Natural Numbers

Problem 601

Simplify the expression $-2(-8 x+10)+9 x$ .

See Solution

Problem 602

Solve linear equation $3(2x-1)-3=0$ for $x$

See Solution

Problem 603

Solve for $x$ where $\frac{x}{4}-2=-10$ .

See Solution

Problem 604

Find the value of $x$ in the equation $\frac{6a}{7b} = \frac{x}{-14b}$ .

See Solution

Problem 605

Solve for $\theta$ given the equation $5+4\cos\theta=6$ .

See Solution

Problem 606

A snowball's radius decreases at $0.1$ cm/min. Find the rate of volume decrease when radius is $11$ cm. (Round answer to 3 decimal places)
$\frac{d V}{d t} = -4 \pi r^2 \frac{d r}{d t} = -4 \pi (11)^2 (0.1) = -\boxed{12.116} \frac{\mathrm{cm}^3}{\min}$

See Solution

Problem 607

Find the value of $d$ given the relationship $d=2.5 r$ and $r=64$ .

See Solution

Problem 608

Show that $y=\sin(t)$ solves the ODE $(\frac{dy}{dt})^2=1-y^2$ . Justify your answer in terms of $t$ .

See Solution

Problem 609

Determine the length of Teresa's workout plans A and B given the number of clients and total training hours on Friday and Saturday. Plan A: $\square$ hour(s) Plan B: $\square$ hour(s)

See Solution

Problem 610

Evaluate the definite integral of $0.25e^{-0.25x}$ .

See Solution

Problem 611

a. Janessa paid $\$ 390.96$ for a 2-year magazine subscription. After receiving 25 magazines in the second year, she cancelled. How many magazines will she receive a refund for? Round up to a whole number.
b. Calculate the pro-rated refund Janessa should receive from the magazine company. Round up to the nearest cent.

See Solution

Problem 612

Find the largest integer value of $t$ that satisfies the inequality $\frac{t}{4} + 2 < 11$ .

See Solution

Problem 613

1. Find $n$ for arithmetic series: a) $t_1=8, t_n=68, S_n=608$ b) $t_1=-6, t_n=21, S_n=75$
2. Find $t_{10}$ and $S_{10}$ for series: a) $5+10+15+\cdots$ b) $10+7+4+\cdots$ c) $(-10)+(-14)+(-18)+\cdots$ d) $2.5+3+3.5+\cdots$
3. a) Sum of multiples of 4 between 1 and 999 b) Sum of multiples of 6 between 1 and 999

See Solution

Problem 614

Solve the equation $6(t+12)=114$ by applying the Distributive Property. Determine the first and last operations needed.

See Solution

Problem 615

Find the square of 8. Find the cube of 7.

See Solution

Problem 616

Find the value of $9^3$ .

See Solution

Problem 617

Find the total temperature change when the temperature increases by $2^{\circ} \mathrm{C}$ each hour for $9 \mathrm{~h}$ .

See Solution

Problem 618

Find the value of the sine function evaluated at $\frac{2 \pi}{3}$ .

See Solution

Problem 619

Find the change in the function $f(x) = 7 - 6x$ from $x = 5$ to $x = 7$ .

See Solution

Problem 620

Solve the inequality $x^2 - 169 < 0$

See Solution

Problem 621

Flights from Dallas to Chicago are on time 80% of the time. 20 flights are randomly selected. Find the probability of exactly 12 on-time flights, fewer than 12 on-time flights, at least 12 on-time flights, and between 10 and 12 on-time flights. Interpret the probabilities.

See Solution

Problem 622

Jared's bicycle rides: given distances and times, find the missing time for 40 miles, assuming constant speed.
\begin{tabular}{|c|c|} \hline Miles (x) & Minutes (y) \\ \hline 6 & 45 \\ \hline 17 & 127.5 \\ \hline 40 & \\ \hline \end{tabular}

See Solution

Problem 623

Find the number where the result of dividing the number by 3 is 4.

See Solution

Problem 624

Find the solutions of the system of linear inequalities $8x + 5y > 40$ and $-6x + 2y \geq -18$ .

See Solution

Problem 625

Solve for the variable $v$ in the equation $1.4 = -6v + 20.6$ .

See Solution

Problem 626

Solve the equation $24+0.44x=19+1.69x$ and select the correct answer from the options provided.

