| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.73 |
| Score | 0% | 55% |
If the base of this triangle is 8 and the height is 2, what is the area?
| 45\(\frac{1}{2}\) | |
| 8 | |
| 52\(\frac{1}{2}\) | |
| 45 |
The area of a triangle is equal to ½ base x height:
a = ½bh
a = ½ x 8 x 2 = \( \frac{16}{2} \) = 8
The endpoints of this line segment are at (-2, 0) and (2, -8). What is the slope-intercept equation for this line?
| y = -2x - 4 | |
| y = 3x - 4 | |
| y = -\(\frac{1}{2}\)x - 1 | |
| y = -\(\frac{1}{2}\)x + 3 |
The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is -4. The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 0) and (2, -8) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-8.0) - (0.0)}{(2) - (-2)} \) = \( \frac{-8}{4} \)Plugging these values into the slope-intercept equation:
y = -2x - 4
If a = 7 and x = -8, what is the value of -6a(a - x)?
| 12 | |
| 168 | |
| -630 | |
| 60 |
To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)
-6a(a - x)
-6(7)(7 + 8)
-6(7)(15)
(-42)(15)
-630
Which of the following statements about a triangle is not true?
area = ½bh |
|
sum of interior angles = 180° |
|
exterior angle = sum of two adjacent interior angles |
|
perimeter = sum of side lengths |
A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The perimeter of a triangle is equal to the sum of the lengths of its three sides, the height of a triangle is equal to the length from the base to the opposite vertex (angle) and the area equals one-half triangle base x height: a = ½ base x height.
Solve for x:
x2 - 6x + 23 = 4x - 2
| 1 or -9 | |
| 8 or -9 | |
| -4 or -5 | |
| 5 |
The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:
x2 - 6x + 23 = 4x - 2
x2 - 6x + 23 + 2 = 4x
x2 - 6x - 4x + 25 = 0
x2 - 10x + 25 = 0
Next, factor the quadratic equation:
x2 - 10x + 25 = 0
(x - 5)(x - 5) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, (x - 5) must equal zero:
If (x - 5) = 0, x must equal 5
So the solution is that x = 5