| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.78 |
| Score | 0% | 56% |
Simplify (7a)(4ab) - (4a2)(4b).
| 88ab2 | |
| 12a2b | |
| 44a2b | |
| -12ab2 |
To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.
(7a)(4ab) - (4a2)(4b)
(7 x 4)(a x a x b) - (4 x 4)(a2 x b)
(28)(a1+1 x b) - (16)(a2b)
28a2b - 16a2b
12a2b
Solve for z:
z2 + z - 25 = -3z - 4
| 7 or -1 | |
| 9 or -6 | |
| 3 or -7 | |
| -9 or -9 |
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 + z - 25 = -3z - 4
z2 + z - 25 + 4 = -3z
z2 + z + 3z - 21 = 0
z2 + 4z - 21 = 0
Next, factor the quadratic equation:
z2 + 4z - 21 = 0
(z - 3)(z + 7) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 3) or (z + 7) must equal zero:
If (z - 3) = 0, z must equal 3
If (z + 7) = 0, z must equal -7
So the solution is that z = 3 or -7
If a = c = 4, b = d = 3, what is the area of this rectangle?
| 9 | |
| 45 | |
| 12 | |
| 48 |
The area of a rectangle is equal to its length x width:
a = l x w
a = a x b
a = 4 x 3
a = 12
If side a = 2, side b = 9, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{72} \) | |
| \( \sqrt{85} \) | |
| \( \sqrt{65} \) | |
| \( \sqrt{26} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 22 + 92
c2 = 4 + 81
c2 = 85
c = \( \sqrt{85} \)
The formula for the area of a circle is which of the following?
c = π d |
|
c = π r2 |
|
c = π d2 |
|
c = π r |
The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)2 : a = π r2.