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3 years ago

John writes the proof below to show that the sum of the angles in a triangle is equal to 1800.

Mathematics

1 answer:

tester [92]3 years ago

4 0

Hello, I believe the answer you are looking for is:

- When two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent.

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Draw an example of a composite figure that has a volume between 750 cubic inches and 900 cubic inches

grigory [225]

Volume:

$V \approx 888.02in^3 \\ \\ And, \ 750in^3$

<h2>Explanation:</h2>

A composite figure is formed by two or more basic figures or shapes. In this problem, we have a composite figure formed by a cylinder and a hemisphere as shown in the figure below, so the volume of this shape as a whole is the sum of the volume of the cylinder and the hemisphere:

$V_{total}=V_{cylinder}+V_{hemisphere} \\ \\ \\ V_{total}=V \\ \\ V_{cylinder}=V_{c} \\ \\ V_{hemisphere}=V_{h}$

So:

$V_{c}=\pi r^2h \\ \\ r:radius \\ \\ h:height$

From the figure the radius of the hemisphere is the same radius of the cylinder and equals:

$r=\frac{8}{2}=4in$

And the height of the cylinder is:

$h=15in$

So:

$V_{c}=\pi r^2h \\ \\ V_{c}=\pi (4)^2(15) \\ \\ V_{c}=240\pi in^3$

The volume of a hemisphere is half the volume of a sphere, hence:

$V_{h}=\frac{1}{2}\left(\frac{4}{3} \pi r^3\right) \\ \\ V_{h}=\frac{1}{2}\left(\frac{4}{3} \pi (4)^3\right) \\ \\ V_{h}=\frac{128}{3}\pi in^3$

Finally, the volume of the composite figure is:

$V=240\pi+\frac{128}{3}\pi \\ \\ V=\frac{848}{3}\pi in^3 \\ \\ \\ V \approx 888.02in^3 \\ \\ And, \ 750in^3$

<h2>Learn more:</h2>

Volume of cone: brainly.com/question/4383003

#LearnWithBrainly

4 0

3 years ago

I solved 4, the answer is 11, seconds: 5x+4(x-3)=87 = x=11, but I don't know how to solve number 5, please anyone explain how to

liq [111]

The answer x = 11 is correct for problem 4. Nice work.

Use this x value to find the answer in problem 5. From problem 4, we're told that Romeo runs at a speed of 5 m/s. If he runs for x = 11 seconds,then he runs a total distance of:

5*x =(5 m/s)*(x meters) = (5 m/s)*(11 seconds) = 5*11 = 55 meters

The answer to problem five is 55 meters

8 0

3 years ago

8x + 2+ 4y; x = 9, y = 2

Alchen [17]

Answer: 82

Step-by-step explanation:

We simply need to substitute the values for x and y into the equation

Both variables are already given to us, x=9, y=2

8(9)+2+4(2)

72+2+8