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3 years ago

Find $y$ if the point $(-6,y)$ is on the line that passes through $(-1,7)$ and $(3,-2)$.

Mathematics

1 answer:

vichka [17]3 years ago

6 0

Answer:

y = 18.25

Step-by-step explanation:

The 2-point form of the equation of a line can be used to write the equation of the line through the given points.

y = (y2 -y1)/(x2 -x1)(x -x1) +y1

y = (-2 -7)/(3 -(-1))(x -(-1)) +7

y = -9/4(x +1) +7

For x = -6 this evaluates to ...

y = -9/4(-6 +1) +7 = (9/4)(5) +7 = 45/4 +7

y = 18 1/4

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(1 point) Find the limit, if it exists, or type DNE if it does not exist. A. lim(x,y)→(0,0)(x+5y)2x2+25y2=lim(x,y)→(0,0)(x+5y)2x

statuscvo [17]

Answer:

A. DNE. The limit does not exist.

B. The limit is 0

Step-by-step explanation:

A. lim(x,y)→(0,0)[(x + 5y)/(2x² + 25y²)]

Along the x axis, y = 0, the limit becomes:

lim(x)→(0)[x/2x²]

= lim(x)→(0)[1/2x] = infinity

Along the y axis, x = 0, the limit becomes

lim(y)→(0)[5y/25y²]

= lim(y)→(0)[1/5y] = infinity

DNE

B. lim(x,y)→(0,0)[(2x³ + 7y³)/(x² + y²)

Putting x = rcosθ, and y = rsinθ, the limit becomes

lim(r)→(0)[(2r³cos³θ + 7r³sin³θ)/(r²cos²θ + r²sin²θ)]

Because cos²θ + sin²θ = 1, the limit becomes:

= lim(r)→(0)[r³(2cos³θ + 7sin³θ)/r²]

= lim(r)→(0)[r(2cos³θ + 7sin³θ)]

= 0

The limit is 0

4 0

3 years ago

Which inequality is true

yarga [219]

The inequality that is true is 7π > 21

<h3>How to determine the inequality that is true?</h3>

To do this, we simply test the given inequalities (starting from the first)

The first inequality is represented as

7π > 21

Divide both sides of the inequality by 7

So, we have:

7π/7 > 21/7

Evaluate the quotient of 21 and 7

So, we have:

7π/7 > 3

Evaluate the quotient of 7π and 7

So, we have:

π > 3

The above inequality is true.

This is so because π = 3.14 and 3.14 > 3

Hence, the inequality that is true is 7π > 21

Read more about inequality at

brainly.com/question/24372553

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6 0

1 year ago

Two ships sail between New York and London. One makes the round trip in 12 days. The other takes 16 days. They both leave London

Mariana [72]

In order to find the answer to this question, you would need to find the Greatest Common Factor of 16 and 12 which would be 4 because 4 is the greatest amount that you can divide both 12 and 16 by. So the soonest both ships will leave together again will be in 4 days.

6 0

3 years ago

Read 2 more answers

A customer wants to tile their sunroom using 12" x24" tile which comes 9 pieces to a box the room is 8' by 9'6" calculate how ma

AysviL [449]

The number of pieces The customer will need actually is 38 tiles

The number of tiles in boxes the customer will buy is 45 tiles

Step-by-step explanation:

To solve the problem we will do these steps

1. Change the dimensions of the room from feet to inches

2. Calculate the area of the room

3. Calculate the area of one tile

4. Divide the area of the room by the area of the tile to find the number

of tills

5. Divide the number of tiles by the number of pieces in one box

to find the number of boxes he will need to buy

∵ The dimensions of the room are 8 feet by 9 feet 6 inches

∵ 1 foot = 12 inches

∴ 8 feet = 8 × 12 = 96 inches

∴ 9 feet 6 inches = 9 × 12 + 6 = 108 + 6 = 114 inches

∴ The dimensions of the sun room are 96" by 114"

The area of a rectangle is length × width

∵ Area of the room = 96 × 114 = 10944 inches²

∵ The dimensions of a tile are 12" by 24"

∴ Area of a tile = 12 × 24 = 288 inches²

∵ The number of tiles = Area room ÷ area tile

∴ The number of tiles = 10944 ÷ 288 = 38 tiles

<em>The number of pieces The customer will need is 38 tiles</em>

The tiles come in boxes each box contains 9 pieces

∵ 38 ÷ 9 = 4.22

∴ He will need to buy 5 boxes with 45 tiles

<em>The number of tiles in boxes is 45 tiles</em>

Learn more:

You can learn more about the area of some figures in brainly.com/question/4459688

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4 0

3 years ago

What is the length and width of a 864 square feet

spayn [35]

The area doesn't tell you the dimensions. There are an infinite number of different answers, all with the same area but different dimensions.
Here are a few:
1 ft by 864 ft
2 ft by 432 ft
3 ft by 288 ft
4 ft by 216 ft
8 ft by 108 ft
16 ft by 54 ft
24 ft by 36 ft
27 ft by 32 ft.

The area of each of these is 864 square feet.

3 0

3 years ago