Home / Digital SAT Math Practice Questions – Medium : Linear functions

# Digital SAT Math Practice Questions – Medium : Linear functions

## SAT MAth Practice questions – all topics

• Algebra Weightage: 35%  Questions: 13-15
• Linear equations in one variable
• Linear equations in two variables
• Linear functions
• Systems of two linear equations in two variables
• Linear inequalities in one or two variables

## SAT MAth and English  – full syllabus practice tests

[No- Calc]  Question   Medium

Some values of $$\mathrm{x}$$ and the corresponding values of $$f(x)$$ are given in the table shown.

If there is a linear relationship between $$\mathrm{x}$$ and $$f(\mathrm{x})$$, which of the following equations gives this relationship?

A) $$f(x)=\frac{1}{2} x+\frac{1}{2}$$
B) $$f(x)=\frac{1}{2} x-\frac{1}{2}$$
C) $$f(x)=\frac{1}{6} x+\frac{5}{6}$$
D) $$f(x)=\frac{1}{6} x+\frac{2}{3}$$

Ans:D

To determine the equation representing the linear relationship between $$x$$ and $$f(x)$$, we can use the point-slope form of a linear equation:

$f(x) – f(x_1) = m(x – x_1)$

where $$m$$ is the slope of the line and $$(x_1, f(x_1))$$ is a point on the line.

Let’s choose the point $$(2, 1)$$ as it is the first point in the table.

Substituting the values into the point-slope form:

$f(x) – 1 = m(x – 2)$

Now, let’s calculate the slope $$m$$ using another point, for example, $$(5, 1.5)$$. The slope $$m$$ is given by:

$m = \frac{f(x_2) – f(x_1)}{x_2 – x_1} = \frac{1.5 – 1}{5 – 2} = \frac{0.5}{3} = \frac{1}{6}$

Now, substituting $$m = \frac{1}{6}$$ and $$(x_1, f(x_1)) = (2, 1)$$ into the equation:

$f(x) – 1 = \frac{1}{6}(x – 2)$

$f(x) – 1 = \frac{1}{6}x – \frac{1}{3}$

$f(x) = \frac{1}{6}x – \frac{1}{3} + 1$

$f(x) = \frac{1}{6}x + \frac{2}{3}$

So, the equation representing the linear relationship between $$x$$ and $$f(x)$$ is:

D) $$f(x) = \frac{1}{6}x + \frac{2}{3}$$

[No calc]  Question   medium

Which equation has no solution?
A. 4(𝑥 + 1) = 𝑥 + 4
B. 4(𝑥 + 1) = 𝑥 + 1
C. 4(𝑥 + 1) = 4𝑥 + 4
D. 4(𝑥 + 1) = 4x

Ans: D

We need to determine which equation has no solution. To do this, we’ll solve each equation and check if it leads to a contradiction.

A. $$4(x+1)=x+4$$ becomes $$4x + 4 = x + 4$$, which simplifies to $$3x = 0$$, leading to $$x = 0$$. So, this equation has a solution.

B. $$4(x+1)=x+1$$ simplifies to $$4x + 4 = x + 1$$, which leads to $$3x = -3$$, giving $$x = -1$$. So, this equation has a solution.

C. $$4(x+1)=4x+4$$ becomes $$4x + 4 = 4x + 4$$, which simplifies to $$0 = 0$$, indicating all $$x$$ are solutions. So, this equation has infinite solutions.

D. $$4(x+1)=4x$$ simplifies to $$4x + 4 = 4x$$, which leads to $$4 = 0$$, showing a contradiction. Hence, this equation has no solution.

Therefore, the answer is D.

[Calc]  Question  Medium

Line $$k$$ is defined by $$y=2 x+14$$. Line $$j$$ is perpendicular to line $$k$$ in the $$x y$$-plane. What is the slope of line $$j$$ ?
A) $$-\frac{1}{2}$$
B) $$\frac{1}{14}$$
C) $$\frac{1}{2}$$
D) 2

A

Line $$k$$ is defined by $$y = 2x + 14$$.

