Question 1

Use an equation to solve the problem.
-Joe Pearlman received a $2.75 \%$ pay decrease. His salary after the decrease was $\$ 36,955$. What was his salary before the decrease?
A) $\$ 37,997.25$
B) $\$ 37,999.725$
C) $\$ 38,000$
D) $\$ 39,045$

Accepted Answer

The answer of Use an equation to solve the problem.
-Joe...

Question 2

Use an equation to solve the problem.
-A square of side $x$ inches is cut out of each corner of an 8 in. by 12 in. piece of cardboard, and the sides folded up to form an open-topped box. Use your graphing calculator to determine the dimensions of cut-out squares that will produce the box of maximum volume.
(Hint: you will first need to write the volume of the box $\mathrm { V }$ as a function of $x$.)
A) $1.7$ inches by $1.7$ inches
B) $1.8$ inches by $1.8$ inches
C) $1.6$ inches by $1.6$ inches
D) $1.4$ inches by $1.4$ inches

Accepted Answer

The answer of Use an equation to solve the problem.
-A...

Question 3

Use an equation to solve the problem.
-When a number, half of the number, and a third of the number are added together, the sum is 275 . Find the three numbers.

Accepted Answer

The answer of Use an equation to solve the problem.
-When...

Question 4

Write the specified quantity as a function of the specified variable.
-The base of an isosceles triangle is half as long as the two equal sides. Write the area of the triangle as a function of the length of the base.
A) $A = 7 b$
B) $\mathrm { A } = \frac { 15 } { 16 } \mathrm {~b} ^ { 3 }$
C) $A = \frac { \sqrt { 15 } } { 4 } b ^ { 2 }$
D) $A = \frac { 15 } { 16 } b ^ { 2 }$

Accepted Answer

Given that the base of the isosceles triangle is half as long as the two equal sides, let the length of the base be $b$, and the length of the equal sides be $2b$. The height $h$ of the triangle can be found using the Pythagorean theorem in one of the right triangles formed by dropping a perpendicular from the apex to the base: $h = \sqrt{(2b)^2 - \left(\frac{b}{2}\right)^2} = \sqrt{4b^2 - \frac{b^2}{4}} = \sqrt{\frac{16b^2 - b^2}{4}} = \sqrt{\frac{15b^2}{4}} = \frac{\sqrt{15}b}{2}$. The area $A$ of the triangle is $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times b \times \frac{\sqrt{15}b}{2} = \frac{\sqrt{15}}{4}b^2$.

Question 5

Choose the one alternative that best completes the statement or answers the question.
Write a mathematical expression for the quantity described verbally.
-The revenue when each item sells for $\$ 31,416$.
A) $31,416 - x$
B) $31,416 + x$
C) $31,416 x$
D) $x - 31,416$

Accepted Answer

Revenue is calculated by multiplying the price per item by the number of items sold, hence $31,416 x$.

Question 6

Use an equation to solve the problem.
-A tire of a moving bicycle has radius 16 inches. If the tire is making 3 rotations per second, find the bicycle's speed in miles per hour.
A) 19.7 mph
B) 5.7 mph
C) 17.1 mph
D) 18.6 mph

Accepted Answer

The answer of Use an equation to solve the problem.
-A...

Question 7

Write the specified quantity as a function of the specified variable.
-A circle is inscribed in a square. Write the area of the square as a function of the radius.
A) $\mathrm { A } = 2 \mathrm { r } ^ { 2 }$
B) $\mathrm { A } = 2 \mathrm { r }$
C) $\mathrm { A } = \mathrm { r } ^ { 3 }$
D) $A = 4 r ^ { 2 }$

Accepted Answer

The diameter of the circle is equal to the side length of the square. Since the diameter is twice the radius ($2r$), the area of the square ($A$) is the side length squared, which is $(2r)^2 = 4r^2$.

Question 8

Use an equation to solve the problem.
-If Gloria received a $4 \%$ raise and is now making $\$ 24,960$ a year, what was her salary before the raise?
A) $\$ 24,000$
B) $\$ 22,960$
C) $\$ 23,960$
D) $\$ 25,000$

Accepted Answer

Gloria's new salary is 104% of her old salary. So, if $x$ is her old salary, $1.04x = 24,960$. Solving for $x$ gives $x = \frac{24,960}{1.04} = \$24,000$.

