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3 years ago

The vertex of the graph of y = -4(x + 3)2 + 2 is ( , )

Mathematics

1 answer:

andrezito [222]3 years ago

6 0

Answer:

Step-by-step explanation:

This quadratic is of the form

$y=-a(x-h)^2+k$ where h and k are the coordinates of the vertex. Notice that inside the parenthesis it very specifically follows the format (<u>x -</u> h)². That means that if you have something like what we have here, ( x + 3)^2, it was originally (x - (-3))^2, and the value for h is -3. k is much simpler to determine. Our 2 at the end is a +2, so the k is 2. The vertex then is (-3, 2).

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The perimeter of a triangle is 32 feet. One side of the triangle is 3 times the second side. The third side is 12 feet longer

Ivenika [448]

We have a triangle whose perimeter is 32 feet. Some information regarding the sides of the triangle is given:

GiveN:

One side is 3 times the second side.
Third side is 12 feet longer than the second side.

As we can see that, two sides of the triangle are defined the second sides. It means First and third side can be expressed in the form of second side.

So let the second side be x

Then,

First side = 3x
And, third side = x + 12

We know that, perimeters is the sum of the lengths of all sides of the triangle, So it can be written as:

$3x + x + x + 12 = 32$

Solving it further,

$5x + 12 = 32$

Subtracting 12 from both sides,

$5x + 12 - 12 = 32 - 12$

$5x = 20$

Dividing 5 from both sides,

$\frac{5x}{5} = \frac{20}{5}$

$x = 4$

Then,

First side = 3x = 12 feet
Second side = 4 feet
Third side = x + 12 = 16 feet

And we are done with the answer !!

#CarryOnLearning

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4 0

3 years ago

Courtney is twice as old as Andre and three years older than Natalie. Courtney is half Shari's age. The difference between Shari

lesantik [10]

The question does not seem complete, but I'll represent the statement mathematically and look for their ages each. This is because the worst they can ask for is their ages.

Let C stand for Courtney's age, A for Andrei's age, N for Natalie's age and S for Shari's age. From the question we can deduce the following:

C = 2A

C = N + 3

C = S/2

S - N = C + A

S = 2C, N = C - 3 and A = C/2, therefore we have

2C - (C - 3) = C + C/2

C + 3 = C + C/2

C/2 = 3 and C = 6

A = C/2

A= 6/2

A = 3

N = C - 3

N = 6 - 3

N = 3

S = 2C

S = 2 x 6

S = 12.

C = 6, A = 3, N = 3 and S = 12

8 0

3 years ago

The graph of which function(s) will contain the point (4, 12)? y = x + 8 y = 3x y = 2x y = x + 6

Alex777 [14]

Answer:

y=x+8 and y=3x

Step-by-step explanation:

The Given point is (4,12)

now we can substitute the point in each of the function and check wether it lies on it or not.

A. y=x+8

substitute y=12,x=4

12=4+8=12 which is true

B. y=3x

substitute y=12,x=4

12=3*4=12 which is true

C. y=2x

substitute y=12,x=4

12=2*4=8 which is not true

D. y=x+6

substitute y=12,x=4

12=4+6=10 . which is not true

Therefore option A and B are correct.

4 0

3 years ago

Can someone please help me

aniked [119]

#1 √ 75

Answer : 5√3 or ≈ 8.66025

#2 √ 48

Answer : 4√3 or ≈ 6.9282

#3 √ 128

Answer : 8√2 or ≈ 11.31371

#4 √ 300

Answer : 10√3 or ≈ 17.32051

~~

#5 √⅔

Answer :

$\frac{ \sqrt{6} }{3} = 0.816497$

#6 √16/4

Answer : 2

#7 √ 6/8

Answer :

$\frac{ \sqrt{3} }{2} = 0.866025$

#8 √27/9

Answer : √ 2 or ≈ 1.73205

~~

I hope that helps you out!!

Any more questions, please feel free to ask me and I will gladly help you out!!

~Zoey

5 0

4 years ago

Find the domain and range. state whether each set of ordered pairs is a function or not.

Gre4nikov [31]

Answer:

Set A is a function

set B is not a function

3 0

3 years ago