To find the slope of line $$j$$, which is perpendicular to line $$k$$, we know that the product of the slopes of perpendicular lines is -1.

The slope of line $$k$$ is 2. So, the slope of line $$j$$ will be the negative reciprocal of 2.

$\text{Slope of } j = -\frac{1}{\text{Slope of } k} = -\frac{1}{2}$

Therefore, the answer is:
$\boxed{A) \, -\frac{1}{2}}$

[No calc]  Question    medium

Line k is shown in the xy-plane. Line j (not shown) is perpendicular to line k. What is the slope of line j?

Ans: 5/2, 2.5

Since line K is passing through points (-5,0) and (0,-2).

$\text { slope of } k=m_k=\frac{y_2-y_1}{x_2-x_1}$

Substitute the given points $$(-5,0)$$ and $$(0,-2)$$ :
$m_k=\frac{-2-0}{0-(-5)}=\frac{-2}{5}$

Since line $$j$$ is perpendicular to line $$k$$, the slope of line $$j\left(m_j\right)$$ is the negative reciprocal of the slope of line $$k$$.

$m_j=-\frac{1}{m_k}=-\frac{1}{\left(\frac{-2}{5}\right)}=\frac{5}{2}$

Thus, the slope of line $$j$$ is:
$m_j=\frac{5}{2}$

[Calc]  Question Medium

The equation of line $$k$$ is $$y=7 x+2$$. What is the slope of a line that is parallel to line $$k$$ in the $$x y$$-plane?

7

The equation of line $$k$$ is given by:
$y = 7x + 2$

The slope-intercept form of a line is $$y = mx + b$$, where $$m$$ represents the slope. Here, the slope $$m$$ of line $$k$$ is 7. For a line to be parallel to line $$k$$ in the $$xy$$-plane, it must have the same slope.

Thus, the slope of a line parallel to line $$k$$ is:
$\boxed{7}$

[Calc]  Question  Medium

The table shows several values of $$x$$ and their corresponding values of $$y$$, where $$k$$ is a nonzero constant. If the relationship between $$x$$ and $$y$$ is linear, which of the following defines this relationship?

A) $$y=2 x(k+1)$$
B) $$y=k x$$
C) $$y=-2 k x$$
D) $$y=-2 k-x-1$$

Ans:A

slope $$m$$:
$m = \frac{y_2 – y_1}{x_2 – x_1}$

Using the points $$(0, 0)$$ and $$(1, 2k + 2)$$:
$m = \frac{(2k + 2) – 0}{1 – 0} = 2k + 2$

The linear equation in slope-intercept form $$y = mx + b$$ has $$b = 0$$ from the point $$(0, 0)$$, so:
$y = (2k + 2)x$

Thus, the equation defining this relationship is:
$\boxed{y = 2x(k+1)}$

[Calc]  Question   Medium

In 1845, a family had $18.00 to purchase flour and bacon for their trip along the Oregon Trail to California. The graph shows the possible combinations of flour and bacon, in hundreds of pounds, they could purchase. Based on the graph, what was the price of 100 pounds of flour ? A) 1.00 B) 2.00 C) 2.50 D) 5.00 ▶️Answer/Explanation B) 2.00 From the graph, we can observe that the family can purchase different combinations of flour and bacon. The total budget for both items is$18.00.

Let’s look at a few points on the graph to understand the relationship between flour and bacon:

• When they purchase 0 hundreds of pounds (0 pounds) of flour, they can purchase 4 hundreds of pounds (400 pounds) of bacon.
• When they purchase 9 hundreds of pounds (900 pounds) of flour, they can purchase 0 hundreds of pounds (0 pounds) of bacon.

