| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
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If a = c = 9, b = d = 5, and the blue angle = 60°, what is the area of this parallelogram?
| 6 | |
| 45 | |
| 28 | |
| 48 |
The area of a parallelogram is equal to its length x width:
a = l x w
a = a x b
a = 9 x 5
a = 45
Solve for x:
x - 8 > -7 - 8x
| x > 2 | |
| x > \(\frac{1}{9}\) | |
| x > 1\(\frac{1}{4}\) | |
| x > \(\frac{2}{7}\) |
To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the > sign and the answer on the other.
x - 8 > -7 - 8x
x > -7 - 8x + 8
x + 8x > -7 + 8
9x > 1
x > \( \frac{1}{9} \)
x > \(\frac{1}{9}\)
Solve for z:
z2 - 4z - 15 = -5z + 5
| 4 or -5 | |
| -1 or -9 | |
| 2 or -2 | |
| 2 or -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:
z2 - 4z - 15 = -5z + 5
z2 - 4z - 15 - 5 = -5z
z2 - 4z + 5z - 20 = 0
z2 + z - 20 = 0
Next, factor the quadratic equation:
z2 + z - 20 = 0
(z - 4)(z + 5) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 4) or (z + 5) must equal zero:
If (z - 4) = 0, z must equal 4
If (z + 5) = 0, z must equal -5
So the solution is that z = 4 or -5
Solve for b:
b2 + 4b - 45 = 0
| -2 or -6 | |
| 4 or -9 | |
| 5 or -9 | |
| 9 or 6 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
b2 + 4b - 45 = 0
(b - 5)(b + 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 5) or (b + 9) must equal zero:
If (b - 5) = 0, b must equal 5
If (b + 9) = 0, b must equal -9
So the solution is that b = 5 or -9
Which types of triangles will always have at least two sides of equal length?
equilateral and isosceles |
|
equilateral and right |
|
isosceles and right |
|
equilateral, isosceles and right |
An isosceles triangle has two sides of equal length. An equilateral triangle has three sides of equal length. In a right triangle, two sides meet at a right angle.