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Bond [772]
2 years ago
14

Determine the value of each variable in the figure below. Keep answers in simplest radical form.

Mathematics
1 answer:
Tanzania [10]2 years ago
7 0

Answer:

  a = 21

  b = 63

  c = 42√3

  d = 21√3

Step-by-step explanation:

The sides of a 30°-60°-90° triangle have the ratios 1 : √3 : 2. The given side (42) is the longest side of the smallest triangle, and the shortest side of the largest triangle.

That means the other sides of the smallest triangle will be ...

  a = 42/2 = 21

  a+b = 2(42) = 84

  b = (a+b) -a = 84 -21 = 63

  d = 21√3 . . . . middle-length side of the smallest triangle

  c = 42√3 . . . . middle-length side of the largest triangle

The values of the variables are ...

  • a = 21
  • b = 63
  • c = 42√3
  • d = 21√3

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a car travels the first 15 km of the journey at an average speed 60km/h and the remaining 40 km at an average speed of 30 km/h f
rewona [7]

Answer:

the average speed of the whole journey is 45 km/h

Step-by-step explanation:

The computation of the average speed of the whole journey is shown below:

Average speed is

= (Speed 1 + speed 2) ÷ 2

= (60 km/h + 30 km/h) ÷ 2

= 90 km/h ÷ 2

= 45 km/h

Hence, the average speed of the whole journey is 45 km/h

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3 years ago
The legs of the drafting table form vertical angles. Find the measures of ∠1, ∠2 and ∠3.
Leviafan [203]

Answer:

m∡1 = 95°

m∡2 = 85°

m∡3 = 95°

Step-by-step explanation:

m∡1 + 85 = 180;   m∡1 = 95°

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m∡3 = m∡1 = 95° because they are vertical and congruent

4 0
3 years ago
Read 2 more answers
The length of a rectangle is seven inches more than its width. Its area is 78 square inches. Find the width and length of the re
Alekssandra [29.7K]

Answer:

Length: 23.38

Width: 3.34

Step-by-step explanation:

First I drew out a diagram so that I could visibly see the problem. [ a rectangle with 7x on one side and x on the other.

So to find the area you multiply length time width and 7x times x is 7x^2. The actual area is given: 78, so you set that equal to 7x^2.

Then you want to divide by 7 to get 11.14. Then you want to take the square root of 11.14 to get 3.338 which rounds to 3.34 {try not to round until the very end]. This gives you the width of the rectangle, so to find the length you would have to multiply x by 7 to get 23.38. When you multiply the length and width (3.34 x 23.38) you get 78.08 which can round to 78.

7x^2 = 78

x^2 = 78/7

x^2= 11.142...

x = sqrt(1.142...)

x = 3.338 --> 3.34 --> width

3.34 x 7 --> 23.38 --> length

3.34 x 23.38 --> 70.8

8 0
3 years ago
Read 2 more answers
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