$

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Problem 319

$3 b-39=-78$

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Problem 320

$6 x+2(x+4)$

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Problem 321

$-\frac{1}{2}=-\frac{5}{6}+\frac{1}{4} a$

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Problem 322

Oliver earns $\$ 12$ per hour doing extra lawn chores for his neighbor. They also pay him $\$ 40$ each month for cutting the grass. Which equation could be used to graph Oliver's earnings for the month? $y=2 x+12$ $y=56 x$ $y=40 x+12$ $y=12 x+40$

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Problem 323

$\frac{1}{3}=\frac{1}{6} x+\frac{3}{4}$

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Problem 324

$14 x-9=10 x+3$

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Problem 325

Question Show Examples
A group of friends wants to go to the amusement park. They have no more than $\$ 425$ to spend on parking and admission. Parking is $\$ 14.75$ , and tickets cost $\$ 18.75$ per person, including tax. Which inequality can be used to determine $x$ , the maximum number of people who can go to the amusement park?
Answer $425 \leq 18.75(x+14.75)$ Submit Answer $425 \geq 14.75+18.75 x$ $425 \leq 14.75+18.75 x$ $425 \geq 18.75(x+14.75)$

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Problem 326

In this pyramid, the value of the top brick is found by adding the values of the two bottom bricks.
What expression should replace the question mark? Simplify your answer fully.

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Problem 327

$4x - 8 = 4x +$

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Problem 328

Determine whether the solution of each equation below is the same as the solution of $2 b+5 b=28$ . Select Yes or No for each equation. $-\frac{1}{4} b=-1$ Yes No $12 b+3-3 b+5=44$ Yes No $5 b+4=3 b-4$ Yes No $-2(-3 b+4.8)=14.4$ Yes No

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Problem 329

JAYDEN
Bode and Grace solve the equation $1.2=6(4-0.4 g)-4.8$ for $g$ in different ways. Bode begins solving by dividing both sides of the equation by 6 and then adding 4.8 to both sides. Grace begins solving by adding 4.8 to both sides of the equation and then dividing both sides by 6 . Whose strategy is best? Why? Grace's strategy is best because adding 4.8 to both sides of the equation means that the left side will simplify to the whole number 5 . Grace's strategy is best because first adding 4.8 then dividing by 6 will solve the equation in the fewest number of steps. Bode's strategy is best because adding 4.8 after dividing by 6 will eliminate a term on the right side of the equation. Bode's strategy is best because first dividing by 6 then adding 4.8 will solve the equation in the fewest number of steps.

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Problem 330

Given $g(x)=-5 x+1$ , find $g(3)$ .
Answer Attempt 1 out of 2

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Problem 331

Describe how the graphs of $f(x)$ and $g(x)$ are related.
13. $f(x)=x$ and $g(x)=x+6$
14. $f(x)=x^{2}$ and $g(x)=\frac{3}{4} x^{2}$

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Problem 332

math/algebra-1/write-a-linear-inequality-from-a-graph
This is the graph of a linear inequality. Write the inequality in slope-intercept form.
Write your answer with y first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form. $\square$

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Problem 333

Learn with an example Watch a video
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. A company that teaches self-improvement seminars is holding one of its seminars in Greenwood. The company pays a flat fee of $\$ 95$ to rent a facility in which to hold each session. Additionally, for every attendee who registers, the company must spend $\$ 11$ to purchase books and supplies. Each attendee will pay $\$ 12$ for the seminar. Once a certain number of attendee register, the company will be breaking even. How many attendees will that take? What will be the company's total expenses and revenues?
Once $\square$ attendees have registered, the company's expenses and receipts will both total \\square$ Submit

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Problem 334

i-Ready JAYDEN
Which statement describes the solution to the equation $a+5(2 a-1)+3=11 a-2$ ? The equation has no solution. The equation has exactly one solution, $a=\frac{2}{11}$ . The equation has exactly one solution, $a=-4$ . The equation has infinitely many solutions.

