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2 years ago

What is the value of x? A. 3 B. 9 C. 15 D. 30

Mathematics

1 answer:

ra1l [238]2 years ago

7 0

Answer:

C. 15

Step-by-step explanation:

Assuming that these segments formed from each parallel line are proportional, x/5 = x-6/3.

Now cross multiply by multiplying each denominator by the opposite numerator, this is so the denominators or bottom numbers of each fraction will cancel.

x/5 = x–6/3 → (3)(x/5) = (3)(x–6/3) → 3x/5 = x–6 →

(5)(3x/5) = (5)(x–6) → 3x = 5(x–6) → 3x = 5x – 30.

The last step is to do the basic algebra to find x:

3x = 5x – 30

–5x –5x

[5x will cancel when you subtract both sides by 5x]

-2x = -30

(-1) (-1)

[2 negatives make a positive when -1 is multiplied by an expression with a negative coefficient]

2x = 30

÷2 ÷2

[divide both sides by 2 to simplify 2x to x]

x = 15

_____

You can also check that both sides are proportional because

5 → x

x = 15

5 → 15

3 → x – 6

x = 15

3 → 9

5 × 3 = 15

3 × 3 = 9

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2 years ago

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Answer:

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2 years ago

PLEASE HELP :((((

sertanlavr [38]

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5 0

2 years ago

If 12% of the air leaks out of Brian's bicycle tire every day, what percent of the air will be left after 2 days? After a week?

Leni [432]

Answer:

77.44%

49.87%

Step-by-step explanation:

If 12% leaks everyday, on the first day 12% would leak, leaving 100 - 125 = 88% of air

on the second day, 12% of 88% would leak = 0.88 x 0.12 = 0.1056

Air left on the second day = 88% - 10.56% = 77.44%

After a week = (100 - 12%)^7 = 49.87%

6 0

2 years ago

Please I’ve attached the question can you help me

Andreyy89

Answer:

1. n[(A U B) - C] = {23, 24, 27, 29, 33, 36, 37, 39, 41, 42, 43, 45, 47, 48, 51, 53, 54, 57, 59, 61, 63}

2. n[(A - B) U C] = n[A U C] = {6, 10, 12, 15, 20, 23, 29, 30, 31, 37, 41, 43, 47, 53, 59, 60, 61}

3. D. I, II and III.

Step-by-step explanation:

U = {21, 22, 23, ..., 64}

A prime number is a number that can be divided only by 1 and itself.

A = {23, 29, 31, 37, 41, 43, 47, 53, 59, 61}

B = {24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63}

C = {6, 10, 12, 15, 20, 30, 60}

1. Find n[(A U B) - C]

n(A U B) = {23, 24, 27, 29, 30, 33, 36, 37, 39, 41, 42, 43, 45, 47, 48, 51, 53, 54, 57, 59, 60, 61, 63}

n[(A U B) - C] = {23, 24, 27, 29, 30, 33, 36, 37, 39, 41, 42, 43, 45, 47, 48, 51, 53, 54, 57, 59, 60, 61, 63} - {6, 10, 12, 15, 20, 30, 60}

Since only 30 and 60 are common to n(A U B) and C, we therefore remove them it and have:

n[(A U B) - C] = {23, 24, 27, 29, 33, 36, 37, 39, 41, 42, 43, 45, 47, 48, 51, 53, 54, 57, 59, 61, 63}

2. Find n[(A - B) U C]

To get n(A - B) we remove all the elements of B in A. Since there are no common elements between A and B, we therefore have:

A - B = A = {23, 29, 31, 37, 41, 43, 47, 53, 59, 61}

C = {6, 10, 12, 15, 20, 30, 60}

Therefore, we have:

n[(A - B) U C] = n[A U C] = {6, 10, 12, 15, 20, 23, 29, 30, 31, 37, 41, 43, 47, 53, 59, 60, 61}

3. Which of the following is/are true?

I. A ∩ B = A ∩ C

A ∩ B = ∅

A ∩ C = ∅

Therefore, A ∩ B = A ∩ C is true.

II. A - B = A - C

A - B = A = {23, 29, 31, 37, 41, 43, 47, 53, 59, 61}

A - C = A = {23, 29, 31, 37, 41, 43, 47, 53, 59, 61}

Therefore, A - B = A - C is true.

III. A ∩ (B ∪ C) = ∅

A = {23, 29, 31, 37, 41, 43, 47, 53, 59, 61}

B U C = {6, 10, 12, 15, 20, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63}

Therefore, A ∩ (B ∪ C) = ∅ is true.

Therefore, the correct option is D i.e. I, II and III are true.

4 0

2 years ago