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Vinil7 [7]
3 years ago
5

In the diagram below, triangle abc ~ triangle dec . What is the value of x? A. 28 b. 24 c. 22 d. 26

Mathematics
1 answer:
Lesechka [4]3 years ago
4 0

Answer:

Option A.

Step-by-step explanation:

From the figure attached,

Given : ΔABC ~ ΔDEC

By the property of similarity,

"Corresponding sides of the similar triangles are proportional"

\frac{\text{AB}}{ED}=\frac{BC}{EC}=\frac{AC}{DC}

Since, \frac{\text{AB}}{ED}=\frac{AC}{DC}

\frac{42}{6}=\frac{x}{(32-x)}

6x = 42(32 - x)

6x = 1344 - 42x

6x + 42x = 1344

48x = 1344

x = \frac{1344}{48}

x = 28 units

Therefore, Option (A). x = 28 units will be the answer.

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2
Zigmanuir [339]

Answer:

The weight of the water in the pool is approximately 60,000 lb·f

Step-by-step explanation:

The details of the swimming pool are;

The dimensions of the rectangular cross-section of the swimming pool = 10 feet × 20 feet

The depth of the pool = 5 feet

The density of the water  in the pool = 60 pounds per cubic foot

From the question, we have;

The weight of the water in Pound force = W = The volume of water in the pool given in ft.³ × The density of water in the pool given in lb/ft.³ × Acceleration due to gravity, g

The volume of water in the pool = Cross-sectional area × Depth

∴ The volume of water in the pool = 10 ft. × 20 ft. × 5 ft. = 1,000 ft.³

Acceleration due to gravity, g ≈ 32.09 ft./s²

∴ W = 1,000 ft.³ × 60 lb/ft.³ × 32.09 ft./s² = 266,196.089 N

266,196.089 N ≈ 60,000 lb·f

The weight of the water in the pool ≈ 60,000 lb·f

6 0
3 years ago
Which of the following are incorrect expressions for slope? Check all that apply.
Crazy boy [7]
Pretty sure it’s B and D
7 0
2 years ago
A diver is 25 feet below sea level. After he swims up 15 feet toward the surface, what is his elevation?
Nataly [62]
The person above me is right!! I kinda got confused because i thought it was asking what sea level is the diver now BUT its asking for the elevation, so you need to subtract.
7 0
3 years ago
A coordinate map of the local grocery store is shown below. Hot dogs are located at the point (6,4) Mustard is located at the po
deff fn [24]

The distance between the 2 locations = 7 units

Step-by-step explanation:

Step 1:

Given,

Location of Hot dogs = (6,4)

Location of Mustard = (6,-3)

We need to find the distance between the two locations

Step 2:

Since the x coordinates of both the location are the same , they lie in the same line.

The first location is 4 units above the x axis and the second location is 3 units below the x axis.

Hence the distance between the 2 locations 4-(-3) = 7 units

Step 3 :

Answer :

The distance between the 2 locations = 7 units

8 0
3 years ago
On a 10-item test, three students in Professor Hsin's advanced chemistry seminar received scores of 2, 5, and 8, respectively. F
Inessa [10]

Answer:

For this distribution of test scores, the standard deviation is equal to the square root of 9

D) 9

Step-by-step explanation:

We need to know the standard deviation formula:

S=\sqrt{\frac{sum(x-Am)^2}{n-1} } (1)

Where:

S: Standard deviation

sum: Summation

x: Sample values

Am: Arithmetic mean

n:   Number of terms, in this case 3

Now, we need to know the arithmetic mean of the sample values: 2, 5 and 8

Am=\frac{2+5+8}{3} = 5

To know the standard deviation we need to have the summation of each term minus the arithmetic mean squared.

(x-Am)^2 of each term:

(2-5)^2=9\\(5-5)^2=0\\(8-5)^2=9

Now, we can find the standard deviation:

S=\sqrt{\frac{9+0+9}{3-1} } \\S=\sqrt{\frac{18}{2} } \\S=\sqrt{9}

The standard deviation is equal to the square root of 9

4 0
3 years ago
Read 2 more answers
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