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forsale [732]
3 years ago
9

Find the value of n so that the line perpendicular to the line with the equation -2y + 4 = 6x + 8 passes through the points at (

n, -4) and (2, -8).
Mathematics
1 answer:
kolezko [41]3 years ago
6 0
If the line must be perpendicular to the equation, that means the slope is the reciprocal of the one in the given equation. So first we find that, the slope of the given equation. 

- 2y + 4 = 6x + 8
- 2y = 6x + 4
 
y = - 3x - 2

So the slope of the given equation is - 3x. That means the slope of our perpendicular equation must be 1/3x 

Now to find the value of n, plug in our given information and perpendicular slope into the slope equation:

Slope = (Y₂ - Y₁ ) / (X₂ - X₁)

1/3 = (- 8 - (-4)) / (2 - n)
1/3 = (- 8 + 4) / (2 - n)
1/3 = ( - 4) / (2 - n)

Multiply both sides by (2 - n) to get the binomial out of the denominator

(1/3)(2 - n) = - 4

Multiply both sides by 3 to isolate the binomial

2 - n = - 4(3)
2 - n = - 12

Subtract 2 from both sides to isolate the variable

- n = - 14

Divide by - 1 to get rid of the negative.

n = 14. Your coordinate is ( 14, - 4)

Now to find the equation that is perpendicular. 

y = 1/3x + b

Plug in either of the coordinates. I'm going to use the ordered pair we just found. 

- 4 = 1/3(14) + b
- 4 = 14/3 + b
- 12/3 = 14/3 + b

Subtract 14/3 on both sides.

- 26/3 = b

Your equation is y = 1/3x - 26/3


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Kenneth wants to sew a tent, including the bottom so that it is entirely enclosed. He has a rectangular piece of canvas with dim
Vadim26 [7]

Based on the calculations, the depth of tent is equal to 12 feet.

<h3>How to calculate the depth of the tent?</h3>

Based on the diagram (see attachment) and information provided, we can logically deduce the following parameters (points):

  • Triangle ABC is an isosceles triangle (AB = AC).
  • The front and back of the triangle are identical triangles.
  • Side AD is perpendicular side BC.
  • CD is the midpoint of BC i.e CD = BC/2 = 6/2 = 3 feet.

Next, we would determine the height of the right-angled triangle (ADC) by applying Pythagorean theorem:

AC² = AD² + DC²

AD² = AC² - DC²

AD² = 5² - 3²

AD² = 25 - 9

AD² = 16

AD = √16

AD = 4 feet.

Also, we would determine the area of the triangle (ABC):

Area = 1/2 × b × h

<u>Where:</u>

  • b is the base area.
  • h is the height.

Substituting the given parameters into the formula, we have;

Area = 1/2 × 6 × 4

Area = 12 feet².

Depth of tent = 3 × height of ADC

Depth of tent = 3 × 4

Depth of tent = 12 feet.

Read more on area of triangle here: brainly.com/question/21917592

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7 0
1 year ago
Question 2(Multiple Choice Worth 5 points)
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it C Step 2, the exponents in the denominator are added during multiplication

hope it helps!

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3 years ago
A square base of a pyramid has the dimensions 5 yards by 5 yards. The height of one of the triangular faces is 12 yards. How can
-Dominant- [34]

Answer:

145 yards squared

Step-by-step explanation:

So the area of the base is area of a square with side length of 5 yards 5*5=25

The area of one triangular face base times height divided by two and then simply multiplied by 4 because there are 4 triangular faces.

(\frac{5*12}{2} )*4 = 120

So the total surface area is 25+120=145 yards squared

4 0
3 years ago
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