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Aleks04 [339]
3 years ago
9

The lengths of two sides of a right triangle are 5 inches and 8 inches. What is the difference between the two possible

Mathematics
2 answers:
wolverine [178]3 years ago
4 0

Answer: B. 3.2 inches

Step-by-step explanation: I took the test and i got it right

3241004551 [841]3 years ago
3 0

Answer:

Option 2 - 3.2 inches.                      

Step-by-step explanation:

Given : The lengths of two sides of a right triangle are 5 inches and 8 inches.

To find : What is the difference between the two possible  lengths of the third side of the triangle?

Solution :

According to question, it is a right angle triangle

Applying Pythagoras theorem,

H^2=P^2+B^2

Where, H is the hypotenuse the longer side of the triangle

P is the perpendicular

B is the base

Assume that H=8 inches and B = 5 inches

Substitute the value in the formula,

8^2=P^2+5^2

64=P^2+25

P^2=64-25

P^2=39

P=\sqrt{39}

P=6.24

Assume that P=8 inches and B = 5 inches

Substitute the value in the formula,

H^2=8^2+5^2

H^2=64+25

H^2=89

H=\sqrt{89}

H=9.43

Therefore, The possible length of the third side of the triangle is

L=H-P

L=9.43-6.24

L=3.19

Therefore, The difference between the two possible  lengths of the third side of the triangle is 3.2 inches.

So, Option 2 is correct.

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Create a 5th degree trinomial that has a constant term of 3.
erastovalidia [21]

Answer:

4x^5\:+\:9x^2\:+\:3 is a trinomial having three terms, with degree 5 and the constant term '3'.

Step-by-step explanation:

Considering the trinomial

4x^5\:+\:9x^2\:+\:3

As the polynomial contains 3 terms, so it is a trinomial.

As the highest power of the variable 'x' is 5, so the degree of this polynomial is 5.

Any term with no variable is called a constant term. so, 3 is a term with no variable. Therefore, the constant term is 3.

Therefore, 4x^5\:+\:9x^2\:+\:3 is a trinomial having three terms, with degree 5 and the constant term '3'.

8 0
3 years ago
Please help!
UkoKoshka [18]

The values of x in the triangles and the angles in the rhombus are illustrations of tangent ratios

  • The values of x in the triangles are 21.4 units, 58 degrees and 66 degrees
  • The angles in the rhombus are 44 and 46 degrees, respectively

<h3>How to determine the values of x?</h3>

<u>Triangle 1</u>

The value of x is calculated using the following tangent ratio

tan(25) = 10/x

Make x the subject

x = 10/tan(25)

Evaluate

x = 21.4

<u>Triangle 2</u>

The value of x is calculated using the following tangent ratio

tan(x) = 8/5

Evaluate the quotient

tan(x) = 1.6

Take the arc tan of both sides

x = arctan(1.6)

Evaluate

x = 58

<u>Triangle 3</u>

The value of x is calculated using the following tangent ratio

tan(x) = 0.34/0.15

Evaluate the quotient

tan(x) = 2.27

Take the arc tan of both sides

x = arctan(2.27)

Evaluate

x = 66

<h3>How to calculate the angles of the rhombus?</h3>

The lengths of the diagonals are:

L1 = 2 in

L2 = 5 in

Represent the angles with x and y.

The measures of the angles are calculated using the following tangent ratios

tan(0.5x) = 2/5 and y = 90 - x

Evaluate the quotient

tan(0.5x) = 0.4

Take the arc tan of both sides

0.5x = arctan(0.4)

Evaluate

0.5x = 22

Divide by 0.5

x = 44

Recall that:

y = 90 - x

This gives

y = 90 - 44

Evaluate

y = 46

Hence, the angles in the rhombus are 44 and 46 degrees, respectively

Read more about tangent ratio at:

brainly.com/question/13347349

5 0
2 years ago
a pollster wishes to estimate the proportion of united states voters who favor capital punishment. how large a sample is needed
olasank [31]

The sample size must be 543 so the sample proportion is will not differ by 5%

We are given the following in the question:

Margin of error = 5%

Confidence interval:

p ±z√(p'(1 - p')/n)

Margin of error =

p = ±z√(p'(1 - p')/n)

Since no particular proportion is given, we take

p' = 0.5

Z critical at α 0.02 is ± 2.33

Putting values, we get,

p = ±z√(p'(1 - p')/n)

2.33 x √(0.5(1 - 0.5)/n)

√n = 2.33x 0.5/0.05

n = 542.89 = 543

Thus, the sample size must be 543 so the sample proportion is will not differ by 5%

To learn more about confidence interval refer here

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