PLEASE HELP Describe the graph of the function f(x) = x3 − 18x2 + 107x − 210. Include the y-intercept, x-intercepts, and the shape of the graph.

Answers

Answer 1

Answer: f(x) = x³ - 18x² + 107x - 210

X - Intercept: f(x) = x³ - 18x² + 107x - 210
   0 = x³ - 18x³ + 107x - 210
       0 = x³ - 7x² - 11x² + 77x + 30x - 210
       0 = x²(x) - x²(7) - 11x(x) + 11x(7) + 30(x) - 30(7)
         0 = x²(x - 7) - 11x(x - 7) + 30(x - 7)
   0 = (x² - 11x + 30)(x - 7)
   0 = (x² - 6x - 5x + 30)(x - 7)
   0 = (x(x) - x(6) - 5(x) + 5(6))(x - 7)
   0 = (x(x - 6) - 5(x - 6))(x - 7)
   0 = (x - 5)(x - 6)(x - 7)
   0 = x - 5   or 0 = x - 6 or 0 = x - 7
+ 5 + 5 + 6 + 6 + 7 + 7
   5 = x or    6 = x or    7 = x
Solution Set: {5, 6, 7}

Y - Intercept: f(x) = x³ - 18x² + 107x - 210
      f(x) = (0)³ - 18(0)² + 108(0) - 210)
      f(x) = 0 - 18(0) + 0 - 210
    f(x) = 0 - 0 - 210
    f(x) = 0 - 210
    f(x) = -210

Shape of the Graph: Odd Degree Polynomials With a Positive Leading Coefficient

Answer 2

Answer:

X - Intercept: f(x) = x³ - 18x² + 107x - 210

0 = x³ - 18x³ + 107x - 210

0 = x³ - 7x² - 11x² + 77x + 30x - 210

0 = x²(x) - x²(7) - 11x(x) + 11x(7) + 30(x) - 30(7)

0 = x²(x - 7) - 11x(x - 7) + 30(x - 7)

0 = (x² - 11x + 30)(x - 7)

0 = (x² - 6x - 5x + 30)(x - 7)

0 = (x(x) - x(6) - 5(x) + 5(6))(x - 7)

0 = (x(x - 6) - 5(x - 6))(x - 7)

0 = (x - 5)(x - 6)(x - 7)

0 = x - 5 or 0 = x - 6 or 0 = x - 7

+ 5 + 5 + 6 + 6 + 7 + 7

5 = x or 6 = x or 7 = x

Solution Set: {5, 6, 7}

Y - Intercept: f(x) = x³ - 18x² + 107x - 210

f(x) = (0)³ - 18(0)² + 108(0) - 210)

f(x) = 0 - 18(0) + 0 - 210

f(x) = 0 - 0 - 210

f(x) = 0 - 210

f(x) = -210

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Find the surface area of the cone in terms of pi.

Answers

Answer:

First option is the correct choice.

Step-by-step explanation:

$SA=\pi r^2+\pi r l\n\n=\pi \left(3\right)^2+\pi \left(3\right)\left(8\right)\n\n=33\pi \:ft^2$

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Dad is 4 times as old as his son Jim. In 10 years, Dad's age will be 20 years more than twice Jim's age. How old is Jim?If D = dad's age now and J = Jim's age now, which of the following systems could be used to solve the problem?

a. D = 4J and D + 10 = 2J + 20
b. D = 4J and D + 10 = 2(4J + 10) + 20
c. D = 4J and D + 10 = 2(J + 10) + 20

Answers

Let's focus on the "In 10 years" part

in 10 years
D will be (D + 10)
and J will be (J + 10)

"twice Jim's age" would then be 2(J + 10)
and
"20 years more than" that would be 2(J + 10) + 20

so
the answer with
D + 10 = 2(J + 10) + 20
would be your answer
that is, C.

Answer: The correct answer would be C:

Step-by-step explanation:

D=4J and D+10=2(J+10)+20

Solve #1 pls, I need to find the shortest side, median side, and longest side

Answers

Answer:

Shortest side = 39 cm.

Median side = 65 cm.

Longest side = 91 cm.

Step-by-step explanation:

The perimeter in total is 195 cm. The ratio of the sides are 3 : 5 : 7.

First, find how much parts there are as a whole, by combining the ratios:

3 + 5 + 7 = 15 parts.

Divide the total of parts from the total measurement:

195/15 = 13

Each part has the measurement of 13 cm.

1 part = 13 cm.

Use the following ratio to solve for each of the sides:

Shortest side: 3

3 x 13 = 39

Shortest side = 39 cm.

Median side: 5

5 x 13 = 65

Median side = 65 cm.

Longest side: 7

7 x 13 = 91

Longest side = 91 cm.

Check. Combine all side measurements together. They should equal 195:

39 + 65 + 91 = 195

(39 + 65) + 91 = 195

(104) + 91 = 195

195 = 195 (True).

Which expression can be used to convert 22 Australian dollars to US dollars assume 1.2 Australian dollar equals to US dollars

Answers

1 USD = 1.2 AUD, therefore you get the AUD if you multiply the USD by 1.2. You need the other way around, so AUD/1.2 = USD.

A total of 180 students went on a field trip. There were 3 buses. If each bus had the same number of students on it, how many students were on each bus? Explain how to solve using compatible numbers.