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astraxan [27]
3 years ago
8

If f(x)=x^3-9x^2+11x+21f(x)=x 3 −9x 2 +11x+21 and x-3x−3 is a factor of f(x)f(x), then find all of the zeros of f(x)f(x) algebra

ically.

Mathematics
1 answer:
Ivanshal [37]3 years ago
6 0

Answer:

x = -1, 3, and 7

Step-by-step explanation:

Using grouping:

f(x) = x³ − 9x² + 11x + 21

f(x) = x³ − 9x² + 18x − 7x + 21

f(x) = x (x² − 9x + 18) − 7 (x − 3)

f(x) = x (x − 6) (x − 3) − 7 (x − 3)

f(x) = (x² − 6x) (x − 3) − 7 (x − 3)

f(x) = (x² − 6x − 7) (x − 3)

f(x) = (x + 1) (x − 7) (x − 3)

To use long division, see the picture.

The zeros are x = -1, 3, and 7.

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What is the equation of the line that passes through the point (6, 8) and has a slope 1/2
Korvikt [17]

Answer:

y=1/2x+5

Step-by-step explanation:

Plug it into the formula for a point and a slope.

(y-(y(subscript 1)))=(m)(x-(x(subscript 1)))

Y-8=1/2(x-6)

Then multiply the 1/2 to the x and -6. After you do that, move everything so that it has y by itself on the left. Your ending should be y=1/2x+5.

7 0
2 years ago
Anthony has two cube-shaped pots with an interior edge length of 8 inches and two cube-shaped pots with an interior edge length
weqwewe [10]

He will have left 154.75 inches³ after he fills each pot full of soil

Step-by-step explanation:

The formula of the volume of a cube is V = s³, where s is the length of its side.

Remember:

  • 1 foot 12 inches
  • 1 foot² = (12)² inches² = 144 inches²
  • 1 foot³ = (12)³ inches³ = 1728 inches³

∵ Anthony has two cube-shaped pots with an interior edge

  length of 8 inches

∴ s = 8

- use the formula of the volume

∴ The volume of each pot = (8)³ = 512 inches³

∴ The volume of the two pots = 512 × 2 = 1024 inches³

∵ He has another two cube-shaped pots with an interior edge

  length of 6.5 inches

∴ s = 6.5

∴ The volume of each pot = (6.5)³ = 274.625 inches³

∴ The volume of the two pots = 274.625 × 2 = 549.25 inches³

∵ He wants to fill each pot full of potting soil

- The volume of soil he uses to fill the 4 pots is equal the volume

  of the four pots

∵ The total volume of pots = 1024 + 549.25 = 1573.25 inches³

∴ The total soil he uses = 1573.25 inches³

∵ His bag of potting soil is one cubic foot

∵ 1 cubic feet = 1728 cubic inches

- To find the quantity of soil he not used subtract the total volume

    of the 4 pots from the volume of the soil in his bag

∴ The soil he will left = 1728 - 1573.25 = 154.75 inches³

He will have left 154.75 inches³ after he fills each pot full of soil

Learn more:

You can learn more about the word problems in brainly.com/question/10557938

#LearnwithBrainly

6 0
3 years ago
Can someone help me with rounding this problem to the tenth? id appreciate it
mezya [45]

4/13.6 = 0

(X/3)/4 = 24

x^2-(7*x)+12 > 0

(1/2)*x^2 = -7

(1/3)*p^2 = 1/4

My friend did this one let me know if it's right or wrong. <3

4 0
3 years ago
If sally got 28 questions correct and received 70% on the exam, how many questions were on the exam
Furkat [3]

Answer: 40

Step-by-step explanation:

Number of correct questions Sally got = 28 questions

Percentage of correct questions answered= 70% on the exam,

Total number of questions in the exam = Unknown

Let the total questions in the exam be represented as y.

Since Sally got 70% correctly, this will be:

70% of y = 28

70/100 × y = 28

0.7 × y = 28

0.7y = 28

Divide both side by 0.7

0.7y/0.7 = 28/0.7

y = 40

There are 40 questions in the exam.

7 0
3 years ago
Identify each function shown in the tables below as either linear or exponential
Gala2k [10]
Which table? I’ll answer you in the comments
6 0
3 years ago
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