See Solution

Problem 627

Translate Chau's height decreased by 16 is 60 into an equation using variable $c$ to represent Chau's height.

See Solution

Problem 628

Simplify expressions like $a^3$ , $6yx$ , $4x^2$ , $15x^2y$ , and $-4y^2z^2$ .

See Solution

Problem 629

Determine the tire lifespan warranty that will replace no more than $10\%$ of tires, given a normal distribution with $\mu=47,700$ miles and $\sigma=2,000$ miles.

See Solution

Problem 630

Identify whether $7-8(x+3)$ is an expression or an equation.

See Solution

Problem 631

Expand $(6-x)^{2}$ using special product of binomials and choose correct answer: (A) $36+12x-x^{2}$ (B) $36-12x+x^{2}$ (C) $6-36x-x^{2}$ (D) $6-12x+x^{2}$

See Solution

Problem 632

Reduce the ratio $0.13: 0.052$ to its smallest terms.

See Solution

Problem 633

Find the value of $x$ that satisfies the equation $\frac{2 x}{x-2}-1=\frac{4}{x-2}$ .

See Solution

Problem 634

Calculate the daily energy consumption of a light bulb that uses $7650$ watt-hours in $4$ days and $6$ hours.

See Solution

Problem 635

Find the distance between the point $(-2,7)$ and the line $6x + 4y + 1 = 0$ .

See Solution

Problem 636

Find the value of $y=a b^{x}$ given $a=1600, b=.25, x=12$ , rounded to 7 decimal places.

See Solution

Problem 637

Find all complex solutions to the cubic equation $f(x) = x^3 - 8x^2 + 21x - 20$ .

See Solution

Problem 638

Solve the equation $-4 x = 16 x^{2}$ for $x$ .

See Solution

Problem 639

Evaluate $y=x^5$ when $x=4$ . Round the result to five decimal places.

See Solution

Problem 640

Find the value of $a^{2} + 3b/c - 2d$ when $a=3, b=8, c=2$ , and $d=5$ .

See Solution

Problem 641

Determine the nature of the roots based on the discriminant value of $64$ .

See Solution

Problem 642

Which transformation turns a figure around a point? $\{1\text{. reflection}, 2\text{. translation}, 3\text{. rotation}, 4\text{. none of the above}\}$

See Solution

Problem 643

Find the value of $(-870 \div 5) \cdot(-6)$ .

See Solution

Problem 644

Calculate the area of a circle with radius 7.

See Solution

Problem 645

Multiplicar y simplificar: $(z-10)(z+10)$

See Solution

Problem 646

Evaluate $\frac{\sqrt{x-3}}{9}$ when $x=12$ . Options: A) $\frac{1}{3}$ B) 1 C) 3 D) 81.

See Solution

Problem 647

A. Probability that none of the 32 people are Independent: $\left(1 - 0.12\right)^{32}$
B. Probability that fewer than 6 are Independent: $\sum_{i=0}^{5} \binom{32}{i} \left(0.12\right)^{i} \left(1 - 0.12\right)^{32-i}$
C. Probability that more than 3 people are Independent: $1 - \sum_{i=0}^{3} \binom{32}{i} \left(0.12\right)^{i} \left(1 - 0.12\right)^{32-i}$

See Solution

Problem 648

Find the equation of the line passing through the point $(4,5)$ and parallel to the $x$ -axis.

See Solution

Problem 649

Solve for the value of $v$ that satisfies the equation $5.2-(2 \div v)=5.1$ .

See Solution

Problem 650

Resolver para $g$ donde $9g=W$ .

See Solution

Problem 651

Write a quadratic function $h$ with zeros at -4 and -5.

See Solution

Problem 652

Prove that the function $f(x)=x^{7}+8 x-2$ has at most one real root using Rolle's Theorem. Show it has exactly one using the Intermediate Value Theorem.

See Solution

Problem 653

A plane flies 2316 mi with the wind and 2004 mi against the wind. Find the wind speed $\square \mathrm{mph}$ given the plane's cruising speed is $540 \mathrm{mph}$ .

