Equation

Problem 14001

Find $x$ given that $m \angle BJK = 146 + 2x$ , $m \angle IJK = 172^\circ$ , and $m \angle IJB = 2x + 26$ .

See Solution

Problem 14002

Solve for $c$ in the equation $6 c + 1 = -2$ .

See Solution

Problem 14003

Solve for $c$ in the equation $6 c + 1 = -2$ .

See Solution

Problem 14004

Find $m \angle N F E$ given $m \angle G F N=4x+10$ , $m \angle N F E=14x+3$ , and $m \angle G F E=157^{\circ}$ .

See Solution

Problem 14005

Find $m \angle I H G$ given $m \angle Z H G=11 x-1$ , $m \angle I H Z=24^{\circ}$ , and $m \angle I H G=12 x+13$ .

See Solution

Problem 14006

Find $x$ if $m \angle G F Z=38^{\circ}$ , $m \angle Z F E=2x+125$ , and $m \angle G F E=x+163$ .

See Solution

Problem 14007

Find 2 values of $\theta$ in $[0, 2\pi)$ such that $\cot \theta = 3.2041$ .

See Solution

Problem 14008

Solve for $x$ in the equation: $-2(x+2)-7=-3$ .

See Solution

Problem 14009

In 2015, North Dakota had 545,027 drivers and Wyoming had 422,450. Estimate total drivers by rounding to the nearest ten thousand. Is your estimate reasonable?

See Solution

Problem 14010

Find the perimeter and area of a trapezoid with bases 13.4 and 14.7 units, and height 11.2 units. Round area to the nearest tenth.

See Solution

Problem 14011

Find $m \angle H I W$ given $m \angle W I J=10 x$ , $m \angle H I J=145^{\circ}$ , and $m \angle H I W=2 x+13$ .

See Solution

Problem 14012

Find the perimeter and area of a triangle with height 11.2, sides 14.7, 13.4, and base 13.4. Round area to nearest tenth.

See Solution

Problem 14013

Find $m \angle F G H$ given $m \angle F G B=105^{\circ}$ and $m \angle B G H=54^{\circ}$ .

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Problem 14014

Calculate the final score based on weights: midterm (5\%), project (15\%), homework (30\%), final (50\%). Scores: midterm 66, project 99, homework 76, final 72. What is the final score and letter grade?

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Problem 14015

Find the distance over which a force of 200 N does 800 J of work. Options: a. $40 \mathrm{~m}$ b. $20 \mathrm{~m}$ c. $4 \mathrm{~m}$ d. $2 \mathrm{~m}$

See Solution

Problem 14016

Calculate the geometric mean of $1.106$ , $1.073$ , and $1.038$ to find the average growth factor. Round to four decimal places.

See Solution

Problem 14017

Find $m \angle W V U$ given $m \angle Z V U=62^{\circ}$ and $m \angle W V Z=50^{\circ}$ .

See Solution

Problem 14018

In January, 611,749 domestic and 106,909 international passengers used Terminal 4. Find the total number of passengers.

See Solution

Problem 14019

Let the original price be $x$ . Write the equation: $360 = \frac{2}{5}x$ . Find $x$ .

See Solution

Problem 14020

Find $m \angle L M N$ if $m \angle F M N=99^{\circ}$ and $m \angle L M F=36^{\circ}$ .

See Solution

Problem 14021

The number minus 18 equals 9. Find the number. $x - 18 = 9$

See Solution

Problem 14022

Find the smaller of two consecutive numbers whose sum is -33. Let the numbers be $x$ and $x+1$ .

See Solution

Problem 14023

Write the equation for savings $s$ after $m$ months, starting with \$374 and saving \$26 monthly.

See Solution

Problem 14024

Find the reference angle for $\theta=-\frac{29 \pi}{12}$ and the coterminal angle $\theta_{C}=\frac{19 \pi}{12}$ in quadrant IV. What is $\theta_{R}$ ?

See Solution

Problem 14025

Solve the equation: $x + 6 = x$ .

