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Sophie [7]
3 years ago
10

What is the slope of the line whose equation is 12=4x−6y? Enter your answer in the box.

Mathematics
1 answer:
swat323 years ago
5 0
Slope= 2/3
Explanation- adding 6y on both sides and subtracting 12 on both sides of eq, 12 + 6y -12=4x+6y-6y-12
6y = 4x-12
Divide by 6 on both sides of eq, we get y=4/6 x -12/6
y=2/3 x-2
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Consider the following function. f(x) = (x + 5)2/3 (a) Find the critical numbers of f. (Enter your answers as a comma-separated
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Step-by-step explanation:

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3 0
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Let 0 be an acute angle of a right triangle. Evaluate the other five trigonometric functions of 0.
Paraphin [41]

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How do you do this question?
mihalych1998 [28]

Answer:

C) π/6

Step-by-step explanation:

The area under the curve from x=-π/2 to x=k is 3 times the area under the curve from x=k to x=π/2.

\int\limits^k_{-\frac{\pi }{2}} {cos\ x} \, dx = 3\int\limits^{\frac{\pi }{2}}_k {cos\ x} \, dx\\sin\ x\ |^{k}_{-\frac{\pi }{2}} = 3\ sin\ x\ |^{\frac{\pi }{2}}_k\\(sin\ k - (-1)) = 3\ (1 - sin\ k)\\sin\ k + 1 = 3 - 3\ sin\ k\\4\ sin\ k = 2\\sin\ k = \frac{1}{2}\\k = \frac{\pi}{6}

Graph: desmos.com/calculator/mezlen9hb4

3 0
3 years ago
Write an equation in slope intercept form for the line that passes through (-1, -2) and (3, 4)
LenaWriter [7]

Answer:

The slope-intercept form of the line equation  is:

  • y=\:\frac{3}{2}x\:-\frac{1}{2}

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

  • m is the slope
  • b is the y-intercept

Given the points

  • (-1, -2)
  • (3, 4)

Determining the slope between (-1, -2) and (3, 4)

\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(-1,\:-2\right),\:\left(x_2,\:y_2\right)=\left(3,\:4\right)

m=\frac{4-\left(-2\right)}{3-\left(-1\right)}

m=\frac{3}{2}

Thus, the slope of the line is:

m = 3/2

substituting m = 3/2 and the point (3, 4) in the slope-intercept form of the line equation

y = mx+b

4=\frac{3}{2}\left(3\right)+b

switch sides

\frac{3}{2}\left(3\right)+b=4

\frac{9}{2}+b=4

subtract 9/2 from both sides

\frac{9}{2}+b-\frac{9}{2}=4-\frac{9}{2}

b=-\frac{1}{2}

now substituting m = 3/2 and b = -1/2 in the slope-intercept form of the line equation

y = mx+b

y=\:\frac{3}{2}x\:+\:\left(-\frac{1}{2}\right)

y=\:\frac{3}{2}x\:-\frac{1}{2}

Therefore, the slope-intercept form of the line equation  is:

  • y=\:\frac{3}{2}x\:-\frac{1}{2}
8 0
3 years ago
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