Which lines are parallel to 8x + 2y = 7? select all that apply. a. y − 1 = 4(x + 8) b. y = −4x + 15 c. 16x + 4y = 9 d. y = −4x

The general form of the straight line equation is y = m·x + c

The lines that are parallel to 8·x + 2·y = 7, are;

B. y = -4·x + 15

C. 16·x + 4·y = 9

D. y = -4·x

The reason the above values are correct are as follows;

The given line is 8·x + 2·y = 7

Required:

To find the line parallel to the given line, 8·x + 2·y = 7

Solution:

Two lines are parallel if they have the same slope but different y-intercept

The slope of the given line is given by the value of m when the line is represented in the form y = m·x + c

8·x + 2·y = 7

2·y = 7 - 8·x

Dividing both sides by two gives;

Therefore;

The slope of the line is therefore, m = -4

The y-intercept of the line, c =

We check the slope of each of the given lines as follows;

Option A; y - 1 = 4·(x + 8)

The slope of the line in option A is 4·x, therefore, oy - 1 = 4·(x + 8), is not parallel to 8·x + 2·y = 7

Option B. y = -4·x + 15

The slope of the line in option B is also m =  -4·x, and the y-intercept is c = 15, is different from the y-intercept of the given function

Therefore, the line y = -4·x + 15, is parallel to 8·x + 2·y = 7

Option C. 16·x + 4·y = 9

The line given by the equation in option C. can be rearranged as follows;

4·y = 9 - 16·x

Therefore, we have;

Therefore, the slope of the equation in option C, is also m = -4

Therefore, the equation in option C. is also parallel to the given equation

Option D. y = -4·x

The slope of the function in option D, given in the form of y = m·x + c is m = -4, and c = 0

Therefore, the equation in option D is also parallel to the given function

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8x + 2y = 7

2y = -8x + 7

y = -4x + 7/2; this line has slope equal -4

Parallel lines, slope is the same so slope of parallel line is also -4

A.y − 1 = 4(x + 8); slope m = 4....FALSE

B.    y = −4x + 15;  slope m = - 4....TRUE

C.16x + 4y = 9;  4y  = -16x + 9 so y = -4x + 9/4; slope m = - 4....TRUE

D.y = −4x; slope m = - 4....TRUE

Answer

B.    y = −4x + 15

C.16x + 4y = 9

D.y = −4x

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9