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storchak [24]
3 years ago
11

How can I do substitution method in Algebra 2? The equations are y= x^2-2x-3 and y=x^2+5x+11

Mathematics
1 answer:
Nikitich [7]3 years ago
7 0

\bf \begin{cases} \boxed{y} = x^2-2x-3\\ y = x^2+5x+11 \end{cases}\qquad\qquad \stackrel{\textit{substituting on the 2nd equation}}{\boxed{x^2-2x-3} = x^2+5x+11} \\\\\\ ~~\begin{matrix} x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ -2x-3= ~~\begin{matrix} x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ +5x+11\implies -2x-3=5x+11\implies -3=7x+11 \\\\\\ -14=7x\implies \cfrac{-14}{7}=x\implies \blacktriangleright -2=x \blacktriangleleft

\bf \stackrel{\textit{since we know that }y = x^2-2x-3}{y=(-2)^2-2(-2)-3} \implies y = 4+4-3\implies \blacktriangleright y = 5 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (-2,5)~\hfill

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Find x, y, and z<br><br> x = 39<br> x = 29<br> y = 61<br> y = 29<br> z = 61<br> z = 29
nikdorinn [45]

answer:

x = 29

y = 29

z = 61

step-by-step explanation:

all angles in a triangle must equal 180 degrees.

we were already given the angle degree of 61 degrees so we must include that in our formula to determine the degree of y.

the line in the middle already gives us two more angles because they both are 90 degrees for being a perfect quarter turn.

so to figure out y,

we must add 61+90 and then subtract the sum of that from 180.

so, 61+90 = 150 and 180-151 = 29

therefore,

we can conclude that y = 29

now, to determine the degrees of x and z we do the same thing.

we already know one angle equals 90 degrees.

180-90 = 90

that concludes that x and z must have a sum of 90.

if we use our choices,

39+61 = 100 (no)

39+29 = 68 (no)

29+61 = 90 (CORRECT)

29+29 = 28 (no)

<em>therefore, x = 29 and z = 61</em>

<em></em>

<em>so, in total :</em>

<em>x = 29</em>

<em>y = 29</em>

<em>z = 61</em>

<em></em>

<em>hope this helps :)   </em>

<em>-audrey <3 </em>

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In order to find this probability we can use excel with the following code:

=GAMMA.DIST(40;5,8,TRUE)-GAMMA.DIST(1,5,8,TRUE)

And we got:

P(1 \leq X \leq 40)=0.560

b) P(X \geq 40)=1-P(X

In order to find this probability we can use excel with the following code:

=1-GAMMA.DIST(40,5,8,TRUE)

And we got:

P(X \geq 40)=1-P(X

Step-by-step explanation:

Previous concepts

The Gamma distribution "is a continuous, positive-only, unimodal distribution that encodes the time required for \alpha events to occur in a Poisson process with mean arrival time of \beta"

Solution to the problem

Let X the random variable that represent the lifetime for transistors

For this case we have the mean and the variance given. And we have defined the mean and variance like this:

\mu = 40 = \alpha \beta  (1)

\sigma^2 =320= \alpha \beta^2  (2)

From this we can solve \alpha and [/tex]\beta[/tex]

From the condition (1) we can solve for \alpha and we got:

\alpha= \frac{40}{\beta}    (3)

And if we replace condition (3) into (2) we got:

320= \frac{40}{\beta} \beta^2 = 40 \beta

And solving for \beta = 8

And now we can use condition (3) to find \alpha

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So then we have the parameters for the Gamma distribution. On this case X \sim Gamma (\alpha= 5, \beta=8)

Part a

For this case we want this probability:

P(1 \leq X \leq 40)

In order to find this probability we can use excel with the following code:

=GAMMA.DIST(40;5,8,TRUE)-GAMMA.DIST(1,5,8,TRUE)

And we got:

P(1 \leq X \leq 40)=0.560

Part b

For this case we want this probability:

P(X \geq 40)=1-P(X

In order to find this probability we can use excel with the following code:

=1-GAMMA.DIST(40,5,8,TRUE)

And we got:

P(X \geq 40)=1-P(X

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We factor each group:

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Group 2: 5k ^ 2 (4k-3)

Rewriting we have:

5 (5k ^ 2 (4k-3) +6 (4k-3)) =\\5 ((5k ^ 2 + 6) (4k-3))

Answer:

5 (5k ^ 2 + 6) (4k-3)

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3 years ago
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