| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.55 |
| Score | 0% | 71% |
When two lines intersect, adjacent angles are __________ (they add up to 180°) and angles across from either other are __________ (they're equal).
obtuse, acute |
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vertical, supplementary |
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supplementary, vertical |
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acute, obtuse |
Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).
If a = 4, b = 7, c = 9, and d = 3, what is the perimeter of this quadrilateral?
| 13 | |
| 19 | |
| 23 | |
| 22 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 4 + 7 + 9 + 3
p = 23
Which of the following is not a part of PEMDAS, the acronym for math order of operations?
addition |
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division |
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exponents |
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pairs |
When solving an equation with two variables, 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.)
If side a = 4, side b = 1, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{17} \) | |
| \( \sqrt{61} \) | |
| 10 | |
| \( \sqrt{52} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 42 + 12
c2 = 16 + 1
c2 = 17
c = \( \sqrt{17} \)
Solve for a:
a2 + 17a + 52 = 2a - 4
| 5 or -4 | |
| -7 or -8 | |
| 8 or 6 | |
| 7 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:
a2 + 17a + 52 = 2a - 4
a2 + 17a + 52 + 4 = 2a
a2 + 17a - 2a + 56 = 0
a2 + 15a + 56 = 0
Next, factor the quadratic equation:
a2 + 15a + 56 = 0
(a + 7)(a + 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a + 7) or (a + 8) must equal zero:
If (a + 7) = 0, a must equal -7
If (a + 8) = 0, a must equal -8
So the solution is that a = -7 or -8