If they buy 900 pounds of flour, they can buy 0 pounds of bacon:
\begin{aligned} & 9 F=18 \\ & F=\frac{18}{9}=2.00 \end{aligned}

Thus, the price of 100 pounds of flour is 2.00 , which matches option B.
So, the correct answer is:
B)

[Calc]  Question   Medium

How many solutions does the equation 2(x + 3) + x = 3(x + 2) have?
A) Zero
B) Exactly one
C) Exactly two
D) Infinitely many

D) Infinitely many

To determine how many solutions the equation $$2(x + 3) + x = 3(x + 2)$$ has, we need to simplify and solve it.

1. Expand both sides:
$2(x + 3) + x = 3(x + 2)$
$2x + 6 + x = 3x + 6$

2. Combine like terms:
$3x + 6 = 3x + 6$

3. Subtract $$3x + 6$$ from both sides:
$3x + 6 – 3x – 6 = 0$
$0 = 0$

This is a true statement, meaning the equation is an identity and holds for all values of $$x$$. Therefore, there are infinitely many solutions.

To solve the system of equations and find the value of $$5x – 2y$$:

1. The given system of equations is:
$4x – 8y = -1 \quad \text{(1)}$
$x + 6y = -10 \quad \text{(2)}$

2. Solve equation (2) for $$x$$:
$x = -10 – 6y$

3. Substitute $$x$$ into equation (1):
$4(-10 – 6y) – 8y = -1$
$-40 – 24y – 8y = -1$
$-40 – 32y = -1$

4. Solve for $$y$$:
$-32y = 39$
$y = -\frac{39}{32}$

5. Substitute $$y$$ back into the expression for $$x$$:
$x = -10 – 6\left(-\frac{39}{32}\right)$
$x = -10 + \frac{234}{32}$
$x = -10 + 7.3125$
$x = -2.6875$

6. Find the value of $$5x – 2y$$:
$5x – 2y = 5(-2.6875) – 2\left(-\frac{39}{32}\right)$
$5x – 2y = -13.4375 + \frac{78}{32}$
$5x – 2y = -13.4375 + 2.4375$
$5x – 2y = -11$

Thus, the value of $$5x – 2y$$ is:
$\boxed{-11}$

$\boxed{D}$

[No calc]  Question   medium

The graph of a line in the xy-plane passes through the point with coordinates (6,2) and crosses the x– axis at the point with coordinates (10,0). The line crosses the y-axis at the point with coordinates (0,b). What is the value of b ?

Ans: 5

To determine the value of $$b$$, where the line crosses the $$y$$-axis, given that the line passes through the points $$(6, 2)$$ and $$(10, 0)$$:

Find the slope $$m$$ of the line:
$m = \frac{y_2 – y_1}{x_2 – x_1} = \frac{0 – 2}{10 – 6} = \frac{-2}{4} = -\frac{1}{2}$

Use the slope-intercept form $$y = mx + b$$. Substitute the coordinates of one of the points (using $$(6, 2)$$) and the slope:
$2 = -\frac{1}{2}(6) + b$

Solve for $$b$$:
$2 = -3 + b$
$b = 2 + 3$
$b = 5$

[Calc]  Question  Medium

In the linear function g, $$g(-2)=\frac{3}{4}$$ and $$g(3)=\frac{9}{2}$$. Which equation defines g ?

A. $$g(x)=\frac{3}{4}x+\frac{9}{4}$$

B. $$g(x)=\frac{3}{4}x+\frac{9}{2}$$

C. $$g(x)=\frac{15}{4}x-\frac{27}{4}$$

D. $$g(x)=\frac{15}{4}x+\frac{33}{4}$$

Ans: A

we can follow these steps:

Step 1: Find the slope $$m$$

The formula for the slope $$m$$ between two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ is:
$m = \frac{y_2 – y_1}{x_2 – x_1}$

Substituting the given points:
$m = \frac{\frac{9}{2} – \frac{3}{4}}{3 – (-2)}$

To simplify the numerator:
$\frac{9}{2} – \frac{3}{4} = \frac{18}{4} – \frac{3}{4} = \frac{18 – 3}{4} = \frac{15}{4}$

