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3 years ago

There are 3 consecutive integers that have a sum of 36. What are the integers?

Mathematics

1 answer:

Mnenie [13.5K]3 years ago

4 0

Answer:

Step-by-step explanation:

The consecutive integers are increasing by 1

k ← the smallest integer

k+1 ← the middle integer

k+1+1 = k+2 ← the largest integer

k + k+1 + k+2 = 36

3k + 3 = 36

÷3 ÷3

k + 1 = 12

-1 -1

k = 11

k+1 = 11 + 1 = 12

k+2 = 11 + 2 = 13

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A palm tree is supported by two guy wires as shown in the diagram below. Which trig expression can be used to find the height on

Volgvan

Answer:

D. $tan(30^\circ+45^\circ)$ is the correct answer.

Step-by-step explanation:

The given situation can be represented as a figure attached in answer area.

B is the base of tree.

C is the base of wires.

A and D are the end of 2 wires supporting the tree.

$\angle DCB =45^\circ\\\angle ACB =75^\circ\\$

Here, we need to find the Height of the tree which is represented the by side AB.

and we are given that bases of wires and tree base are at a distance 4 ft.

i.e. side BC = 4 ft

If we look at the $\triangle ABC$ , we are given the base BC and the $\angle ACB$ , and the perpendicular is to be find out.

We can use trigonometric identity:

$tan\theta =\dfrac{Perpendicular}{Base}$

$tan 75^\circ = \dfrac{AB}{BC}\\\bold {tan (45+30)^\circ }= \dfrac{AB}{4}\\\Rightarrow AB = \bold {tan (45+30)^\circ } \times 4 = 14.93\ ft$

Hence, D. $tan(30^\circ+45^\circ)$ is the correct answer.

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2 years ago

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sergeinik [125]

Answer:

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2 years ago

For every 12 slices of pizza sold at Ping's Pizza Shop,

kaheart [24]

Answer:

3:5 Is the ratio because there are five pieces of cheese.

Step-by-step explanation:

If there are 12 pieces, then you can add 4 and 3 together and get 7 and then you can take 7 from 12 and get 5 which is how many cheese pieces there are. Now you know that there are 3 slices of pepperoni and 5 pieces of cheese. Therefore the ratio is 3:5.

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3 years ago

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3 years ago

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horrorfan [7]

Answer: (5+√2) and (3+√2)

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Difference = 2

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2 years ago