Quick Algebra questions please :)
1 answer:
1. -4x² + 11x + 2 = 0
x = -(11) ± √((11)² - 4(-4)(2))
2(-4)
x = -11 ± √(121 + 32)
-8
x = -11 ± √(153)
-8
x = -11 ± 3√(17)
-8
x = -11 ± 3(4.1)
-8
x = -11 ± 12.3
-8
x = -11 + 12.3 or x = -11 - 12.3
-8 -8
x = 1.3 or x = -23.3
-8 -8
x = -0.1625 or x = 2.9125
x ≈ -0.2 or x ≈ 2.9
The answer is B.
2. 4x² - 3 = 11x
4x² - 11x - 3 = 0
x = -(-11) ± √((-11)² - 4(4)(-3))
2(4)
x = 11 ± √(121 + 48)
8
x = 11 ± √(169)
8
x = 11 ± 13
8
x = 11 + 13 or x = 11 - 13
8 8
x = 24 or x = -2
8 8
x = 3 or x = -0.25
The answer is C.
3. g(x) = -1(x + 2)² + 5
g(x) = -1(x + 2)(x + 2) + 5
g(x) = -1(x(x + 2) + 2(x + 2)) + 5
g(x) = -1(x(x) + x(2) + 2(x) + 2(2)) + 5
g(x) = -1(x² + 2x + 2x + 4) + 5
g(x) = -1(x² + 4x + 4) + 5
g(x) = -1(x²) - 1(4x) - 1(4) + 5
g(x) = -x² - 4x - 4 + 5
g(x) = -x² - 4x + 1
x = -(11) ± √((11)² - 4(-4)(2))
2(-4)
x = -11 ± √(121 + 32)
-8
x = -11 ± √(153)
-8
x = -11 ± 3√(17)
-8
x = -11 ± 3(4.1)
-8
x = -11 ± 12.3
-8
x = -11 + 12.3 or x = -11 - 12.3
-8 -8
x = 1.3 or x = -23.3
-8 -8
x = -0.1625 or x = 2.9125
x ≈ -0.2 or x ≈ 2.9
The answer is B.
2. 4x² - 3 = 11x
4x² - 11x - 3 = 0
x = -(-11) ± √((-11)² - 4(4)(-3))
2(4)
x = 11 ± √(121 + 48)
8
x = 11 ± √(169)
8
x = 11 ± 13
8
x = 11 + 13 or x = 11 - 13
8 8
x = 24 or x = -2
8 8
x = 3 or x = -0.25
The answer is C.
3. g(x) = -1(x + 2)² + 5
g(x) = -1(x + 2)(x + 2) + 5
g(x) = -1(x(x + 2) + 2(x + 2)) + 5
g(x) = -1(x(x) + x(2) + 2(x) + 2(2)) + 5
g(x) = -1(x² + 2x + 2x + 4) + 5
g(x) = -1(x² + 4x + 4) + 5
g(x) = -1(x²) - 1(4x) - 1(4) + 5
g(x) = -x² - 4x - 4 + 5
g(x) = -x² - 4x + 1
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Step-by-step explanation:
Answer:
When Ø = 300°, Ø = 60 degrees.
When Ø = 225°, Ø = 45 degrees.
When Ø = 480°, Ø = 60 degrees.
When Ø = -210°, Ø = 30 degrees.
Step-by-step explanation:
Reference angles are in Quadrant I (0° to 90°).
1. Find 300° (Quadrant IV) on the unit circle. Since it's in Quadrant IV, you use 360 - 300 = 60° to get your answer.
2. Find 225° (Quadrant III) on the unit circle. Since it's in Quadrant III, you use 225 - 180 = 45° to get your answer.
3. The angle 480° is not on the unit circle. To find its corresponding angle between 0° and 360°, use 480 - 360 = 120°. Then, find 120° (Quadrant II) on the unit circle. Since it's in Quadrant II, you use 180 - 120 = 60° to get your answer.
4. The angle -210° is not on the unit circle. To find its corresponding angle between 0° and 360°, use -210 + 360 = 150°. Then, find 150° (Quadrant II) on the unit circle. Since it's in Quadrant II, you use 180 - 150 = 30° to get your answer.