See Solution

Problem 654

Classic Movie DVDs are on sale from June 19-25. 60 titles available. 2 for $\$ 15.00$ , 3 for $\$ 20.00$ , or 5 for $\$ 30.00$ with coupon. After June 25, $\$ 8.50$ each. Cost of 5 DVDs on June 26 is $\$ 32.50$ .

See Solution

Problem 655

Solve the equation $\frac{8}{x}+\frac{7}{6 x}=\frac{-5}{6}$ for $x$ .

See Solution

Problem 656

Find a vector $\vec{b}$ with opposite direction of $\vec{a}$ and $|\vec{b}|=3$ , where $\vec{a}$ is a nonzero vector.

See Solution

Problem 657

Solve for $x$ in the equation $\frac{x+3}{4}=\frac{5}{2}$ . Simplify the solution.

See Solution

Problem 658

Find the exact value of $\cot \frac{-11 \pi}{6}$ .

See Solution

Problem 659

Find the integer closest to $x$ such that $2^{x} = 100$ .

See Solution

Problem 660

Find complex solutions of $9 x^3 - 17 x^2 + 43 x + 5 = 0$ using possible rational roots: $\pm 1, \pm 1/3, \pm 1/9, \pm 5, \pm 5/3, \pm 5/9$ .

See Solution

Problem 661

Solve the absolute value equation: $|2x+1| = 9$

See Solution

Problem 662

Solve for $x$ in the equation $\frac{3}{8} x=48$ . Simplify the solution.

See Solution

Problem 663

Solve the equation $10-c=-3$ and express the solution as an integer or simplified fraction.

See Solution

Problem 664

Solve the linear equation $12p - 0.7 = 5p + 3.2$ for the variable $p$ .

See Solution

Problem 665

Find the average velocity of an object moving along a vertical line with position $L(t)=-3t^2+t+8$ (m) at time $t$ (s) for the given intervals: [3s, 9s], [2s, 7s], [5s, 8s].

See Solution

Problem 666

Find the domain of the function $f(x) = \frac{9}{x^2 - 5x}$ . Express the answer in interval notation.

See Solution

Problem 667

Write a story to match the equation $x + 2.5 = 10$ .

See Solution

Problem 668

Graph the parabola $y=\frac{1}{2}(x-4)^{2}$ representing a bird's height over time as it lands. Find 3 points on the graph.

See Solution

Problem 669

Find the derivative of $f(x)=\sqrt{5 x-10}$ using the limit definition.

See Solution

Problem 670

Solve $F g = 5$ for the variable $F$ , accounting for capitalization.

See Solution

Problem 671

Find the time (in h) to administer $3 \mathrm{L}$ IV at $40 \mathrm{drops} / \mathrm{min}$ with $10 \mathrm{drops} / \mathrm{mL}$ drop factor.

See Solution

Problem 672

Find the quotient of 36.75 divided by 5.25.

See Solution

Problem 673

Solve $a=2b-5c$ for $b$ . Options: (A) $\frac{a-5c}{2}=b$ (B) $\frac{a+5c}{2}=b$ (C) $\frac{a-2b}{5}=c$ (D) $\frac{a+2b}{5}=c$

See Solution

Problem 674

Choose the expression equivalent to $\frac{\tan \left(\frac{3 \pi}{5}\right)-\tan \left(\frac{13 \pi}{30}\right)}{1+\tan \left(\frac{3 \pi}{5}\right) \tan \left(\frac{13 \pi}{30}\right)}$ : $\sin \left(\frac{3 \pi}{5}+\frac{13 \pi}{30}\right) \tan \left(\frac{3 \pi}{5}-\frac{13 \pi}{30}\right) \tan \left(\frac{3 \pi}{5}+\frac{13 \pi}{30}\right) \cos \left(\frac{3 \pi}{5}-\frac{13 \pi}{30}\right)$

See Solution

Problem 675

Find the radius $r$ given the formula for the area $A$ of a circle: $A = \pi r^2$ .

See Solution

Problem 676

Find the simple interest rate $r$ for a loan with principal $P=\$2300$ , future value $A=\$2775$ , and duration $t=3$ months.

See Solution

Problem 677

Karen is saving $\$ 60$ per week. After $W$ weeks, the total amount in the savings account is $S = 350 + 60W$ . The total amount after 18 weeks is $\$ 1,430$ .

