| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.23 |
| Score | 0% | 65% |
Solve for z:
z2 - 12z + 35 = 0
| 5 or 7 | |
| 7 or -8 | |
| 7 or 1 | |
| -3 or -9 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
z2 - 12z + 35 = 0
(z - 5)(z - 7) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 5) or (z - 7) must equal zero:
If (z - 5) = 0, z must equal 5
If (z - 7) = 0, z must equal 7
So the solution is that z = 5 or 7
Find the value of a:
-a + y = -1
-7a + 9y = -9
| \(\frac{7}{9}\) | |
| 4 | |
| \(\frac{5}{7}\) |
You need to find the value of a so solve the first equation in terms of y:
-a + y = -1
y = -1 + a
then substitute the result (-1 - -1a) into the second equation:
-7a + 9(-1 + a) = -9
-7a + (9 x -1) + (9 x a) = -9
-7a - 9 + 9a = -9
-7a + 9a = -9 + 9
2a = 0
a = \( \frac{0}{2} \)
a =
A(n) __________ is two expressions separated by an equal sign.
problem |
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formula |
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expression |
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equation |
An equation is two expressions separated by an equal sign. The key to solving equations is to repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.
What is the area of a circle with a diameter of 8?
| 16π | |
| 2π | |
| 4π | |
| 5π |
The formula for area is πr2. Radius is circle \( \frac{diameter}{2} \):
r = \( \frac{d}{2} \)
r = \( \frac{8}{2} \)
r = 4
a = πr2
a = π(42)
a = 16π
What is 8a4 + 5a4?
| 40a4 | |
| 40a8 | |
| 13a4 | |
| 13a8 |
To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.
8a4 + 5a4 = 13a4