For f(x) = 3x^3 - 9x^2 - 5x + 2

A. Find f(-1)

B. Find f(2)

Answer:

[tex]\displaystyle \textcolor{black}{4.}\:[-3, -5][/tex]

[tex]\displaystyle \textcolor{black}{3.}\:[8, -1][/tex]

[tex]\displaystyle \textcolor{black}{2.}\:[4, -7][/tex]

[tex]\displaystyle \textcolor{black}{1.}\:[3, -2][/tex]

Step-by-step explanation:

When using the Elimination method, you eradicate one pair of variables so they are set to zero. It does not matter which pair is selected:

[tex]\displaystyle \left \{ {{2x - 3y = 9} \atop {-5x - 3y = 30}} \right.[/tex]

{2x - 3y = 9

{⅖[−5x - 3y = 30]

[tex]\displaystyle \left \{ {{2x - 3y = 9} \atop {-2x - 1\frac{1}{5}y = 12}} \right. \\ \\ \frac{-4\frac{1}{5}y}{-4\frac{1}{5}} = \frac{21}{-4\frac{1}{5}} \\ \\ \boxed{y = -5, x = -3}[/tex]

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[tex]\displaystyle \left \{ {{x - 2y = 10} \atop {x + 3y = 5}} \right.[/tex]

{x - 2y = 10

{⅔[x + 3y = 5]

[tex]\displaystyle \left \{ {{x - 2y = 10} \atop {\frac{2}{3}x + 2y = 3\frac{1}{3}}} \right. \\ \\ \frac{1\frac{2}{3}x}{1\frac{2}{3}} = \frac{13\frac{1}{3}}{1\frac{2}{3}} \\ \\ \boxed{x = 8, y = -1}[/tex]

_______________________________________________

[tex]\displaystyle \left \{ {{y = -3x + 5} \atop {y = -8x + 25}} \right.[/tex]

{y = −3x + 5

{−⅜[y = −8x + 25]

[tex]\displaystyle \left \{ {{y = -3x + 5} \atop {-\frac{3}{8}y = 3x - 9\frac{3}{8}}} \right. \\ \\ \frac{\frac{5}{8}y}{\frac{5}{8}} = \frac{-4\frac{3}{8}}{\frac{5}{8}} \\ \\ \boxed{y = -7, x = 4}[/tex]

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[tex]\displaystyle \left \{ {{y = -x + 1} \atop {y = 4x - 14}} \right.[/tex]

{y = −x + 1

{¼[y = 4x - 14]

[tex]\displaystyle \left \{ {{y = -x + 1} \atop {\frac{1}{4}y = x - 3\frac{1}{2}}} \right. \\ \\ \frac{1\frac{1}{4}y}{1\frac{1}{4}} = \frac{-2\frac{1}{2}}{1\frac{1}{4}} \\ \\ \boxed{y = -2, x = 3}[/tex]

_______________________________________________

I am joyous to assist you at any time.

Answer: 10 × 3 + 4 + 5 × 2 + 1 + 3 × 100 = 345

Answer:

the largest Angle has a measure of 360 degrees

Answer:

40; 0.1 and 0.16

Step-by-step explanation:

a. We know that p(w)=230(1.1)^W represents the number of specialty items produced at the old factory.

This equation is in the form of an exponential growth function:

f(x)=a(1+r)^x

where a is the initial value, r is the growth rate, and x is the number of time intervals.

That means that for p(w)=230(1.1)^W:

230 is the initial value, and 0.1 is the growth rate. (1.1-1)

Therefore, for week 0, there were 230 specialty items produced at the old factory.

We can also plug in 0 for w (0 time intervals) to get the same answer

That would look like:

p(0)=230(1.1)^0

p(0)=230(1)

p(0)=230

On the other hand, for the new factory, if you go find 0 on the x-axis, you'll notice that 190 specialty items were produced in week 0.

230-190=40

This means that our answer for a is that 40 more specialty items were produced at the old factory than the new factory.

_____

b. Our first step for this question would be to find the equation for the graph.

