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3 years ago

Given the following information, determine which lines are parallel and what justifies them being parallel.

Mathematics

1 answer:

kow [346]3 years ago

8 0

Answers:

Blank 1 = p and q

Blank 2 = Consecutive interior angles converse

=================================================

Explanation:

There's a lot of visual noise here, meaning there's a lot of lines and angles to potentially distract. I recommend redrawing things but only drawing lines p and q, and the transversal cut line t. Furthermore, I would mark only angle 8 and angle 13. See the diagram below.

The diagram is optional, but hopefully you can see that the angles are same side interior angles, aka consecutive interior angles. That's why we go with the consecutive interior angles converse

If we drop the "converse" portion, then that theorem says parallel lines lead to supplementary consecutive interior angles. The converse just reverses the flow of the logic.

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Blababa [14]

Answer:

$a)\: \frac{3}{2} \pi$

$b) \:\frac{47}{5} \pi$

Step-by-step explanation:

$y=3\sqrt x,\:\:y=3,\:\:x=0$

a) about the line y = 3

$3\sqrt x=3$ ⇒ $x = 1$ is the intersection point

So,

$V=\int\limits^1_0\pi(3-3\sqrt x)^2\:dx=\pi\int\limits^1_0(9-18\sqrt x+9x)\:dx=\\\\=\pi(9x-12x^{3/2}+9/2x^2)|^1_0=\pi(9-12+9/2)=\frac{3}{2} \pi$

b) about the line x = 5

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So,

$V = \int\limits^3_0\pi([5-0]^2-[5-y^2/9]^2)\:dy=\pi\int\limits^3_0(25-25+10y^2/9-y^4/81)\:dy=\\\\=\pi(10y^3/27-y^5/405)|^3_0=\pi(10-3/5)=\frac{47}{5} \pi$

8 0

4 years ago

Use the distributive property to remove the parentheses.<br> - 4(5u - 3y-1)

schepotkina [342]

Answer:

-20u + 12y + 4

Step-by-step explanation:

We have the equation -4(5u - 3y - 1) and are asked to use the <u>distributive property</u> to remove the parenthesis.

When using the distributive property, you have to multiply the number outside the parenthesis to all numbers inside the parenthesis, do as followed :

-4(5u - 3y - 1)

(5u(-4) -3y(-4) -1(-4))

-20u + 12y + 4

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3 years ago

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rosijanka [135]

Answer:all lines are straight

Step-by-step explanation:

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2 years ago

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Tasya [4]

Answer:

Step-by-step explanation:

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3 years ago

Solve the equation for x, where x is a real number (5 points): <br> 3x^2 + 8x + 2 = 0

g100num [7]

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4 0

3 years ago