See Solution

Problem 14026

Solve for $x$ in the equation $x+(x+33)=200$ .

See Solution

Problem 14027

Rahquez and Hu have 203 books total. If Rahquez has 35 more than Hu, find how many books Hu has.

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Problem 14028

Solve the equation: $\frac{1}{2} x + \frac{1}{2} x = x + 1$ .

See Solution

Problem 14029

Solve the equation: $\frac{1}{3}(9 x+3)=3 x+1$ .

See Solution

Problem 14030

Find the reference angle for $\theta=570^{\circ}$ and the angle $\theta_{C}=210^{\circ}$ in quadrant III. What is $\theta_{R}=\square^{\circ}$ ?

See Solution

Problem 14031

Four times a number minus two equals -58. Find the number.
A) Write the equation: $4x - 2 = -58$ . B) Solve for $x$ : $x =$

See Solution

Problem 14032

An organism has $20 \mathrm{~g}$ of carbon-14. After 11,400 years (2 half-lives), how much remains? a) 0 g b) 2.5 g c) 5 g d) 10 g

See Solution

Problem 14033

Solve for $x$ : $2 x + 4 = -(-7 x + 6)$ .

See Solution

Problem 14034

Estimate the age of a fossil with $16 \mathrm{~g}$ of carbon-14 from an initial $32 \mathrm{~g}$ .

See Solution

Problem 14035

A $15 \mathrm{~cm}$ wire is cut into two pieces. The longer piece is $5 \mathrm{~cm}$ longer than the shorter. Find the shorter piece's length.

See Solution

Problem 14036

What percentage of carbon-14 is left after 34,200 years? a $0 \%$ b $1.56 \%$ c $3.02 \%$ d $10.5 \%$

See Solution

Problem 14037

Solve for $\square$ in the equations: a) $8 \cdot \square=40$ , b) $8+\square=40$ , c) $21 \div \square=7$ , d) $21-\square=7$ , e) $21 \cdot \square=7$ .

See Solution

Problem 14038

Calculate the total cost for 8 items at \$25 each plus a \$17.50 fee. Total \$ (\#\#\#.\#)

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Problem 14039

Find three consecutive natural numbers that add up to 1074. What are the numbers in increasing order?

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Problem 14040

A cable provider charges \$75 installation and \$39.96/month. A satellite provider has free installation and \$13.32/month. When is total cost equal for both after owning 3 TVs?

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Problem 14041

Find the values for the following equations given $a=11$ and $b=3$ : $2a + 3b$ , $a^2 - b + 10$ , $(ab)^2 - (a+b)^2$ .

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Problem 14042

A rental car company charges \ $30 plus 20 cents per mile. Model the total cost with$ m$ as miles driven.

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Problem 14043

Find the reference angle for $\theta=-420^{\circ}$ and the least nonnegative coterminal angle. $\theta_{\mathrm{C}}=$

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Problem 14044

Find the probabilities of these spins: red first, cyan second, blue third; blue first, blue second, red third; red on all spins.

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Problem 14045

Two cyclists, 42 miles apart, meet in 2 hours. One cycles twice as fast. Find the faster cyclist's speed in $\mathrm{mi} / \mathrm{h}$ .

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Problem 14046

Let your brother's age be $x$ . Then your cousin's age is $x + 8$ . Three years ago, $x + 8 - 3 = 2(x - 3)$ . Find $x$ .

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Problem 14047

Solve $|2x + 3| + 9 = 20$ . Find the values of $x$ .

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Problem 14048

Find the probability of correctly guessing both answers in a 2-question quiz with 3 choices each. Round to one decimal place.

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Problem 14049

What is the tire's load capacity at 26 psi if it is 196 lb less than 1949 lb at 32 psi?

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Problem 14050

Solve the equation: $\frac{56}{80} = x$ . What is the value of $x$ ?

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Problem 14051

What is the probability that both of two randomly chosen students wear glasses if $20\%$ of students do? Round to three decimal places.

