10. A movie theater offers a reward program that charges a yearly membership fee and a discounted rate per movie ticket. The total cost for a reward program member to see 5 movies is $40 and the total cost for 12 movies is $75. Assume the relationship is linear. Write the equation of the function in the form y=mx+b, where x represents the number of movies and y represents the total cost.
Official Time: 14:43:23 Question 2 [10 points]
Find the characteristic polynomial of A. Use x for the variable in your polynomial.
A=⎣⎡1000−1−200−102205802⎦⎤
characteristic polynomial of A is: 0
SUBMIT AND MARK
Otricial Time: 14:44:47 Question 1 [10 points]
Find the characteristic polynomial of A. Use x for the variable in your polynomial. You do not need to factor your polynomial.
A=⎣⎡100−9010120−11⎦⎤
characteristic polynomial of A is: 0
SUBMIT AND MARK
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Question 10 (2 points)
Statement: A function is a relation where each input can be paired with only one output. Choose if the statement is true or false.
True
False
View hint for Question 10
Express as a single logarithm and simplify, if possible.
41logcx+4logcy−5logcx41logcx+4logcy−5logcx=□
(Type your answer using exponential notation. Use integers or fractions for any numbers in the expression.)
3. Malik's salary is $25,500 per year, which he expects will increase by a constant dollar amount annually. In 12 years, his salary will have doubled. Assuming salar increases take place only at the end of a full year, how many years must Malik wait until his salary is at least \$40,000 annually?
Reason Abstractly During a test flight, Jeri's rocket reached a height of 18 yards above the ground. This was 7 yards less than the height that Devon's rocket reached. Did Devon's rocket reach a height greater than 23 yards? Explain.
Choose the best answer and explanation.
A) no; If I solve the equation x−7=18 to find the height that Devon's rocket reached, I find that Devon's rocket reached a height of 18−7, or 11 yards. Because 11<23, Devon's rocket did not reach a height greater than 23 yards.
B) no; If I solve the equation x+7=18 to find the height that Devon's rocket reached, I find that Devon's rocket reached a height of 18−7, or 11 yards. Because 11<23, Devon's rocket did reach a height greater than 23 yards.
C) yes; If I solve the equation x−7=18 to find the height that Devon's rocket reached, I find that Devon's rocket reached a height of 18+7, or 25 yards. Since 25>23, Devon's rocket did reach a height greater than 23 yards.
D) yes; If I solve the equation x+7=18 to find the height that Devon's rocket reached, Ifind that Devon's rocket reached a height of 18+7, or 25 yards. Because 25>23, Devon's rocket did reach a height greater than 23 yards.
For each inequality, choose the statement that describes its solution. If applicable, give the solution.
(a) 3(4−u)+3u>16
No solution
u रे □u>□
All real numbers are solutions
(b) 3(5v+2)≤13v+16
No solution
v≤□v≥□
All real numbers are solutions
Check here for instructional material to complete this problem.
A person's annual salary increases by $10,650 over a 6 -year period. Find the average rate of change of the salary per year. The average rate of change is $□ per year.
(Round to the nearest dollar.)
Find the sum of the pair of complex numbers.
21+65i,65+21i The sum is □ .
(Simplify your answer. Type your answer in the form a + bi. Use integers or fractions for any numbers in the expressic
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
REASONING
a. Rewrite 2x+46x4+2x2−16x2+24x+32 as q(x)+d(x)π(x) using long division.
2x+46x4+2x3−16x2+24x+32=□∫x3−□x2+□∫x+□ , remainder
□ Part B
b. What does the remainder indicate in this problem? Because the remainder is Select Choice v,2x+4 is a Select Choice v of 6x4+2x3−16x2+24x+32.
□
Name
Practice
Period Date
Go Online You can complete your homework online 1. Gennaro is considering two job offers as a part-time sales person. Company A will pay him $12.50 for each item he sells, plus a base salary of $500 at the end of the month. The amount Company B will pay him at the end of the month is shown in the table. Compare the functions' initial values and rates of change. Then determine how much more Gennaro would make at Company A if he sells
\begin{tabular}{c|c|c}
\hline \begin{tabular}{c}
Number of \\
Items Sold, x
\end{tabular} & \begin{tabular}{c}
Total \\
Earned (\),y
\end{tabular} \\
\hlineS$ & 5 & 425 \\
\hline 10 & 500 \\
\hline 15 & 575 \\
\hline
\end{tabular} 28 items by the end of the month. (Example 1)
Algebra II 3. Write an equation for the line perpendicular to y=4x−3 through the point (2,0) using point-slope form, then simplify into standard form.
y=4x−3
Check here for instructional material to complete this problem.
