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3 years ago

What is the value of x? Enter your answer in the box. x =

Mathematics

1 answer:

Svetllana [295]3 years ago

6 0

Answer:

Step-by-step explanation:

The two triangles are similar and therefore we can set up a proportion

9/(9 + 72) = (3x - 20)/(3x - 20 + 56) Combine like terms on the right

9/(81) = (3x - 20)/(3x + 36) Cross multiply

9(3x + 36) = 81 (3x - 20) Remove the brackets.

27x + 324 +1620 = 243x Add 1620 to both sides

27x + 324 + 1620 = 243x Subtract 27x from both

1944 = 216x divide both sides by 216

x = 9

If you feel comfortable canceling the size of the numbers can be reduced.

9/81 = 1/9

1/9 = (3x - 20)/(3x + 36)

3x + 36 = 9(3x - 20)

3x + 36 = 27x - 180

36 + 180 = 24x

216 = 24x

216/24 = x

x = 9

There is another cancelation possible, but this is simple enough.

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The response to a question has three alternatives: A, B, and C. A sample of 120 responses provides 60 A, 12 B, and 48 C. Show th

zimovet [89]

Answer:

CLASS FREQUENCIES RELATIVE FREQUENCIES

A 60 0.5

B 12 0.1

C 48 0.4

TOTAL 120 1

Step-by-step explanation:

Given that;

the frequencies of there alternatives are;

Frequency A = 60

Frequency B = 12

Frequency C = 48

Total = 60 + 12 + 48 = 120

Now to determine our relative frequency, we divide each frequency by the total sum of the given frequencies;

Relative Frequency A = Frequency A / total = 60 / 120 = 0.5

Relative Frequency B = Frequency B / total = 12 / 120 = 0.1

Relative Frequency C = Frequency C / total = 48 / 120 = 0.4

therefore;

CLASS FREQUENCIES RELATIVE FREQUENCIES

A 60 0.5

B 12 0.1

C 48 0.4

TOTAL 120 1

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2 years ago

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Ber [7]

Answer:

Step-by-step explanation:

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3 years ago

Two trains leave stations 272 miles apart at the same time. One train travles 75 miles per hour while the other travles at 95 mi

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102 miles for them to meet up

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3 years ago

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jeka94

Answer:

Step-by-step explanation:

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2 years ago

Sqrt(2x-6)=3-x<br> Solve for x

soldi70 [24.7K]

Answer:

x = 3

Step-by-step explanation:

$\sqrt{2x - 6} = 3 - x$

Square both sides of the equation

$2x - 6 = (3 - x)^{2} = 9 - 6x + x^{2} \\$

$x^{2} - 8x + 15 = 0\\$

(x - 3)(x - 5) = 0

x = 3 or 5

Now, you must always check your results because a result may not satisfy the original equation.

If x = 3, then $\sqrt{2x - 6} = \sqrt{2(3) - 6} = \sqrt{6 - 6} = \sqrt{0} = 0$ and 3 - x = 3 - 3 = 0

So 3 satisfies the original.

If x = 5, then $\sqrt{2(5) - 6} = \sqrt{10 - 6} = \sqrt{4} = 2$ , but 3 - x = 3 - 5 = -2. Therefore, 5 does NOT satisfy the original equation.

That means that x = 3 is the solution to the equation.

5 0

2 years ago