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Problem 14052

Katrina has 60 GB of storage; her father has 10 times that. How much storage does he have? Show your work.

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Problem 14053

One angle is $66^{\circ}$ , and the third angle is $57^{\circ}$ more than half the second angle. Find the second and third angles.

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Problem 14054

Solve the equation $2|2x+3|=|x-3|$ for the values of $x$ . What are the solutions?

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Problem 14055

Brigeth has 5 chocolate chip, 5 peanut butter, 4 sugar, and 9 oatmeal cookies. Find the probability of selecting 2 chocolate chip cookies.

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Problem 14056

Given $z=6+2 i$ , prove that $z-i z=8-4 i$ and $|z|^{2}+|i z|^{2}=|z-i z|^{2}$ .

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Problem 14057

Two similar triangles have sides $7x$ and $70$ for the first, and $120$ and $60$ for the second. Find $x$ .

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Problem 14058

Katrina saved \$200. Her father spent 10 times that. What is the cost of her father's computer? Explain your answer.

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Problem 14059

Theodore's bill was \$ 899, with \$ 335 for parts. If labor costs \$ 47/hour, how many hours of labor were needed?
(A) Write an equation using $x$ . (B) Solve for $x$ . Answer: The number of labor hours was

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Problem 14060

A jar has 6 red marbles (1-6) and 8 blue marbles (1-8). Find the probabilities for these scenarios:
a) If a blue marble is chosen, what's the chance it's numbered 3? b) If a marble with number 1 is chosen, what's the chance it's blue?

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Problem 14061

Solve $9 y - 2 x = 1$ for $y$ . The solution is $y = \frac{2 x + 1}{9}$ .

See Solution

Problem 14062

Find three consecutive odd integers that sum to 63 using the expression $2n + 1$ .

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Problem 14063

Fill in the blanks: a. 4 times 3 is $12$ . b. 10 times 9 is $90$ . c. 700 is 10 times $70$ . d. 8,000 is $10$ times 800.

See Solution

Problem 14064

Theodore's total bill was \ $899, with \$ 335 for parts. If labor costs \$ 47 per hour, how many hours of labor ($ x$) were needed?

See Solution

Problem 14065

Solve the equation: $\frac{3}{4}(x+6)=-\frac{1}{4} x$ . What is the solution?

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Problem 14066

An executive earns a yearly total of 83600 dollars, including a 7400 dollar bonus. Find her monthly salary $S$ .

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Problem 14067

Determine if $y$ is a function of $\alpha$ for: A) $x^{2}=y-7$ , B) $y^{2}=x+1$ .

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Problem 14068

Solve for $l$ in the perimeter formula of a rectangle: $p=2 l+2 w$ . What is the expression for $l$ ?

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Problem 14069

What is the probability that at least one of four randomly selected people has been vaccinated if $66\%$ are vaccinated? Round to three decimal places.

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Problem 14070

Calculate: $3 \times(4-3)=$

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Problem 14071

A room is 6 m longer than wide, with a perimeter of 36 m. Find the length and width of the room.

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Problem 14072

Aaron filled the bird bath with 58 ounces. After blue jays drank 3.18 and a vulture drank $14 \frac{2}{5}$ , how much is left?

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Problem 14073

Tomas's grandfather is 100 years old and 10 times Tomas's age. Find Tomas's age.

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Problem 14074

Choose between two cell phone plans: Plan 1 at 21 cents/min and Plan 2 at \$29.95 + 9 cents/min. Find when costs equal.
$C_{1} = 0.21t$ $C_{2} = 29.95 + 0.09t$
Find $t$ where $C_{1} = C_{2}$ .

See Solution

Problem 14075

Jodie spent $30 \frac{1}{4}$ seconds climbing and 11.78 seconds on ropes. How much time is left to reach 73.4 seconds?

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Problem 14076

At the fair, the male to female ratio is $5:2$ . With 175 people total, how many males are there?

