Write the equation of the line that passes through the given point and is parallel to the given line. Write the answer in slope-intercept formP(-6,3), y + 3x = -12
Can anyone help me on this one? Thanks!

Answers

Answer 1

Answer: $General\ formula:\ny=ax+b\n\ny+3x=-12\ny=-3x-12\n\nLine\ is\ parallel\ to\ the\ given\ when\ a=-\-3}\ny=-3x+b\n\nPasses\ through\ P(-6,3):\n3=(-3)*(-6)+b\n3-18=b\nb=-15\n\nAnswer:\ y=-3x-15$

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How many solutions are there to the following system of equations?4x – 14y = 6
–2x + 7y = –3

A.
1

B.
2

C.
infinitely many

D.
0

Answers

$4x-14y=6 \n-2x+7y=-3 \ \ \ |* 2 \n \n4x-14y=6 \n\underline{-4x+14y=-6} \n4x-4x-14y+14y=6-6 \n0=0 \n always \ true \n \n\boxed{\hbox{infinitely many solutions}} \Leftarrow \hbox{answer C}$

If f(x) = 3x + 3, g(x) = 3x + 3, and h(x) = x + 3, what is [g o f o h](–5)?A: –30
B: –24
C: –15
D: –6

Answers

Answer:

The correct answer is D. -6

Step-by-step explanation:

f(x) = 3x + 3

g(x) = 3x + 3

h(x) = x + 3

We need to find : [g o f o h](–5)

⇒ [g o f o h](–5)

⇒ [g o f]h(-5)

⇒ [g o f](-5 + 3)

⇒ [g o f](-2)

⇒ [g]f(-2)

⇒ [g](3 × -2 + 3)

⇒ [g](-6 + 3)

⇒ g(-3)

⇒ 3 × -3 + 3

⇒ -9 + 3

⇒ -6

Therefore, The correct answer is D. -6

The answer would be -6.
Start by substituting -5 into the 'h' function.
h(-5) = -5 + 3 = -2
Now substitute this answer into the 'f' function.
f(-2) = 3(-2) + 3 = -3
now substitute this answer into the 'g' function
g(-3) = 3(-3) + 3 = -6
D is your answer

List all the angles that are congruent to the given angle (72 degrees).1/2
72°
3
d
4/5
7/6
HELP!

Answers

Answer:

<2, <5, and <7.

Step-by-step explanation:

<2 and 72°, are vertical angles. Vertical angles are congruent. Therefore, <2 ≅ 72°.

<7 and 72° are corresponding angles. Corresponding angles are congruent, therefore, <7 ≅ 72°.

<5 and 72° are alternate interior angles. Alternate interior angles are congruent, therefore, <5 ≅ 72°.

Angles that are congruent to 72° are <2, <5, and <7.

PT=x+2, TR=y, QT=2x, TS=y+3

Answers

After consideration I'm not sure but I think x=3 and y=6 I'm not a math whiz but this made sense to me.

Find the missing value of a triangle one leg is 12 and the long side is 20 what is the other leg?

Answers

Simple,

using the Pythagorean Theorem...

$a^(2) + b^(2) = c^(2)$

You have the hypotenuse (C) and one of the legs (A)

So, plug in what you know...

$12^(2)+ b^(2) = 20^(2)$

144+ $b^(2)$ =400

Now,isolate $b^(2)$

$144+ b^(2) =400$
-144 -144

Leaving you with...

$b^(2) =256$

So, now, $√(256)$ , to find what b is..

b=16

Thus, your answer.

IF this is a 'right' triangle, then we can calculate an answer.
If it's NOT a right triangle, then no answer is possible.

I'm going to assume that it's a right triangle, because you did say
that one 'leg' is 12, and you want the length of the other 'leg'. It's
common to refer to the two short sides of a right triangle as 'legs'.

In "Tales of Pythagoras", we learned that in a right triangle ...

(Longest side)² = (one leg)² + (the other leg)²

In your triangle ...

   (20)²       = (12)² + (the other leg)²

      (400)    = (144) + (the other leg)²

Subtract 144 from each side: (The other leg)² = (400 - 144) = 256

   The other leg    = √256 = 16 .

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