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3 years ago

9. What is the slope of the line through the points (-2, -1) and (4, 3)?

Mathematics

1 answer:

Fofino [41]3 years ago

4 0

Step-by-step explanation:

given points,

(-2, -1) and (4,3)

we know,

slope of line = y_2 - y_1/ x_2 - x_1

x_1 and y_1 = -2 , -1

x_2 and y_2 = 4 , 3

according to the formula

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

→ 3 + 1/4 + 2

→ 4/6

→ 2/3

or (2,3)

therefore, slope of the given line is (2,3).

Hope this answer helps you dear!

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How does the ratio of surface area to volume change as the shapes get smaller

svet-max [94.6K]

The ratio of the surface area to the volume will decrease

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3 years ago

Orlando invested $16,000 in an eight-year CD bearing 6.5% simple annual interest, but needed to withdraw $3,500 after five years

baherus [9]

Answer:

Therefore, the correct option is OPTION C.

Step-by-step explanation:

If Orlando had not made his early withdrawal, the amount of money he would have earned is:

F = 0.065($16,000)(8) = $8.320

Given that he withdraw $3500, he now earns:

F1 = (0.065)($16,000)(5) + ($12,500)(0.065)(3)

F1 = $5200 + $2437.5 = $7637.5

And now we have to take into acount the year of penalty, which is one year’s worth of interest on the amount withdrawn.

Penalty= $3500(0.065)(1) = $227.5

So the total money he earns now is: $7637.5 - $227.5 = $7410

Then, the amunt of money he could have earn but he didn't is:

Money = $8.320 - $7410 = $910

Therefore, the correct option is OPTION C.

6 0

3 years ago

Read 2 more answers

21. Who is closer to Cameron? Explain.

pickupchik [31]

Problem 21

<h3>Answer: Jamie is closer</h3>

-----------------------

Explanation:

A = Arthur's location = (20,35)
J = Jamie's location = (45,20)
C = Cameron's location = (65,40)

To find out who's closer to Cameron, we need to compute the segment lengths AC and JC. Then we pick the smaller of the two lengths.

We use the distance formula to find each length

Let's find the length of AC.

$A = (x_1,y_1) = (20,35)\\\\C = (x_2,y_2) = (65,40)\\\\d = \text{Distance from A to C} = \text{length of segment AC}\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(20-65)^2 + (35-40)^2}\\\\d = \sqrt{(-45)^2 + (-5)^2}\\\\d = \sqrt{2025 + 25}\\\\d = \sqrt{2050}\\\\d \approx 45.2769257\\\\$

The distance from Arthur to Cameron is roughly 45.2769257 units.

Let's repeat this process to find the length of segment JC

$J = (x_1,y_1) = (45,20)\\\\C = (x_2,y_2) = (65,40)\\\\d = \text{Distance from J to C} = \text{length of segment JC}\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(45-65)^2 + (20-40)^2}\\\\d = \sqrt{(-20)^2 + (-20)^2}\\\\d = \sqrt{400 + 400}\\\\d = \sqrt{800}\\\\d \approx 28.2842712\\\\$

Going from Jamie to Cameron is roughly 28.2842712 units

We see that segment JC is shorter than AC. Therefore, Jamie is closer to Cameron.

=================================================

Problem 22

<h3>Answer: Arthur is closest to the ball</h3>

-----------------------

Explanation:

We have these key locations:

A = Arthur's location = (20,35)
J = Jamie's location = (45,20)
C = Cameron's location = (65,40)
B = location of the ball = (35,60)

We'll do the same thing as we did in the previous problem. This time we need to compute the following lengths:

These segments represent the distances from a given player to the ball. Like before, the goal is to pick the smallest of these segments to find out who is the closest to the ball.

The steps are lengthy and more or less the same compared to the previous problem (just with different numbers of course). I'll show the steps on how to get the length of segment AB. I'll skip the other set of steps because there's only so much room allowed.

$A = (x_1,y_1) = (20,35)\\\\B = (x_2,y_2) = (35,60)\\\\d = \text{Distance from A to B} = \text{length of segment AB}\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(20-35)^2 + (35-60)^2}\\\\d = \sqrt{(-15)^2 + (-25)^2}\\\\d = \sqrt{225 + 625}\\\\d = \sqrt{850}\\\\d \approx 29.1547595\\\\$

Segment AB is roughly 29.1547595 units.

If you repeated these steps, then you should get these other two approximate segment lengths:

JB = 41.2310563

CB = 36.0555128

-------------

So in summary, we have these approximate segment lengths

AB = 29.1547595
JB = 41.2310563
CB = 36.0555128

Segment AB is the smallest of the trio, which therefore means Arthur is closest to the ball.

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2 years ago

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chubhunter [2.5K]

-52

Step-by-step explanation:

8.4-2.22+12.4-4.22=

=32-44+48-88=

=-132+80=

=-52

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3 years ago

Can someone pls help me with this problem?

Alex787 [66]

<u></u>

For the first blank, since the output increases by 5 for each increase of 1 for the input, the answer is 13+2(5) = 23.
For the second blank, since the output increased by 10 compared to 23, the input increased by 2. So, the answer is 5 + 2 = 7.
We know the output is of the form 5x+b for some constant b. If we test input of 1 and an output of 3, we get an input of 1 gives 5+b, which is equal to 3, meaning b=-2. So, the answer is 5x-2.

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2 years ago