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Problem 335

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
Oscar and Roger started out at their houses and are biking towards each other. Oscar started out first, and has already gone 4 kilometers. He bikes at a constant speed of 4 kilometers per hour. Roger just left, and rides at 6 kilometers per hour. When the boys meet halfway between their houses, they will continue to the park together. How far will each boy have ridden? How long will that take?
Oscar and Roger will have each biked $\square$ kilometers in $\square$ hours.

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Problem 336

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
A daycare center in Princeton currently has 9 assistant caregivers and 7 senior caregivers. Since demand is high, the owner is going to be hiring 2 assistant caregivers per month and 3 senior caregivers per month. Her goal is to have a larger staff, including an equal number of assistant caregivers and senior caregivers. How long will that take? How many of each type will there be?
After $\square$ months, there will be $\square$ of each type of caregiver.
Submit

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Problem 337

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
When Dave does 8 push-ups and 5 sit-ups, it takes a total of 23 seconds. In comparison, he needs 68 seconds to do 20 push-ups and 16 sit-ups. How long does it take Dave to do each kind of exercise?
It takes Dave $\square$ seconds to do a push-up and $\square$ seconds to do a sit-up. Submit

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Problem 338

3. At the end of yesterday's soccer game between Team Why and Team Zed, Team Why had scored 3 goals and Team Zed had scored 2 goals. At half-time of the game, Team Why had scored $y$ goals and Team Zed had scored $z$ goals. If $y \geq 0$ and $z \geq 0$ , how many possibilities are there for the ordered pair of integers $(y, z)$ ? (In soccer, each team's score is always a non-negative integer that never decreases as the game proceeds.)

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Problem 339

What system of equations does the graph show?
Write the equations in slope-intercept form. Simplify any fractions. $y=$ $\square$

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Problem 340

You are choosing between two differènt cell phone plans. The first plan charges a rate of 22 cents per minute. The second plan charges a monthly fee of $\$ 29.95$ plus 10 cents per minute. How many minutes would you have to use in a month in order for the second plan to be preferable? Round up to the nearest whole minute.

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Problem 341

Aaliyah went into a grocery store and bought 5 peaches and 6 mangos, costing a total of $\$ 17.75$ . Tristan went into the same grocery store and bought 2 peaches and 3 mangos, costing a total of \$8. Write a system of equations that could be used to determine the price of each peach and the price of each mango. Define the variables that yoù use to write the system.
Answer Attempt 1 out of 2
Let $\square$ $\square$
Let $\square$ $\square$ System of Equations: $\square$ $\square$

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Problem 342

Write the equation of this line in slope-intercept form.

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Problem 343

Simplify by clearing parentheses and combining like terms. $4(y+7)-28=$

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Problem 344

1-2 Solve each equation or formula for the variable indicated.
8. $u=v w+z$ , for $v$ (9) $x=b-c d$ , for $c$
10. $f g-9 h=10 j$ , for $g$
11. $10 m-p=-n$ , for $m$

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Problem 345

Solve the system by the addition method. $\begin{array}{l} x+y=4 \\ x-y=-2 \end{array}$

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Problem 346

7. (MIP Identify Structure Determine the rate of change for a horizontal line. Explain why this rate of change makes sense.

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Problem 347

Solve the given system of equations $\begin{array}{l} 5 x+2 y-5 z=-6 \\ 2 x-4 y+2 z=-4 \\ 4 x-5 y+4 z=-17 \end{array}$

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Problem 348

near function in which the rate of change 3 and the initial value is -10 . You wrote the quation $y=-3 x+(-10)$ to represent the nction. Your classmate wrote $y=-3 x-1$ ho is correct? Justify your response.

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Problem 349

Solve the given system of equations. $\begin{array}{l} 3 x+2 y-3 z=-13 \\ 2 x-4 y+2 z=-14 \\ 4 x-5 y+4 z=-16 \end{array}$
Select the correct choice below and fill in any answer boxes within your choice. A. There is one solution. The solution set is $\{(\square, \square, \square)\}$ . (Simplify your answers.) B. There are infinitely many solutions. C. There is no solution.