We can immediately recognize that this is an exponential growth function, similar to the other equation.

As a reminder, exponential growth functions are in the form: f(x)=a(1+r)^x

We can put it in terms of production and weeks:

p(w)=a(1+r)^w

We know that the initial value is 190 by the graph.

p(w)=190(1+r)^w

Now we just need to find the growth rate:

We can do this by choosing a value (other than the first point) and plugging it in.  Let's use (1, 220) which is in the form (w, p)

Plug it in to the equation:

220=190(1+r)^1

220=190(1+r)

Distribute

220=190+190r

Subtract 190 from both sides

30=190r

Divide 190 from both sides

r=0.1578947368 (round how your teacher asks)

Next, all we have to do is find the growth rate for the old factory:

p(w)=230(1.1)^W

1.1=1+r

Therefore, r=0.1

The growth rate at the old factory is 0.1.

When comparing them, we'll realize that the growth rate at the new factory is about 0.06 higher.

#1

For old factory

So

[tex]\\ \rm\dashrightarrow p(0)=230(1.1)^0=230(1)=230[/tex]

For nEW factory

Difference:-

40 items were more produced

#2

For old factory

[tex]\\ \rm\dashrightarrow 230(1+0.1)^t[/tex]

For new factory

Find slope:-

[tex]\\ \rm\dashrightarrow m=\dfrac{220-190}{1}=30[/tex]

Find growth rate

New factory has greater growth rate

The missing length is 18

Using Pythagorean rule

Hyp^2 = Opp^2 + adj^2

Opp^2 = hyp^2 - adj^2

Opp^2 = 30^2 - 24^2

Opp^2 = 900 - 576

Opp^2 = 324

Opp = sqrt ( 324 )

Opp = 18

Answer:

The point at f(-3) is at (-3,1).

Step-by-step explanation:

To find the y-value of a function at a specific point by using the graph, keep in mind that the x-axis is the axis that lies horizontally on the graph.

So, look along the horizontal line through the center until you find where x = -3. Now find the corresponding y-value to that x-value by looking above or below that point until you find where it intersects the graph. When you find that point, look to see what number the point corresponds with on the y-axis. In this case, it corresponds to y = 1.

Remember that ordered pairs are formatted as (x,y).

Hope this helps.

The area of a parallelogram is the product of:

   --> length of the base and the height

Thus the area = 7 * 5 = 35 square feet

Hope that helps!

Answer:

so first you want to mulitply the 5,5,5.8, and 8 together to get 1160 then take away 464 from 1160 to get 696. then you add all of the numbers up to get 719.8 ten subtract .75 from that and you get 719.05. then take the cubic feet and get 200 then taky away 200 from 719.05 and get 519.05 then do that again

Step-by-step explanation:

219.05

Answer:

Center: (3,-1)

Radius: 3

Step-by-step explanation:

Given:

[tex]\displaystyle \large{x^2+y^2-6x+2y+1=0}[/tex]

First, we have to convert the following standard circle equation to this:

[tex]\displaystyle \large{(x-h)^2+(y-k)^2=r^2}[/tex]

where h is horizontal shift, k is vertical shift and r is radius.

That means we have to complete the square for both x-term and y-term.

Rearrange the equation:

[tex]\displaystyle \large{x^2-6x+y^2+2y+1=0}\\\displaystyle \large{(x^2-6x)+(y^2+2y+1)=0}[/tex]

For [tex]\displaystyle \large{y^2+2y+1}[/tex], can be converted to perfect square as [tex]\displaystyle \large{(y+1)^2}[/tex]. Hence:

[tex]\displaystyle \large{(x^2-6x)+(y+1)^2=0}[/tex]

For the x-terms, we have to find another value that can complete the square. We know that [tex]\displaystyle \large{(a\pm b)^2 = a^2 \pm 2ab + b^2}[/tex].

For [tex]\displaystyle \large{x^2-6x}[/tex] can be [tex]\displaystyle \large{x^2-2(x)(3)+3^2 \to x^2-6x+9}[/tex]. So our another value is 9.

