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Genrish500 [490]
2 years ago
8

Which function's graph has x-intercepts at x = - 2 and x = 4 , and a vertex at point (1, - 18) ?

Mathematics
1 answer:
Irina18 [472]2 years ago
5 0

Answer: (x+2)(2x-8)

if you let x = 1 it give h(x) = -18

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P(x) =x and q(x) = x-1Given:minimum x and Maximum x: -9.4 and 9.4minimum y and maximum y: -6.2 and 6.2Using the rational functio
Arte-miy333 [17]

we have the following function

\frac{p(x)}{g(x)}=\frac{x}{x\text{ -1}}

where x is between -9.4 and 9.4 and y is between -6.2 and 6.2.

We will first draw the function

from the graph, we can see that the zeroes are all values of x for which the graph crosses the x -axis

In this case, we see that that the only zero is at x=0.

Now, we have that the asymptotes are lines to which the graph of the function get really close to. On one side, we can see that as x goes to infinity or minus infinity, the values of the function get really close to 1. So the graph has a horizontal asymptote at y=1. Also, we can see that as x gets really close to 1, the graph gets really close to the vertical line x=1. So the graph has a vertical asymptote at x=1.

Recall that the domain of a function is the set of values of x for which the function is defined. From our graph, we can see that graph is not defined when x=1. So the domain of the function is the set of real numbers except x=1. Now, recall that the range of the function is the set of y values of the graph. From the picture we can see that the graph has a y coordinate for every value of y except for y=1. So, this means that the range of the function is the set of real numbers except y=1.

From the graph, we can see that we cannot draw the graph having a continous drawing. That is, imagine we take a pencil and start on one point on the graph on the left side. We can draw the whole graph on the left side, but we cannot draw the graph on the right side without lifting the pencil up. As we have to "lift the pencil up" this means that the graph is not continous

Finally note that as we have a vertical asymptote at x=1 and horizontal asymptote at y=1 we have that when y is 1 or x is 1, the function y=f(x)/g(x) is undefined

5 0
1 year ago
Line segment AB has a length of 4 units. It is translated 2 units to the right on a coordinate plane to obtain line segment A'B'
JulijaS [17]
4 units, because a translation is a rigid motion, meaning it preserves segment length.

8 0
3 years ago
What is -5 2/3 divided by -3?
sweet [91]
The answer to this question is 1.88888888889 or rounded to 2.0
6 0
3 years ago
What’s the answer but you also have to simplify
Jlenok [28]

Answer:

<em><u>The</u></em><em><u> </u></em><em><u>answer</u></em><em><u> </u></em><em><u>is</u></em><em><u> </u></em><em><u>9x</u></em><em><u>²</u></em><em><u> </u></em><em><u>+</u></em><em><u> </u></em><em><u>3x</u></em><em><u> </u></em><em><u>-</u></em><em><u> </u></em><em><u>2</u></em><em><u>.</u></em>

Step-by-step explanation:

1) Collect like terms.

(7x^{2}  +  {2x}^{2} ) + ( - 2x + 5x) + (8 - 10)

2) Simplify.

{9x}^{2}  + 3x - 2

<em><u>Therefor</u></em><em><u>,</u></em><em><u> </u></em><em><u>the</u></em><em><u> </u></em><em><u>answer</u></em><em><u> </u></em><em><u>is</u></em><em><u> </u></em><em><u>9x</u></em><em><u>²</u></em><em><u> </u></em><em><u>+</u></em><em><u> </u></em><em><u>3x</u></em><em><u> </u></em><em><u>-</u></em><em><u> </u></em><em><u>2</u></em>.

6 0
3 years ago
(4) A spherical balloon is being inflated so that its diameter is increasing at a constant rate of 6 cm/min. How quickly is the
fredd [130]

In terms of its radius r, the volume of the balloon is

V(r)=\dfrac{4\pi}3r^3

The diameter d is twice the radius, so that in terms of its diameters, the balloon's volume is given by

V(d)=\dfrac{4\pi}3\left(\dfrac d2\right)^3=\dfrac\pi6d^3

Differentiate both sides with respect to time t:

\dfrac{\mathrm dV}{\mathrm dt}=\dfrac\pi2d^2\dfrac{\mathrm dd}{\mathrm dt}

The diameter increases at a rate of \frac{\mathrm dd}{\mathrm dt}=6\frac{\rm cm}{\rm min}. When the diameter is d=50\,\mathrm{cm}, we have

\dfrac{\mathrm dV}{\mathrm dt}=\dfrac\pi2(50\,\mathrm{cm})^2\left(6\frac{\rm cm}{\rm min}\right)=7500\pi\dfrac{\mathrm{cm}^3}{\rm min}

or about 23,562 cc/min (where cc = cubic centimeters)

5 0
3 years ago
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