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Problem 350

A roller skating rink charges a skate rental fee and an hourly rate to skate. The total cost to skate for 2 hours is $\$ 9.50$ and for 5 hours is $\$ 18.50$ . Assume the relationship is linear. Find and interpret the rate of change and initial value. Then write the equation of the function in the form $y=m x+b$ where $x$ represents the number of hours and $y$ represents the total cost. (Example 3)

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Problem 351

Taryn conducted a science experiment on saturation. She added sugar to a sugar-water solution at different intervals. The graph shows how much sugar was in the solution at different times.
Which equation represents Taryn's situation, where $x$ is the number of minutes and $y$ is the tablespoons of sugar? $y=x+1$ $y=2 x+1$ $y=x$ $y=\frac{1}{2} x+1$

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Problem 352

Practice Go Online (3. A cleaning service charges an initial fee plus an hourly rate. The total cost for different numbers of hours, including the initial fee, is shown on the graph. Find and interpret the rate of change and initial value. Then write the equation of the function in the form $y=m x+b$ . (Example 1) $y=28 x+20$

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Problem 353

Complete the process of solving the equation. Fill in the missing term on each line. Simplify any fractions. \begin{tabular}{|l|l|} \hline $6 b+1=7$ & \\ $6 b$ & $=\square$ \\ $\dot{I}$ & $=\square$ \\ Subtract 1 from both sides \\ & Divide both sides by 6 \end{tabular}

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Problem 354

What value of $r$ is a solution to this equation? $\begin{array}{l} 7 r+19=89 \\ r=10 \quad r=12 \end{array}$ Submit

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Problem 355

Solve the system by the substitution method $\begin{aligned} x y & =30 \\ 3 x-y & =-9 \end{aligned}$

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Problem 356

What value of $r$ is a solution to this equation? $10+\frac{r}{3}=14$ $r=-12$ $r=12$

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Problem 357

Solve for $c$ . $2 c+2=6$ $c=$ $\square$ Submit

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Problem 358

Solve for $y$ . $\begin{array}{l} 3 y-14=1 \\ y=\square \end{array}$ Submit

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Problem 359

Determine if $(4,-9,4)$ is a solution of the system. $\begin{aligned} x+y+z & =-1 \\ x-2 y-z & =18 \\ 2 x-y-2 z & =9 \end{aligned}$
Choose the correct answer below. The ordered triple is a solution to the system. The ordered triple is not a solution to the system.

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Problem 360

Use Gauss elimination $\left\{\begin{array}{l} x+2 y-z=-3 \\ 3 x-y+2 z=8 \\ 2 x+y-3 z=-5 \end{array}\right.$

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Problem 361

Fill in the table

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Problem 362

16) $1=\frac{x+8}{22}$

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Problem 363

15) $-6=-8+\frac{p}{4}$

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Problem 364

13) $1=\frac{x+6}{26}$

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Problem 365

Determine whether the function given in the table is linear, exponential, or neither. If the function is linear, find a linear function that models the data; if it is exponential, find an exponential function that models the data. \begin{tabular}{|c|c|} \hline $\mathbf{x}$ & $\mathbf{f}(\mathbf{x})$ \\ \hline-1 & 1 \\ \hline 0 & 6 \\ \hline 1 & 11 \\ \hline 2 & 16 \\ \hline 3 & 21 \\ \hline \end{tabular}
Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. The function is exponential. An exponential function that models the data is $f(x)=$ $\square$ $\square$ . (Simplify your answer.) B. The function is linear. A linear function that models the data is $f(x)=5 x+4$ . $\square$ (Simplify your answer.).

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Problem 366

Use the graph to solve the compound inequality $-3 \leq y_{1} \leq 2$ . Write your answer in interval notation

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Problem 367

$-44=-4-2 b$

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Problem 368

$\text{Let } x \text{ be a number that is more than 10. Write and solve an equation to find the value of } x.$
$x = 10 + a$
$\text{where } a > 0$
$\text{For example, if } a = 5, \text{ then } x = 10 + 5 = 15.$
$\text{Thus, } x \text{ can be any number greater than 10, such as 11, 12, 13, \ldots}$
$\text{The solution is } x > 10.$

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Problem 369

Read the description of a proportional relationship.
Zoe is thrilled to be cast as Juliet in her school's production of Romeo and Julier, but she has lot of lines to memorize! There is a proportional relationship between the number of days Zoe has been memorizing her lines, $x$ , and the total number of lines she has memorized, $y$ .
The equation that models this relationship is $y=5 x$ . How many lines will Zoe have memorized after 3 days? Write your answer as a whole number or decimal. $\qquad$ lines

