| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.81 |
| Score | 0% | 56% |
The dimensions of this trapezoid are a = 5, b = 4, c = 6, d = 7, and h = 4. What is the area?
| 24 | |
| 12\(\frac{1}{2}\) | |
| 34 | |
| 22 |
The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:
a = ½(b + d)(h)
a = ½(4 + 7)(4)
a = ½(11)(4)
a = ½(44) = \( \frac{44}{2} \)
a = 22
Which of the following statements about a parallelogram is not true?
the perimeter of a parallelogram is the sum of the lengths of all sides |
|
opposite sides and adjacent angles are equal |
|
the area of a parallelogram is base x height |
|
a parallelogram is a quadrilateral |
A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).
What is 4a - 2a?
| 8a | |
| 6 | |
| 2a | |
| 2 |
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.
4a - 2a = 2a
Solve for c:
c2 - 12c + 13 = -2c + 4
| -1 or -8 | |
| 1 or 9 | |
| 2 or -1 | |
| 5 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:
c2 - 12c + 13 = -2c + 4
c2 - 12c + 13 - 4 = -2c
c2 - 12c + 2c + 9 = 0
c2 - 10c + 9 = 0
Next, factor the quadratic equation:
c2 - 10c + 9 = 0
(c - 1)(c - 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 1) or (c - 9) must equal zero:
If (c - 1) = 0, c must equal 1
If (c - 9) = 0, c must equal 9
So the solution is that c = 1 or 9
Which types of triangles will always have at least two sides of equal length?
equilateral and isosceles |
|
equilateral, isosceles and right |
|
isosceles and right |
|
equilateral 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.