Now, calculate the slope:
$m = \frac{\frac{15}{4}}{5} = \frac{15}{4} \cdot \frac{1}{5} = \frac{15}{20} = \frac{3}{4}$

Step 2: Find the y-intercept $$b$$

Using the slope-intercept form $$y = mx + b$$, we need to find $$b$$ using one of the points. We can use $$g(-2) = \frac{3}{4}$$:

$\frac{3}{4} = \frac{3}{4}(-2) + b$

Solve for $$b$$:
$\frac{3}{4} = -\frac{3}{2} + b$

Add $$\frac{3}{2}$$ to both sides:
$\frac{3}{4} + \frac{3}{2} = b$

Convert $$\frac{3}{2}$$ to a common denominator:
$\frac{3}{2} = \frac{6}{4}$

$\frac{3}{4} + \frac{6}{4} = \frac{9}{4}$

So, $$b = \frac{9}{4}$$.

Step 3: Write the equation

The equation of the line $$g(x)$$ with slope $$\frac{3}{4}$$ and y-intercept $$\frac{9}{4}$$ is:
$g(x) = \frac{3}{4}x + \frac{9}{4}$

[Calc]  Question   Medium

The graph of the linear function/is shown. What is they-coordinate of they-intercept of the graph off?

3/2

Since the line y = f(x) passing through (0,1.5) and (3,0) and having y intercept of 3/2

[No- Calc]  Question   Medium

Line $$\mathrm{m}$$ is shown in the xy-plane. Line p (not shown) is perpendicular to line $$\mathrm{m}$$. Which of the following could be the equation of line $$p$$ ?

A) $$\frac{1}{2} x+7$$
B) $$2 x+7$$
C) $$-\frac{1}{2} x+7$$
D) $$-2 x+7$$

Ans:A

To determine which of the given equations could be the equation of line $$p$$, we need to use the fact that $$p$$ is perpendicular to line $$m$$. The slope of line $$m$$ is given as $$-2$$. For two lines to be perpendicular, the product of their slopes must be $$-1$$. Therefore, if the slope of line $$m$$ is $$-2$$, the slope of line $$p$$ must be the negative reciprocal of $$-2$$.

The negative reciprocal of $$-2$$ is:

$\frac{1}{2}$

So, the slope of line $$p$$ must be $$\frac{1}{2}$$.

find which line has a slope of $$\frac{1}{2}$$:

A) $$\frac{1}{2} x + 7$$

The slope is $$\frac{1}{2}$$.

B) $$2x + 7$$

The slope is $$2$$.

C) $$-\frac{1}{2} x + 7$$

The slope is $$-\frac{1}{2}$$.

D) $$-2x + 7$$

The slope is $$-2$$.

The correct equation for line $$p$$ that has a slope of $$\frac{1}{2}$$ is:

$\boxed{\frac{1}{2} x + 7}$

[Calc]  Question  Medium

Line k passes through the points (1,1) and in the xy-plane. If the equation for line k is written in the form y=mx+b , where m and b are constants, what is the value of m ?

Ans: 5

To find the slope $$m$$ of the line passing through the points $$(1, 1)$$ and $$(2, 6)$$, we use the slope formula:

$m = \frac{y_2 – y_1}{x_2 – x_1}$

Substitute the given points $$(x_1, y_1) = (1, 1)$$ and $$(x_2, y_2) = (2, 6)$$:

$m = \frac{6 – 1}{2 – 1} = \frac{5}{1} = 5$

So, the value of $$m$$ is $$5$$.

Therefore, the slope $$m$$ of the line is:

$m = 5$

[Calc]  Question   medium

If 4(x + 1) = 16 , what is the value of x + 1 ?

