| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.54 |
| Score | 0% | 51% |
If a = c = 1, b = d = 4, and the blue angle = 73°, what is the area of this parallelogram?
| 16 | |
| 4 | |
| 8 | |
| 6 |
The area of a parallelogram is equal to its length x width:
a = l x w
a = a x b
a = 1 x 4
a = 4
Find the value of b:
4b + x = 5
-9b - 3x = 7
| \(\frac{9}{17}\) | |
| -2\(\frac{7}{34}\) | |
| 7\(\frac{1}{3}\) |
You need to find the value of b so solve the first equation in terms of x:
4b + x = 5
x = 5 - 4b
then substitute the result (5 - 4b) into the second equation:
-9b - 3(5 - 4b) = 7
-9b + (-3 x 5) + (-3 x -4b) = 7
-9b - 15 + 12b = 7
-9b + 12b = 7 + 15
3b = 22
b = \( \frac{22}{3} \)
b = 7\(\frac{1}{3}\)
Which types of triangles will always have at least two sides of equal length?
isosceles and right |
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equilateral, isosceles and right |
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equilateral and right |
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equilateral and isosceles |
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.
For this diagram, the Pythagorean theorem states that b2 = ?
a2 - c2 |
|
c2 - a2 |
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c2 + a2 |
|
c - a |
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, \(c = \sqrt{a + b}\)
Solve for x:
7x + 1 = \( \frac{x}{6} \)
| -1\(\frac{1}{47}\) | |
| -\(\frac{6}{41}\) | |
| 1\(\frac{1}{3}\) | |
| \(\frac{18}{29}\) |
To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.
7x + 1 = \( \frac{x}{6} \)
6 x (7x + 1) = x
(6 x 7x) + (6 x 1) = x
42x + 6 = x
42x + 6 - x = 0
42x - x = -6
41x = -6
x = \( \frac{-6}{41} \)
x = -\(\frac{6}{41}\)