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3 years ago

Find the measure of angle ABC

Mathematics

2 answers:

Julli [10]3 years ago

7 0

In every triangle, the sum of the interior angles is 180°. The sum of the angles of this triangle is

$32+(2x-15)+(x-5) = 2x+x+32-15-5 = 3x+12$

and we want this sum to be 180, so we can write the following equation:

$3x+12 = 180$

subtract 12 from both sides:

$3x = 168$

divide both sides by 3:

$x = \cfrac{168}{3} = 56$

Now we can plug this value for x in the expressions for the two unknown angle to get their value:

$B = x-5 = 56-5 = 51,\quad C = 2x-15 = 2\cdot 56-15 = 112-15 = 97$

enot [183]3 years ago

4 0

You will get x as 56 and angle ABC as 51°

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What are the two solutions of 2x^2 = -X^2 - 5x - 1?

Sidana [21]

Answer:

Step-by-step explanation:

Let's solve 2x^2 = -X^2 - 5x - 1. Consolidate all terms on the left side and write 0 on the right side:

3x^2 + 5x + 1 = 0. This is a quadratic equation. Let's solve it for x using the quadratic formula:

a = 3, b = 5, c = 1, and so the discriminant is b^2 - 4ac = 5^2 - 4(3)(1) = 13. Because the discriminant is positive, we know that there are two distinct, real roots; the graphs of y = 2x^2 and y = x^2 - 5x - 1 intersect in two places whose x-coordinates are the real roots mentioned above.

Answer A is not correct as stated, but would be correct if we were to replace "the y-coordinates" with "the x-coordinates."

Answer C would be correct if and only if we write y = x^2 - 5x - 1.

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IrinaVladis [17]

Answer:

The height of the tree is 19.81 m

Step-by-step explanation:

Trigonometric Ratios

The ratios between the sides of a right triangle are called trigonometric ratios.

If any of the acute angles is chosen as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides and the hypotenuse.

The image shows a right triangle with a tree and the ground forming a right angle and an elevation angle of 33°.

This angle of 33° has a side of 30.5 m as its adjacent leg and the height of the tree X as the opposite side.

The trigonometric ratio that relates both legs is the tangent:

$\displaystyle \tan 33^\circ=\frac{X}{30.5}$

Solving for X

$X=30.5\cdot \tan 33^\circ$

Using a calculator:

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gizmo_the_mogwai [7]

Answer:

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2 years ago

Read 2 more answers

A Gallup poll showed that 30% of Americans are satisfied with teh way things are going in the United States. Suppose a sample of

weeeeeb [17]

Answer:

Mean of the binomial distribution μ= 6

Variance of the binomial distribution λ² = 4.2

Step-by-step explanation:

Explanation:-

The probability a Gallup poll showed that 30% of Americans are satisfied with the way things are going in the United States.

p = 30% = 0.3

q =1-p = 1- 0.3 =0.7

a sample of 20 Americans is selected as part of a study of the state of the nation

size of the sample 'n' =20

we will use binomial distribution

mean:-

Mean of Americans who are satisfied with the way things are going in the United States (μ) = np

μ= 20 X 0.3

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Variance:-

Variance of Americans who are satisfied with the way things are going in the United States λ² = n p q = 20 X(0.3)(0.7)

λ² = 4.2

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