[tex]\displaystyle \large{(x^2-6x+9-9)+(y+1)^2=0}[/tex]

From above, we add -9 because the original expression isn’t actual perfect square.

Separate -9 out of [tex]\displaystyle \large{x^2-6x+9}[/tex]:

[tex]\displaystyle \large{(x^2-6x+9)-9+(y+1)^2=0}[/tex]

Transport -9 to add another side:

[tex]\displaystyle \large{(x^2-6x+9)+(y+1)^2=9}[/tex]

Complete the square:

[tex]\displaystyle \large{(x-3)^2+(y+1)^2=9}[/tex]

Finally, we have our needed equation to find radius and center. The coordinate of center is defined as the point (h,k) from [tex]\displaystyle \large{(x-h)^2+(y-k)^2=r^2}[/tex] and the radius is defined as r.

Hence, from the equation:

The coordinate of center is (3,-1) with radius equal to 3.

Answer:

Rs 200

Step-by-step explanation:

100/104×Rs 208

Rs 200

S.P = 208

4%×208=8.32

208-8.38=199.68

Therefore, C.P = ₹199.68

so approximately C.P = ₹200

Answer:

  (a)  140 sandwiches

Step-by-step explanation:

The total number sold can be found from the given relation:

  56 sandwiches = 40% × total sold

__

Dividing by the coefficient of the variable, we find ...

  total sold = (56 sandwiches)/0.40 = 140 sandwiches

The total number of sandwiches sold last week was 140.

Answer:

D. f(x) = x - 4

Step-by-step explanation:

If you plug in the x values for the expression x - 4:

3 - 4 = -1
4 - 4 = 0
5 - 4 = 1
6 - 4 = 2
This means that the function rule is f(x) = x - 4
Hope this helps :)

Answer:

the answer is shown below

I truly hope this helps you -TJ

Step-by-step explanation:

here you go

Answer:

D

Step-by-step explanation:

Edge

The fact that the angles in a triangle add up to 180 indicates that it is actually a square). There are also four right triangles, each with a base and a height. The Pythagorean Theorem is reached when a2 + b2 = c2.

Answer: 15 miles per gallon

Step-by-step explanation:

135 divided by 9

15 miles per gallon

rate:

[tex]\sf \dfrac{distance}{amount \ of \ oil}[/tex]

[tex]\rightarrow \dfrac{135}{9}[/tex]

[tex]\sf \rightarrow15 \ miles \ per \ gallon[/tex]

Answer:

10%

Step-by-step explanation:

1/10  = 10%

The equation of the ravine function is an illustration of a quadratic function

It will take 1.5 seconds for the music player to fall to the bottom of the ravine

The equation of the function is given as:

[tex]t = \sqrt{\frac{8t + 24}{16}}[/tex]

Take the square of both sides

t² = (8t + 24)/16

Multiply both sides by 16

16t² = 8t + 24

Divide through by 8

2t² = t + 3

Set the equation to 0

2t² - t - 3 = 0

Expand the equation

2t² + 2t- 3t - 3 = 0

Factorize the equation to 0

2t(t + 1)- 3(t + 1) = 0

Factor out t + 1

(2t- 3)(t + 1) = 0

Expand

2t- 3 = 0 or t + 1 = 0

Solve for t

t= 1.5 or t =- 1

Time cannot be negative.

So, we have:

t = 1.5

Hence, it will take 1.5 seconds for the music player to fall to the bottom of the ravine

Read more about quadratic functions at:

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total mass = mass of a bag of candy + mass of a chocolate bar

total mass = 80g +110g = 190g

Answer:

The order of operations says that operations must be done in the following order: parentheses, exponents, multiplication, division, addition, and subtraction. You can also create a little phrase to go along with this, like "Please Excuse My Dear Aunt Sally." Whatever you choose, make sure that you know all six steps of the order of operations very well. The order of operations tells us the order to solve steps in expressions with more than one operation. First, we solve any operations inside of parentheses or brackets. Second, we solve any exponents. Third, we solve all multiplication and division from left to right.

