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2 years ago

2. Consider the function, f(x)=x^3+x^2-9x-9

Mathematics

1 answer:

Sedaia [141]2 years ago

5 0

The intercepts of the graph are:

x-axis interception: $\left(-1,\:0\right),\:\left(-3,\:0\right),\:\left(3,\:0\right)$ .

y-axis interception: $\left(0,\:-9\right)$ .

See the graph of the function $f(x)=x^3+x^2-9x-9$ in the attached image.

<h3>Constructing a graph</h3>

For constructing a graph we have the following steps:

Determine the range of values for x of your graph.

For this exercise, for example, we can define a range -4<x<4. In others words, the values of x will be in this interval.

Determine the points

Replace these x-values in the given equation. For example:

When x=-4, we will have: $\left(-4\right)^3+\left(-4\right)^2-9\left(-4\right)-9=-21$ . Do this for the all x-values of your ranges.

See the results for this step in the attached table.

Draw the graph

Mark the points <u>x</u> and<u> y</u> that you found in the last step. After that, connect the dots to draw the graph.

The attached image shows the graph for the given function.

<h3>Find the x- and y-intercepts</h3>

The intercepts are points that crosses the axes of your plot. From your graph is possible to see:

x-axis interception points (y=f(x)=0) are: $\left(-1,\:0\right),\:\left(-3,\:0\right),\:\left(3,\:0\right)$ .

y-axis interception point (x=0) is: $\left(0,\:-9\right)$ .

Learn more about intercepts of the graph here:

brainly.com/question/4504979

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The graph of F(x) shown below has the same shape as the graph of G(x) = x^2 but it is shifted down 5 units and to the left 4 uni

grandymaker [24]

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$\bf \bullet \textit{ flips it sideways if } B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}$

with that template in mind, let's see

down by 5 units, D = -5

to the left by 4 units, C = +4

$\bf G(x)=x^2\implies G(x)=1(1x+\stackrel{C}{0})^2+\stackrel{D}{0} \\\\\\ \begin{cases} D=-5\\ C=+4 \end{cases}\implies F(x)=1(1x+\stackrel{C}{4})^2\stackrel{D}{-5}\implies F(x)=(x+4)^2-5$

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2 years ago

the area for any square is given by the function y=x squared where is the length of a side of the area square and y is the area

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12.25 inches. the equation to find that would be 3.5 squared or 3.5 times 3.5

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3 years ago

FORM A CUBIC POLYNOMIAL WHOSE ZEROS ARE -3,-1 AND 2

Firdavs [7]

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3 years ago

In a chemical plant, 24 holding tanks are used for final product storage. Four tanks are selected at random and without replacem

Damm [24]

Answer:

a) P(A) = 0,4607 or P(A) = 46,07 %

b) P(B) = 0,7120 or 71,2 %

c) P(C) = 0,2055 or P(C) = 20,55 %

Step-by-step explanation:

We will use two concepts in solving this problem.

1.- The probability of an event (A) is for definition:

P(A) = Number of favorable events/ Total number of events FE/TE

2.- If A and B are complementary events ( the sum of them is equal to 1) then:

P(A) = 1 - P(B)

a) The total number of events is:

C ( 24,4) = 24! / 4! ( 24 - 4 )! ⇒ C ( 24,4) = 24! / 4! * 20!

C ( 24,4) = 24*23*22*21*20! / 4! * 20!

C ( 24,4) = 24*23*22*21/4*3*2

C ( 24,4) = 24*23*22*21/4*3*2 ⇒ C ( 24,4) = 10626

TE = 10626

Splitting the group of tanks in two 6 with h-v and 24-6 (18) without h-v

we get that total number of favorable events is the product of:

FE = 6* C ( 18, 3) = 6 * 18! / 3!*15! = 18*17*16*15!/15!

FE = 4896

Then P(A) ( 1 tank in the sample contains h-v material is:

P(A) = 4896/10626

P(A) = 0,4607 or P(A) = 46,07 %

b) P(B) will be the probability of at least 1 tank contains h-v

P(B) = 1 - P ( no one tank with h-v)

Again Total number of events is 10626

The total number of favorable events for the ocurrence of P is C (18,4)

FE = C (18,4) = 18! / 14!*4! = 18*17*16*15*14!/14!*4!

FE = 18*17*16*15/4*3*2 = 3060

Then P = 3060/10626

P = 0,2879

And the probability we are looking for is

P(B) = 1 - 0,2879

P(B) = 0,7120 or 71,2 %

c) We call P(C) the probability of finding exactly 1 tank with h-v and t-i

having 4 with t-i tanks is:

reasoning the same way but now having 4 with t-i (impurities) number of favorable events is:

FE = 6*4* C(14,2) = 24 * 14!/12!*2!

FE = 24* 14*13*12! / 12!*2

FE = 24*14*13/2 ⇒ FE = 2184

And again as the TE = 10626

P(C) = 2184/ 10626

P(C) = 0,2055 or P(C) = 20,55 %

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3 years ago

9 – 2k = 25 what is k

worty [1.4K]

Answer:

k = - 8

Step-by-step explanation:

Subtract 9 from both sides to get the constants on one side and the variables on the other

9 - 2k = 25

- 2k = 25 - 9

Simplify

- 2k = 16

Divide by -2 on both sides to isolate the variable, then simplify once more.

- 2k/ -2 = 16/ -2

k = 16/ -2

k = -8

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3 years ago

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