Find the approximate slope of the line that contains the points (−3.1,5.9) and (−2.7,2.4). State whether the line is increasing, decreasing, horizontal, or vertical. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The slope is □
(Type an integer or decimal rounded to two decimal places as needed.)
B. The slope is undefined.
Question 1 of 5, Step 1 of 1
Correct Use any convenient method to solve the following system of equations. If the system is dependent, express the solution set in terms of one of the variables. Leave all fractional answers in fraction form.
⎩⎨⎧x+5yy−3z−3x−y+6z===121032 Answer
Keypad
Keyboard Shortcuts Selecting an option will display any text boxes needed to complete your answer.
Only One Solution Inconsistent System
O Dependent System
8. The tape diagram shows the ratio of the hours of work done by you and a friend. Ypeand your frie worked a total of 24 hours. How many hours did you work? You:
\begin{tabular}{|c|c|c|c|}
\hline 4 & 5 & e & ln \\
\hline
\end{tabular} Your friend: □
Question 1 of 12, Step 1 of 2
Correct The price of a meal plus a 12% delivery charge comes to a total cost of $16.80. What was the price of the meal? Step 1 of 2: Describe the above situation as a linear equation using " x " or " y " as variable names to describe the unknowns.
Find all zeros of the function: k(x)=12x2−23x+5.
The zeros are x=□ Find all zeros of the function: g(x)=x2−3x−18.
The zeros are x=□
Find all zeros of the function: m(x)=2x2−5x−63.
The zeros are x=□
Question Help:
Video
A mass attached to the end of a spring is set in motion. The mass is observed to oscillate up and down, completing 12 complete cycles every 6.00 s What is the period T of the oscillation?
T=□
s What is the frequency f of the oscillation?
f=□
Hz
5. 2(x+14)+(2x−14)= 6. (11x−8)+7(x−1)= 7. Write a linear expression in simplest form to represent the perimeter of the triangle at the right. Then find the perimeter if the value of x is 10 millimeters. (Example 6) 8. A rectangle has side lengths (2x−5) meters and (2x+6) meters. Write a linear expression in simplest form to represent the perimeter. Find the perimeter if the value of x is 12 meters. (Example 6)
19 Find the sum of (x+5),(−4x−2), and (2x−1). Add. 10. (−3.5x+1.7)+(9.1x−0.3)= 11. (0.5x+15)+(8.2x−16.6)=
Lesson 6 Add Linear Expre
Solve the system of equations by the substitution method.
y=75x+72y=41x+4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is □ 3. (Type an ordered pair.)
B. There are infinitely many solutions.
C. There is no solution.
Solve the system of equations by the addition method.
16x−3y4x+2y=−49=−26 Select the correct choice below and fill in any answer boxes present in your choice.
A. The solution set is □ \}. (Simplify your answer. Type an ordered pair.)
B. There are infinitely many solutions.
C. There is no solution.
Question 9
0/1pt
3
19
Detarls The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 300 people entered the park, and the admission fees collected totaled 750 dollars. How many children and how many adults were admitted?
□ children were admitted.
□ adults were admitted.
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Which of the following is the set of all real numbers x such that x+2>x+5 ?
A. The set containing only zero
B. The set containing all nonnegative real numbers
C. The set containing all negative real numbers
D. The set containing all real numbers
E. The empty set
The formulas below are the cost and revenue functions for a company that manufactures and sells small radios.
C(x)=24,000+38x and R(x)=40x
a. Use the formulas shown to write the company's profit function, P, from producing and selling x radios.
b. Find the company's profit if 20,000 radios are produced and sold.
a. The company's profit function is P(x)= :
□
(Simplify your answer.)
At least one of the answers above is NOT correct.
(1 point)
A batter hits a baseball. The ball's height (in feet) after t seconds is given by h(t)=−16t2+62t+4.
a) What is the height of the ball when it is hit? The height is □ 4 feet.
b) When will the height be at 20 feet? The ball will be a height of 20 feet in 0.28,3.6□ seconds. If there are two times, enter them separated by a comma. If there is no time, enter "never". Round to two decimal places.
c) When will the ball reach its maximum height? The ball will reach a maximum height in □ 1.94 seconds. Round to two decimal places.
d) What is the ball's maximum height? The ball's maximum height is □ feet. Note: You can earn partial credit on this problem.
