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Komok [63]
3 years ago
15

Which equation describes the graph a) y=-2|x|-1 b) y=2|x|+1 c) y=-2|x|+1 d) y=2|x|-1

Mathematics
1 answer:
Alecsey [184]3 years ago
8 0

Answer:

D: y=2|x|-1

Step-by-step explanation:

We need to find the equation which describes the graph

The general form of equation for this graph is y=|x|

The graph opens upwards so its positive

We cannot choose option (a) and option (d) because it has -2

Lets check with option b  and d

In the graph, the y values starts at -1. (0,-1) is the vertex.

Lets plug in (0,-1)  and check with option b

y=2|x|+1

-1= 2|0|+1

-1=+1, its false.

Lets check with option (d)

y=2|x|-1

-1= 2|0|-1

-1=-1, its true

Option D is the answer

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Please show your work and explain it.
Maru [420]

Answer:

f(x)=\dfrac{x+2}{2(x-2)}

Step-by-step explanation:

Remember when you divide fractions, you need to get the reciprocal of the divisor and multiply. So your first simplification would be:

\dfrac{x^2+4x+4}{x^2-6x+8}\div\dfrac{6x+12}{3x-12}\\\\=\dfrac{x^2+4x+4}{x^2-6x+8}\times\dfrac{3x-12}{6x+12}\\\\=\dfrac{(x^2+4x+4)(3x-12)}{(x^2-6x+8)(6x+12)}

Next we factor what we can so we can further simplify the rest of the equation:

=\dfrac{(x^2+4x+4)(3x-12)}{(x^2-6x+8)(6x+12)}\\\\=\dfrac{(x+2)(x+2)(3x-12)}{(x^2-6x+8)(6(x+2))}\\\\

We can now cancel out (x+2)

=\dfrac{(x+2)(3x-12)}{(x^2-6x+8)(6)}

Next we factor out even more:

=\dfrac{(x+2)(3)(x-4)}{(x-2)(x-4)(6)}

We cancel out x-4 and reduce the 3 and 6 into simpler terms:

=\dfrac{(x+2)(1)}{(x-2)(2)}

And we can now simplify it to:

=\dfrac{x+2}{2(x-2)}

6 0
3 years ago
E price of a large pizza increased from $21 to $26. what is the percent of increase in the cost of pizza? round to the nearest p
rodikova [14]
Percent increase=increase/original times 100

increase=26-21=5
original=21

so
5/21 times 100=0.23809523809523809523809523809524 times 100=23.809523809523809523809523809524
round
24%

so 24% increase

7 0
3 years ago
MARSVECTORCALC6 3.4.020. My Notes A rectangular box with no top is to have a surface area of 64 m2. Find the dimensions (in m) t
ioda

Answer:

We would have

                                    l =w =\frac{8\sqrt{3}}{3} \\h = \frac{8\sqrt{3}}{6}

where " l " is  length, " w"  is width and "h" is height.

Step-by-step explanation:

Step 1

Remember that

         Surface area for a box with no top = lw+2lh+2wh = 64

where " l " is  length, " w"  is width and "h" is height.

 Step 2.

Remember as well that

                              Volume of the box = l*w*h

Step 3

 We can now use lagrange multipliers.  Lets say,

                                    F(l,w,h) = lwh

and

                                g(l,w,h) = lw+2lh+2wh = 64

By the lagrange multipliers method we know that                            

 

                                                     \nabla F  = \lambda \nabla g

Step 4

Remember that

                          \nabla F  = (wh,lh,lw)

and

                      \nabla g = (w+2h,l+2h , 2w+2l)

So basically you will have the system of equations

                              wh = \lambda (w+2h)\\lh = \lambda (l+2h)\\lw = \lambda (2w+2l)

Now, remember that you can multiply the first eqation, by "l" the second equation by "w" and the third one by "h" and you would get

                                   lwh = l\lambda (w+2h)\\\\lwh = w\lambda (l+2h)\\\\lwh = h\lambda (2w+2l)

Then you would get

                      l\lambda (w+2h) = w\lambda (l+2h) =  h\lambda (2w+2l)

You can get rid of \lambda from these equations and you would get

                         lw+2lh = lw+2wh =  2wh+2lh

And from those equations you would get

                                             l = w =2h

Now remember the original equation

                                    lw+2lh+2wh = 64

If we plug in what we just got, we would have

                                 l^{2} + l^{2} + l^2   =  64 \\3l^{2} = 64 \\l = w = \frac{8\sqrt{3} }{3} \\h = \frac{8\sqrt{3} }{6}

                       

                                                 

7 0
3 years ago
A pencil box contains five
KonstantinChe [14]

Answer:

red pencil=5/24

yellow pencil=6/24

Blue pencil=8/24

Orange pencil=3/24

purple pencil=2/24

5 0
2 years ago
The pyramid shown has a square base that is 24 inches on each side. The slant height is 20 inches. What is the surface area of t
kondaur [170]

Answer:

Surface area of pyramid = 1536 square inches.

Step-by-step explanation:

Surface area of a pyramid with the square base will be = surface area of base + 4× slant surfaces of the pyramid

area of square base = 24×24 = 576 inches²

area of one slant side of pyramid = (1/2)×side × slant height = (24×20)/2 = 240 square inches

Therefore surface area of complete pyramid = 4×area of slant side + surface area of square base = 4×240 + 576 = 960 + 576 = 1536 square inch.

7 0
3 years ago
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