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Anon25 [30]
3 years ago
9

if Paula wants the tops of the latter to reach exactly 8 feet up the building, what is x, the distance between the building and

the base of the latter in feet​

Mathematics
1 answer:
cluponka [151]3 years ago
5 0

Answer:

6 ft

Step-by-step explanation:

Since the distance between the bottom of the ladder and the wall forms a right angle that is across from the ladder, you can use the Pythagorean Theorem to solve for the value of 'x':

a² + b² = c², where 'a' and 'b' are the legs of the triangle and 'c' is the diagonal or hypotenuse.  

Using 8 for 'a' and 10 for 'c':

8² + x² = 10²

64 + x² = 100

Subtract 64 from both sides:

64 - 64 + x² = 100 - 64 or x² = 36

Take the square root of both sides:

√x² = √36

x = 6 ft

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Jane's favorite fruit punch consists of pear, pineapple, and plum juices in the ratio 5:2:3. C How many cups of pear juice shoul
Gala2k [10]

This question is incomplete

Complete Question

Jane’s favorite fruit punch consists of pear, pineapple, and plum juices in the ratio 5:2:3.

a) How much of each juice is needed to make 25 liters of this punch?

b) How much punch can she make if she has only 6 cups of plum juice?

c) How many cups of pear juice should she use to make the quantity of punch from part (b)?

Answer:

a)For pear =

12.5 liters

For Pineapple

= 5 liters

For plum

= 7.5 liters

b) 20 cups of punch

c) 10 cups of pear juice

Step-by-step explanation:

Jane’s favorite fruit punch consists of pear, pineapple, and plum juices in the ratio 5:2:3.

The total proportion is :

5 + 2 + 3 = 10

a) How much of each juice is needed to make 25 liters of this punch?

For pear =

5/10 × 25 = 12.5 liters

For Pineapple

= 2/10 × 25 = 5 liters

For plum

= 3/10 × 25 = 7.5 liters

b) How much punch can she make if she has only 6 cups of plum juice?

The ratio of plum juice is 3

6 cups / 3 = 2 cups per portion

Since 2 equals 2/3 of 3,

The quantity of pineapple juice = 2/3 of the plum juice

2/3 x 6 cups = 4 cups

Since 5 equals 5/3 of 3, the amount of pear juice amount 5/3 of the plum juuce

5/3 x 6 cups = 10 cups

So, the number of cups are

Pear juice = 10 cups

Pineapple juice = 4 cups

Plum juice 6 cups

Total=( 10 + 4 + 6) = 20 cups of punch

c) How many cups of pear juice should she use to make the quantity of punch from part (b)?

10 cups of pear juice can be used to make the quantity of punch in part b

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Answer:

21 3/4 - 13 1/8 = 8 5/8 ft longer

Step-by-step explanation:

We subtract the blue rope from the green rope

21 3/4 - 13 1/8

We need to get a common denominator of 8

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21 6/8 - 13 1/8

8 5/8

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