Question 9

Use an equation to solve the problem.
-Between 1990 and 2000 the population of a certain city grew from 202,000 to 239,700 . What was the percentage increase in the population of the city?
A) $18.7 \%$
B) $19.6 \%$
C) $15.7 \%$
D) $1.9 \%$

Accepted Answer

The percentage increase in population is calculated by the formula $\frac{{\text{New Population} - \text{Old Population}}}{{\text{Old Population}}} \times 100$. Substituting the given values, we get $\frac{{239,700 - 202,000}}{{202,000}} \times 100 = 18.7\%$.

Question 10

Use an equation to solve the problem.
-One positive number is twice another positive number. The sum of the two numbers is 360 . Find the two numbers.
A) 180,180
B) 120,122
C) 120,240
D) 60,300

Accepted Answer

Let the smaller number be x. Then the larger number is 2x. The equation is x + 2x = 360. Solving for x gives x = 120, so the two numbers are 120 and 240.

Question 11

Use an equation to solve the problem.
-On Monday, an investor bought 100 shares of stock. On Tuesday, the value of the shares went up $5 \%$. How much did the investor pay for the 100 shares if he sold them Wednesday morning for $\$ 1470.00$ ?
A) $\$ 1543.50$
B) $\$ 1420.00$
C) $\$ 1450.00$
D) $\$ 1400.00$

Accepted Answer

The investor sold the shares for $1470 after a 5% increase. Let $ x $ be the original price. Then $ x \times 1.05 = 1470 $. Solving for $ x $, we get $ x = 1400 $.

Question 12

Write the specified quantity as a function of the specified variable.
-The base of an isosceles triangle is a fourth as long as the two equal sides. Write the area of the triangle as a function of the length of the base.
A) $A = \frac { \sqrt { 15 } } { 4 } b ^ { 2 }$
B) $A = \frac { 63 } { 8 } b ^ { 3 }$
C) $A = 2 b ^ { 2 }$
D) $A = \frac { 3 \sqrt { 7 } } { 4 } b ^ { 2 }$

Accepted Answer

The answer of Write the specified quantity as a function...

Question 13

Write the specified quantity as a function of the specified variable.
-One leg of a right triangle is three times as long as the other. Write the length of the hypotenuse as a function of the length of the shorter leg.
A) $c = 2 a$
B) $c = 10 a ^ { 2 }$
C) $c = 2 \sqrt { a }$
D) $c = a \sqrt { 10 }$

Accepted Answer

Given a right triangle where one leg is three times as long as the other, let the shorter leg be $a$ and the longer leg be $3a$. By the Pythagorean theorem, $c^2 = a^2 + (3a)^2 = a^2 + 9a^2 = 10a^2$, so $c = a\sqrt{10}$.

Question 14

Write the specified quantity as a function of the specified variable.
-The height of a right circular cylinder equals its diameter. Write the volume of the cylinder as a function of its radius.
A) $V = \pi r ^ { 3 }$
B) $V = 4 \pi r$
C) $V = 2 \pi r ^ { 3 }$
D) $V = \frac { 1 } { 2 } \pi r ^ { 3 }$

Accepted Answer

The answer of Write the specified quantity as a function...

Question 15

Write the specified quantity as a function of the specified variable.
-The base of an isosceles triangle is a third as long as the two equal sides. Write the perimeter of the triangle as a function of the length of the base.
A) $P = \frac { 8 } { 3 } b$
B) $P = < \frac { 5 } { 3 } b$
C) $P = 7 b$
D) $P = 5 b$

Accepted Answer

The answer of Write the specified quantity as a function...

Question 16

Use an equation to solve the problem.
-When a number is added to its double and its triple, the sum is 138 . Find the three numbers.
A) $23,46,138$
B) $46,69,92$
C) $46,69,138$
D) $23,46,69$

Accepted Answer

Let the number be $x$. Its double is $2x$ and its triple is $3x$. According to the problem, $x + 2x + 3x = 138$. Simplifying, $6x = 138$, so $x = 23$. Therefore, the numbers are $23$, $46$, and $69$.

Question 17

Write the specified quantity as a function of the specified variable.
-A square is inscribed in a circle. Write the area of the square as a function of the radius.
A) $A = r$
B) $A = 2 r$
C) $\mathrm { A } = 2 \mathrm { r } ^ { 2 }$
D) $A = 4 r ^ { 2 }$

Accepted Answer

The diagonal of the square is equal to the diameter of the circle, so if the radius is $r$, the diameter (and thus the diagonal of the square) is $2r$. Using the Pythagorean theorem in a right triangle formed by half the diagonal and two sides of the square, if the side of the square is $s$, then $s^2 + s^2 = (2r)^2$, leading to $2s^2 = 4r^2$, and thus $s^2 = 2r^2$. Since the area of the square ($A$) is $s^2$, it follows that $A = 2r^2$.

