| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.50 |
| Score | 0% | 70% |
If a = c = 6, b = d = 1, what is the area of this rectangle?
| 36 | |
| 8 | |
| 6 | |
| 24 |
The area of a rectangle is equal to its length x width:
a = l x w
a = a x b
a = 6 x 1
a = 6
Which of the following is not true about both rectangles and squares?
the lengths of all sides are equal |
|
the area is length x width |
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all interior angles are right angles |
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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).
A right angle measures:
180° |
|
90° |
|
45° |
|
360° |
A right angle measures 90 degrees and is the intersection of two perpendicular lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.
If c = 3 and z = -7, what is the value of 2c(c - z)?
| 90 | |
| 60 | |
| -27 | |
| 20 |
To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)
2c(c - z)
2(3)(3 + 7)
2(3)(10)
(6)(10)
60
Solve for z:
z2 - 5z - 21 = z - 5
| 3 or -3 | |
| 2 or -2 | |
| -2 or 8 | |
| 8 or 3 |
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:
z2 - 5z - 21 = z - 5
z2 - 5z - 21 + 5 = z
z2 - 5z - z - 16 = 0
z2 - 6z - 16 = 0
Next, factor the quadratic equation:
z2 - 6z - 16 = 0
(z + 2)(z - 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 2) or (z - 8) must equal zero:
If (z + 2) = 0, z must equal -2
If (z - 8) = 0, z must equal 8
So the solution is that z = -2 or 8