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Problem 370

In a flash of sheer brilliance, Kenneth invents a time machinel The machine uses a small nuclear reactor to generate the electricity it needs to travel back in time. There is a proportional relationship between how many years Kenneth wants to travel back in time, $x$ , and how much electricity (in megawatts) his time machine needs, $y$ .
The equation that models this relationship is $y=2 x$ . How far back in time can Kenneth's machine travel using 12 megawatts of electricity? Write your answer as a whole number or decimal. $\square$ years

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Problem 371

Read the description of a proportional relationship.
In a flash of sheer brilliance, Kenneth invents a time machine! The machine uses a small nuclear reactor to generate the electricity it needs to travel back in time. There is a proportional relationship between how many years Kenneth wants to travel back in time, $x$ , and how much electricity (in megawatts) his time machine needs, $y$ .
The equation that models this relationship is $y=2 x$ . How much electricity does Kenneth's time machine need to travel back 8 years? Write your answer as a whole number or decimal. $\square$ megawatts

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Problem 372

Read the description of a proportional relationship.
Every day after school, Jeremiah and his sister Grace play their favorite video game, Wizarding Legends. The goal of the game is to earn power points by defeating goblins. There is a proportional relationship between the number of goblins defeated, $x$ , and the number of power points earned, $y$ .
Today, Jeremiah earns 42 power points defeating 14 goblins. Write the equation for the relationship between $x$ and $y$ . $y=$ $\square$

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Problem 373

16. $3 n-n+7=25$

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Problem 374

(3) A marine biologist is studying how fast a dotphin swims. The delphin swims at a constant speed for 5 seconds. The distance it swims is 55 meters. The relationship between time and distance for the trip is proportiona? a. Make a graph showing the change in the dolphin's distance over time. How far does the dolphin swim in 1 second? Show your work.

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Problem 375

$-3 x+2=-10 x+30$
Simplify your answer as much as possible. $x=$

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Problem 376

Solve for $y$ . $5 y+9=17 y-4 y+81$
Simplify your answer as much as possible.

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Problem 377

Solve the inequality for $w$ . $17<w+6$
Simplify your answer as much as possible.

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Problem 378

rind the domain and tne tarlys
Write your answers as inequalities, using $x$ or $y$ as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer. (a) domain: $\square$ (b) range: $\square$ Empty All set reals

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Problem 379

A line has a slope of $-\frac{7}{9}$ and includes the points $(3, w)$ and $(-6,-1)$ . What is the value of $w$ ? $w=$

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Problem 380

A line has a slope of $-\frac{3}{2}$ and includes the points $(5,0)$ and $(3, v)$ . What is the value of $v$ ? $v=$

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Problem 381

Factor the algebraic expression. $\begin{array}{r} 40 \mathrm{a}+35 \\ 40 \mathrm{a}+35= \end{array}$ $\square$ (Factor completely.)

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Problem 382

Id the range and the domain of the function shown.
Write your answers as inequalities, using $x$ or $y$ as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer. (a) range: $\square$ (b) domain: $\square$ Empty All set reals Explanation Check

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Problem 383

Solve the equation: $-6 c+21=81$

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Problem 384

$-\frac{2}{3}(x+12)+\frac{2}{3} x=-\frac{5}{4} x+2$

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Problem 385

Simplify the expression: Video $6 h+4 h+6 h-4 h+3 h$ $\square$ Submit

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Problem 386

Jose wants to spend no more than $\$ 30$ on apples and grapes for the month. Apples cost $\$ 1.50$ per pound, and grapes cost $\$ 2$ per pound. Jose also wants his monthly caloric intake from apples and grapes to be greater than 2,000 calories. He determines that 1 pound of apples has 200 calories and 1 pound of grapes has 300 calories. Let a represent the number of pounds of apples and $g$ represent the number of pounds of grapes.
Which system of inequalities can be used to determine the number of pounds of apples and the number of pounds of grapes that Jose can buy for a month? (a) $\left\{\begin{array}{l}1.5 a+2 g \geq 30 \\ 200 a+300 g>2,000\end{array}\right.$ (b) $\left\{\begin{array}{l}1.5 a+2 g \leq 30 \\ 200 a+300 g>2,000\end{array}\right.$ (C) $\left\{\begin{array}{l}2 a+1.5 g \leq 30 \\ 300 a+200 g>2,000\end{array}\right.$ (d) $\left\{\begin{array}{l}2 a+1.5 g \geq 30 \\ 200 a+300 g<2,000\end{array}\right.$

