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3 years ago

Find the point, M, that divides segment AB into a ratio of 4:7 if A is at (-33,0) and B is at (0, 44).

Mathematics

1 answer:

Amanda [17]3 years ago

5 0

Answer:

(-21, 16)

Step-by-step explanation:

A is at (-33, 0) and B is at (0, 44),

A point that divides the line segment in a ratio of 4:7 also divides the differences of the x-and y-coordinates in the same ratio.

If we divide each distance into 11 equal parts and choose a length 4/11 of the distance, the other part will be 7/11 of the distance. The two parts will be in a ratio of 4:7.

For the x-coordinate,

x₂ - x₁ = 0 - (-33) = 0 + 33 = 33

(4/11) × 33 = 12

-33 + 12 = -21

The x-coordinate of M is (-21, 0).

For the y-coordinate,

y₂ - y₁ = 44 - 0 = 44

(4/11) × 44 = 16

0 + 16 = 16

The y-coordinate of M is (0, 16).

The coordinates of M are then (-21, 16).

The diagram below shows the point M that divides AB in a 4/7 ratio.

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Alenkasestr [34]

The question is an annuity question with the present value of the annuity given.
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Kara ate 2 7/9 of the raisins she packed. Which box shows the decimal equivalent of the amount of raisins she ate? Box A: 2.777

vivado [14]

Answer: Box A, 2.777

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When using a calculator or long division, you should find that

7/9 = 0.7777...

where the 7s go on forever

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3 years ago

216 divided by 31

Aleksandr-060686 [28]

Answer:

6 r 30

Step-by-step explanation:

Step 1:

Start by setting it up with the divisor 31 on the left side and the dividend 216 on the right side like this:

3 1 ⟌ 2 1 6

Step 2:

The divisor (31) goes into the first digit of the dividend (2), 0 time(s). Therefore, put 0 on top:

3 1 ⟌ 2 1 6

Step 3:

Multiply the divisor by the result in the previous step (31 x 0 = 0) and write that answer below the dividend.

3 1 ⟌ 2 1 6

Step 4:

Subtract the result in the previous step from the first digit of the dividend (2 - 0 = 2) and write the answer below.

3 1 ⟌ 2 1 6

- 0

Step 5:

Move down the 2nd digit of the dividend (1) like this:

3 1 ⟌ 2 1 6

- 0

2 1

Step 6:

The divisor (31) goes into the bottom number (21), 0 time(s). Therefore, put 0 on top:

0 0

3 1 ⟌ 2 1 6

- 0

2 1

Step 7:

Multiply the divisor by the result in the previous step (31 x 0 = 0) and write that answer at the bottom:

0 0

3 1 ⟌ 2 1 6

- 0

2 1

Step 8:

Subtract the result in the previous step from the number written above it. (21 - 0 = 21) and write the answer at the bottom.

0 0

3 1 ⟌ 2 1 6

- 0

2 1

- 0

2 1

Step 9:

Move down the last digit of the dividend (6) like this:

0 0

3 1 ⟌ 2 1 6

- 0

2 1

- 0

2 1 6

Step 10:

The divisor (31) goes into the bottom number (216), 6 time(s). Therefore put 6 on top:

0 0 6

3 1 ⟌ 2 1 6

- 0

2 1

- 0

2 1 6

Step 11:

Multiply the divisor by the result in the previous step (31 x 6 = 186) and write the answer at the bottom:

0 0 6

3 1 ⟌ 2 1 6

- 0

2 1

- 0

2 1 6

1 8 6

Step 12:

Subtract the result in the previous step from the number written above it. (216 - 186 = 30) and write the answer at the bottom.

0 0 6

3 1 ⟌ 2 1 6

- 0

2 1

- 0

2 1 6

- 1 8 6

3 0

You are done, because there are no more digits to move down from the dividend.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 216 divided by 31 calculated using Long Division is:

30 Remainder

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3 years ago