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aalyn [17]
3 years ago
5

The measure of angle DBE is (0.1x - 22) and the measure of angle CBE is (0.3x - 54). Find the value of x.

Mathematics
1 answer:
ElenaW [278]3 years ago
8 0

The measure of angle DBE is (0.1x - 22) and the measure of angle CBE is (0.3x - 54). The value of x is 415

Step-by-step explanation:

Given that,

The measure of angle DBE   (0.1x - 22)

The measure of angle CBE (0.3x - 54)

<u>Step 1</u>

As per the  Angle Addition Postulate,

m∠DBE+m∠CBE=m∠DBC

<u> Step 2</u>

Since∠ DBC is a right angle as indicated by the square symbol, then m∠DBC=90°.

Hence,

(0.1x-22)+(0.3x-54)= 90

<u>Step 3</u>

Lets solve the equation  for x

We know that 0.4x-76= 90

0.4x= 166

x=166/0.4

x=415

<u>Step 4</u>

<u>Answer :</u> The value of x is 415

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Step-by-step explanation:

Continuous Random Variable:

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6 0
3 years ago
Determine the domain of the function (fog)(x) where f(x)=3x-1/x-4 and g(x)=x+1/x
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Answer: (-∞,-1) ∪ (0,+∞)

Step-by-step explanation: The representation fog(x) is a representation of composite function, meaning one depends on the other.

In this case, fog(x) means:

fog(x) = f(g(x))

fog(x) = 3(x+\frac{1}{x} )-\frac{1}{x+\frac{1}{x} } -4

fog(x)=3x+\frac{3}{x} -\frac{1}{\frac{x^{2}+x}{x} } -4

fog(x)=3x+\frac{3}{x} -\frac{x}{x^{2}+x} -4

fog(x)=\frac{3x^{2}(x^{2}+x)+3(x^{2}+x)-x-4x(x^{2}+x)}{x(x^{2}+x)}

fog(x)=\frac{3x^{4}+3x^{3}+3x^{2}+3x-x-4x^{3}+4x^{2}}{x(x^{2}+x)}

fog(x)=\frac{3x^{4}-x^{3}-x^{2}+2x}{x(x^{2}+x)}

This is the function fog(x).

The domain of a function is all the values the independent variable can assume.

For fog(x), denominator can be zero, so:

x(x^{2}+x) \neq 0

If x = 0, the function doesn't exist.

x^{2}+x \neq0

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x+1\neq0

x\neq-1

<u>Therefore, the domain of this function is: </u><u>-∞ < -1 or x > 0</u>

5 0
3 years ago
In Scott’s backyard, he has a windmill that makes 5 ¾ of a turn every hour. How many turns does it make for 1 ½ hours?
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Answer: 8 5/8 turns

Step-by-step explanation:

Hi, to answer this question we have to simply to multiply the number of turns that the windmill makes per hour (5 3/4) by the time asked (1 ½ hours).

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In conclusion, the windmill makes 8 5/8 turns in 1 1/2 hours.

3 0
3 years ago
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