What is the multiple zero and multiplicity of f(x) = x3 − 8x2 + 16x?



multiple zero = −4; multiplicity = 2


multiple zero = 2; multiplicity = 4


multiple zero = 4; multiplicity = 2


multiple zero = 2; multiplicity = −4

The equation of the line which is parallel to the line 3x+4y=8 and passes through the point (2,-5) is y = -3/4x - 1/2.

The given equation is 3x+4y=8, which is a linear equation. To make this simpler, we can isolate 'y' to make it in the form 'y = mx + b', where 'm' is the slope. When we do this, we get y = -3/4x + 2, so the slope of this line is -3/4.

Next, we know that parallel lines have the same slope. Therefore, the equation of the line parallel to the given line and passing through (2, -5) will also have a slope of -3/4. Using the point-slope form of a line, which is y – y1 = m(x – x1), where (x1, y1) is a point on the line, and 'm' is the slope, we can substitute the given values.

Therefore, y - (-5) = -3/4(x - 2), simplifying this gives us the equation of our line: y = -3/4x - 1/2.

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Answer: 6

Step-by-step explanation:

y'' by implicit differentiation is y'' = -16x/5y^3.

To find y'' by implicit differentiation, we need to differentiate both sides of the equation .4x3 + 5y3 = 9 twice with respect to x.

First, we differentiate both sides once with respect to x to find dy/dx. This gives us:

12x^2 + 15y^2 (dy/dx) = 0

Next, we differentiate both sides once again with respect to x to find d^2y/dx^2 (y''). This gives us:

24x + 30y^2 (dy/dx) + 15y^2 (d^2y/dx^2) = 0

We can now solve for d^2y/dx^2 (y'') by substituting dy/dx from the first equation into the second equation. This gives us:

24x + 30y^2 (-12x^2/15y^2) + 15y^2 (d^2y/dx^2) = 0

Simplifying this equation, we get:

d^2y/dx^2 = -16x/5y^3

Therefore, y'' = -16x/5y^3.

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the line of the graph is vertical since both x coordinates are the same ( both are -2)

so the equation would be x = -2

Linear algebra

I've always had trouble with graphs and it's much better if the algebra is similar to arthemetic

Answer:

-8π + 32

6.8675

Step-by-step explanation:

So we know that the are of the square is 64, and we know that the equation for the are of the shaded region is Area of square - 1/4 area of circle with a radius of 4√2 - area of 90/45/45 triangle with side lengths of 8 and 8.

s = square area

c = circle area

t = triangle area

∆ = shaded region area

∆ = s - 1/4c - t

input the numbers that we have for those variables:

∆ = 64 - 1/4(100.53) - 32

∆ = 64 - 25.1325 - 32

∆ = 32 - 25.1325

shade region approximate ≈ 6.8675

or to get an exact answer in terms of pi

∆ = 64 - 1/4(32π) - 32

∆ = 32 - 8π

shaded region = -8π + 32

just added this because it is hard to pick out the actual answer in the other person's answer.

I would say that this person has lost out on 2 years salary while in school plus 5 year repayment period. Total amount divided over 5 years is:

( (2+5)(45,000) + 30,000 ) / 5 =

(7(45,000)+30,00)/5 = 69,000 salary

Answer:

69,000

Step-by-step explanation:

Given,

There is loss of 45,000 per year for two years,

So, the total lost = 2 × 45000 = 90,000

Also, the cost of school going = 30,000

∴ the total recovering amount = 90,000 + 30,000 = 120,000

If this amount must recover in 5 years or less than 5,

Then, the minimum recovering amount per year = [tex]\frac{120000}{5}[/tex] = 24,000

Now, the original salary per year  = 45,000

Hence, the new salary per year = original salary + recovering amount

= 45,000 + 24,000

= 69,000

Answer:

C

Step-by-step explanation:

Last month, more rain fell compared to two months ago, and there was less variation in the daily rainfall.

To determine whether more rain fell two months ago or last month, we need to compare the mean daily rainfall and the mean absolute deviation for both months. Two months ago, the mean daily rainfall was 9.4 cm with a mean absolute deviation of 3.5 cm. Last month, the mean daily rainfall was 11.5 cm with a mean absolute deviation of 1.6 cm.

Thus, based on this information, we can conclude that more rain fell last month. The mean daily rainfall was higher and the mean absolute deviation was lower. This indicates that there was less variation in the amount of rain that fell each day last month compared to two months ago.

The possible pairs that fulfil the statement → "The product of two consecutive even integers is 80" are -

(8, 10)

(- 10, - 8)

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given product of two consecutive even integers is 80.

Assume that the first integer is [n]. Then the second integer will be [n + 2]. According to the question, we can write -

n x (n + 2) = 80

n² + 2n = 80

n² + 2n - 80 = 0

n² + 10n - 8n - 80 = 0

n(n + 10) - 8(n + 10)

(n - 8)(n + 10) = 0

n = 8  and n = - 10

If → n = 8 then (n + 2) = 10.

If → n = - 10 then (n + 2) = -8.

Therefore, the possible pairs that fulfil the statement → "The product of two consecutive even integers is 80" are -

(8, 10)

(- 10, - 8)

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Final answer:

The consecutive even integers whose product is 80 are 8 and 10. This is found by setting up an equation for consecutive even integers and factoring the number 80.

Explanation:

The question is asking to find two consecutive even integers whose product is 80. When two numbers are consecutive even integers, they can be represented as n and n + 2, where n is an even integer. To find these numbers, we set up the equation n(n + 2) = 80.

First, we need to find two numbers that multiply to give 80. We can start by listing the factors of 80: 1 x 80, 2 x 40, 4 x 20, 5 x 16, 8 x 10. Since we are looking for even integers, we pick the pairs where both numbers are even: 4 x 20, 8 x 10. However, the numbers must also be consecutive even integers, which is the case for the pair 8 and 10, but not for 4 and 20.

Therefore, the pair of consecutive even integers that multiply to give 80 are 8 and 10.

5000 x (1+0.078/12)^54

5000 x (1.0065)^54

$7094.37

 Option A

x<-7

Given :

[tex]4 - (x + 2) < -3(x + 4)[/tex]

Explanation :

Solve the given inequality for x by applying algebraic properties

We use order of operation to simplify the left and right side of inequality

[tex]4- (x + 2) < -3(x + 4)\\4-x-2<-3x-12\\-x+2 < -3x -12\\Add\; 3x \; on \; both \; sides\\2x+2<-12\\Subtract\; 2\; from \; both \; sides\\2x<-14\\Divide \; both \; sides \; by 2\\x<-7[/tex]

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Answer:

C.)p ↔ (q ∧ r)

Step-by-step explanation:

I scored a 100 on my quiz

from x15 to x 25 is 4 - -16 = -20 degree change

25 -15 = 10000 feet

-20/10 = -2 degrees every 1000 feet

Answer: The  average rate of change of the function between x = 15 to x = 25  is -2 degrees Celsius per thousand feet and represents the rate of change of temperature per thousand feet.

Step-by-step explanation:

The average rate of change of a function y=f(x) from [tex]x_1\ to\ x_2[/tex]is given by :-

[tex]k=\frac{f(x_2)-f(x_1)}{x_2-x_1}=\frac{-6-4}{20-15}[/tex]

Now, by the given table the average rate of change of the function between x = 15 to x = 25 will be :_

[tex]k=\frac{-16-4}{25-15}=\frac{-20}{10}=-2[/tex]

Hence, the  average rate of change of the function between x = 15 to x = 25  is -2 degrees Celsius per thousand feet and represents the rate of change of temperature per thousand feet.