A) 3

B) 4

C) 11

B) 4

To find the value of $$x + 1$$ in the equation $$4(x + 1) = 16$$:

Divide both sides of the equation by 4:
$\frac{4(x + 1)}{4} = \frac{16}{4}$
$x + 1 = 4$

[Calc]  Question   medium

The equation 0.95c + 0.05n = 8.87 represents the density of a copper-zinc alloy, where c is the density, in grams per cubic centimeter (g/cm3), of copper, n is the density, in g/$$cm^3$$, of zinc, and 8.87 g/$$cm^3$$ is the density of the alloy. The density of copper is 8.96 g/$$cm^3$$. What is the density of zinc, in g/$$cm^3$$ ?

A) 0.09

B) 0.47

C) 7.16

D) 8.51

C) 7.16

Given the equation $$0.95c + 0.05n = 8.87$$ representing the density of a copper-zinc alloy, where $$c$$ is the density of copper and $$n$$ is the density of zinc, and knowing the density of copper is $$8.96 \, \text{g/cm}^3$$, we can solve for the density of zinc.

Substitute the known value of the density of copper ($$c = 8.96 \, \text{g/cm}^3$$) into the equation:
$0.95(8.96) + 0.05n = 8.87$
$8.512 + 0.05n = 8.87$

Subtract $$8.512$$ from both sides:
$0.05n = 8.87 – 8.512$
$0.05n = 0.358$

Divide both sides by $$0.05$$:
$n = \frac{0.358}{0.05}$
$n = 7.16$

So, the density of zinc is $$7.16 \, \text{g/cm}^3$$.

[No calc]  Question  medium

The graph of the linear function f is shown. Which equation defines f ?

A) f(x)=$$\frac{3}{2}x-8$$

B) f(x)=$$\frac{3}{2}x+5$$

C) f(x)=$$\frac{1}{3}x-8$$

D) f(x)=$$\frac{1}{3}x+5$$

A) f(x)=$$\frac{3}{2}x-8$$

To find the slope of a line passing through two points $$\left(x_1, y_1\right)$$ and $$\left(x_2, y_2\right)$$, you can use the formula:
slope $$=\frac{y_2-y_1}{x_2-x_1}$$
Given the points $$(0,-8)$$ and $$(8,4)$$ :
$$x_1=0$$
$$y_1=-8$$
$$x_2=8$$
$$y_2=4$$

Now, plug these values into the formula:
$\text { slope }=\frac{4-(-8)}{8-0}=\frac{4+8}{8}=\frac{12}{8}=\frac{3}{2}$

$y=m x+b$
where $$m$$ is the slope and $$b$$ is the $$y$$-intercept.

The slope $$(m)$$ is $$\frac{3}{2}$$.
The $$y$$-intercept $$(b)$$ is -8 .

Plug these values into the slope-intercept form:
$y=\frac{3}{2} x-8$

[Calc]  Question  medium

Line k is defined by y = −x + 5. Line j is parallel to line k on the xy-plane. What is the slope of line j?

A) -1

B) $$\frac{-1}{5}$$

C) 1

D) 5

A) -1

Given that line $$k$$ is defined by the equation $$y = -x + 5$$, we need to determine the slope of line $$j$$, which is parallel to line $$k$$.

The slope-intercept form of a line is $$y = mx + b$$, where $$m$$ is the slope.

For line $$k$$, the equation $$y = -x + 5$$ has a slope $$m = -1$$.

Since line $$j$$ is parallel to line $$k$$, it must have the same slope.

The slope of line $$j$$ is:A) -1

[Calc]  Question  medium

The table shows the results of a survey on the average amount of money d, in dollars, consumers would be willing to spend on a product and their corresponding age a, in years. Which equation could represent this linear relationship?

A) d = −2a + 92

B) d = $$− \frac{1}{2}$$ a + 92

C)  d = 2a −8

D) d = 2a − 40

A) d = −2a + 92

We need to find which equation could represent the linear relationship between the average amount of money $$d$$ consumers are willing to spend and their age $$a$$, based on the given data points.

