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3 years ago

What is the vertex of the function h(x)=|x+6|+3

Mathematics

1 answer:

meriva3 years ago

8 0

Answer:

(-6, 3)

Step-by-step explanation:

The function f(x) = a |x − h| + k has its vertex at (h, k).

In this case, the vertex is (-6, 3).

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nirvana33 [79]

Answer:

13. 15

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7 0

2 years ago

What is the inverse of x^2-4x+5

lisabon 2012 [21]

we are given

$f(x)=x^2-4x+5$

Since, we have to find inverse of this function

step-1: we set f(x)=y

$y=x^2-4x+5$

step-2: switch x and y

$x=y^2-4y+5$

step-3: Solve for y

$y^2-4y+(5-x)=0$

now, we can use quadratic formula

$y=\frac{4+\sqrt{4^2-4(5-x)} }{2}$

$f^{-1}(x)=\sqrt{x-1}+2$

$f^{-1}(x)=-\sqrt{x-1}+2$ ..............Answer

6 0

3 years ago

Find the volume of a pyramid with a square base, where the side length of the base is

nlexa [21]

Answer:

336.8 cubic meter or 336.8m³

Step-by-step explanation:

In other to solve the above question we would be using the volume of a square based pyramid.

The formula for the volume of a square based pyramid is

1/3a²h

In the above question we are given the following values as:

Side length of the base = a = 11.1 m

Height of the pyramid = h = 8.2m

Volume of the square based pyramid = 1/3 × 11.1² × 8.2

= 336.774 cubic meter or 336.774 m³

Approximately to the nearest tenth = 336.8 cubic meter or 336.8m³

8 0

3 years ago

Luna mixes 3/4 of orange juice and 3/8 of cranberry juice and then she gave mags 5/8 cup of juice and we have to turn it into an

Gennadij [26K]

Answer: 1/2

Step-by-step explanation:

The question is for us to calculate the amount of juice that's left.

We are told that Luna mixes 3/4 of orange juice and 3/8 of cranberry juice. The amount of juice mixed will be:

= 3/4 + 3/8

= 6/8 + 3/8

= 9/8

= 1 1/8

We are then told that she gave Mags 5/8 cup of juice. The amount of juice that's then left will be:

= 1 1/8 - 5/8

= 4/8

= 1/2

1/2 cup of juice will be left

8 0

3 years ago

Part

goldfiish [28.3K]

When a shape is rotated, it must be rotated around a point.

To determine the location of the new triangle, Sonja must subtract (5,-1) from the coordinates of the original triangle, before rotating by $90^o$ .

From the question, we have:

$C = (5,-1)$ --- the center of rotation

Let the vertices of the triangle be (x,y).

First, she must subtract the coordinates of the center of rotation from the vertices of the triangle.

This gives:

$(x,y) \to (x - 5, y + 1)$

Then the vertices are rotated by $90^o$

The rule of $90^o$ rotation is:

$(x,y) \to (-y,x)$

So, we have:

$(x - 5,y + 1) \to (-y - 1,x - 5)$

From the attachment, the coordinates of the triangle are: (0,2), (0,5) and (4,2)

After rotation, the coordinates are calculated as follows:

$(0,2) \to (-2-1,0-5) \to (-3,-5)$

$(0,5) \to (-5-1,0-5) \to (-6,-5)$

$(4,2) \to (-2-1,4-5) \to (-3,-1)$

Hence, the coordinates are: (-3,-5), (-6,-5) and (-3,-1)