| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.26 |
| Score | 0% | 45% |
Find the value of b:
5b + y = -8
7b + 8y = -7
| -1\(\frac{8}{11}\) | |
| -1\(\frac{5}{8}\) | |
| -1\(\frac{13}{37}\) | |
| -2\(\frac{3}{8}\) |
You need to find the value of b so solve the first equation in terms of y:
5b + y = -8
y = -8 - 5b
then substitute the result (-8 - 5b) into the second equation:
7b + 8(-8 - 5b) = -7
7b + (8 x -8) + (8 x -5b) = -7
7b - 64 - 40b = -7
7b - 40b = -7 + 64
-33b = 57
b = \( \frac{57}{-33} \)
b = -1\(\frac{8}{11}\)
Which types of triangles will always have at least two sides of equal length?
isosceles and right |
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equilateral and right |
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equilateral and isosceles |
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equilateral, isosceles and right |
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.
Solve for a:
5a + 8 > \( \frac{a}{-8} \)
| a > -1\(\frac{23}{41}\) | |
| a > -1\(\frac{11}{14}\) | |
| a > 2\(\frac{2}{35}\) | |
| a > -\(\frac{3}{23}\) |
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 > sign and the answer on the other.
5a + 8 > \( \frac{a}{-8} \)
-8 x (5a + 8) > a
(-8 x 5a) + (-8 x 8) > a
-40a - 64 > a
-40a - 64 - a > 0
-40a - a > 64
-41a > 64
a > \( \frac{64}{-41} \)
a > -1\(\frac{23}{41}\)
Which of the following statements about a parallelogram is not true?
opposite sides and adjacent angles are equal |
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the perimeter of a parallelogram is the sum of the lengths of all sides |
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a parallelogram is a quadrilateral |
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the area of a parallelogram is base x height |
A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).
Which of the following statements about parallel lines with a transversal is not correct?
all acute angles equal each other |
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all of the angles formed by a transversal are called interior angles |
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same-side interior angles are complementary and equal each other |
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angles in the same position on different parallel lines are called corresponding angles |
Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other. Same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°).