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3 years ago

What does 30 ≤ x + 10 ≤ 80 simplify to

Mathematics

1 answer:

MakcuM [25]3 years ago

4 0

Answer:

20 ≤ x ≤ 70

Step-by-step explanation:

Given that:

30 ≤ x + 10 ≤ 80

By solving the left half inequality first:

30 ≤ x + 10

Subtracting 10 from both sides:

30 - 10 ≤ x + 10 -10

20 ≤ x

Now solving inequality of right half:

x + 10 ≤ 80

Subtracting 10 from both sides:

x + 10 -10 ≤ 80 - 10

x ≤ 70

So after simplification we get:

20 ≤ x ≤ 70

I hope it will help you!

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A triangle has two constant sides of length 5 feet and 7 feet. The angle between these two sides is increasing at a rate of 0.9

o-na [289]

Answer: $12.74 ft^2/s$

Step-by-step explanation:

Given

Two sides of triangle of sides 5 ft and 7 ft

and angle between them is increasing at a rate of 0.9 radians per second

let $\theta$ is the angle between them thus

Area of triangle when two sides and angle between them is given

$A=\frac{ab\sin C}{2}$

$A=\frac{5\times 7\times \sin \theta }{2}$

Differentiate w.r.t time

$\frac{\mathrm{d} A}{\mathrm{d} t}=\frac{35\cos theta }{2}\times \frac{\mathrm{d} \theta }{\mathrm{d} t}$

at $\theta =\frac{\pi }{5}$

$\frac{\mathrm{d} A}{\mathrm{d} t}=\frac{35\times cos(\frac{\pi }{5})}{2}\times 0.9$

$\frac{\mathrm{d} A}{\mathrm{d} t}=12.74 ft^2/s$

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3 years ago

The nile river is 6690 kilometers long.This is 394 kilometers longer than the Amazon River.How long is the Amazon River?

valentinak56 [21]

Answer:

The nile river is 6690 kilometers long.This is 394 kilometers longer than the Amazon River.How long is the Amazon River?

6690-394=6296 kilometers

Step-by-step explanation:

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2 years ago

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a patients dose of medication increased from 100mg to 150mg. What is the percent increase in medication?

lord [1]

Answer:

The answer is 50% increase. Hope this helped!

Step-by-step explanation:

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3 years ago

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14. What is the reflection image of (5, -3) across the line y = -x? (3, -5) (3, 5) (-3, 5) (-3, -5)

Nata [24]

Answer:

The reflection image of (5, -3) across the line y = -x is (3, -5).

Step-by-step explanation:

You can find the reflection equation by putting the value of x and y in the line given one by one.

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3 years ago

What is 37.5 percent of 80

Leya [2.2K]

37.5*0.010=.375 (or press % button on calculator)
80*.375=30

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3 years ago