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Figure it
thomure 6 In Figure 1, a person uses a pulley to lift a bell. The person pulls down on the rope at a constant speed. Power P1 is delvered to the bell and it moves upward at a constant speed. In Figure 2, the person uses a double pulley. The person pulls down on the rope at the same constant speed. The bell again moves upward at a constant speed, but the speed of the bell is half the speed of the bell in Figure 1 . The power delivered to the bell in Figure 2 is P2. Which of the following correctly compares P2 to P1 and provides a valid justification?
(A) P2<P1, because in Figure 2 the force exerted on the bell is the same but it is moving with less speed than in Figure 1.
(B) P2<P1, because in Figure 2 the force exerted on the bell is less than in Figure 1.
(C) P2=P1, because in Figure 2 the speed is half that in Figure 1 , but the force on the bell is twice that in Figure 1.
(D) P2=P1, because in Figure 2 the person is doing the same amount of work on the bell as in Figure 1.
y=ax2+bx+c
to model the shape of the arch.
(a) Use the surveyed points to set up a system of linear equations for the
⎩⎨⎧100a+10b+c100225a+15b+c1600a+40b+c=54
(b) Solve the system using Cramer's Rule.
y=−3750
8. A marine biologist measures the presence of a pollutant in an ocean and concludes that the concentration, C, in parts per million ( ppm ) as a function of the population, P, of the neighbouring town is given by C(P)=1.38P+97.4. The population of the town, in thousands, can be modelled by P(t)=12(1.078)t where t is the time in years since the first measurement.
a. Determine an equation, in simplified form, for the concentration of pollutant as a function of the number of years since the first measurement. [ 3 marks]
b. What reasonable restrictions should be placed on the function's domain and range? [2 marks]
c. The first measurement was taken in January 2018. Adapt the formula in part (a) to create an equation for the concentration as a function of the number of months since January 2020. [3 marks]
d. In which year will the concentration reach 180 ppm? [ 3 marks]
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Get a similar question You can retry this question oetow The population of a country was 119 million in 1982 and the continuous exponential growth rate was estimated at 3.5% per year. Assuming that the population of the country continues to follow an exponential growth model, find the projected population in 1997. Round your answer to 1 decimal place.
The approximate population in 1997 is □ million people
Enter an integer or decimal number [more..]
The following steps are used to rewrite the polynomial expression (x+4y+z)(x−7y).
Step 1: x(x−7y)+4y(x−7y)+z(x−7y) Step 2: x2−7xy+4yx−28y2+zx−7zy Step 3: x2−7xy+4xy−28y2+xz−7yz Step 4: x2−3xy−28y2+xz−7yz Identify the property used in each of the steps: Step 1: Step 2: Step 3:
1.) During a sale at a local department store, you buy three sweatshirts and two pairs of jeans for $85.50. Later you return to the same store and buy three more sweatshirts and four more pairs of jeans for $123. What is the sale price of each sweatshirt and pair of jeans?
4.5 Exponential and Logarithmic Equations and Applications
Question 8 of 26 (2 points) I Question Attempt: 2 of Unilimited
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13 Solve the equation. Write the solution set with the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places.
2t=19
There is no solution, }.
The exact solution set is □ \}
t≈□
\begin{tabular}{|c|c|c|}
\hline \multicolumn{3}{|l|}{} \\
\hline □ln□ & □log□ & log D \\
\hline ㅁ & □□ & □ \\
\hline × & & 5 \\
\hline
\end{tabular}
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Dec 3
6:56
Find all the zeros. Write the answer in exact form.
t(x)=x3−5x2+4x+6 If there is more than one answer, separate them with commas.
Select "None" if applicable.
The zeros of t(x) : □
Solve the equation. Write the solution set with the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places.
2700=16,200e−0.2x
There is no solution, \{\}.
The exact solution set is □}.
x≈□
Solve for x.
−2+x32=x−x3 If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".
x=□
No
solution
1□ □,□,…
Neronica lives on a straight road that goes east and west She starts from a point 5 . miles west of her home and drives a certain distance to the store. The store is more than 321 miles east of her home. Let d represent the distance Veronica drove.
Which inequality represents this situation?
−5.1+d≥−321−5.1+d≥321−5.1+d>321−5.1+d>−321
Alex needs to represent this statement as an inequality.
Half of a number is more than one and one-third.
Drag and drop a symbol to correctly complete the inequality.
PRACTICE 4 Make Sense of Problems Mauricio hits a baseball 4 times as often as Tony each game. He also hits 20 baseballs every Monday at practice. How many baseballs will Mauricio hit this week if Tony hits 4 balls at the game Saturday?