| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.85 |
| Score | 0% | 57% |
What is the circumference of a circle with a radius of 11?
| 22π | |
| 10π | |
| 8π | |
| 18π |
The formula for circumference is circle diameter x π. Circle diameter is 2 x radius:
c = πd
c = π(2 * r)
c = π(2 * 11)
c = 22π
Solve for y:
y2 - 5y + 8 = 2y - 2
| -1 or -6 | |
| 4 or 3 | |
| 4 or -2 | |
| 2 or 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:
y2 - 5y + 8 = 2y - 2
y2 - 5y + 8 + 2 = 2y
y2 - 5y - 2y + 10 = 0
y2 - 7y + 10 = 0
Next, factor the quadratic equation:
y2 - 7y + 10 = 0
(y - 2)(y - 5) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (y - 2) or (y - 5) must equal zero:
If (y - 2) = 0, y must equal 2
If (y - 5) = 0, y must equal 5
So the solution is that y = 2 or 5
Find the value of a:
-a + x = -6
6a + 3x = 2
| -2\(\frac{1}{12}\) | |
| 2\(\frac{2}{9}\) | |
| -\(\frac{4}{7}\) | |
| \(\frac{5}{16}\) |
You need to find the value of a so solve the first equation in terms of x:
-a + x = -6
x = -6 + a
then substitute the result (-6 - -1a) into the second equation:
6a + 3(-6 + a) = 2
6a + (3 x -6) + (3 x a) = 2
6a - 18 + 3a = 2
6a + 3a = 2 + 18
9a = 20
a = \( \frac{20}{9} \)
a = 2\(\frac{2}{9}\)
What is 7a2 + 6a2?
| 42a4 | |
| 42a2 | |
| 1 | |
| 13a2 |
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.
7a2 + 6a2 = 13a2
The dimensions of this cylinder are height (h) = 2 and radius (r) = 6. What is the surface area?
| 96π | |
| 104π | |
| 90π | |
| 14π |
The surface area of a cylinder is 2πr2 + 2πrh:
sa = 2πr2 + 2πrh
sa = 2π(62) + 2π(6 x 2)
sa = 2π(36) + 2π(12)
sa = (2 x 36)π + (2 x 12)π
sa = 72π + 24π
sa = 96π