See Solution

Problem 678

TechWiz sells MP3 ( $35 profit) and DVD ($ 18 profit) players. Last week, they sold 137 total. Find the total profit. Total profit = $35x +$ 18(137 - x), where $x$ is the number of MP3 players sold.

See Solution

Problem 679

Find the value of $d$ that satisfies the equation $d + 9 = 23$ .

See Solution

Problem 680

Find the capital position (CP) when the selling price (SP) is $Rs. 0.924$ and the gain is 10%.

See Solution

Problem 681

Convert the given units to find the product of two quantities.

See Solution

Problem 682

Find the simplified form of $(3^2 y^4)^{-2}$ . A. $-81 y^{8}$ B. $-\frac{y^{8}}{12}$ C. $9 y^{2}$ D. $y^{2}$ E. $\frac{1}{81 y^{8}}$

See Solution

Problem 683

Simplify the expression $\frac{8}{x^{2}-8 x}-\frac{x}{8 x-64}$ .

See Solution

Problem 684

Find the amount of wrapping paper needed to cover a $5$ in. by $7$ in. cylindrical gift box, including the top, bottom, and sides. Use $\pi = 3.14$ . Round to the nearest tenth of a square inch.

See Solution

Problem 685

Find the value of the linear function $P(x)=-7x+9$ . Determine the value of $P(-2)$ .

See Solution

Problem 686

Find the length of the adjacent side of a rectangular garden with total area $8 x^{2} - 12 x + 4$ sq. ft. and one side measuring $2 x - 2$ ft.

See Solution

Problem 687

Radioactive fallout from a 1981 nuclear lab explosion is described by $f(x) = 1000(0.5)^{\frac{x}{30}}$ , where $f(x)$ is the remaining amount (kg) $x$ years later. Determine $f(40)$ and if the area will be safe by 2021.

See Solution

Problem 688

Find the period of the function $y = \tan(4x) + 1$ .

See Solution

Problem 689

Multiply two decimal numbers: $0.7 \times 0.7$

See Solution

Problem 690

Simplify the rational expression $\frac{v+\frac{64}{v^{2}}}{1+\frac{4}{v}}$ .

See Solution

Problem 691

Find the missing value in the scale: $1: \square = 17: 51$ . Options: A) 3, B) 0.4, C) 0.08, D) 0.02.

See Solution

Problem 692

Select the constraint $x_{1} - x_{5} \leq 1$ to ensure that if project 1 is chosen, project 5 must not be chosen.

See Solution

Problem 693

Determine if the function $y=f(x)$ with given $(x,y)$ pairs is linear or nonlinear. If linear, find the slope.

See Solution

Problem 694

Find the third term in $(x+y)^{8}$ when $x=0.3$ and $y=0.7$ .

See Solution

Problem 695

Find $n(B)$ if $n(A \times B)=92$ and $n(A)=23$ .

See Solution

Problem 696

Complete the expansion of $(y-z)^{3}$ using Pascal's Triangle.
$y^{3}-3y^{2}z+3yz^{2}-z^{3}$

See Solution

Problem 697

Find the greatest common factor (GCF) of the terms $35c + 14b - 7$ and simplify the expression.

See Solution

Problem 698

Solve for $x$ in the equation $x+5.15=23.85$ .

See Solution

Problem 699

Find all possible values of $x$ in the equation $x^2 = 1/36$ .

See Solution

Problem 700

Find the solutions to the equation $\cos x = -\sqrt{2}/2$ for $0 \leq x < 2\pi$ .

See Solution

1 ...4 5 6 7 8 9 10 ...28

Natural Numbers

Problem 601

Simplify the expression −2(−8x+10)+9x-2(-8 x+10)+9 x−2(−8x+10)+9x.

Problem 602

Solve linear equation 3(2x−1)−3=03(2x-1)-3=03(2x−1)−3=0 for xxx

Problem 603

Solve for xxx where x4−2=−10\frac{x}{4}-2=-104x​−2=−10.

Problem 604

Find the value of xxx in the equation 6a7b=x−14b\frac{6a}{7b} = \frac{x}{-14b}7b6a​=−14bx​.

Problem 605

Solve for θ\thetaθ given the equation 5+4cos⁡θ=65+4\cos\theta=65+4cosθ=6.

Problem 606

Problem 607

Find the value of ddd given the relationship d=2.5rd=2.5 rd=2.5r and r=64r=64r=64.