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Problem 387

$\begin{array}{r} 16 a+14=14 \\ 16 a=0 \end{array}$ $a=$ $\square$ Divide both sides by 16

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Problem 388

2) $(-2,0) ; \begin{array}{l}8 x-3 y=-16 \\ 50=-9 x-2 y\end{array}$

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Problem 389

State whether the growth (or decay) is linear or exponential, and answer the associated question. The value of a house is increasing by $\$ 1500$ per year. If it is worth $\$ 170,000$ today, what will it be worth in three years?
Is the increase in value linear or exponential? linear exponential
What will the house be worth in three years? $\$$ $\square$

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Problem 390

$9 x=19$ and $y=38$

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Problem 391

$(7,-4) ; \begin{array}{l}9 b+4 a=-8 \\ 6 a+5 b-42=0\end{array}$

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Problem 392

Part 2 of 2
Four glasses of milk and 3 snack bars have a total of 81 carbohydrates (carbs), and 3 glasses of milk and 4 snack bars have a total of 80 carbs. Determine how many carbs are in one glass of milk and in one snack bar.
There are $\square$ carbs in one glass of milk.
There are $\square$ carbs in in one snack bar.

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Problem 393

B) Check whether $(6,9)$ is a solution of the systems of linear equations. 5) $s+7 t=69$ $6 t+4 s=78$ 6) $\begin{array}{l} -2 p+5 q=34 \\ -7 q=-61-8 p \end{array}$ C) Write a system of linear equations that has the solution $(4,3)$ .

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Problem 394

Find the domain and the range of the function shown
Write your answers as inequalities, using $x$ or $y$ as ap Or, you may instead click on "Empty set" or "All reals (a) domain: $\square$ (b) range: $\square$ Empty set All reals

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Problem 395

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution. $\begin{aligned} 5 x+y & =-3 \\ -5 x-y & =3 \end{aligned}$
Answer One Solution No Solutions Submit Answer Infinitely Many Solutions

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Problem 396

Use the Read-Draw-Write process to solve the problem.
2. Shen and Liz set up chairs in a classroom. Liz makes 6 rows of 4 chairs. Shen says there are 2 fewer chairs than they need.
How many chairs do they need?

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Problem 397

To grow his ranch, a rancher is purchasing some bulls, which cost $\$ 5,100$ apiece, and some cows, which cost $\$ 1,000$ apiece. He doesn't want to spend more than $\$ 21,000$ at this time.
Write the inequality in standard form that describes this situation. Use the given numbers and the following variables. $x=$ the number of bulls $y=$ the number of cows

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Problem 398

(就) Function $A$ and Function $B$ are linear functions.
Function A
Function B \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-10 & -5 \\ \hline 5 & -2 \\ \hline 10 & -1 \\ \hline \end{tabular}
Which statement is true?
The $y$ -value of Function A when $x=-5$ is greater than the $y$ -value of Function $B$ when $x=-5$ .
The $y$ -value of Function A when $x=-5$ is less than the $y$ -value of Function B when $x=-5$ .

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Problem 399

Write a linear function for the data in the table. \begin{tabular}{|c|c|c|c|c|c|} \hline $\mathbf{x}$ & 0 & 1 & 2 & 3 & 4 \\ \hline $\mathbf{y}$ & 1 & -0.5 & -2 & -3.5 & -5 \\ \hline \end{tabular}
The linear function for the data in the table is $\square$

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Problem 400

Graph the equation $y=-10 x$ on the coordinate plane.

