| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.89 |
| Score | 0% | 58% |
The dimensions of this cube are height (h) = 3, length (l) = 7, and width (w) = 1. What is the surface area?
| 246 | |
| 70 | |
| 62 | |
| 188 |
The surface area of a cube is (2 x length x width) + (2 x width x height) + (2 x length x height):
sa = 2lw + 2wh + 2lh
sa = (2 x 7 x 1) + (2 x 1 x 3) + (2 x 7 x 3)
sa = (14) + (6) + (42)
sa = 62
Which of the following statements about a triangle is not true?
area = ½bh |
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exterior angle = sum of two adjacent interior angles |
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perimeter = sum of side lengths |
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sum of interior angles = 180° |
A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The perimeter of a triangle is equal to the sum of the lengths of its three sides, the height of a triangle is equal to the length from the base to the opposite vertex (angle) and the area equals one-half triangle base x height: a = ½ base x height.
If side a = 6, side b = 3, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{82} \) | |
| \( \sqrt{106} \) | |
| 5 | |
| \( \sqrt{45} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 62 + 32
c2 = 36 + 9
c2 = 45
c = \( \sqrt{45} \)
Find the value of c:
-5c + x = 4
-7c - 2x = -1
| 1\(\frac{9}{23}\) | |
| -\(\frac{1}{13}\) | |
| -\(\frac{7}{17}\) |
You need to find the value of c so solve the first equation in terms of x:
-5c + x = 4
x = 4 + 5c
then substitute the result (4 - -5c) into the second equation:
-7c - 2(4 + 5c) = -1
-7c + (-2 x 4) + (-2 x 5c) = -1
-7c - 8 - 10c = -1
-7c - 10c = -1 + 8
-17c = 7
c = \( \frac{7}{-17} \)
c = -\(\frac{7}{17}\)
The formula for the area of a circle is which of the following?
a = π r2 |
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a = π d2 |
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a = π r |
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a = π d |
The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)2 : a = π r2.