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3 years ago

Given the graphs of f(x) = x – 4 and g(x) = –2x – 7, what is the solution to the equation f(x) = g(x)?

Mathematics

1 answer:

STatiana [176]3 years ago

4 0

Answer:

C) -1

Step-by-step explanation:

we have the following functions:

$f(x)=x-4$

and

$g(x)=-2x-7$

to find the solution of $f(x) = g(x)$

what you need to do is to match the two functions:

$f(x) = g(x)\\x-4=-2x-7$

and now we solve this equation for x.

we move the -2x to the left as a +2x, and the -4 on to the right as a +4

$x+2x=-7+4$ :

and we add the quantities on both sides:

$3x=-3$

dividing by 3:

$x=-3/3\\\\x=-1$

the solution to the equation is

C) -1

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The height of a ball above the ground as a function of time is given by the function h(t)=−32t2+8t+3 where h is the height of th

gavmur [86]

Answer:

0.125 seconds.

Step-by-step explanation:

We have been given that the height of a ball above the ground as a function of time is given by the function $h(t)=-32t^2+8t+3$ , where h is the height of the ball in feet and t is the time in seconds.

We can see that our given equation is a downward opening parabola as its leading coefficient is negative. The maximum point will be vertex of parabola.

To find the time, when the ball would be at its maximum height, we need to find the x-coordinate of vertex.

Using formula $\frac{-b}{2a}$ , we will find the x-coordinate of vertex of parabola as:

$\frac{-b}{2a}$

$\frac{-8}{2*-32}$

$\frac{-8}{-64}$

$\frac{1}{8}$

$0.125$

Therefore, the ball will be at a maximum height after 0.125 seconds.

6 0

3 years ago

Evaluate the definite integral

Georgia [21]

$\displaystyle\int_{x=9}^{x=10}x\sqrt{x-9}\,\mathrm dx$

Let $y=x-9$ , so that $x=y+9$ and $\mathrm dx=\mathrm dy$ . The integral is then equivalent to

$\displaystyle\int_{y=0}^{y=1}(y+9)\sqrt y\,\mathrm dy=\int_0^1(y^{3/2}+9y^{1/2})\,\mathrm dy=\dfrac{32}5$