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vredina [299]
1 year ago
7

Find the equation of the line through (-9,6) that is perpendicular to the line through (7,8),

Mathematics
1 answer:
Setler [38]1 year ago
7 0

Step-by-step explanation:

I assume as "equation" we mean the slope-intercept form :

y = ax + b

"a" is the slope of the line (y coordinate change / x coordinate change when going from one point to another on the line). b is the y-intercept (the y value when x = 0).

we get the slope by finding the perpendicular slope of the first line.

the slope of the first line when going from (-3, -9) to (7, 8) :

x changes by + 10 (from -3 to +7).

y changes by + 17 (from -9 to +8).

so, that slope is 17/10.

the perpendicular slope is turning the original slope upside-down and flips the sign :

-10/17

so, a = -10/17

now, as we have only the slope and a point of the new line, we can use the point-slope form to stay and then transfer into the slope-intercept form.

y - y1 = a(x - x1)

where "a" is again the slope, and (x1, y1) is a point on the line

y - -6 = -10/17 × (x - -9)

y + 6 = -10/17 × (x + 9) = -10/17 × x - 90/17

y = -10/17 × x - 90/17 - 6 =

= -10/17 × x - 90/17 - 102/17 =

= -10/17 × x - 192/17

so, the equation is (in a maybe nicer way)

y = -1/17 × (10x + 192)

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Find the volume of the triangular prism to the right
tigry1 [53]

Answer:

V = 567 ft³

Step-by-step explanation:

V = Bh

<em>[note: a capital 'B' represents the </em><em>area</em><em> of the base] </em>

<em />

The right triangle is the triangular prism's base.

Because the triangle's height (9 ft) and it's base are the same value (9 ft), we can solve to find the area.

  • We can identify the base easily because the base and the top of the prism are exactly the same shape

Area of triangular base:

 A = \frac{bh}{2}

 A = \frac{1}{2} (9 ⋅ 9)

 A = \frac{1}{2} (81)

 A = 40.5

We have 'B' for the triangular prism's formula, so next we need 'h'. 14 ft is provided as the prism's height, so we just need to multiply 40.5 and 14 for our answer.

Volume of triangular prism:

 V = Bh

 V = (40.5)(14)

 V = 567 ft³

3 0
3 years ago
2.5x=-10 what is the answer
Maru [420]

Answer: -4

Step-by-step explanation:

2.5x = -10

1. divide -10 by 2.5

2. x = -4

4 0
2 years ago
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Aiden bought some noteboks and book covers for the upcoming school year.He bought a total of 13 items.Each notebook costs $1.37,
NARA [144]
Answer: Aiden bought 8 notebooks and 5 covers.

This is a system of equations problem. To solve this, we have to write 2 different equations and then solve them.

Our equations are:

x + y = 13
1.37x + 1.08y = 16.36

Where x is the number of notebooks and y is the number of covers.

To solve these equations, you can use anyone of these methods:
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The easiest way would be to graph them with a graphing calculator and find the point of intersection.
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A pump fills 25 of a tank in 23 hour. At this rate, how much of the tank will the pump fill in an hour?
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60% or 3/5 of the tank will be filled in an hour.

The pump will fill 2/5 of the tank in 2/3 hours.

In order to find out how much of the tank will be filled in an hour, use direct proportion and assume portion of the tank that will be filled up in an hour is x.

<em>2/5 of tank        :            2/3 hours </em>

<em>x of tank            :             1 hour </em>

Cross multiply to get:

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x = 2/5 ÷ 2/3

x = 2/5 x 3/2

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In conclusion, 60% of the tank will be filled in an hour.

<em>Find out more at brainly.com/question/14336804.</em>

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