To determine which of the given equations could represent this linear relationship, we’ll check the slope and y-intercept for each option.

Option A: $$d = -2a + 92$$

Check with some data points:
For $$a = 25$$:
$d = -2(25) + 92 = -50 + 92 = 42$
For $$a = 28$$:
$d = -2(28) + 92 = -56 + 92 = 36$

Both points satisfy this equation.

For completeness, let’s check another point:
For $$a = 33$$:
$d = -2(33) + 92 = -66 + 92 = 26$

This point also satisfies the equation.

We can reasonably conclude that this equation fits all the given data points.

The correct answer is:A) $$d = -2a + 92$$

[Calc]  Question Medium

For the linear function f, f(2) = 10 and the graph of y = f(x) in the xy-plane has a slope of 3. Which equation defines f ?

A) f(x)=2x+12
B) f(x)=2x+8
C) f(x)=3x+10
D) f(x)=3x+4

Ans: D

To find the equation of the linear function $$f$$ given $$f(2) = 10$$ and the slope $$m = 3$$, we use the point-slope form of a linear equation: $$y = mx + b$$.

Given:
Slope $$m = 3$$
Point $$(2, 10)$$

We can use the point-slope form to find $$b$$:
$f(x) = 3x + b$

Substitute $$x = 2$$ and $$f(2) = 10$$:
$10 = 3(2) + b$
$10 = 6 + b$
$b = 4$

Thus, the equation of the function $$f$$ is:
$f(x) = 3x + 4$

[No- Calc]  Question  Medium

A line in the xy-plane has a slope of 1 and passes through the point (0, 2). Which is an equation of the line?

A) y=x/2

B) y=2x

C) y = x+2

D) y=x-2

Ans: C

The line has a slope of $$1$$ and passes through the point $$(0, 2)$$. We can use the point-slope form of the equation for a line:

$y – y_1 = m(x – x_1)$

Substituting $$m = 1$$, $$x_1 = 0$$, and $$y_1 = 2$$:

$y – 2 = 1(x – 0)$

$y – 2 = x$

Adding $$2$$ to both sides:

$y = x + 2$

So, the equation of the line is C) $$y = x + 2$$

[Calc]  Question  Medium

For the linear function, f, the table shows several values of x and their corresponding values of f(x). What is the y-intercept of the graph of y = f(x) in the xy-plane?
A) (0,-3)
B) (0,-1)
C) (0, 2)
D) (0,4)

Ans: C

To find the $$y$$-intercept of the linear function $$f(x)$$, we need to determine the equation of the line in the form $$f(x) = mx + b$$, where $$m$$ is the slope and $$b$$ is the $$y$$-intercept.

First, we find the slope $$m$$ using two points from the table. Let’s use the points $$(-4, 14)$$ and $$(-2, 8)$$.

The formula for the slope $$m$$ is:
$m = \frac{f(x_2) – f(x_1)}{x_2 – x_1}$

Substitute the values:
$m = \frac{8 – 14}{-2 – (-4)}$
$m = \frac{-6}{2}$
$m = -3$

Now that we have the slope $$m = -3$$, we use one of the points to find the $$y$$-intercept $$b$$. Using the point $$(-2, 8)$$:

The equation of the line is:
$f(x) = -3x + b$

Substitute $$(-2, 8)$$ into the equation:
$8 = -3(-2) + b$
$8 = 6 + b$
$b = 2$

Therefore, the $$y$$-intercept is $$b = 2$$

[No- Calc]  Question   Medium

Which linear equation has exactly one solution?
A) $$y=5-y$$
B) $$y=y-5$$
C) $$y=y+5$$
D) $$y+5=5+y$$

Ans:A

A linear equation has exactly one solution when it represents a horizontal line.

Among the options:

A) $$y = 5 – y$$

This equation simplifies to $$2y = 5$$, which means $$y = \frac{5}{2}$$. This represents a horizontal line at $$y = \frac{5}{2}$$, which intersects the y-axis at exactly one point.