Question 18

Solve the problem.
-Sue invested $10,000, part at 5.9% annual interest and the balance at 6.7% annual interest. How much is invested at each rate if a 1-year interest payment is $645.52?
A) $2960 at 5.9% and $4160 at 6.7%
B) $3160 at 5.9% and $6840 at 6.7%
C) $3060 at 5.9% and $6940 at 6.7%
D) $6940 at 5.9% and $3060 at 6.7%

Accepted Answer

Let x be the amount invested at 5.9%, then (10000 - x) is invested at 6.7%. The equation is 0.059x + 0.067(10000 - x) = 645.52. Solving this gives x = 3060, so $3060 is invested at 5.9% and $6940 at 6.7%.

Question 19

Choose the one alternative that best completes the statement or answers the question.
Write a mathematical expression for the quantity described verbally.
-The profit consists of a franchise fee of $\$ 100,000$ plus $20 \%$ of all sales
A) $0.2 + 100,000 x$
B) $20 x + 100,000$
C) $( 0.2 x + 100,000 )$
D) $\$ 100,000 - 0.2$

Accepted Answer

The correct expression is $0.2x + 100,000$, where $x$ represents the sales. This captures the $20\%$ of sales ($0.2x$) plus the franchise fee ($100,000$).

Question 20

Use an equation to solve the problem.
-A construction company builds a swimming pool with a perimeter of $50 \mathrm {~m}$. The length is $3 \mathrm {~m}$ more than the width. Find the dimensions of the swimming pool?
A) $19 \mathrm {~m} \times 11 \mathrm {~m}$
B) $9 \mathrm {~m} \times 11 \mathrm {~m}$
C) $14 \mathrm {~m} \times 3 \mathrm {~m}$
D) $14 \mathrm {~m} \times 11 \mathrm {~m}$

Accepted Answer

The answer of Use an equation to solve the problem.
-A...

Quiz 1: Functions and Graphs

Use an equation to solve the problem. -Joe Pearlman received a $2.75 \%$ pay decrease. His salary after the decrease was $\$ 36,955$ . What was his salary before the decrease?

Use an equation to solve the problem. -When a number, half of the number, and a third of the number are added together, the sum is 275 . Find the three numbers.

Write the specified quantity as a function of the specified variable. -The base of an isosceles triangle is half as long as the two equal sides. Write the area of the triangle as a function of the length of the base.

Choose the one alternative that best completes the statement or answers the question. Write a mathematical expression for the quantity described verbally. -The revenue when each item sells for $\$ 31,416$ .

Use an equation to solve the problem. -A tire of a moving bicycle has radius 16 inches. If the tire is making 3 rotations per second, find the bicycle's speed in miles per hour.

Write the specified quantity as a function of the specified variable. -A circle is inscribed in a square. Write the area of the square as a function of the radius.

Use an equation to solve the problem. -If Gloria received a $4 \%$ raise and is now making $\$ 24,960$ a year, what was her salary before the raise?

Use an equation to solve the problem. -Between 1990 and 2000 the population of a certain city grew from 202,000 to 239,700 . What was the percentage increase in the population of the city?

Use an equation to solve the problem. -One positive number is twice another positive number. The sum of the two numbers is 360 . Find the two numbers.

Use an equation to solve the problem. -On Monday, an investor bought 100 shares of stock. On Tuesday, the value of the shares went up $5 \%$ . How much did the investor pay for the 100 shares if he sold them Wednesday morning for $\$ 1470.00$ ?

Write the specified quantity as a function of the specified variable. -The base of an isosceles triangle is a fourth as long as the two equal sides. Write the area of the triangle as a function of the length of the base.

Write the specified quantity as a function of the specified variable. -One leg of a right triangle is three times as long as the other. Write the length of the hypotenuse as a function of the length of the shorter leg.

Write the specified quantity as a function of the specified variable. -The height of a right circular cylinder equals its diameter. Write the volume of the cylinder as a function of its radius.

Write the specified quantity as a function of the specified variable. -The base of an isosceles triangle is a third as long as the two equal sides. Write the perimeter of the triangle as a function of the length of the base.

Use an equation to solve the problem. -When a number is added to its double and its triple, the sum is 138 . Find the three numbers.

Write the specified quantity as a function of the specified variable. -A square is inscribed in a circle. Write the area of the square as a function of the radius.

Solve the problem. -Sue invested $10,000, part at 5.9% annual interest and the balance at 6.7% annual interest. How much is invested at each rate if a 1-year interest payment is $645.52?