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Problem 14077

Find $p$ and $q$ if $3+2i$ is a root of $z^{2}+pz+q=0$ with $p, q \in \mathbb{R}$ .

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Problem 14078

A room is 3 times longer than wide with a perimeter of 64 m. Find the length and width in meters.

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Problem 14079

What is the probability of drawing a King or an odd-valued card from a standard deck? Provide your answer as a fraction or decimal (3 decimal places).

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Problem 14080

Find values of $x$ such that $y_{1}=\frac{x-4}{4}, y_{2}=\frac{x-11}{5}$ and $y_{1}-y_{2}=1$ . Choose A, B, or C.

See Solution

Problem 14081

Solve for $W$ in the equation $S=2 L H+(2 L+2 H) W$ .

See Solution

Problem 14082

Solve the equation $f(x p + u) = j + a$ for $f$ and $p$ . Find: $f =$ and $p =$ .

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Problem 14083

Sheena earned \ $12/hour, got a \$340 bonus, and made \$1216 total. What does$ x=73$ represent?

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Problem 14084

Calculate work done with $5 \mathrm{~N}$ force moving an object 25 meters. Choices: 5 J, 20 J, 30 J, 125 J.

See Solution

Problem 14085

Find $P(A$ or $B)$ given $P(A)=0.4$ , $P(B)=0.5$ , and $P(A \text{ and } B)=0.3$ . Round to two decimal places.

See Solution

Problem 14086

Manfred's gym costs \$25 yearly plus a monthly fee. After 3 years, he paid \$579. Find his monthly payment.

See Solution

Problem 14087

Find $P(B)$ given $P(A)=0.4$ , $P(A \text{ or } B)=0.95$ , and $P(A \text{ and } B)=0.3$ . Round to two decimal places.

See Solution

Problem 14088

Find the probability that a randomly selected student is taking a math or English class, given $68\%$ in math, $75\%$ in English, and $60\%$ in both. Round your answer to two decimal places.

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Problem 14089

Find values of $x$ where $y_{1} + y_{2} = y_{3}$ with $y_{1}=\frac{3}{x+3}$ , $y_{2}=\frac{5}{x+2}$ , $y_{3}=\frac{12x+5}{x^2+5x+6}$ .

See Solution

Problem 14090

What is the probability of drawing a heart or an ace from a standard deck of cards? Round your answer to three decimal places.

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Problem 14091

Solve for $y$ : $\frac{x}{2}+\frac{y}{9}=1$ . What is $y$ ?

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Problem 14092

7.65 m equals how many cm?

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Problem 14093

Calculate the area of a triangle with base 10m and height 8m using $Area = \frac{1}{2} \cdot base \cdot height$ .

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Problem 14094

Find all values of $x$ such that $y_{1} + y_{2} = y_{3}$ , where $y_{1}=\frac{4}{x+6}, y_{2}=\frac{5}{x+3}, y_{3}=\frac{12 x+30}{x^{2}+9 x+18}$ . Choices: A, B, C.

See Solution

Problem 14095

Mr. Michaels has 40 m of wire. After wiring 16 lamps (0.45 m each), 12 wall lights (0.7 m each), and 1 floor lamp (2.6 m), how much is left? A) 7.2 m B) 18.2 m C) 21.8 m D) 15.6 m

See Solution

Problem 14096

Find the width of a 70" TV with a 16:9 aspect ratio. Options: $80.33^{\prime \prime}$ , $39.4^{\prime \prime}$ , $61^{\prime \prime}$ , $44.8^{\prime \prime}$ .

See Solution

Problem 14097

Solve for $x$ in the equation: $y_{1}=\frac{3}{x+6}, y_{2}=\frac{4}{x+4}, y_{3}=\frac{9 x+28}{x^{2}+10 x+24}$ , where $y_{1}+y_{2}=y_{3}$ .

See Solution

Problem 14098

Find $x$ such that $y_{1}=\frac{3}{x+6}, y_{2}=\frac{4}{x+4}, y_{3}=\frac{9x+28}{x^2+10x+24}$ and $y_{1}+y_{2}=y_{3}$ .