So, the correct answer is:

A) $$y = 5 – y$$

[Calc]  Question  Medium

Bridges have spaces between their sections to allow for expansion and contraction caused by temperature variation. This space is known as the gap width. The size of the gap width w(T), in inches, is a linear function of temperature T, in degrees Fahrenheit ($$^{\circ }F$$). For a certain bridge, the gap width is 2.875 inches at 40$$^{\circ }F$$ and is 1.875 inches at 100°F. Which of the following defines the relationship between temperature and gap width?

A) $$w(T)=-\frac{1}{60}(T-40)+2.875$$

B) $$w(T)=-\frac{1}{60}(T-40)-2.875$$

C) $$w(T)=60(T-40)+2.875$$

D) $$w(T)=60(T-40)-2.875$$

Ans: A

We are given that the gap width $$w(T)$$ is a linear function of temperature $$T$$. We are also provided with two points on this line: $$T = 40^\circ \text{F}$$ corresponds to $$w = 2.875 \text{ inches}$$, and $$T = 100^\circ \text{F}$$ corresponds to $$w = 1.875 \text{ inches}$$.

We can use the point-slope form of the equation of a line to find the linear function that represents the relationship between temperature and gap width.

The point-slope form is given by $$y – y_1 = m(x – x_1)$$, where $$(x_1, y_1)$$ is a point on the line, and $$m$$ is the slope.

Using the point $$(40, 2.875)$$, and $$(100, 1.875)$$, we can find the slope:

$m = \frac{{1.875 – 2.875}}{{100 – 40}} = -\frac{1}{60}$

Now, we can use either point to find the equation. Let’s use the point $$(40, 2.875)$$:

$w – 2.875 = -\frac{1}{60}(T – 40)$

$w = -\frac{1}{60}(T – 40) + 2.875$

So, the relationship between temperature and gap width is given by option $$\mathbf{A}$$ – $$w(T) = -\frac{1}{60}(T – 40) + 2.875$$.

Questions

Which of the following is a graph of a system of equations with no solution?

Ans: A

Questions

$P=P_o+\rho g h$

The equation above gives the total pressure, $P$, on an object submerged in a fluid, where $P_o$ is the pressure at the fluid’s surface, $\rho$ is the density of the fluid, $g$ is the acceleration due to gravity, and $h$ is the depth to which the object is submerged. What is $h$ in terms of $P, P_o, \rho$, and $g$ ?

A. $\frac{p g}{P-P_o}$
B. $\frac{P-P_o^o}{\rho g}$
C. $\frac{P+P_o}{\rho g}$
D. $P+P_o+\rho g$

Ans: B

Questions

In the $$xy$$-plane above, line $$m$$ is perpendicular to line $$l$$ (not shown). Which of the following could be an equation of line $$l$$ ?

1. $$5x + 3y + 3 = 0$$
2. $$5x — 3y + 3 = 0$$
3. $$3x — 5y + 15 = 0$$
4. $$3x + 5y — 15 = 0$$

Ans: A

Question

Under the right conditions, giant sequoia trees are the fastest-growing conifer on Earth. In good growing conditions, a giant sequoia tree will form a 1-inch growth ring each year, increasing the size of its trunk diameter by 2 inches per year. This relationship is represented in the graph below. A giant sequoia tree can also grow 4 feet vertically every three years.

Which of the following equations represents the relationship between the diameter, in inches, of a giant sequoia tree’s trunk and that tree’s age, in years?

1. $$y = x-2$$
2. $$y = x+2$$
3. $$y = \frac{1}{2}x$$
4. $$y = 2x$$

Ans: D

Questions

The table above shows selected values for the function $$h$$. In the $$xy$$-plane, the graph of $$y =h(x)$$ is a line. What is the value of $$h(8)$$ ?

1. 15
2. 19
3. 21
4. 22