Step-by-step explanation:

hope this helps :)

Answer:

h=3/2. V=3(root)3

Step-by-step explanation:

This is the war between the communist governmrnt of Vietnam North and the South Vietnam.  The United States of America were the main ally of the Vietnam south during the war.

The communist Vietnam North later united with the south with a common name Socialist Reepublic of Vietnam, After a fierce onslaught that took the life of about 58000 americans and over 2 million Vietnamese.

The influence of the Vietnam war in United States today

1. End of the drafts

The drafts is the method of conscription to the military that requires vitually every male between the age of 18 - 25 in United States to register with the selective service. since the end of the Vietnam war in 1975 the draft stopped hence no penalty for not registering to the draft.

2. Granting 18 years old the right to vote

26th Amendment of the United States Constitution gave right to vote to the 18 years old citizens. Today 18 tear old American has right to vote. This was evolvement of the war and still holds till date.

3. It is easier getting into a war than getting out of a war

Americans was pulling out of the Vietnam war when they suffered the huge massacre. This lesson was helpful for president George H W Bush during the 1991 Persian Gulf War were he systematically exited after liberating Kuwait

Read more on Vietnam war here: https://brainly.com/question/24845081

Using sampling concepts, it is found that it is not a random sample, as it considers only the books in her bedroom, hence books from other people in the household are likely to not be considered.

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which has to involve all groups in the population.

In this problem, a random sample should involve the books of all people in the household, not only Jamaya's. Hence, it is not a random sample, as it considers only the books in her bedroom, hence books from other people in the household are likely to not be considered.

More can be learned about sampling concepts at https://brainly.com/question/25122507

Answer:

30 ft.³

Step-by-step explanation:

3ft. × 5ft. × 2ft. = 30 ft.³

Please rate!! I hope this helps!!

Answer:

$710,000

Step-by-step explanation:

The computation of the owner’s equity at the end of the year is given below:

We know that

The accounting equation equals to

Total assets = Total liabilities + owners equity

where,

Total assets = $800,000 + $150,000 = $950,000

And, the total liabilities = $300,000 - $60,000 = $240,000

So, the owners equity at the end of the year would be

= $950,000 - $240,000

= $710,000

Answer: 121.875 ounces of orange dye

Step-by-step explanation: 8 ÷ 195 = 24.375

24.375 x 5 = 121.875

Step-by-step explanation:

after x^2-4x-5 do sum and product

From the given price function, we have;

(a) [tex] \frac{dp}{dq} = - 13[/tex]

(b) The point elasticity of demand is 0.0256; inelastic demand

(c) $46.6

(d) Increase

a. The given function is presented as follows;

[tex]p = 50 \times (151 - q) ^{0.02 \times \sqrt{q + 19} } [/tex]

Differentiating the above function with a graphing calculator and setting q = 150 gives;

[tex] \frac{dp}{dq} = - 13[/tex]

b. The point elasticity of demand is given by the formula;

[tex] e \: = \frac{dq}{dp} \times \frac{p}{q} [/tex]

When q = 150, we have;

P = 50

Which gives;

[tex]e \: = \frac{1}{13} \times \frac{50}{150} = 0.0256[/tex]

The point elasticity of demand, E = 0.0256

c. If the quantity demanded decreases from 150 to 140 units, we have;

[tex]0.0256 \: = \frac{1}{13} \times \frac{p}{140} = [/tex]

Which gives;

p = 46.6

d. Given that increase in price, from 46.6 to 50, increases the quantity demanded from 140 to 150, therefore;

R = p × q

Learn more about elasticity of demand here;

https://brainly.com/question/19141990

The loss in producer surplus as a result of the tax given the information in the diagram is  $9000.

Producer surplus is the difference between the price of a good and the least price the seller is willing to sell the product

The dead weight loss of tax can be determined by calculating the reduction in total surplus as a result of the tax

Loss = (1/2 x 600 x 40) - (1/2 x 300 x 20)

12000  - 3000 = $9000

Please find attached the complete question. To learn more about surplus, please check: https://brainly.com/question/25816093