Problem 608

Show that y=sin⁡(t)y=\sin(t)y=sin(t) solves the ODE (dydt)2=1−y2(\frac{dy}{dt})^2=1-y^2(dtdy​)2=1−y2. Justify your answer in terms of ttt.

Problem 609

Determine the length of Teresa's workout plans A and B given the number of clients and total training hours on Friday and Saturday. Plan A: □\square□ hour(s) Plan B: □\square□ hour(s)

Problem 610

Evaluate the definite integral of 0.25e−0.25x0.25e^{-0.25x}0.25e−0.25x.

Problem 611

Problem 612

Find the largest integer value of ttt that satisfies the inequality t4+2<11\frac{t}{4} + 2 < 114t​+2<11.

Problem 613

Problem 614

Solve the equation 6(t+12)=1146(t+12)=1146(t+12)=114 by applying the Distributive Property. Determine the first and last operations needed.

Problem 615

Find the square of 8. Find the cube of 7.

Problem 616

Find the value of 939^393.

Problem 617

Find the total temperature change when the temperature increases by 2∘C2^{\circ} \mathrm{C}2∘C each hour for 9 h9 \mathrm{~h}9 h.

Problem 618

Find the value of the sine function evaluated at 2π3\frac{2 \pi}{3}32π​.

Problem 619

Find the change in the function f(x)=7−6xf(x) = 7 - 6xf(x)=7−6x from x=5x = 5x=5 to x=7x = 7x=7.

Problem 620

Solve the inequality x2−169<0x^2 - 169 < 0x2−169<0

Problem 621

Flights from Dallas to Chicago are on time 80% of the time. 20 flights are randomly selected. Find the probability of exactly 12 on-time flights, fewer than 12 on-time flights, at least 12 on-time flights, and between 10 and 12 on-time flights. Interpret the probabilities.

Problem 622

Jared's bicycle rides: given distances and times, find the missing time for 40 miles, assuming constant speed.\begin{tabular}{|c|c|} \hline Miles (x) & Minutes (y) \\ \hline 6 & 45 \\ \hline 17 & 127.5 \\ \hline 40 & \\ \hline \end{tabular}

Problem 623

Find the number where the result of dividing the number by 3 is 4.

Problem 624

Find the solutions of the system of linear inequalities 8x+5y>408x + 5y > 408x+5y>40 and −6x+2y≥−18-6x + 2y \geq -18−6x+2y≥−18.

Problem 625

Solve for the variable vvv in the equation 1.4=−6v+20.61.4 = -6v + 20.61.4=−6v+20.6.

Problem 626

Solve the equation 24+0.44x=19+1.69x24+0.44x=19+1.69x24+0.44x=19+1.69x and select the correct answer from the options provided.

Problem 627

Translate Chau's height decreased by 16 is 60 into an equation using variable ccc to represent Chau's height.

Problem 628

Simplify expressions like a3a^3a3, 6yx6yx6yx, 4x24x^24x2, 15x2y15x^2y15x2y, and −4y2z2-4y^2z^2−4y2z2.

Problem 629

Determine the tire lifespan warranty that will replace no more than 10%10\%10% of tires, given a normal distribution with μ=47,700\mu=47,700μ=47,700 miles and σ=2,000\sigma=2,000σ=2,000 miles.

Problem 630

Identify whether 7−8(x+3)7-8(x+3)7−8(x+3) is an expression or an equation.

Problem 631

Expand (6−x)2(6-x)^{2}(6−x)2 using special product of binomials and choose correct answer: (A) 36+12x−x236+12x-x^{2}36+12x−x2 (B) 36−12x+x236-12x+x^{2}36−12x+x2 (C) 6−36x−x26-36x-x^{2}6−36x−x2 (D) 6−12x+x26-12x+x^{2}6−12x+x2

Problem 632

Reduce the ratio 0.13:0.0520.13: 0.0520.13:0.052 to its smallest terms.

Problem 633

Find the value of xxx that satisfies the equation 2xx−2−1=4x−2\frac{2 x}{x-2}-1=\frac{4}{x-2}x−22x​−1=x−24​.

Problem 634

Calculate the daily energy consumption of a light bulb that uses 765076507650 watt-hours in 444 days and 666 hours.

