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alexdok [17]
2 years ago
15

Solve the following proportion: (round to the nearest tenths place if necessary)

Mathematics
2 answers:
romanna [79]2 years ago
8 0

Solution:

<u>Note that:</u>

  • 4/7 = 10/x

To find the solution to the proportion, we will need to simplify the equation (4/7 = 10/x)

  • 4/7 = 10/x
  • => 4x = 70
  • => x = 70/4 = 35/2 = 17.5.

Hoped this helped!

maks197457 [2]2 years ago
7 0

Answer:

x = 17.5

Step-by-step explanation:

4/7 = 10/x

4x = 70

x = 70/4

x = 17.5

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Answer:

Exercise 1: The length of the unknown leg is 4 inches.

Exercise 3: The following straws can be used to construct the triangle: b) 3\,in, c) 4.5\,in, d) 6.5\,in, e) 10\,in, f) 13.5\,in

Exercise 4: Possible options of this exercise: 1) (2, 4, 5), 2) (4, 5, 6), 3) (5, 6, 10), 4) (1, 2, 11), 5) (1, 4, 11), 6) (1, 10, 11)

Step-by-step explanation:

Exercise 1:

Let suppose that triangle represented in the figure is a right triangle, the length of the missing leg is determined by Pythagorean Theorem:

y = \sqrt{l^{2}-x^{2}} (1)

Where:

l - Hypotenuse, in inches.

x - Known leg, in inches.

y - Unknown leg, in inches.

If we know that l = 11\,in and x = 10\,in, then the length of the unknown leg is:

y = \sqrt{21}

Since 4 is the least whole number closest to \sqrt{21}, then we conclude that the length of the unknown leg is 4 inches.

Exercise 3:

The range of possible lengths for the missing side of the triangle is represented by the following simultaneous inequality:

x + y > l > x-y (2)

Where:

x - Greater side, in inches.

y - Lesser side, in inches.

l - Missing side, in inches.

If we know that x = 8\,in and y = 6\,in, then we have the following range of missing sides:

14\,in > l > 2\,in

The following straws can be used to construct the triangle: b) 3\,in, c) 4.5\,in, d) 6.5\,in, e) 10\,in, f) 13.5\,in

Exercise 4:

Let check each pair to determine possible constructions by means of the inequality used in Exercise 3:

(i) x = 4\,in, y = 2\,in

6\,in>l>2\,in

Possible choices: 5 inches.

(ii) x = 5\,in, y = 2\,in

7\,in > l > 3\,in

Possible choices: 4 inches, 6 inches.

(iii) x = 6\,in, y = 2\,in

8\,in > l > 4\,in

Possible choices: 5 inches, 6 inches.

(iv) x = 10\,in, y = 2\,in

12\,in > l > 8\,in

Possible choices: None.

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9\,in > l > 1\,in

Possible choices: 2 inches, 6 inches.

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10\,in > l > 2\,in

Possible choices: 5 inches.

(vii) x = 10\,in, y = 4\,in

14\,in > l > 6\,in

Possible choices: None.

(viii) x = 6\,in, y = 5\,in

11\,in > l > 1\,in

Possible choices: 2 inches, 4 inches, 10 inches.

(ix) x = 10\,in, y = 5\,in

15\,in > l > 5\,in

Possible choices: 6 inches.

(x) x = 10\,in, y = 6\,in

16\,in > l > 4\,in

Possible choices: 5 inches.

Possible options of this exercise: 1) (2, 4, 5), 2) (4, 5, 6), 3) (5, 6, 10), 4) (1, 2, 11), 5) (1, 4, 11), 6) (1, 10, 11)

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