See Solution

Problem 14099

Find $x$ when $y=0$ for the equation $y=2[x-(3-x)]-3(x+1)$ . Choose A, B, or C for the solution.

See Solution

Problem 14100

Find $x$ values where $y=0$ for $y=\frac{x+6}{3x-12}-\frac{7}{x-4}-\frac{2}{3}$ . Choices: A, B, C.

See Solution

1 ...138 139 140 141 142 143 144 ...188

Equation

Problem 14001

Find xxx given that m∠BJK=146+2xm \angle BJK = 146 + 2xm∠BJK=146+2x, m∠IJK=172∘m \angle IJK = 172^\circm∠IJK=172∘, and m∠IJB=2x+26m \angle IJB = 2x + 26m∠IJB=2x+26.

Problem 14002

Solve for ccc in the equation 6c+1=−26 c + 1 = -26c+1=−2.

Problem 14003

Solve for ccc in the equation 6c+1=−26 c + 1 = -26c+1=−2.

Problem 14004

Find m∠NFEm \angle N F Em∠NFE given m∠GFN=4x+10m \angle G F N=4x+10m∠GFN=4x+10, m∠NFE=14x+3m \angle N F E=14x+3m∠NFE=14x+3, and m∠GFE=157∘m \angle G F E=157^{\circ}m∠GFE=157∘.

Problem 14005

Find m∠IHGm \angle I H Gm∠IHG given m∠ZHG=11x−1m \angle Z H G=11 x-1m∠ZHG=11x−1, m∠IHZ=24∘m \angle I H Z=24^{\circ}m∠IHZ=24∘, and m∠IHG=12x+13m \angle I H G=12 x+13m∠IHG=12x+13.

Problem 14006

Find xxx if m∠GFZ=38∘m \angle G F Z=38^{\circ}m∠GFZ=38∘, m∠ZFE=2x+125m \angle Z F E=2x+125m∠ZFE=2x+125, and m∠GFE=x+163m \angle G F E=x+163m∠GFE=x+163.

Problem 14007

Find 2 values of θ\thetaθ in [0,2π)[0, 2\pi)[0,2π) such that cot⁡θ=3.2041\cot \theta = 3.2041cotθ=3.2041.

Problem 14008

Solve for xxx in the equation: −2(x+2)−7=−3-2(x+2)-7=-3−2(x+2)−7=−3.

Problem 14009

In 2015, North Dakota had 545,027 drivers and Wyoming had 422,450. Estimate total drivers by rounding to the nearest ten thousand. Is your estimate reasonable?

Problem 14010

Find the perimeter and area of a trapezoid with bases 13.4 and 14.7 units, and height 11.2 units. Round area to the nearest tenth.

Problem 14011

Find m∠HIWm \angle H I Wm∠HIW given m∠WIJ=10xm \angle W I J=10 xm∠WIJ=10x, m∠HIJ=145∘m \angle H I J=145^{\circ}m∠HIJ=145∘, and m∠HIW=2x+13m \angle H I W=2 x+13m∠HIW=2x+13.

Problem 14012

Find the perimeter and area of a triangle with height 11.2, sides 14.7, 13.4, and base 13.4. Round area to nearest tenth.

Problem 14013

Find m∠FGHm \angle F G Hm∠FGH given m∠FGB=105∘m \angle F G B=105^{\circ}m∠FGB=105∘ and m∠BGH=54∘m \angle B G H=54^{\circ}m∠BGH=54∘.

Problem 14014

Calculate the final score based on weights: midterm (5\%), project (15\%), homework (30\%), final (50\%). Scores: midterm 66, project 99, homework 76, final 72. What is the final score and letter grade?

Problem 14015

Find the distance over which a force of 200 N does 800 J of work. Options: a. 40 m40 \mathrm{~m}40 m b. 20 m20 \mathrm{~m}20 m c. 4 m4 \mathrm{~m}4 m d. 2 m2 \mathrm{~m}2 m

Problem 14016

Calculate the geometric mean of 1.1061.1061.106, 1.0731.0731.073, and 1.0381.0381.038 to find the average growth factor. Round to four decimal places.

