Question 1

Solve the formula $$C = 2\pi r$$ for $$r.$$

Accepted Answer

$$r = \dfrac{C}{2\pi}$$

Question 2

A chemist uses the formula $$V = lwh to $$calculate the volume of a rectangular container. If the chemist wants to solve for $$h in $$terms of $$V$$, $$l$$, and $$w$$, which is the correct rearrangement?

Accepted Answer

$$h = \dfrac{V}{lw}$$

Question 3

Solve the formula $$C = 5/9(F - 32)$$ for $$F. $$This formula is used to convert Celsius to Fahrenheit in weather reports.

Accepted Answer

$$F = \dfrac{9}{5}C + 32$$

Question 4

A business uses the formula $$P = b + 1.5t to $$calculate profit $$P$$ based on base profit $$b$$ and time $$t. $$Solve for $$t.$$

Accepted Answer

$$t = \dfrac{P - b}{1.5}$$

Question 5

Solve the formula $$2x + 3y = 7$$ for $$y.$$

Accepted Answer

$$y = \dfrac{7 - 2x}{3}$$

Question 6

In physics, the formula $$F = mv^2$r is $$used to calculate force. Solve for $$m.$$

Accepted Answer

$$m = \dfrac{F}{v^2$r}$$

Question 7

Solve the formula $$abc + b = 2a$$ for $$b.$$

Accepted Answer

$$b = \dfrac{2a}{ac + 1}$$

Question 8

A bank uses the formula $$I = Prt to $$calculate interest. Solve for $$t.$$

Accepted Answer

$$t = \dfrac{I}{Pr}$$

Question 9

Solve the formula $$x = ya + yz$$ for $$y.$$

Accepted Answer

$$y = \dfrac{x}{a + z}$$

Question 10

Solve the formula $$xa + yb = 1$$ for $$x.$$

Accepted Answer

$$x = \dfrac{1 - yb}{a}$$

Question 11

Solve the formula $$pr + pw = m$$ for $$p.$$

Accepted Answer

$$p = \dfrac{m}{r + w}$$

Question 12

Solve the formula $$A = \dfrac{1}{2}bh$$ for $$b.$$

Accepted Answer

$$b = \dfrac{2A}{h}$$

Question 13

A painter uses the formula $$S = 2WH + 2WL to $$calculate the surface area of a wall. Solve for $$H.$$

Accepted Answer

$$H = \dfrac{S - 2WL}{2W}$$

Question 14

Solve the formula $$y + mx_2$ = mx_1$ for m$.

Accepted Answer

$$m = \dfrac{y}{x_1$ - x_2$}$$

Question 15

Solve the formula $$p = 23a - 10$$ for $$a.$$

Accepted Answer

$$a = \dfrac{p + 10}{23}$$

Question 16

Solve the formula $$x + 7y = 1$$ for $$y.$$

Accepted Answer

$$y = \dfrac{1 - x}{7}$$

Question 17

A scientist uses the formula $$C = 5/9(F - 32) to $$convert Fahrenheit to Celsius. What is the first step to solve for $$F$$?

Accepted Answer

Multiply both sides by $$\dfrac{9}{5} to $$clear the fraction.

Question 18

Solve the formula $$I = Prt$$ for $$r.$$

Accepted Answer

$$r = \dfrac{I}{Pt}$$

Question 19

Solve the formula $$abc + b = 2a$$ for $$c.$$

Accepted Answer

$$c = \dfrac{2a - b}{ab}$$

Solving Formulas for a Specified Variable (Section 1.5 Study Notes)

Guida di studio - Domande di pratica

Study guide - Flashcard