which of the following describes the roots of the polynomial function f(x)=(x-3)^4(x+6)^2

Answer:

The length of the ladder is 7.21 feet

Step-by-step explanation:

Let

y = Height of the wall

x = Distance between the wall and the ladder (bottom)

L = Length of the ladder

So, the given parameters are:

[tex]\frac{dy}{dt} = -2ft/s[/tex]

When [tex]x = 4; \frac{dx}{dt} = 3ft/s[/tex]

The ladder, the wall and the ground forms a right-angled triangle where the hypotenuse is the length of the ladder; So:

[tex]L^2 = x^2 + y^2[/tex]

Differentiate with respect to time

[tex]2L\frac{dL}{dt} = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]

The length of the ladder does not change with time. So:

[tex]2L*0 = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]

[tex]0 = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]

Rewrite as:

[tex]2x\frac{dx}{dt} =- 2y\frac{dy}{dt}[/tex]

Divide both sides by 2

[tex]x\frac{dx}{dt} =- y\frac{dy}{dt}[/tex]

Recall that:

[tex]\frac{dy}{dt} = -2ft/s[/tex] and  [tex]x = 4; \frac{dx}{dt} = 3ft/s[/tex]

So:

[tex]4 * 3 = -y * -2[/tex]

[tex]12 = 2y[/tex]

[tex]6 = y[/tex]

[tex]y = 6[/tex]

Substitute [tex]y = 6[/tex] and [tex]x =4[/tex] in: [tex]L^2 = x^2 + y^2[/tex]

[tex]L^2 =4^2 + 6^2[/tex]

[tex]L^2 =52[/tex]

[tex]L = \sqrt{52[/tex]

[tex]L = 7.21ft[/tex]

Answer:

y=2/3x+7

Step-by-step explanation:

y-y1=m(x-x1)

y-11=2/3(x-6)

y=2/3x-12/3+11

y=2/3x-4+11

y=2/3x+7

Answer:

384 ft²

Step-by-step explanation:

12x16x2=384

Answer:

20

Step-by-step explanation:

120*1/5= 24

120*1/3= 40

120*3/10= 36

120-24-40-36= 20

Answer:

1800.02 kilometers

Step-by-step explanation:

1 kilometer = 1000 meters

1800020 meters = 1800.02 kilometers

Answer:

x = 6

Step-by-step explanation:

8x + 7x = 90

15x = 90

15x/15 = 90/15

x = 6

Answer:

around 13.18

Step-by-step explanation:

the middle square is 2*2 = 4

the triangle then is 2^2 + 6^2 = 40  -> sqrt40 = 6.325

and then 2^2 + 2^2 = 8 -> sqrt8 = 2.828

4+6.325+2.828 = 13.18

Answer:

8

Step-by-step explanation:

because since it is a square all sides are the same length you can either add 2+2+2+2 or you can do 2x2=4x2 which equals 8

Answer:

D

Step-by-step explanation:

Answer:

1/2 of the possibilities are even number

Step-by-step explanation:

Add all of the sides together, you get 12, count on even numbers until you get to 12. 2,4,6,8,10,12. that's six numbers which is half of 12. so half of the possibilities are even.

Answer:

2

Step-by-step explanation:

6x2=12

6z=12=2

12/2=6

Answer:

a term

Step-by-step explanation:

Answer:

x = 8

The value of 'x' is 8

Step-by-step explanation:

2/3(8)=12

2/(24)=12

Good luck!!

Answer:

x ≤ 1

Step-by-step explanation:

8 + 4x [tex]\geq[/tex] 12

4x [tex]\geq[/tex] 12 - 8

4x ≥ 4

Dividing both sides by 4 gives;

x ≤ 1

Answer:

give me sec waitttttttt give me sec

9514 1404 393

Answer:

  z = 47 at (x, y) = (3, 8)

Step-by-step explanation:

In the attached graph, the inequalities are graphed as their opposites, so the feasible solution region is the white area of the graph. The dashed boundary lines are part of the feasible region. The vertex of the feasible region that is farthest from the origin is ...

  (x, y) = (3, 8)

The value of z there is 5·3 +4·8 = 47.

The maximum value of z is 47 at the point (x, y) = (3, 8).

Answer:

Step-by-step explanation:

Apply the Distributive Rule

3(6x+2) = 3·6x + 3·2 = 18x + 6

Answer:

164 ft squared

Step-by-step explanation:

Answer:

B) (5, -3)

Step-by-step explanation:

Answer:

44250

Step-by-step explanation:

delta math

Answer:

y = 8x

Step-by-step explanation:

Slope intercept form is y = mx + b

y = y coordinate

m = slope, rise over run

x = x coordinate

b = y-intercept, where the line crosses the y-axis.

y = mx + b

y = 80/10x + 0

y = 8x + 0

y = 8x

Answer:

y=-8x

Step-by-step explanation:

Answer-> the average weight of chipmunks is 87 grams. About half of the chipmunks weigh more than 87 grams

Answer:

D is correct

Step-by-step explanation:

Biologists studying wildlife in the state parks want to estimate the average weight of chipmunks. They measured the weights of 5 chipmunks from each of 10 parks. The mean of the data was 91 grams, and the median was 87 grams. Which predictions match the data?

About one-half of the chipmunks weigh more than 91 grams.

The average weight of the chipmunks is 87 grams.

About one-half of the chipmunks weigh more than 87 grams.

The average weight of the chipmunks is 91 grams.

Answer:

786240 different license plates.

Step-by-step explanation:

The required number of plates that can be used is 2,599,974.

Given that,
State-issued license plates use the scheme of one letter followed by five digits, how many plates could it used is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Maxium five-digit number = 99999
Total letters = 26
Number of plates = 26 × 99999 = 2,599,974

Thus, the required number of plates that can be used is 2,599,974.

Learn more about simplification here:

https://brainly.com/question/12501526

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Answer:

At most 5

At least 0

Step-by-step explanation:

22 - 17 = 5

You can't have no more than 5, and you can have none join at all.

Answer:

At the most, it will be 5

At least  it will be 0

You can't have anymore than 5, and you can have none join at all.

Step-by-step explanation:

22 - 17 = 5

You can't have anymore than 5, and you can have none meet at all.

Answer:

Step-by-step explanation:

y=-4x+2

Answer:

y=2x-4

Step-by-step explanation:

Becuase the x axis croses -4, so you would draw a line starting at the bottom through negative 4. Then since their is a positive 2 you would keep drawing the line on the untill you see a 2 which would be on the y axis.

Answer:

C

Step-by-step explanation:

Answer:

7

Step-by-step explanation: