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Find the value of b:
b + z = 8
5b - 7z = -6
| 4\(\frac{1}{6}\) | |
| -\(\frac{1}{2}\) | |
| -\(\frac{9}{40}\) | |
| \(\frac{49}{50}\) |
You need to find the value of b so solve the first equation in terms of z:
b + z = 8
z = 8 - b
then substitute the result (8 - 1b) into the second equation:
5b - 7(8 - b) = -6
5b + (-7 x 8) + (-7 x -b) = -6
5b - 56 + 7b = -6
5b + 7b = -6 + 56
12b = 50
b = \( \frac{50}{12} \)
b = 4\(\frac{1}{6}\)
Which of the following statements about parallel lines with a transversal is not correct?
same-side interior angles are complementary and equal each other |
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all acute angles equal each other |
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angles in the same position on different parallel lines are called corresponding angles |
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all of the angles formed by a transversal are called interior 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°).
Solve for z:
z2 - 5z - 5 = -4z + 1
| 7 or -4 | |
| 8 or -6 | |
| -2 or 3 | |
| -2 or -6 |
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 - 5z - 5 = -4z + 1
z2 - 5z - 5 - 1 = -4z
z2 - 5z + 4z - 6 = 0
z2 - z - 6 = 0
Next, factor the quadratic equation:
z2 - z - 6 = 0
(z + 2)(z - 3) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 2) or (z - 3) must equal zero:
If (z + 2) = 0, z must equal -2
If (z - 3) = 0, z must equal 3
So the solution is that z = -2 or 3
On this circle, line segment AB is the:
diameter |
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chord |
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radius |
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circumference |
A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).
Solve for c:
-6c - 7 < \( \frac{c}{-8} \)
| c < -1\(\frac{9}{47}\) | |
| c < -\(\frac{16}{55}\) | |
| c < \(\frac{3}{5}\) | |
| c < \(\frac{5}{7}\) |
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.
-6c - 7 < \( \frac{c}{-8} \)
-8 x (-6c - 7) < c
(-8 x -6c) + (-8 x -7) < c
48c + 56 < c
48c + 56 - c < 0
48c - c < -56
47c < -56
c < \( \frac{-56}{47} \)
c < -1\(\frac{9}{47}\)