| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.69 |
| Score | 0% | 54% |
Solve for x:
x2 - 10x + 4 = -4x - 5
| 1 or 1 | |
| -2 or -3 | |
| 8 or -3 | |
| 3 |
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 - 10x + 4 = -4x - 5
x2 - 10x + 4 + 5 = -4x
x2 - 10x + 4x + 9 = 0
x2 - 6x + 9 = 0
Next, factor the quadratic equation:
x2 - 6x + 9 = 0
(x - 3)(x - 3) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, (x - 3) must equal zero:
If (x - 3) = 0, x must equal 3
So the solution is that x = 3
Factor y2 - 6y + 8
| (y + 4)(y + 2) | |
| (y - 4)(y - 2) | |
| (y + 4)(y - 2) | |
| (y - 4)(y + 2) |
To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 8 as well and sum (Inside, Outside) to equal -6. For this problem, those two numbers are -4 and -2. Then, plug these into a set of binomials using the square root of the First variable (y2):
y2 - 6y + 8
y2 + (-4 - 2)y + (-4 x -2)
(y - 4)(y - 2)
If c = -5 and y = -9, what is the value of -3c(c - y)?
| -6 | |
| 60 | |
| 630 | |
| 42 |
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.)
-3c(c - y)
-3(-5)(-5 + 9)
-3(-5)(4)
(15)(4)
60
The dimensions of this cube are height (h) = 5, length (l) = 3, and width (w) = 4. What is the surface area?
| 118 | |
| 16 | |
| 94 | |
| 214 |
The surface area of a cube is (2 x length x width) + (2 x width x height) + (2 x length x height):
sa = 2lw + 2wh + 2lh
sa = (2 x 3 x 4) + (2 x 4 x 5) + (2 x 3 x 5)
sa = (24) + (40) + (30)
sa = 94
If the length of AB equals the length of BD, point B __________ this line segment.
bisects |
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trisects |
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intersects |
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midpoints |
A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.