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3 years ago

On the set of axes, solve the following system of equations graphically for all values of

1 answer:

4 0

Y = x² + 4x - 5
y = 2x

x² + 4x - 5 = 2x
 - 2x - 2x
x² + 2x - 5 = 0
x = -(2) ± √((2)² - 4(1)(-5))
 2(1)
x = -2 ± √(4 + 20)
 2
x = -2 ± √(24)
 2
x = -2 ± 2√(6)
 2
x = -1 ± √(6)
x = -1 + √(6) U x = -1 - √(6)
y = 2x
y = 2(-1 ± √(6))
y = 2(-1) ± 2√(6)
y = -2 ± 2√(6)
(x, y) = (-1 ± √(6), -2 ± 2√(6))

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A huge trucking firm determines that its fleet of trucks averages a mean of 12.4 miles per gallon with a standard deviation of 1

Jlenok [28]

Answer:

$P(x$

Step-by-step explanation:

From the question we are told that

Sample mean $\=x=12.4$

Standard deviation $\sigma=1.2miles\ per\ gallon$

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$P(x$

Therefore The probability that a randomly selected truck averages fewer than 10 miles per gallon

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8 0

3 years ago

If 180°<α<270°, cos ⁡α= −8/17, 270°<β<360°, and sin β= −4/5, what is sin⁡(α+β)?

mars1129 [50]

Answer:

$\sin(\alpha+\beta) = -0.153$

Step-by-step explanation:

Let determine the angles behind each trigonometric expression:

$\cos \alpha = -\frac{8}{17}$

$\alpha = \cos^{-1}\left(-\frac{8}{17} \right)$

Given that $180^{\circ}< \alpha < 270^{\circ}$ , the value of $\alpha$ is:

$\alpha \approx 241.928^{\circ}$

$\sin \beta = -\frac{4}{5}$

$\beta = \sin^{-1}\left(-\frac{4}{5} \right)$

Given that $270^{\circ}< \beta$ , the value of $\beta$ is:

$\beta \approx 306.870^{\circ}$

The sine function of the sum of angles can be determined by the following identity:

$\sin(\alpha + \beta)=\sin \alpha \cdot \cos \beta + \sin \beta \cdot \cos \alpha$

If $\alpha \approx 241.928^{\circ}$ and $\beta \approx 306.870^{\circ}$ , then:

$\sin (241.928^{\circ}+306.870^{\circ}) = (\sin 241.928^{\circ}) \cdot (\cos 306.870^{\circ}) + (\sin 306.870^{\circ})\cdot (\cos 241.928^{\circ})$ $\sin(241.928^{\circ}+306.870^{\circ}) = -0.153$