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Taya2010 [7]
3 years ago
6

Angles ∝ and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of β

if β < ∝.
sin(7x - 15) = cos(3x + 5)

A) 10°
B) 35°
C) 55°
D) 80°
Mathematics
2 answers:
Nadya [2.5K]3 years ago
7 0
We know that
in a right triangle
(∝ + β)=90°-------> by complementary angles
so
sin ∝ = cos β
sin(7x - 15) = cos(3x + 5)
Let 
∝=7x-15
β=3x+5

therefore

(7x-15)+(3x+5)=90 \\ 10x-10=90 \\ 10x=90+10 \\ x= \frac{100}{10}
x=10°

∝=7x-15-----------> ∝=7*10-15-------> ∝=55°
β=3x+5------------> β=3*10+5-------> β=35°

the answer is
 β=35°

arlik [135]3 years ago
5 0
Ok so cos(x) = sin(90-x) so using that you can get sin(7x-15) = sin(90-(3x+5)) so 7x-15 = -3x+85. 10x = 100 and x = 10. Use that to find the 2 angles are 55 and 35
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Answer:

The equations represent the line that is parallel to 3x - 4y = 7 and pass through the point (-4,-2) are:

  • y+2=\frac{3}{4}\left(x+4\right)
  • 3x - 4y = -4

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

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  • b is the y-intercept

Given the line

3x - 4y = 7

writing in the slope-intercept form

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dividing both sides by 4

4y/4 = 3/4x - 7/4

y = 3/4x - 7/4

Now, comparing with the slope-intercept form of the line equation

y = 3/4x - 7/4

The slope of the line m = 3/4

We know that parallel lines have the same slopes.

Therefore, the slope of the parallel line is: 3/4

now we have,

The point (-4, -2)

The slope m of parallel line = 3/4

Given the point-slope form of the line equation

y-y_1=m\left(x-x_1\right)

where m is the slope of the line and (x₁, y₁) is the point

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

\:y-\left(-2\right)=\frac{3}{4}\left(x-\left(-4\right)\right)

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

Thus, the equation in the point-slope form of the line equation is:

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

Simplifying the equation

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

Subtract 3 from both sides

y+2-2=\frac{3}{4}\left(x+4\right)-2

y=\frac{3}{4}x+1

Multiplying the equation by 4

4y = 3x + 4

3x - 4y = -4

Therefore, the equations represent the line that is parallel to 3x - 4y = 7 and pass through the point (-4,-2) are:

  • y+2=\frac{3}{4}\left(x+4\right)
  • 3x - 4y = -4
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