| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.66 |
| Score | 0% | 53% |
If the base of this triangle is 3 and the height is 1, what is the area?
| 55 | |
| 35 | |
| 67\(\frac{1}{2}\) | |
| 1\(\frac{1}{2}\) |
The area of a triangle is equal to ½ base x height:
a = ½bh
a = ½ x 3 x 1 = \( \frac{3}{2} \) = 1\(\frac{1}{2}\)
A(n) __________ is to a parallelogram as a square is to a rectangle.
quadrilateral |
|
triangle |
|
rhombus |
|
trapezoid |
A rhombus is a parallelogram with four equal-length sides. A square is a rectangle with four equal-length sides.
Solve 8a + 9a = -4a - 6z - 2 for a in terms of z.
| \(\frac{5}{8}\)z + \(\frac{5}{8}\) | |
| \(\frac{1}{2}\)z + \(\frac{7}{10}\) | |
| -1\(\frac{3}{5}\)z + \(\frac{1}{5}\) | |
| -1\(\frac{1}{4}\)z - \(\frac{1}{6}\) |
To solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.
8a + 9z = -4a - 6z - 2
8a = -4a - 6z - 2 - 9z
8a + 4a = -6z - 2 - 9z
12a = -15z - 2
a = \( \frac{-15z - 2}{12} \)
a = \( \frac{-15z}{12} \) + \( \frac{-2}{12} \)
a = -1\(\frac{1}{4}\)z - \(\frac{1}{6}\)
Solve for y:
y2 + 7y + 11 = y + 2
| 9 or -1 | |
| -3 | |
| 5 or 1 | |
| 5 or -7 |
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 + 7y + 11 = y + 2
y2 + 7y + 11 - 2 = y
y2 + 7y - y + 9 = 0
y2 + 6y + 9 = 0
Next, factor the quadratic equation:
y2 + 6y + 9 = 0
(y + 3)(y + 3) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, (y + 3) must equal zero:
If (y + 3) = 0, y must equal -3
So the solution is that y = -3
What is 7a2 - 8a2?
| a24 | |
| 15a4 | |
| 56a2 | |
| -1a2 |
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 - 8a2 = -1a2