Problem 635

Find the distance between the point (−2,7)(-2,7)(−2,7) and the line 6x+4y+1=06x + 4y + 1 = 06x+4y+1=0.

Problem 636

Find the value of y=abxy=a b^{x}y=abx given a=1600,b=.25,x=12a=1600, b=.25, x=12a=1600,b=.25,x=12, rounded to 7 decimal places.

Problem 637

Find all complex solutions to the cubic equation f(x)=x3−8x2+21x−20f(x) = x^3 - 8x^2 + 21x - 20f(x)=x3−8x2+21x−20.

Problem 638

Solve the equation −4x=16x2-4 x = 16 x^{2}−4x=16x2 for xxx.

Problem 639

Evaluate y=x5y=x^5y=x5 when x=4x=4x=4. Round the result to five decimal places.

Problem 640

Find the value of a2+3b/c−2da^{2} + 3b/c - 2da2+3b/c−2d when a=3,b=8,c=2a=3, b=8, c=2a=3,b=8,c=2, and d=5d=5d=5.

Problem 641

Determine the nature of the roots based on the discriminant value of 646464.

Simplify the expression $-2(-8 x+10)+9 x$ .

Solve linear equation $3(2x-1)-3=0$ for $x$

Solve for $x$ where $\frac{x}{4}-2=-10$ .

Find the value of $x$ in the equation $\frac{6a}{7b} = \frac{x}{-14b}$ .

Solve for $\theta$ given the equation $5+4\cos\theta=6$ .

Find the value of $d$ given the relationship $d=2.5 r$ and $r=64$ .

Show that $y=\sin(t)$ solves the ODE $(\frac{dy}{dt})^2=1-y^2$ . Justify your answer in terms of $t$ .

Determine the length of Teresa's workout plans A and B given the number of clients and total training hours on Friday and Saturday. Plan A: $\square$ hour(s) Plan B: $\square$ hour(s)

Evaluate the definite integral of $0.25e^{-0.25x}$ .

Find the largest integer value of $t$ that satisfies the inequality $\frac{t}{4} + 2 < 11$ .

Solve the equation $6(t+12)=114$ by applying the Distributive Property. Determine the first and last operations needed.

Find the value of $9^3$ .

Find the total temperature change when the temperature increases by $2^{\circ} \mathrm{C}$ each hour for $9 \mathrm{~h}$ .

Find the value of the sine function evaluated at $\frac{2 \pi}{3}$ .

Find the change in the function $f(x) = 7 - 6x$ from $x = 5$ to $x = 7$ .

Solve the inequality $x^2 - 169 < 0$

Jared's bicycle rides: given distances and times, find the missing time for 40 miles, assuming constant speed.
\begin{tabular}{|c|c|} \hline Miles (x) & Minutes (y) \\ \hline 6 & 45 \\ \hline 17 & 127.5 \\ \hline 40 & \\ \hline \end{tabular}

Find the solutions of the system of linear inequalities $8x + 5y > 40$ and $-6x + 2y \geq -18$ .

Solve for the variable $v$ in the equation $1.4 = -6v + 20.6$ .

Solve the equation $24+0.44x=19+1.69x$ and select the correct answer from the options provided.

Translate Chau's height decreased by 16 is 60 into an equation using variable $c$ to represent Chau's height.

Simplify expressions like $a^3$ , $6yx$ , $4x^2$ , $15x^2y$ , and $-4y^2z^2$ .

Determine the tire lifespan warranty that will replace no more than $10\%$ of tires, given a normal distribution with $\mu=47,700$ miles and $\sigma=2,000$ miles.

Identify whether $7-8(x+3)$ is an expression or an equation.

Expand $(6-x)^{2}$ using special product of binomials and choose correct answer: (A) $36+12x-x^{2}$ (B) $36-12x+x^{2}$ (C) $6-36x-x^{2}$ (D) $6-12x+x^{2}$

Reduce the ratio $0.13: 0.052$ to its smallest terms.

Find the value of $x$ that satisfies the equation $\frac{2 x}{x-2}-1=\frac{4}{x-2}$ .

Calculate the daily energy consumption of a light bulb that uses $7650$ watt-hours in $4$ days and $6$ hours.

Find the distance between the point $(-2,7)$ and the line $6x + 4y + 1 = 0$ .