Problem 14017

Find m∠WVUm \angle W V Um∠WVU given m∠ZVU=62∘m \angle Z V U=62^{\circ}m∠ZVU=62∘ and m∠WVZ=50∘m \angle W V Z=50^{\circ}m∠WVZ=50∘.

Problem 14018

In January, 611,749 domestic and 106,909 international passengers used Terminal 4. Find the total number of passengers.

Problem 14019

Let the original price be xxx. Write the equation: 360=25x360 = \frac{2}{5}x360=52​x. Find xxx.

Problem 14020

Find m∠LMNm \angle L M Nm∠LMN if m∠FMN=99∘m \angle F M N=99^{\circ}m∠FMN=99∘ and m∠LMF=36∘m \angle L M F=36^{\circ}m∠LMF=36∘.

Problem 14021

The number minus 18 equals 9. Find the number. x−18=9x - 18 = 9x−18=9

Problem 14022

Find the smaller of two consecutive numbers whose sum is -33. Let the numbers be xxx and x+1x+1x+1.

Problem 14023

Write the equation for savings sss after mmm months, starting with \$374 and saving \$26 monthly.

Problem 14024

Find the reference angle for θ=−29π12\theta=-\frac{29 \pi}{12}θ=−1229π​ and the coterminal angle θC=19π12\theta_{C}=\frac{19 \pi}{12}θC​=1219π​ in quadrant IV. What is θR\theta_{R}θR​?

Problem 14025

Solve the equation: x+6=xx + 6 = xx+6=x.

Problem 14026

Solve for xxx in the equation x+(x+33)=200x+(x+33)=200x+(x+33)=200.

Problem 14027

Rahquez and Hu have 203 books total. If Rahquez has 35 more than Hu, find how many books Hu has.

Problem 14028

Solve the equation: 12x+12x=x+1\frac{1}{2} x + \frac{1}{2} x = x + 121​x+21​x=x+1.

Problem 14029

Solve the equation: 13(9x+3)=3x+1\frac{1}{3}(9 x+3)=3 x+131​(9x+3)=3x+1.

Problem 14030

Find the reference angle for θ=570∘\theta=570^{\circ}θ=570∘ and the angle θC=210∘\theta_{C}=210^{\circ}θC​=210∘ in quadrant III. What is θR=□∘\theta_{R}=\square^{\circ}θR​=□∘?

Problem 14031

Four times a number minus two equals -58. Find the number. A) Write the equation: 4x−2=−584x - 2 = -584x−2=−58. B) Solve for xxx: x=x = x=

Problem 14032

An organism has 20 g20 \mathrm{~g}20 g of carbon-14. After 11,400 years (2 half-lives), how much remains? a) 0 g b) 2.5 g c) 5 g d) 10 g

Problem 14033

Solve for xxx: 2x+4=−(−7x+6)2 x + 4 = -(-7 x + 6)2x+4=−(−7x+6).

Problem 14034

Estimate the age of a fossil with 16 g16 \mathrm{~g}16 g of carbon-14 from an initial 32 g32 \mathrm{~g}32 g.

Problem 14035

A 15 cm15 \mathrm{~cm}15 cm wire is cut into two pieces. The longer piece is 5 cm5 \mathrm{~cm}5 cm longer than the shorter. Find the shorter piece's length.

Problem 14036

What percentage of carbon-14 is left after 34,200 years? a 0%0 \%0% b 1.56%1.56 \%1.56% c 3.02%3.02 \%3.02% d 10.5%10.5 \%10.5%

Problem 14037

Solve for □\square□ in the equations: a) 8⋅□=408 \cdot \square=408⋅□=40, b) 8+□=408+\square=408+□=40, c) 21÷□=721 \div \square=721÷□=7, d) 21−□=721-\square=721−□=7, e) 21⋅□=721 \cdot \square=721⋅□=7.