Choose the one alternative that best completes the statement or answers the question. Write a mathematical expression for the quantity described verbally. -The profit consists of a franchise fee of $\$ 100,000$ plus $20 \%$ of all sales

Use an equation to solve the problem. -A construction company builds a swimming pool with a perimeter of $50 \mathrm {~m}$ . The length is $3 \mathrm {~m}$ more than the width. Find the dimensions of the swimming pool?

Quiz 1: Functions and Graphs

Use an equation to solve the problem. -Joe Pearlman received a 2.75%2.75 \%2.75% pay decrease. His salary after the decrease was $36,955\$ 36,955$36,955 . What was his salary before the decrease?

Use an equation to solve the problem. -When a number, half of the number, and a third of the number are added together, the sum is 275 . Find the three numbers.

Write the specified quantity as a function of the specified variable. -The base of an isosceles triangle is half as long as the two equal sides. Write the area of the triangle as a function of the length of the base.

Choose the one alternative that best completes the statement or answers the question. Write a mathematical expression for the quantity described verbally. -The revenue when each item sells for $31,416\$ 31,416$31,416 .

Use an equation to solve the problem. -A tire of a moving bicycle has radius 16 inches. If the tire is making 3 rotations per second, find the bicycle's speed in miles per hour.

Write the specified quantity as a function of the specified variable. -A circle is inscribed in a square. Write the area of the square as a function of the radius.

Use an equation to solve the problem. -If Gloria received a 4%4 \%4% raise and is now making $24,960\$ 24,960$24,960 a year, what was her salary before the raise?

Use an equation to solve the problem. -Between 1990 and 2000 the population of a certain city grew from 202,000 to 239,700 . What was the percentage increase in the population of the city?

Use an equation to solve the problem. -One positive number is twice another positive number. The sum of the two numbers is 360 . Find the two numbers.

Use an equation to solve the problem. -On Monday, an investor bought 100 shares of stock. On Tuesday, the value of the shares went up 5%5 \%5% . How much did the investor pay for the 100 shares if he sold them Wednesday morning for $1470.00\$ 1470.00$1470.00 ?

Write the specified quantity as a function of the specified variable. -The base of an isosceles triangle is a fourth as long as the two equal sides. Write the area of the triangle as a function of the length of the base.

Write the specified quantity as a function of the specified variable. -One leg of a right triangle is three times as long as the other. Write the length of the hypotenuse as a function of the length of the shorter leg.

Write the specified quantity as a function of the specified variable. -The height of a right circular cylinder equals its diameter. Write the volume of the cylinder as a function of its radius.

Write the specified quantity as a function of the specified variable. -The base of an isosceles triangle is a third as long as the two equal sides. Write the perimeter of the triangle as a function of the length of the base.

Use an equation to solve the problem. -When a number is added to its double and its triple, the sum is 138 . Find the three numbers.

Write the specified quantity as a function of the specified variable. -A square is inscribed in a circle. Write the area of the square as a function of the radius.

Solve the problem. -Sue invested $10,000, part at 5.9% annual interest and the balance at 6.7% annual interest. How much is invested at each rate if a 1-year interest payment is $645.52?

Choose the one alternative that best completes the statement or answers the question. Write a mathematical expression for the quantity described verbally. -The profit consists of a franchise fee of $100,000\$ 100,000$100,000 plus 20%20 \%20% of all sales

Use an equation to solve the problem. -A construction company builds a swimming pool with a perimeter of 50 m50 \mathrm {~m}50 m . The length is 3 m3 \mathrm {~m}3 m more than the width. Find the dimensions of the swimming pool?

Use an equation to solve the problem. -Joe Pearlman received a $2.75 \%$ pay decrease. His salary after the decrease was $\$ 36,955$ . What was his salary before the decrease?

Choose the one alternative that best completes the statement or answers the question. Write a mathematical expression for the quantity described verbally. -The revenue when each item sells for $\$ 31,416$ .

Use an equation to solve the problem. -If Gloria received a $4 \%$ raise and is now making $\$ 24,960$ a year, what was her salary before the raise?

Use an equation to solve the problem. -On Monday, an investor bought 100 shares of stock. On Tuesday, the value of the shares went up $5 \%$ . How much did the investor pay for the 100 shares if he sold them Wednesday morning for $\$ 1470.00$ ?

Choose the one alternative that best completes the statement or answers the question. Write a mathematical expression for the quantity described verbally. -The profit consists of a franchise fee of $\$ 100,000$ plus $20 \%$ of all sales

Use an equation to solve the problem. -A construction company builds a swimming pool with a perimeter of $50 \mathrm {~m}$ . The length is $3 \mathrm {~m}$ more than the width. Find the dimensions of the swimming pool?