# Ged Math practice test 3 - online test

Which line running through (3,4) is perpendicular to y = -3x + 4?

y = -3x + 13

y = 3x - 5

A line perpendicular to another line will have a slope that is the negative reciprocal of the slope of that line. This means that, if Line 1 has a slope of m, a perpendicular Line 2 will have a slope of . Line y = -3x + 4 is in slope-intercept form: y=mx+b, where m is the slope and b is the y-intercept. Since m=-3, it has a slope of -3. A line perpendicular to it should have a slope of . Thus, it will have an equation in the form: Only the line is similar to this format. If there were more choices that fit the format, continue: Plug in (3, 4) for (x, y) to solve for b: 4 = 1 + b 4-1=b 3=b Therefore, the correct equation is:

Where does cross the y axis?

(-1,0)

(2,0)

(1,-2)

(0,-2)

The line crosses the y axis when x is equal to zero. Thus, when x = 0, Presented as (x, y), this is the point (0, -2).

Which equation runs through points (1, 6) and (-1, 2)?

y = 2x + 4

y = -2x + 8

y = -4x + 10

y = 4x + 2

Slope, m, is defined as rise over run, or the vertical distance between two points divided by the horizontal distance between the same points: , where and are two points along the line.
To compute for m in the problem use and
The straight-line equation in the slope-intercept form applies, that is:
y = mx + b, where m is the slope and b is the value of y when x = 0 (the y-intercept)
Initially, we know that the equation will be something like this:
y = 2x + b
Since there is only one choice that fits this description, save time by choosing that answer.
However, if there were more than one choices that fit the description, or if it isn't a multiple choice problem, continue:
We need to know b, which we compute by plugging in either of the points given:
If we use (x, y)=(-1, 2):
y = 2x + b
2 = 2(-1) + b
2=-2+b
2+2=b
4=b
Therefore, the correct equation is:
y = 2x + 4
TIP: you can check by using the other given point, (1, 6).

Jim is filling his rectangular pig trough full of slop. The trough is 3 ft wide, 8 ft long, and has a depth of 4 ft. One of the piglets jumps in the trough and the slop rises 2.8 inches.
What is the volume of the trough?

To compute for the volume of the trough, use the formula: Volume = L u00D7 W u00D7 H
The information about 2.8 inches rise in slop is unnecessary because you are asked to find the volume of the trough, not that of the slop.
Be careful to be aware of, and discard, any irrelevant information given in test questions.

A ladder is leaning against an 18 ft building. The bottom of the ladder is 8.5 ft from the building.
Approximately how tall is the ladder?

20 Ft

18 Ft

40 Ft

396 Ft

The problem involves a right triangle, with height equal to the building's height, base equal to the distance of the ladder from the building, and diagonal or hypotenuse equal to the length of the ladder. Height = h = 18 ft Base = b = 8.5 ft Hypotenuse = H = ? For right triangles, there is a special formula for this called the Pythagorean Theorem: The square of the height + the square of the base = the square of the hypotenuse H=19.9 ft = Length of the ladder
TIP: It's easy to arrive at the answer ,
but not as easy looking for the . Since you will be computing manually, review the answer choices and eliminate the unlikely answers. 396 is definitely not the answer because the square root of 396.25 will be a much smaller number. 40 is also out because if you square it,
18 is also eliminated because .
Checking out 20, it is the best answer because , very close to 396.25.

Where do lines y = x - 1 and y = -5x + 11 intersect?

(3, -4)

(2, 1)

(-2, -3)

(-3, -4)

Two lines meet or intersect at a point when their (x, y) coordinates are equal. Simply set the equation of the two straight lines equal to each other. y = x - 1 y = -5x + 11 Equating the two equations, solve for x: x - 1 = -5x + 11 x + 5x = 11 + 1 6x = 12 Substituting x=2 to either of the equations, solve for y: y = x - 1 y = 2 - 1 = 1 The two lines intersect at (2, 1)

In parallelogram ABCD, ∠ = 4x + 8 and ???? = 6x - 10. Find the measure of ∠.

Parallelogram ABCD describes a parallelogram with its 4 angles named as u2220A, u2220B, u2220C, and u2220D. u2220A is opposite u2220C, and u2220B is opposite u2220D. Opposite angles in parallelograms are equal in measure. Hence, the measure of u2220A = u2220C, and the measure of u2220B = u2220D. Given the equations for u2220A and u2220C, we can set them as: u2220A = u2220C 4x + 8 = 6x - 10 8 + 10 = 6x - 4x 18 = 2x 9=x Computing for the measure of u2220A:

Austin, Texas has a statue of Stevie Ray Vaughn that is 12 ft tall. It casts an 8 ft shadow. Doug stops to admire the statue. Doug's shadow is 3.5 ft.
How tall is Doug?

