| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.75 |
| Score | 0% | 55% |
Solve for z:
z2 - 2z - 39 = -z + 3
| -2 or -6 | |
| 7 or 6 | |
| -6 or 7 | |
| 7 or 4 |
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 - 2z - 39 = -z + 3
z2 - 2z - 39 - 3 = -z
z2 - 2z + z - 42 = 0
z2 - z - 42 = 0
Next, factor the quadratic equation:
z2 - z - 42 = 0
(z + 6)(z - 7) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 6) or (z - 7) must equal zero:
If (z + 6) = 0, z must equal -6
If (z - 7) = 0, z must equal 7
So the solution is that z = -6 or 7
If a = c = 4, b = d = 8, and the blue angle = 50°, what is the area of this parallelogram?
| 14 | |
| 25 | |
| 6 | |
| 32 |
The area of a parallelogram is equal to its length x width:
a = l x w
a = a x b
a = 4 x 8
a = 32
A(n) __________ is to a parallelogram as a square is to a rectangle.
triangle |
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quadrilateral |
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trapezoid |
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rhombus |
A rhombus is a parallelogram with four equal-length sides. A square is a rectangle with four equal-length sides.
For this diagram, the Pythagorean theorem states that b2 = ?
c - a |
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c2 - a2 |
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a2 - c2 |
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c2 + a2 |
The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c2) is equal to the sum of the two perpendicular sides squared (a2 + b2): c2 = a2 + b2 or, solved for c, \(c = \sqrt{a + b}\)
Which of the following is not true about both rectangles and squares?
the area is length x width |
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the perimeter is the sum of the lengths of all four sides |
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all interior angles are right angles |
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the lengths of all sides are equal |
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).