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jekas [21]
2 years ago
11

Parallel and perpendicular lines ​

Mathematics
1 answer:
11Alexandr11 [23.1K]2 years ago
3 0

Answer:

A. Slope = -³/2

B. y = -³/2x - 6

C. ³/2x + y = -6

Step-by-step explanation:

A. Slope of the line would be the negative reciprocal of the slope of 2x - 3y = 12, which is written in standard form. Rewrite in slope-intercept form, y = mx + b, where m = slope.

Thus:

2x - 3y = 12

-3y = -2x + 12

y = -2x/-3 + 12/-3

y = ⅔x - 4

The slope of 2x - 3y = 12 is therefore ⅔.

The slope of the line perpendicular to 2x - 3y = 12 would be the negative reciprocal of its slope, ⅔ which is:

-³/2

Therefore, the slope of the line perpendicular to 2x - 3y = 12 is -³/2

B. To find the equation of the line in slope-intercept form, first find the equation in point-slope form using the point given (-6, 3) and slope of the line, -³/2.

Substitute a = -6, b = 3, and m = -³/2 into y - b = m(x - a).

Thus:

y - 3 = -³/2(x - (-6))

y - 3 = -³/2(x + 6)

Rewrite in slope-intercept form, y = mx + b

Multiply both sides by 2

2(y - 3) = -3(x + 6)

2y - 6 = -3x - 18

2y = -3x - 18 + 6

2y = -3x - 12

y = -3x/2 - 12/2

y = -³/2x - 6

C. Rewrite y = -³/2x - 6 in standard form.

y = -³/2x - 6

³/2x + y = -6

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In order to determine the vertex of the given functions, consider that the general form of a quadrati function is:

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1. y = x² + 8x - 6

x = -8/2(1) = -4

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Hence, the vertex is (-4,-22)

2. y = -4x² - 24x - 5

x = -(-24)/2(-4) = -6

y(-6) = -4(-6)² - 24(-6) - 6 = -144 + 144 - 6 = -6

Hence, the vertex is (-6,-6)

3. y = 2x² - 3x + 7

x = -(-3)/2(2) = 3/4 = 0.75

y(3/4) = 2(3/4)² - 3(3/4) + 7 = 18/16 - 9/4 + 7 =5.875

Hence, the vertex is (0.75 , 5.875)

4. y = -x² + 5x - 6

x = -5/2(-1) = 5/2 = 2.5

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5. y = 1/2 x² + 6x - 5

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y(-6) = 1/2 (-6)² + 6(-6) - 5 = -23

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6. y = 4x² + 7

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Total
WITCHER [35]

Answer:

The right answer for the question that is being asked and shown above is that: "d. P(A and B) = x + y." The probability of event A is x, and the probability of event B is y. If the two events are independent, the condition must be true is this d. P(A and B) = x + y

Read more on Brainly.com - brainly.com/question/1295200#readmore

Step-by-step explanation:

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A parallelogram can have one pair or two pairs of parallel sides
Rudiy27

Answer:

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Step-by-step explanation:

Think of a rectangle for a parallelogram. It has 2 pairs of parallel sides which makes it a parallelogram. The same for a square as well as it has 2 parallel pairs. Just remember that a parallelogram always has 2 pairs of parallel sides.

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