All categories

3 years ago

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

You might be interested in

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