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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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irina [24]
5/8 of a liter of syrup, or 0.625
7 0
3 years ago
Determine whether each set of numbers can be the measure of the sides of a triangle. If so, classify the triangle as acute, righ
ElenaW [278]

The following set of numbers 2√3, 4√2, and 3√5, can be the measures of the sides of an obtuse triangle.

A triangle is a polygon with three sides and three vertices.

To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

let a = 2√3, b = 4√2, and c = 3√5

a + b > c     2√3 + 4√2 > 3√5     9.12 > 6.71     True

a + c > b     2√3 + 3√5 > 4√2     10.17 > 5.66    True

b + c > a     4√2 + 3√5 > 2√3     12.37 > 3.46     True

To know what type of triangle based on the length of its side:

1. Take the sum of the squares of the two smaller sides.

(2√3)^2 + (4√2)^2 = 44

2. Compare it to the square of the largest side.

(3√5)^2 = 45

44 < 45

If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.

if they are equal, it is a right triangle

if they are smaller, then it is an obtuse triangle.

Hence, 2√3, 4√2, and 3√5 can be the measure of the sides of an obtuse triangle.

To learn more about types of triangle based on side lengths: brainly.com/question/13619935

#SPJ4

4 0
1 year ago
If you answer this question in full truth you get max points able to be given and brainliest I don't have time to play game answ
asambeis [7]

A)

The formula for direct variation is written as Y = KX, where k is the direct variation you need to solve for.

Y is the total amount raised and X would be the number of attendees:

100 = K5

Divide both sides by 5:

K = 100/5

K = 20

B. The constant of variation is  K  which is 20

C) Using the formula from A: y = kx, replace k with 20 and x with 60 and solve for y:

y = 20 * 60

y = 1200

The total is: $1,200

2. A relationship is proportional when the ratio is a constant number.The relationship is non proportional when the ratio varies between the different values.

8 0
3 years ago
Find the volume of the right triangular prism shown:
LekaFEV [45]

Answer:

960cm³

Step-by-step explanation:

Find the base of the triangle (use phytagoras theorem)

c²= a²+b²

20²= 16²+b²

400=256+b²

b²=400-256

b²= 144

b=

\sqrt{144}

base= 12

Volume: (1/2×b×h)×l

= (1/2×12×16)×10

=(6×16)×10

=96×10

=960cm³

7 0
2 years ago
Write a linear equation in slope intercept form to model the situation and internet company charges $4.95 per month plus $2.50 f
antoniya [11.8K]

Answer:

it cost $39.95 in a month when you use the internet for 14 hours

Step-by-step explanation:

internet company charges $4.95 per month plus $2.50 for each hour

Let x be the amount of hours internet used

for 1 hour, charge is 2.50

for x hours , charge is 2.50x

To get linear equation we use y=mx+b

m is the slope and b is the fixed cost

fixed cost b= 4.95 and slope m = 2.50

So equation becomes y = 2.50x + 4.95

we need to find the cost y for 14 hours

So we plug in 14 for x  and find out y

y = 2.50(14) + 4.95= 39.95


7 0
3 years ago
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