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1 2 3 4 5 6 7 ...76

Linearity

Problem 301

Problem 302

Problem 303

Problem 304

Problem 305

Problem 306

Problem 307

Problem 308

Problem 309

9−2x=359-2 x=359−2x=35

Problem 310

Find the intercepts of the equation. x+2y=6x+2 y=6x+2y=6X-intercept (Blank 1, Blank 2) y-intercept (Blank 3, Blank 4)

Problem 311

−5x−10=10-5 x-10=10−5x−10=10

Problem 312

−8=x+11−2-8=\frac{x+11}{-2}−8=−2x+11​

Problem 313

−12x−17=−89-12 x-17=-89−12x−17=−89

Problem 314

5−x=125-x=125−x=12

Problem 315

8. A car travels 252 miles in 4 hours. Assuming that the distance the car travels varies directly with the time, how far will the car travel in 6 hours?

Problem 316

−7+13x+2x+8-7+13 x+2 x+8−7+13x+2x+8

Problem 317

Translate to a system of equations and solve the system.Three times a number plus three times a second number is fifteen. Four times the first plus twice the second number is fourteen. Find the numbers.

Problem 318

4x−6≥6x−204 x-6 \geq 6 x-204x−6≥6x−20

Problem 319

3b−39=−783 b-39=-783b−39=−78

Problem 320

6x+2(x+4)6 x+2(x+4)6x+2(x+4)

Problem 321

−12=−56+14a-\frac{1}{2}=-\frac{5}{6}+\frac{1}{4} a−21​=−65​+41​a

Problem 322

Problem 323

13=16x+34\frac{1}{3}=\frac{1}{6} x+\frac{3}{4}31​=61​x+43​

Problem 324

14x−9=10x+314 x-9=10 x+314x−9=10x+3

Problem 325

Problem 326

In this pyramid, the value of the top brick is found by adding the values of the two bottom bricks.What expression should replace the question mark? Simplify your answer fully.

Problem 327

4x−8=4x+4x - 8 = 4x +4x−8=4x+

Problem 328

Problem 329

Problem 330

Given g(x)=−5x+1g(x)=-5 x+1g(x)=−5x+1, find g(3)g(3)g(3).Answer Attempt 1 out of 2

Problem 331

Describe how the graphs of f(x)f(x)f(x) and g(x)g(x)g(x) are related.13. f(x)=xf(x)=xf(x)=x and g(x)=x+6g(x)=x+6g(x)=x+614. f(x)=x2f(x)=x^{2}f(x)=x2 and g(x)=34x2g(x)=\frac{3}{4} x^{2}g(x)=43​x2

Problem 332

math/algebra-1/write-a-linear-inequality-from-a-graphThis is the graph of a linear inequality. Write the inequality in slope-intercept form.Write your answer with y first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form. □\square□

Problem 333

Problem 334

Problem 335

Problem 336

Problem 337

Problem 338

Problem 339

What system of equations does the graph show?Write the equations in slope-intercept form. Simplify any fractions. y=y=y= □\square□

Problem 340

Problem 341

Problem 342

Write the equation of this line in slope-intercept form.

Problem 343

Simplify by clearing parentheses and combining like terms. 4(y+7)−28=4(y+7)-28=4(y+7)−28=

Problem 344

1-2 Solve each equation or formula for the variable indicated.8. u=vw+zu=v w+zu=vw+z, for vvv (9) x=b−cdx=b-c dx=b−cd, for ccc10. fg−9h=10jf g-9 h=10 jfg−9h=10j, for ggg11. 10m−p=−n10 m-p=-n10m−p=−n, for mmm

Problem 345

Solve the system by the addition method. x+y=4x−y=−2\begin{array}{l} x+y=4 \\ x-y=-2 \end{array}x+y=4x−y=−2​

Problem 346

7. (MIP Identify Structure Determine the rate of change for a horizontal line. Explain why this rate of change makes sense.

Problem 347

Solve the given system of equations 5x+2y−5z=−62x−4y+2z=−44x−5y+4z=−17\begin{array}{l} 5 x+2 y-5 z=-6 \\ 2 x-4 y+2 z=-4 \\ 4 x-5 y+4 z=-17 \end{array}5x+2y−5z=−62x−4y+2z=−44x−5y+4z=−17​

Problem 348

near function in which the rate of change 3 and the initial value is -10 . You wrote the quation y=−3x+(−10)y=-3 x+(-10)y=−3x+(−10) to represent the nction. Your classmate wrote y=−3x−1y=-3 x-1y=−3x−1 ho is correct? Justify your response.

