MATHEMATICS HIGH SCHOOL

PLEASE HELP Polynomial Graph Studies Polynomials are great functions to use for modeling real-world scenarios where different intervals of increase and decrease happen. But polynomial equations and graphs can be trickier to work with than other function types. In mathematical modeling, we often create an equation to summarize data and make predictions for information not shown on the original display. In this activity, you’ll create an equation to fit this graph of a polynomial function. Part A Describe the type of function shown in the graph. Part B What are the standard form and the factored form of the function? Part C What are the zeros of the function? Part D Use the zeros to find all of the linear factors of the polynomial function. Part E Write the equation of the graphed function f(x), where a is the leading coefficient. Use the factors found in part D. Express the function as the product of its leading coefficient and the expanded form of the equation in standard form. Part F Use the y-intercept of the graph and your equation from part E to calculate the value of a. Part G Given what you found in all of the previous parts, write the equation for the function shown in the graph.

Answers

Answer 1

Answer:

Answer:

Here's what I get

Step-by-step explanation:

Part A

The graph shows a polynomial of odd degree. It is probably a third-degree polynomial — a cubic equation.

Part B

The standard form of a cubic equation is

y = ax³ + bx² + cx + d

The factored form of a cubic equation is

y = a(x - b₁)(x² + b₂x + b₃)

If you can factor the quadratic, the factored form becomes

y = a(x - c₁)(x - c₂)(x - c₃)

Part C

The zeros of the function are at x = -25, x = - 15, and x = 15.

Part D

The linear factors of the function are x + 25, x + 15, and x - 15.

Part E

y = a(x + 25)(x + 15)(x - 15) = a(x + 25)(x² - 225)

y = a(x³ + 25x² - 225x - 5625)

Part F

When x = 0, y = 1.

1 = a[0³ +25(0)² - 225(0) - 5625] = a(0 + 0 - 0 -5625) = -5625a

a = -1/5625

Part G

$y = -(1)/(5625)( x^(3) + 25x^(2) - 225x - 5625)\n\ny = \mathbf{ -(1)/(5625) x^(3) - (1)/(225)x^(2) + (1)/(25) x + 1}$

Answer 2

Answer:

Answer

Actually, the answer should be -0.0007(x+20)(x+5)(x-15)

Step-by-step explanation:

This is continuing off of the previous answer

PART C

The zeros should be (15,0), (-5,0), and (-20,0)

PART D

x - 15, x + 5, and x + 20

PART E

a(x - 15)(x + 5)(x + 20)

Standard: $a(x^(3) + 10x^(2) -275x-1500)$

PART F

The y-intercept is at (0,1), so we replace the x's with 0:

1 = $[(0)x^(3) +10(0)x^(2) -275(0)-1500]$ and this gives us (0+0-0-1500) which also equals -1500

Then we do $(1)/(-1500)$ which gives us -0.0006 repeating which rounds to -0.0007

a= -0.0007

PART G

Just place the numbers where they should go and your answer is

y =-0.0007(x + 20)(x + 5)(x - 15)

the placement for (x + 20) (x + 5) and (x - 15) doesn't matter as long as they are behind -0.0007

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18-6and -18+6 is the same thing

Answers

Answer:

Step-by-step explanation:

18-6=12

-18+6=-12

It is the opposite because rather than subtracting from a positive, you're adding to a negative.

Hope this helps :)

1. Write an algebraic expression for the word phrase ; the quotient of r and 12. A. r .12
B. r*12
C. r - 12
D r + 12

Answers

r ÷ 12 or r/12

Further explanation

Given the word phrase: the quotient of r and 12.

An algebraic expression for it is $\boxed{ \ r / 12 \ or \ r/12 \ or \ (r)/(12) \ }$

Notes:

The quotient is the ratio of two quantities to be divided or the number obtained by division. Synonyms for the quotient are proportion, ratio, or fractions.

An algebraic expression for the quotient of a and b is $\boxed{ \ a / b \ or \ a/b \ or \ (a)/(b) \ }$

'a' is called a dividend
'b' is called a divider
The quotient is the result derived after dividing the dividend by the divisor.

The quotient, a dividend, and a divisor represent the fundamental components of a division equation.

Another example:

A car requires 10 liters of fuel to travel 60 km. Determine the quotient of the distance of the car with fuel (in km/L).

The quotient (or ratio) is

$\boxed{ \ the \ distance / fuel \ consumption \ }$

$\boxed{ \ 60 \ km / 10 \ L \ }$

$\boxed{\boxed{ \ 6 \ km/L \ }}$

Consider the same method as follows.

$\boxed{ \ (the \ distance)/(fuel \ consumption) \ }$

$\boxed{ \ (60 \ km)/(10 \ L) \ }$

$\boxed{\boxed{ \ 6 \ (km)/(L) \ }}$

This means that the car can travel a distance of 6 km for every 1 L of fuel.

Kilometers per liter is a unit used to measure fuel economy and we see this as one example of the use of the quotient (or ratio).

Learn more

10 times as many as (blank) hundreds or 60 hundreds is (blank) thousands brainly.com/question/47704532
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100 is 1/10 of what? brainly.com/question/96535

Keywords: write an algebraic expression, for the word phrase, the quotient of r and 12, a dividend, a divisor, components of a division equation

The difference of a number and 4/ 3 is 11/3. what is the number

Answers

The difference of a number 5 and 4/ 3 is 11/3.

What is subtraction of fractions?

Subtracting fractions include the subtraction of two or more fractions with the same or different denominators. Like fractions can be subtracted directly but for unlike fractions we need to make the denominators same first and then subtract them.

Given that, the difference of a number and 4/ 3 is 11/3.

Let the unknown number be x.

Here, x-4/3 =11/3

x= 11/3+4/3 (Transpose 4/3 to RHS of the equation)

To add like fractions, add the numerators and keep the denominator same. That is

x= 15/3

x=5

Therefore, the unknown number is 5.

To learn more about the subtraction of fractions visit:

brainly.com/question/5220474.

#SPJ2

Answer:

Step-by-step explanation:

15/3 - 4/3 = 11/3

15/3 = 5

Joel earns $1,500 per month. If he spends $375 on rent each month, what percent of his income does he spent on rent?

Answers

So taking part over the whole month you will get % spent.

375/1500 = .25
Convert to percent by multiplying by 100.

.25 x 100 = 25%

He spends 25% of his income on rent each month.

A knitting shop orders yarn from three suppliers in Toronto, Montreal, and Ottawa. One month the shop ordered a total of 108 units of yarn from these suppliers. The delivery costs were $78, $53, and $66 per unit for the orders from Toronto, Montreal, and Ottawa, respectively, with total delivery costs of $6826. The shop ordered the same amount from Toronto and Ottawa. How many units were ordered from each supplier?

Answers

All you need to do is add them all together witch is basic addition

Doris put $4000 in a 2 year cd paying 6% interest, compounding monthly. after 2 years, she withdrew all her money. what was the amount of the withdraw?

Answers

For the answer to the question above asking what was the amount of the withdraw if Doris put $4000 in a 2-year cd paying 6% interest, compounding monthly. after 2 years, she withdrew all her money?

First year Interest: I(1) = 4000[(1.005)^12 - 1] = 246.71 = penalty for early withdrawal
Value after two years: P(2) = 4000(1.005)^24 = 4508.64

Value after 2 years with penalty: V = 4000(1.005^24 - 1.005^12 + 1) = $4261.93

Answer:

Value after two years: P(2) = 4000(1.005)^24 = **** 4508.64 ***

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