Is (x + 5) a factor of f(x) = x3 − 4x2 + 3x + 7?

If y = x+2 were arranged to y= x+1, how would you graph the new function compare with the first one

Kobotan [32]

Hope I was able to help u

8 0

2 years ago

100 Points PLEASE ANSWER ASP! Will Give BRAINLIST!

VikaD [51]

Let's work to solve this system of equations:

y = 2x ~~~~~~~~\gray{\text{Equation 1}}y=2x Equation 1

x + y = 24 ~~~~~~~~\gray{\text{Equation 2}}x+y=24 Equation 2

The tricky thing is that there are two variables, xx and yy. If only we could get rid of one of the variables...

Here's an idea! Equation 11 tells us that \goldD{2x}2x and \goldD yy are equal. So let's plug in \goldD{2x}2x for \goldD yy in Equation 22 to get rid of the yy variable in that equation:

\begin{aligned} x + \goldD y &= 24 &\gray{\text{Equation 2}} \\\\ x + \goldD{2x} &= 24 &\gray{\text{Substitute 2x for y}}\end{aligned}

x+y

x+2x

=24

Equation 2

Substitute 2x for y

Brilliant! Now we have an equation with just the xx variable that we know how to solve:

x+2x3x 3x3x=24=24=243=8Divide each side by 3

Nice! So we know that xx equals 88. But remember that we are looking for an ordered pair. We need a yy value as well. Let's use the first equation to find yy when xx equals 88:

\begin{aligned} y &= 2\blueD x &\gray{\text{Equation 1}} \\\\ y &= 2(\blueD8) &\gray{\text{Substitute 8 for x}}\\\\ \greenD y &\greenD= \greenD{16}\end{aligned}

y

=2x

=2(8)

=16

Equation 1

Substitute 8 for x

Sweet! So the solution to the system of equations is (\blueD8, \greenD{16})(8,16). It's always a good idea to check the solution back in the original equations just to be sure.

Let's check the first equation:

\begin{aligned} y &= 2x \\\\ \greenD{16} &\stackrel?= 2(\blueD{8}) &\gray{\text{Plug in x = 8 and y = 16}}\\\\ 16 &= 16 &\gray{\text{Yes!}}\end{aligned}

y

16

=2x

=

?

2(8)

=16

Plug in x = 8 and y = 16

Yes!

Let's check the second equation:

\begin{aligned} x +y &= 24 \\\\ \blueD{8} + \greenD{16} &\stackrel?= 24 &\gray{\text{Plug in x = 8 and y = 16}}\\\\ 24 &= 24 &\gray{\text{Yes!}}\end{aligned}

x+y

8+16

24

=24

=

?

24

=24

Plug in x = 8 and y = 16

Yes!

Great! (\blueD8, \greenD{16})(8,16) is indeed a solution. We must not have made any mistakes.

Your turn to solve a system of equations using substitution.

Use substitution to solve the following system of equations.

4x + y = 284x+y=28

y = 3xy=3x

4 0

2 years ago

Read 2 more answers

Jobisdone [24]

Remember for any two polygons

Area of polygons is directly proportional to square of sides

So

BC²/XY²=135/15
15²/XY²=9
(15/3)²=XY²
XY=5in

#35

HJ²/XY²=168/378
8²/XY²=0.44
XY²=64/0.44
XY²=145.45
XY\approx 12+

3 0

1 year ago

Read 2 more answers

The number of tickets purchased by an individual for Beckham College's holiday music festival is a uniformly distributed random

Zanzabum

1) Mean: 6.5

2) Standard deviation: 3.2

Step-by-step explanation:

1)

A uniform random distribution is the distribution of a variable that can assume n different values, and each of these values is equally likely to occur.

This means that the probability of occurring of each of these values is the same:

$p(x_1)=p(x_2)=...=p(x_n)$

For a uniform random distribution, the mean of the distribution is simply equal to the median value of the distribution, which is exactly at the center of the distribution itself. It can be calculated as

$\bar x = \frac{1}{2}(a+b)$