| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.54 |
| Score | 0% | 51% |
Which of the following is not true about both rectangles and squares?
the area is length x width |
|
the lengths of all sides are equal |
|
all interior angles are right angles |
|
the perimeter is the sum of the lengths of all four sides |
A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s2).
Which of the following statements about parallel lines with a transversal is not correct?
angles in the same position on different parallel lines are called corresponding angles |
|
all of the angles formed by a transversal are called interior angles |
|
all acute angles equal each other |
|
same-side interior angles are complementary and equal each other |
Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other. Same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°).
The dimensions of this trapezoid are a = 4, b = 3, c = 5, d = 7, and h = 3. What is the area?
| 30 | |
| 9 | |
| 15 | |
| 28 |
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(3 + 7)(3)
a = ½(10)(3)
a = ½(30) = \( \frac{30}{2} \)
a = 15
Solve for y:
y2 - 3y + 14 = 5y - 1
| 7 or 3 | |
| 3 or 5 | |
| 7 or -6 | |
| 7 or 1 |
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 - 3y + 14 = 5y - 1
y2 - 3y + 14 + 1 = 5y
y2 - 3y - 5y + 15 = 0
y2 - 8y + 15 = 0
Next, factor the quadratic equation:
y2 - 8y + 15 = 0
(y - 3)(y - 5) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (y - 3) or (y - 5) must equal zero:
If (y - 3) = 0, y must equal 3
If (y - 5) = 0, y must equal 5
So the solution is that y = 3 or 5
Solve for b:
b2 - 10b + 21 = 0
| 3 or 7 | |
| -4 or -9 | |
| 2 or -7 | |
| 6 or -3 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
b2 - 10b + 21 = 0
(b - 3)(b - 7) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 3) or (b - 7) must equal zero:
If (b - 3) = 0, b must equal 3
If (b - 7) = 0, b must equal 7
So the solution is that b = 3 or 7