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Sphinxa [80]
3 years ago
9

What is the complete factorization of x^2 - 6x + 9

Mathematics
1 answer:
Finger [1]3 years ago
4 0

Answer:

(x-3)^{2}

Step-by-step explanation:

Factor using the perfect square rule.

:)

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(x+6) (z-y)<br>__________<br> (x+y) <br><br><br><br>x= -3<br>y= 4<br>z= 5​
Oksana_A [137]

Answer:

The answer is 4/1

Step by step

So x=-3 y=4 and z=5 so i added - 3 +6 to get positive 3 and z - y to get postive 1. X +y gives you positive 1 also so if u join both you get an improper fraction 4/1

7 0
2 years ago
Help please when I do the guadratic equation I’m doing something wrong
AnnZ [28]

Answer:

Graph A

Step-by-step explanation

The problem: y=2x^2+8x+3

1) You will need to determine the direction of the parabola, If a > 0 then the parabola opens upward, if a < 0 then the parabola opens downward.

2) If when doing this you get an imaginary solution, you would have no x intercepts. The first thing you need to do is find the x intercepts, you can do this by plugging in 0 for y, so this would give you 0=2x^2+8x+3. Once you have this you start by subtracting 3 from both sides, dividing 8 from both side, etc. (If you would like me to elaborate don't hesitate to ask!)

3) To find the graphs y intercept you plug in 0 for x, which gives you y=2(0)^2+8(0)+3, you do the same thing you did during the previous step for y. (Once again, I am willing to elaborate further if you need!)

4) You then need to find the vertex (h,k)

To find h: h= -b/2a

To find k: k = a(h)2 + b(h) + c

5) Once you've worked through this you can graph the point!

Hope this helped!

8 0
3 years ago
F(x) = (128/127)(1/2)x, x = 1,2,3,...7. determine the requested values: round your answers to three decimal places (e.g. 98.765)
Marrrta [24]
A.
\mathbb P(X\le 1)=\mathbb P(X=1)=\dfrac{128}{127}\left(\dfrac12\right)^1=\dfrac{64}{127}

b.
\mathbb P(X>1)=1-\mathbb P(X\le1)=1-\dfrac{64}{127}=\dfrac{63}{127}

c.
\mathbb E(X)=\displaystyle\sum_{x=1}^7 x\,f_X(x)=\frac{64}{127}\sum_{x=1}^7 x\left(\frac12\right)^{x-1}

Suppose f(y)=\displaystyle\sum_{x=0}^7 y^x. Then f'(y)=\displaystyle\sum_{x=1}^7 xy^{x-1}. So if we can find a closed form for f(y), in terms of y, we can find \mathbb E(X) by evaluating the derivative of f(y) at y=\dfrac12.

f(y)=\displaystyle\sum_{x=0}^7 y^x=y^0+y^1+y^2+\cdots+y^6+y^7
y\,f(y)=y^1+y^2+y^3+\cdots+y^7+y^8
f(y)-y\,f(y)=y^0-y^8
(1-y)f(y)=1-y^8
f(y)=\dfrac{1-y^8}{1-y}
\implies f'(y)=\dfrac{7y^8-8y^7+1}{(1-y)^2}
\implies\mathbb E(X)=\dfrac{64}{127}f'\left(\dfrac12\right)=\dfrac{64}{127}\times\dfrac{247}{64}=\dfrac{247}{127}

d.
\mathbb V(X)=\mathbb E(X^2)-\mathbb E(X)^2

We find \mathbb E(X^2) in a similar manner as in (c).

\mathbb E(X^2)=\displaystyle\sum_{x=1}^7 x^2\,f_X(x)=\frac{32}{127}\sum_{x=1}^7x^2\left(\frac12\right)^{x-2}

Now,

f(y)=\displaystyle\sum_{x=0}^7y^x
\implies f'(y)=\displaystyle\sum_{x=1}^7xy^{x-1}
\implies f''(y)=\displaystyle\sum_{x=2}^7x(x-1)y^{x-2}

We know that

f''(y)=-\dfrac{42y^8-96y^7+56y^6-2}{(1-y)^3}
\implies f''\left(\dfrac12\right)=\dfrac{219}{16}

We also have

f''(y)=\displaystyle\sum_{x=2}^7x(x-1)y^{x-2}
f''(y)=\displaystyle\sum_{x=2}^7x^2y^{x-2}-\sum_{x=2}^7xy^{x-2}
f''(y)=\displaystyle\frac1{y^2}\left(\sum_{x=2}^7x^2y^x-\sum_{x=2}^7xy^x\right)
f''(y)=\displaystyle\frac1{y^2}\left(\bigg(\sum_{x=1}^7x^2y^x-y\bigg)-\bigg(\sum_{x=1}^7xy^x-y\bigg)\right)
f''(y)=\displaystyle\frac1{y^2}\left(\sum_{x=1}^7x^2y^x-\sum_{x=1}^7xy^x\right)

so that when y=\dfrac12, we get

\dfrac{219}{16}=4\left(\dfrac{127}{128}\mathbb E(X^2)-\dfrac{127}{128}\mathbb E(X)\right)\implies\mathbb E(X^2)=\dfrac{685}{127}

Then

\mathbb V(X)=\dfrac{685}{127}-\left(\dfrac{247}{127}\right)^2=\dfrac{25,986}{16,129}
6 0
3 years ago
A truck whose bed is 2.5m long,1.5m, and 1.0 m high is delivering sand for a sand sculpture competition.About how many trips mus
serg [7]

The volume of the bed of the truck is 2.5 x 1.5 x 1.0 = 3.75 cubic meters.

total trips = 7 / 3.75 = 1.87, round up to 2.

They will need to make 2 trips.

5 0
3 years ago
I need help bc good at every class but math
Kobotan [32]

Answer:

10

Step-by-step explanation:

5 0
2 years ago
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