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Marianna [84]
3 years ago
8

The length of the segment between the points $(2a, a-4)$ and $(4, -1)$ is $2\sqrt{10}$ units. What is the product of all possibl

e values for $a$? LOTS OF POINTS AND BRAINLIEST TO CORRECT ANSWER!
Mathematics
1 answer:
True [87]3 years ago
5 0

Answer:

-3

Step-by-step explanation:

The length of a segment is

sqrt( ( y2-y1)^2 + (x2-x1) ^2) = 2 sqrt(10)

sqrt( ( a-4 - -1)^2 + (2a -4) ^2) = 2 sqrt(10)

sqrt( ( a-4 +1)^2 + (2a -4) ^2) = 2 sqrt(10)

Combine like terms

sqrt( ( a-3)^2 + (2a -4) ^2) = 2 sqrt(10)

Square each side

( a-3)^2 + (2a -4) ^2) = 4 *(10)

FOIL the left side

a^2 -6a +9   + 4a^2 -16a +16 = 40

Combine like terms

5a^2 -22a +25 = 40

Subtract 40 from each side

5a^2 -22a -15 =0

Factor

(a - 5) (5 a + 3) = 0

Using the zero product property

a-5 =0   5a +3 = 0

a = 5       5a = -3

a=5     a = -3/5

The product of the terms is

5 * -3/5 = -3

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Answer:

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7 0
1 year ago
The distance around a rectangular cafe is 35m . The ratio of length of the cafe to the width is 3:2. Find the dimension of the
marusya05 [52]

Hi there! :)

Answer:

Length = 10.5 m, width = 7 m.

Step-by-step explanation:

Given:

Perimeter, or P = 35 m

Ratio of l to w = 3 : 2

Since the ratio is 3 : 2, let l = 3x, and w = 2x.

We know that the formula for the perimeter of a rectangle is P = 2l + 2w. Therefore:

35 = 2(3x) + 2(2x)

35 = 6x + 4x

35 = 10x

x = 3.5

Plug this value of "x" into each expression to solve for the dimensions:

2(3.5) = w

w = 7 m

3(3.5) = l

l = 10.5 m

Therefore, the dimensions are:

Length = 10.5 m, width = 7 m.

4 0
3 years ago
Taryn is shopping for a Christmas tree. At Home Depot the one she likes is $149.00 and she has a 15% off coupon. At Lowe's the o
Vitek1552 [10]

Answer:

Step-by-step explanation:

At home depot

Price of Christmas tree = $149.00

Discount = 15%

Amount discounted = 15% of $149

Amount discounted = 15/100 * $149

Amount discounted = 15 * 1.49

Amount discounted = $22.35

Amount she paid = $149-$22.35

Amount she paid = $126.65

At Lowe's:

Price of Christmas tree = $175.00

Discount = 260%

Amount discounted = 20% of $175

Amount discounted = 20/100 * $175

Amount discounted = 0.2 * 175

Amount discounted = $35

Amount she paid = $175-$35

Amount she paid at Lowe's = $140

<u><em>From the prices above, it can be seen that Home Depot has a better deal since the price after removing discount is lower than that of Lowe's.</em></u>

<u><em></em></u>

<u><em>Amount she will save will be $140 - $126.65 = $13.35</em></u>

6 0
3 years ago
Becky bought a magazine for $3.90, and the sales tax was 8.25%. How much sales tax did Becky pay on the magazine?
igor_vitrenko [27]

Answer:

32 cents

Step-by-step explanation:

Find 8.25 percent of 3.90:

0.0825*3.90 = 0.32

3 0
3 years ago
Read 2 more answers
Kin made a Picture frame for a square picture with sides that are 5f-4 inches long. Framing the picture adds 2 inches to the len
elena-s [515]

The perimeter of a shape is the sum of its side lengths

The expressions for the perimeter of the frame are 4(l + 2) and 4l + 8

<h3>How to determine the perimeter of the shape</h3>

The side length of the frame is given as l

So, the perimeter of the frame is

:P = 4l

When 2 inches are added to each length, the perimeter of the frame becomes

P =4(l + 2)

Expand

P =4l + 8

Hence, the expressions for the perimeter of the frame are 4(l + 2) and 4l + 8

Read more about perimeter at:

brainly.com/question/24571594

3 0
2 years ago
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