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serious [3.7K]
3 years ago
9

Examine the diagram.

Mathematics
1 answer:
iris [78.8K]3 years ago
5 0

Answer:

5

Step-by-step explanation:

When two lines are crossed by another line (the transversal), the pair of angles on  the opposite and inner side of each of those two lines are called Alternate Interior Angles.  Therefore 5 is the alternate interior angle to 4.

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A building casts a shadow that is 18 ft long. A woman standing near the building is 5.75 ft tall and 4 feet long. What is the he
Lynna [10]

Answer:

25 feet 6 inches

Step-by-step explanation:

Assuming that the woman is standing up straight, you have a situation where you have two similar right triangles. The legs of the smaller triangle are the woman's height and the length of her shadow, and the legs of the larger triangle are the building's height and the length of its shadow. We know that the sides of similar triangles are proportional, so we can write:

5ft8in =2ft=x%2Aft%2F18ft

Now you need to cross-multiply and solve for x, but multiplying feet times feet and inches is a messy calculation. Changing 5 ft 8 inches to 5 and 2/3 feet is messy also. My recommendation is to convert everything to inches, and then convert back to feet and inches when you are done.

5 ft 8 inches = (5 *12) + 8 = 68 inches

4 ft = 4 * 12 = 48 inches, and

18 ft = 18 * 12 = 216 inches.

Now the proportion looks like:

68%2F48=x%2F216, so

48x=14688 after cross-multiplying, and

x=306 after dividing by 48. So the building is 306 inches tall. But we want to know the height of the building in feet and inches. To convert back to feet and inches from inches, just do integer division by 12 where your answer is expressed as a quotient and a remainder. The quotient is the number of feet, and the remainder is the number of inches.

306 = 25 remainder 6, so the answer is 25 feet 6 inches.

Note that this answer makes sense. 5'8" is nearly 6'. 6' is one and a half times 4 feet, so the woman is a little less than one and a half times taller than her shadow is long. One and a half times the building's 18 ft shadow is 27 feet, and that is a little bit more than the 25'6' answer that we

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The chance of winning based on the type of lottery tickets we purchase is 0.05, or 1 in 20. We will play each saturday until we
BigorU [14]

Answer:

Given that the probability of winning is = 0.05

So the probability of losing is = 1 - 0.05 = 0.95.

We are told we have a 1 in 20 chance

Success: 0.05

Failure: 0.95

P(X=4)= 0.95*0.95*0.95*0.05

So the chance is 0.04286 or Option D

6 0
2 years ago
What are the solutions to 7x^2 + 10x - 3 = x^2 +3x? Select all that apply.
kiruha [24]

Answer:

x=1/3 or x=−3/2

Step-by-step explanation:

7x2+10x−3=x2+3x

Step 1: Subtract x^2+3x from both sides.

7x2+10x−3−(x2+3x)=x2+3x−(x2+3x)

6x2+7x−3=0

Step 2: (3x−1)(2x+3)=0

Step 3: Set factors equal to 0.

3x−1=0 or 2x+3=0

x=1/3 or x= −3/2

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3 years ago
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