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3 years ago

Find a cubic function with the given zeros.

Mathematics

1 answer:

tester [92]3 years ago

5 0

The cubic function is $f(x)=x^3+3x^2-46x-168$

Option D is correct

Step-by-step explanation:

We need to find the cubic function with the given zeros -6,7,-4

If -6,7,-4 are zeros of the function then:

x=-6, x=7 and x=-4

=> x+6=0,x-7=0 and x+4=0

Multiplying these terms to find the cubic function:

(x+6)(x-7)(x+4)

Solving:

$(x+6)(x-7)(x+4)\\=(x+6)(x(x+4)-7(x+4))\\=(x+6)(x^2+4x-7x-28)\\=(x+6)(x^2-3x-28)\\=x(x^2-3x-28)+6(x^2-3x-28)\\=x^3-3x^2-28x+6x^2-18x-168\\Combining\,\,like\,\,terms:\\=x^3-3x^2+6x^2-28x-18x-168\\=x^3+3x^2-46x-168$

So, the cubic function is $f(x)=x^3+3x^2-46x-168$

Option D is correct

Keywords: cubic function

Learn more about cubic function at:

#learnwithBrainly

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Hitman42 [59]

Answer:

With replacement, there are 1600 possible outcomes.

Without replacement, there are 1560 possible outcomes.

Step-by-step explanation:

Chosen with replacement:

State is chosen, then put back in the group, then another state can be chosen. In both cases, there will be 40 possible outcomes, as the first taken state is placed back. So

40*40 = 1600

With replacement, there are 1600 possible outcomes.

Chosen without replacement:

State and chosen and is not replaced.

So, for the second state, there will be only 39 possible outcomes.

40*39 = 1560

Without replacement, there are 1560 possible outcomes.

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3 years ago

What is the equation of the line that passes through the point (-5,1) and has a slope of -1/5?

olchik [2.2K]

Answer:

x + 5y = 0

Step-by-step explanation:

y = mx + b

y = -1/5 x + b

1 = -1/5 (-5) + b

1 = 1 + b

b = 0

y = -1/5 x

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3 years ago

The height of the water in a tank decreased 3 inches each week due to evaporation. What is the change in the height of the water

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AlekseyPX

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3 years ago

Read 2 more answers

Solve the system and enter the smallest x-coordinate first

ankoles [38]

Answer:
(2,-3)(6,5)
Step-by-step explanation:
We can use substitution to get the equation: x^2-6x+5 = 2x-7
Solve:
x^2-6x+5 = 2x-7
x^2 = 8x-12
x^2-8x+12 = 0 (we now have a polynomial)
(x-6)(x-2) = 0 (set each equation to equal 0 and solve)
x-6 = 0 --> x=6
x-2 = 0 --> x=2
To get the Y coordinates:
y=2(2)-7 --> y = -3
y = 2(6)-7 --> y = 5

Check work:
5 = 6^2-6(6)+5 --> 5 = 36-36 +5 --> 5=5
-3 = 2^2-6(2)+5 --> -3 = 4-12+5 --> -3=-3

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2 years ago