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Dafna11 [192]
2 years ago
10

Ricardo has a square hot tub. He wants to build a square pool next to it that is a dilation of the hot tub using a scale factor

of 5. Point Q is the center of dilation. Square A B C D is dilated to created square A prime B prime C prime D prime. The length of B prime C prime is 24 feet. If the pool is to be 24 ft on each side, what is the length of one side of the hot tub?
Mathematics
1 answer:
PilotLPTM [1.2K]2 years ago
5 0

Answer:

The length of one side of the hot tub is 4.8ft

Step-by-step explanation:

Given

Shape: Square

k = 5 -- scale factor

B'C' = 24

Required

Side length of ABCD (the hot tub)

From the question, we understand that

ABCD \to D_5 \to A'B'C'D  ABCD dilated by 5 to A'B'C'D

This implies that:

BC * 5 = B'C' i.e. the sides of ABCD is multiplied by 5 to get A'B'C'D

So, we have:

BC * 5 = 24

Divide by 5

BC = 4.8

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13,000 inches equals how many miles
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Answer:

0.205177 mi

Step-by-step explanation:

Step 1: Find conversions

12 in = 1 ft

5280 ft = 1 mi

Step 2: Use Dimensional Analysis

13000 \hspace{2} in(\frac{1 \hspace{2} ft}{12 \hspace{2} in} )(\frac{1 \hspace{2} mi}{5280 \hspace{2} ft} )

0.205177 mi

8 0
3 years ago
How can I prove mathematically that (a / b) + (c / d) = (ad + bc) / bd
wlad13 [49]

Step-by-step explanation:

(a/b) + (c/d)

Find the common denominator.  In this case, bd.  So multiply the first fraction by d/d, and the second fraction by b/b.

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Add the fractions.

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7 0
3 years ago
Work out the value of x
Korvikt [17]

Answer:

117 degrees

Step-by-step explanation:

So we already know that one angle is 38 degrees, so we have that one. The angle, 101 is exterior, and we have to subtract 180 from that to get the interior angle. We get a difference of 79. Since the sum of a triangle's interior angles are 180, we have to add 38+79 to get 117. Then, we have to subtract it from 180 to get the value of the interior angle as 63 degrees. Because x is on the outside, we have to again subtract 63 from 180 to get the missing value of x as 117.

6 0
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Read 2 more answers
A note with a face value 4300 was discounted at 3%. if discount was 21 dollars. find the length of loan in days
Doss [256]
The annual discount is 3%, therefore the total discount for 1 year would be:

4300 × 3 ÷ 100 = 129$

Now, you can set a proportion:

discount : annual discount = loan days : days in one year
21 : 129 = x : 360
 
x = 21 × 360 / 129 = 58.6 days

Hence, the loan duration was 60 days.
6 0
3 years ago
14.   What's the length of a segment that begins at the point (2, 3) and ends at the point (18, 15)? 
Bingel [31]

Answer:

20

Step-by-step explanation:

d = √(xb - xa)2 + (yb - ya)2 =

= √(18 - 2)2 + (15 - 3)2 =

= √162 + 122 = √256 + 144 =

= √400  

= 20


7 0
3 years ago
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