Find the value of $y=a b^{x}$ given $a=1600, b=.25, x=12$ , rounded to 7 decimal places.

Find all complex solutions to the cubic equation $f(x) = x^3 - 8x^2 + 21x - 20$ .

Solve the equation $-4 x = 16 x^{2}$ for $x$ .

Evaluate $y=x^5$ when $x=4$ . Round the result to five decimal places.

Find the value of $a^{2} + 3b/c - 2d$ when $a=3, b=8, c=2$ , and $d=5$ .

Determine the nature of the roots based on the discriminant value of $64$ .

Which transformation turns a figure around a point? $\{1\text{. reflection}, 2\text{. translation}, 3\text{. rotation}, 4\text{. none of the above}\}$

Find the value of $(-870 \div 5) \cdot(-6)$ .

Multiplicar y simplificar: $(z-10)(z+10)$

Evaluate $\frac{\sqrt{x-3}}{9}$ when $x=12$ . Options: A) $\frac{1}{3}$ B) 1 C) 3 D) 81.

Find the equation of the line passing through the point $(4,5)$ and parallel to the $x$ -axis.

Solve for the value of $v$ that satisfies the equation $5.2-(2 \div v)=5.1$ .

Resolver para $g$ donde $9g=W$ .

Write a quadratic function $h$ with zeros at -4 and -5.

Prove that the function $f(x)=x^{7}+8 x-2$ has at most one real root using Rolle's Theorem. Show it has exactly one using the Intermediate Value Theorem.

A plane flies 2316 mi with the wind and 2004 mi against the wind. Find the wind speed $\square \mathrm{mph}$ given the plane's cruising speed is $540 \mathrm{mph}$ .

Classic Movie DVDs are on sale from June 19-25. 60 titles available. 2 for $\$ 15.00$ , 3 for $\$ 20.00$ , or 5 for $\$ 30.00$ with coupon. After June 25, $\$ 8.50$ each. Cost of 5 DVDs on June 26 is $\$ 32.50$ .

Solve the equation $\frac{8}{x}+\frac{7}{6 x}=\frac{-5}{6}$ for $x$ .

Find a vector $\vec{b}$ with opposite direction of $\vec{a}$ and $|\vec{b}|=3$ , where $\vec{a}$ is a nonzero vector.

Solve for $x$ in the equation $\frac{x+3}{4}=\frac{5}{2}$ . Simplify the solution.

Find the exact value of $\cot \frac{-11 \pi}{6}$ .

Find the integer closest to $x$ such that $2^{x} = 100$ .

Find complex solutions of $9 x^3 - 17 x^2 + 43 x + 5 = 0$ using possible rational roots: $\pm 1, \pm 1/3, \pm 1/9, \pm 5, \pm 5/3, \pm 5/9$ .

Solve the absolute value equation: $|2x+1| = 9$

Solve for $x$ in the equation $\frac{3}{8} x=48$ . Simplify the solution.

Solve the equation $10-c=-3$ and express the solution as an integer or simplified fraction.

Solve the linear equation $12p - 0.7 = 5p + 3.2$ for the variable $p$ .

Find the average velocity of an object moving along a vertical line with position $L(t)=-3t^2+t+8$ (m) at time $t$ (s) for the given intervals: [3s, 9s], [2s, 7s], [5s, 8s].

Find the domain of the function $f(x) = \frac{9}{x^2 - 5x}$ . Express the answer in interval notation.

Write a story to match the equation $x + 2.5 = 10$ .

Graph the parabola $y=\frac{1}{2}(x-4)^{2}$ representing a bird's height over time as it lands. Find 3 points on the graph.

Find the derivative of $f(x)=\sqrt{5 x-10}$ using the limit definition.

Solve $F g = 5$ for the variable $F$ , accounting for capitalization.

Find the time (in h) to administer $3 \mathrm{L}$ IV at $40 \mathrm{drops} / \mathrm{min}$ with $10 \mathrm{drops} / \mathrm{mL}$ drop factor.

Solve $a=2b-5c$ for $b$ . Options: (A) $\frac{a-5c}{2}=b$ (B) $\frac{a+5c}{2}=b$ (C) $\frac{a-2b}{5}=c$ (D) $\frac{a+2b}{5}=c$