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3 years ago

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Mathematics

1 answer:

DedPeter [7]3 years ago

6 0

9514 1404 393

Answer:

3. vertical stretch by a factor of 2; shift right 1 and down 1

4. shift left 4 and up 4 (no stretch or shrink)

Step-by-step explanation:

The vertex form equation is ...

y = a(x -h)^2 +k

It represents a vertical stretch of the parent function by a factor of 'a', a right shift of 'h', and an upward shift of 'k'.

Compare the the given equations to the above form to see the transformations.

3. (a, h, k) = (2, 1, -1) ⇒ vertical stretch by a factor of 2; shift right 1, down 1

4. (a, h, k) = (1, -4, 4) ⇒ no vertical stretch; shift left 4, up 4

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Which sets of side lengths could form a triangle? Choose all that apply.

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3 years ago

If O N = 8 x − 8 , L M = 7 x + 4 , N M = x − 5 , and O L = 3 y − 6 , find the values of x and y for which LMNO must be a paralle

posledela

Answer:

$x=12\\y=\frac{13}{3}$

Step-by-step explanation:

For it to be a parallelogram, opposite sides have to be of same length.

OL = NM, and
ON = LM

Using the expressions given, we can make 2 equations:

Equation 1:

$OL=NM\\3y-6=x-5\\-x+3y=1$

Equation 2:

$ON=LM\\8x-8=7x+4\\$

Solving equation 2, we have x:

$8x-8=7x+4\\8x-7x=4+8\\x=12$

Plugging this value of x into equation 1, we can solve for y:

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So,

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3 years ago

Find the median 60,62,64,54,56,28

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Answer:

Step-by-step explanation:

you need to order all the numbers together:

28, 54, 56, 60, 62, 64

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3 years ago

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Suppose the function, g(x), is used to model the height ,y, of a soccer ball, x seconds after the ball is kicked up in the air.

andrey2020 [161]

the ball reaches its maximum height of 15 feet in 2.2 seconds

The ball starts on the ground and travels in a parabolic shape as it reaches a maximum height and then returns to the ground

The ball starts on the ground at 0 seconds so the ball starts at x=0 seconds

the ball reaches its maximum height of 15 feet in 2.2 seconds

So it takes 2.2 second to reach the maximum height

It will take another 2.2 seconds to reach the ground

The time the ball in the air is 2.2 + 2.2 = 4.4

The ball will reach the ground in 4.4 seconds

So the domain for g(x) is {0,4.4}

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3 years ago

The measure of an angle is three more than twice its supplement. What is the measure of the angle?

Zinaida [17]

Answer: the angle is 1°+n×120°

1°, 121°, 241°

Step-by-step explanation:

Angles are taken modulo 360°, so 363° = 3°.

Angle plus supplement gives 180°.

Let a be angle, s be supplement of a.

So s = 180-a. Given a = 3 + 2s

a = 3 + 2(180 - a)

a = 3 + 360 - 2a = 363 - 2a

3a = 363° or 3° or 723°

a = 121° or 1° or 241°

a = 1°

s = 179°

2s = 358°

2s+3 = 361° = 1° (modulo 360)

a = 121°

s = 180-121 = 59°

2s = 118°

2s + 3 = 121°, as required.

a = 241°

s = 360+180-241 = 540-241 = 299

2s = 598

2s + 3 = 601 = 241 (modulo 360)

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3 years ago