Problem 349

Problem 350

Problem 351

$9-2 x=35$

Find the intercepts of the equation. $x+2 y=6$
X-intercept (Blank 1, Blank 2) y-intercept (Blank 3, Blank 4)

$-5 x-10=10$

$-8=\frac{x+11}{-2}$

$-12 x-17=-89$

$5-x=12$

$-7+13 x+2 x+8$

Translate to a system of equations and solve the system.
Three times a number plus three times a second number is fifteen. Four times the first plus twice the second number is fourteen. Find the numbers.

$4 x-6 \geq 6 x-20$

$3 b-39=-78$

$6 x+2(x+4)$

$-\frac{1}{2}=-\frac{5}{6}+\frac{1}{4} a$

$\frac{1}{3}=\frac{1}{6} x+\frac{3}{4}$

$14 x-9=10 x+3$

In this pyramid, the value of the top brick is found by adding the values of the two bottom bricks.
What expression should replace the question mark? Simplify your answer fully.

$4x - 8 = 4x +$

Given $g(x)=-5 x+1$ , find $g(3)$ .
Answer Attempt 1 out of 2

Describe how the graphs of $f(x)$ and $g(x)$ are related.
13. $f(x)=x$ and $g(x)=x+6$
14. $f(x)=x^{2}$ and $g(x)=\frac{3}{4} x^{2}$

math/algebra-1/write-a-linear-inequality-from-a-graph
This is the graph of a linear inequality. Write the inequality in slope-intercept form.
Write your answer with y first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form. $\square$

What system of equations does the graph show?
Write the equations in slope-intercept form. Simplify any fractions. $y=$ $\square$

Simplify by clearing parentheses and combining like terms. $4(y+7)-28=$

1-2 Solve each equation or formula for the variable indicated.
8. $u=v w+z$ , for $v$ (9) $x=b-c d$ , for $c$
10. $f g-9 h=10 j$ , for $g$
11. $10 m-p=-n$ , for $m$

Solve the system by the addition method. $\begin{array}{l} x+y=4 \\ x-y=-2 \end{array}$

Solve the given system of equations $\begin{array}{l} 5 x+2 y-5 z=-6 \\ 2 x-4 y+2 z=-4 \\ 4 x-5 y+4 z=-17 \end{array}$

near function in which the rate of change 3 and the initial value is -10 . You wrote the quation $y=-3 x+(-10)$ to represent the nction. Your classmate wrote $y=-3 x-1$ ho is correct? Justify your response.

Complete the process of solving the equation. Fill in the missing term on each line. Simplify any fractions. \begin{tabular}{|l|l|} \hline $6 b+1=7$ & \\ $6 b$ & $=\square$ \\ $\dot{I}$ & $=\square$ \\ Subtract 1 from both sides \\ & Divide both sides by 6 \end{tabular}

What value of $r$ is a solution to this equation? $\begin{array}{l} 7 r+19=89 \\ r=10 \quad r=12 \end{array}$ Submit

Solve the system by the substitution method $\begin{aligned} x y & =30 \\ 3 x-y & =-9 \end{aligned}$

What value of $r$ is a solution to this equation? $10+\frac{r}{3}=14$ $r=-12$ $r=12$

Solve for $c$ . $2 c+2=6$ $c=$ $\square$ Submit

Solve for $y$ . $\begin{array}{l} 3 y-14=1 \\ y=\square \end{array}$ Submit

Use Gauss elimination $\left\{\begin{array}{l} x+2 y-z=-3 \\ 3 x-y+2 z=8 \\ 2 x+y-3 z=-5 \end{array}\right.$

16) $1=\frac{x+8}{22}$

15) $-6=-8+\frac{p}{4}$

13) $1=\frac{x+6}{26}$

Use the graph to solve the compound inequality $-3 \leq y_{1} \leq 2$ . Write your answer in interval notation

$-44=-4-2 b$

16. $3 n-n+7=25$