5 ft

6 ft

4.75 ft

The proportion of the height of an object versus the length of its shadow will be in the same proportion as that of another object, if both objects being compared are located at approximately the same location and the measurements of the shadows are taken at the same time of day. Thus, the ratio of the statue's actual height over its shadow is equal to the ratio of Doug's height over his own shadow. If we let h be Doug's height, the equation will be: Cross-multiply and you will have: 8h = 12 \u00D7 3.5 8h = 42 Divide both sides by 8 to get the value of just h:

If Hunter scored an average of 76 on his first four tests, what is the minimum he must score on his fifth test in order to have an overall average of 80?

80

86

96

94

First, you will need to find the total of the tests that have already been taken. Multiplying 4 by 76 gives you a total of 304.
Next, you will need to find the total of what you want. There are 5 tests, and you want an average of 80. Multiplying 5 by 80 gives you a total of 400.
Then, you will need to find the difference between the totals on the first 4 tests and all 5 tests. Subtracting 304 from 400 gives you a total of 96.

Meghan raised funds for the Cancer Society for seven straight days. She raised the following amounts: \$525, \$350, \$275, \$630, \$1,010, \$275, and x.
What would the value of x equal if the average funds collected were \$500?

\$375

\$480

\$595

\$435

If the average is \$500, then
(\$525 + \$350 + \$275 + \$630 + \$1,010 + \$275 + x) × 7 = \$500.
Solve for x.
(\$3,065 + x) × 7 = \$500
\$3,065 + x = 7 × \$500 = \$3,500
x = \$3,500 - \$3,065 = \$435

A bus arrives at the bus station every 2 hours, a second bus arrives every 3 hours, and a third bus arrives every 4 hours.
If all 3 buses arrive at 9:00 AM, at what time will all 3 buses next arrive at the same time?

9:00 PM

12:00 PM

3:00 AM

6:00 PM

You must look at each time the third bus arrives and determine if it's evenly divisible by the other two. Therefore, you would look at 4, 8, and 12. Because 12 is the only time that is evenly divisible by the times of buses 1 and 2, you know that the buses will all arrive every 12 hours. 9:00 AM = 12 hours = 9:00 PM.

Solve the following equation:
|2x + 6 - 5x| = 9

x = 1 or x = 5

x = -1 or x = 5

x = -3 or x = -5

x = 3 or x = 5

First, simplify the expression in absolute value: |2x + 6 - 5x| = |6 - 3x | = 9 Because absolute value of a number is its distance from zero, it can be a positive or negative value. Therefore, solve each of the following equations: 6 - 3x = 9 6 - 3x = -9 Solve the first equation. 6 - 3x = 9 -3x = 3 x = -1 Solve the next equation. 6 - 3x = -9 -3x = -15 x = 5 Therefore, x = -1 or x = 5

John adopted his dog exactly 5 years and 12 days ago. At this instant, how many minutes has John had his dog? (Ignore leap years.)

2,217,116 minutes

3,098,732 minutes

2,645,280 minutes

1,872,234 minutes

Start by finding the number of days in 5 years. 1 year = 365 days 1 year x 5 = 365 days x 5 = 1,825 days Add the 12 days. 1,825 days + 12 days = 1,837 days Convert the number of days to hours. 1 day = 24 hours 1 day x 1,837 = 24 hours x 1,837 = 44,088 hours Convert the number of hours to minutes. 1 hour = 60 minutes 1 hour x 44,088 = 60 minutes x 44,088 = 2,645,280 minutes

Which of the following pairs of points both lie on the line whose equation is 4x-2y= 10?

(3,2) and (4,4)

(8,3) and (6,-1)

(2,-2) and (5,5)

(3,1) and (6,7)

Test each pair. Only (3,1) and (6,7) satisfy the equation. 4(3) - 2(1) = 12 - 2 = 10, and 4(6) - 2(7) = 24 - 14 = 10. None of the other pairs work.

|3 + x| = 5
Which of the following options is the correct solution set for the above equation?

{2, 8}

{-8, 2}

{-8, -2}

{-8, 8}

The bars which surround the equation signify “absolute value,” which refers to the distance of a number from zero. Therefore, the outcome can be either positive or negative. The equation |3 + x| = 5 has two solutions: 3 + x = - 5 and 3 + x = 5 Solve the first equation. 3 + x = -5 x = -5 - 3 x = -8 Solve the next equation. 3 + x = 5 x = 5 - 3 x = 2 Therefore, the set of possible solutions is {-8, 2}

Kyle borrows \$12,000 for a period of five years to buy a used car.
If the simple interest rate is 12%, how much will he pay in interest?

\$7,200

\$5,400

\$8,400

\$1,200

To calculate the interest, multiply the amount of the loan by the interest rate by the number of years of the loan: 12,000 x 0.12 x 5 = \$7,200.