Problem 14038

Calculate the total cost for 8 items at \$25 each plus a \$17.50 fee. Total \$ (\#\#\#.\#)

Problem 14039

Find three consecutive natural numbers that add up to 1074. What are the numbers in increasing order?

Problem 14040

Find $x$ given that $m \angle BJK = 146 + 2x$ , $m \angle IJK = 172^\circ$ , and $m \angle IJB = 2x + 26$ .

Solve for $c$ in the equation $6 c + 1 = -2$ .

Solve for $c$ in the equation $6 c + 1 = -2$ .

Find $m \angle N F E$ given $m \angle G F N=4x+10$ , $m \angle N F E=14x+3$ , and $m \angle G F E=157^{\circ}$ .

Find $m \angle I H G$ given $m \angle Z H G=11 x-1$ , $m \angle I H Z=24^{\circ}$ , and $m \angle I H G=12 x+13$ .

Find $x$ if $m \angle G F Z=38^{\circ}$ , $m \angle Z F E=2x+125$ , and $m \angle G F E=x+163$ .

Find 2 values of $\theta$ in $[0, 2\pi)$ such that $\cot \theta = 3.2041$ .

Solve for $x$ in the equation: $-2(x+2)-7=-3$ .

Find $m \angle H I W$ given $m \angle W I J=10 x$ , $m \angle H I J=145^{\circ}$ , and $m \angle H I W=2 x+13$ .

Find $m \angle F G H$ given $m \angle F G B=105^{\circ}$ and $m \angle B G H=54^{\circ}$ .

Find the distance over which a force of 200 N does 800 J of work. Options: a. $40 \mathrm{~m}$ b. $20 \mathrm{~m}$ c. $4 \mathrm{~m}$ d. $2 \mathrm{~m}$

Calculate the geometric mean of $1.106$ , $1.073$ , and $1.038$ to find the average growth factor. Round to four decimal places.

Find $m \angle W V U$ given $m \angle Z V U=62^{\circ}$ and $m \angle W V Z=50^{\circ}$ .

Let the original price be $x$ . Write the equation: $360 = \frac{2}{5}x$ . Find $x$ .

Find $m \angle L M N$ if $m \angle F M N=99^{\circ}$ and $m \angle L M F=36^{\circ}$ .

The number minus 18 equals 9. Find the number. $x - 18 = 9$

Find the smaller of two consecutive numbers whose sum is -33. Let the numbers be $x$ and $x+1$ .

Write the equation for savings $s$ after $m$ months, starting with \$374 and saving \$26 monthly.

Find the reference angle for $\theta=-\frac{29 \pi}{12}$ and the coterminal angle $\theta_{C}=\frac{19 \pi}{12}$ in quadrant IV. What is $\theta_{R}$ ?

Solve the equation: $x + 6 = x$ .

Solve for $x$ in the equation $x+(x+33)=200$ .

Solve the equation: $\frac{1}{2} x + \frac{1}{2} x = x + 1$ .

Solve the equation: $\frac{1}{3}(9 x+3)=3 x+1$ .

Find the reference angle for $\theta=570^{\circ}$ and the angle $\theta_{C}=210^{\circ}$ in quadrant III. What is $\theta_{R}=\square^{\circ}$ ?

Four times a number minus two equals -58. Find the number.
A) Write the equation: $4x - 2 = -58$ . B) Solve for $x$ : $x =$

An organism has $20 \mathrm{~g}$ of carbon-14. After 11,400 years (2 half-lives), how much remains? a) 0 g b) 2.5 g c) 5 g d) 10 g

Solve for $x$ : $2 x + 4 = -(-7 x + 6)$ .

Estimate the age of a fossil with $16 \mathrm{~g}$ of carbon-14 from an initial $32 \mathrm{~g}$ .

A $15 \mathrm{~cm}$ wire is cut into two pieces. The longer piece is $5 \mathrm{~cm}$ longer than the shorter. Find the shorter piece's length.

What percentage of carbon-14 is left after 34,200 years? a $0 \%$ b $1.56 \%$ c $3.02 \%$ d $10.5 \%$

Solve for $\square$ in the equations: a) $8 \cdot \square=40$ , b) $8+\square=40$ , c) $21 \div \square=7$ , d) $21-\square=7$ , e) $21 \cdot \square=7$ .

Find the values for the following equations given $a=11$ and $b=3$ : $2a + 3b$ , $a^2 - b + 10$ , $(ab)^2 - (a+b)^2$ .

A rental car company charges \ $30 plus 20 cents per mile. Model the total cost with$ m$ as miles driven.

Find the reference angle for $\theta=-420^{\circ}$ and the least nonnegative coterminal angle. $\theta_{\mathrm{C}}=$

Two cyclists, 42 miles apart, meet in 2 hours. One cycles twice as fast. Find the faster cyclist's speed in $\mathrm{mi} / \mathrm{h}$ .

Let your brother's age be $x$ . Then your cousin's age is $x + 8$ . Three years ago, $x + 8 - 3 = 2(x - 3)$ . Find $x$ .

Solve $|2x + 3| + 9 = 20$ . Find the values of $x$ .

Solve the equation: $\frac{56}{80} = x$ . What is the value of $x$ ?

What is the probability that both of two randomly chosen students wear glasses if $20\%$ of students do? Round to three decimal places.

One angle is $66^{\circ}$ , and the third angle is $57^{\circ}$ more than half the second angle. Find the second and third angles.

Solve the equation $2|2x+3|=|x-3|$ for the values of $x$ . What are the solutions?

Given $z=6+2 i$ , prove that $z-i z=8-4 i$ and $|z|^{2}+|i z|^{2}=|z-i z|^{2}$ .

Two similar triangles have sides $7x$ and $70$ for the first, and $120$ and $60$ for the second. Find $x$ .

Theodore's bill was \$ 899, with \$ 335 for parts. If labor costs \$ 47/hour, how many hours of labor were needed?
(A) Write an equation using $x$ . (B) Solve for $x$ . Answer: The number of labor hours was

A jar has 6 red marbles (1-6) and 8 blue marbles (1-8). Find the probabilities for these scenarios:
a) If a blue marble is chosen, what's the chance it's numbered 3? b) If a marble with number 1 is chosen, what's the chance it's blue?

Solve $9 y - 2 x = 1$ for $y$ . The solution is $y = \frac{2 x + 1}{9}$ .

Find three consecutive odd integers that sum to 63 using the expression $2n + 1$ .

Fill in the blanks: a. 4 times 3 is $12$ . b. 10 times 9 is $90$ . c. 700 is 10 times $70$ . d. 8,000 is $10$ times 800.

Theodore's total bill was \ $899, with \$ 335 for parts. If labor costs \$ 47 per hour, how many hours of labor ($ x$) were needed?

Solve the equation: $\frac{3}{4}(x+6)=-\frac{1}{4} x$ . What is the solution?

An executive earns a yearly total of 83600 dollars, including a 7400 dollar bonus. Find her monthly salary $S$ .

Determine if $y$ is a function of $\alpha$ for: A) $x^{2}=y-7$ , B) $y^{2}=x+1$ .

Solve for $l$ in the perimeter formula of a rectangle: $p=2 l+2 w$ . What is the expression for $l$ ?

What is the probability that at least one of four randomly selected people has been vaccinated if $66\%$ are vaccinated? Round to three decimal places.

Calculate: $3 \times(4-3)=$

Aaron filled the bird bath with 58 ounces. After blue jays drank 3.18 and a vulture drank $14 \frac{2}{5}$ , how much is left?

Choose between two cell phone plans: Plan 1 at 21 cents/min and Plan 2 at \$29.95 + 9 cents/min. Find when costs equal.
$C_{1} = 0.21t$ $C_{2} = 29.95 + 0.09t$
Find $t$ where $C_{1} = C_{2}$ .