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4 years ago

What is the coefficient of the term x7y in the expansion of (x + y)^8?

1 answer:

3 0

The coefficient for x^7*y is equal to 8Choose7 which is 8!/7! which is 8, or answer b. Pascal's triangle may be used to capture this as well, or use the exponent as above.

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Amy has a piece of wood that measures 42 inches. The model shows the length remaining after she cut a piece from the 42-inch pie

Hitman42 [59]

Answer:

She has 42 pieces of wood each of 1 inch of length.

Step-by-step explanation:

Amy has 42 inches piece of wood.

She has to cut an inch.

After cutting pieces of inch each she counts the pieces to be 42.

Mathematically

Total length / unit lenght = Number of pieces

42 inches/ 1 inch= 42 pieces.

She has 42 pieces of wood each of 1 inch of length.

6 0

3 years ago

Martin is two years younger than three times his daughter Ada’s age. The sum of their ages is 54. If Ada’s age is given by a, th

Igoryamba

Answer:

Martin is 40 and Ada is 14

Step-by-step explanation:

Martin's age = m
Ada's age = a

Martin is two years younger than three times his daughter Ada’s age:

m = 3a - 2

The sum of their ages is 54:

m + a = 54

Solving this equation for m:

m = 54 - a

Eliminate m:

3a - 2 = 54 - a

Solve for a:

3a + a = 54 + 2
4a = 56
a = 56/4
a = 14

Find m:

m = 54 - 14 = 40

Martin is 40 and Ada is 14

8 0

3 years ago

A line passes through the points (4, 9) and (12, 20). What is the slope of the line?

Mashutka [201]

Answer:

$\frac{11}{8}$

Step-by-step explanation:

→ State the gradient formula

( y₂ - y₁ ) ÷ ( x₂ - x₁ )

→ Find x₁ , x₂ , y₁ and y₂

x₁ = 4 , x₂ = 12 , y₁ = 9 and y₂ = 20

→ Substitute in the values

$\frac{20-9}{12-4}$

→ Simplify

$\frac{11}{8}$

4 0

3 years ago

Sally is filling glass containers in the shape of cylinders with different colors of sand. Each cylinder has a radius of 4 inche

ryzh [129]

Part A.
We are given the total volume of the amount of sand she will want to fill
we are also given the shape and dimensions of the cylinders
Total volume of the sand = 1,000
Cylinder= radius 4 in, and height 8 in
the volume of a cylinder is V=πr^2h
We will solve for the volume of the cylinders
V=πr^2hV=π(4)^2*(10)
V = π (16) * (10)
V = π 160
The volume of the cylinders she wants to fill is 502.65 in^3
How many cylinders will she need
Well,
1000/502.65 ≈ 1.98
She will need two cylinder cans to fill with the 1,000 in^3 of sand

Part B.
To see if this is true, we find the half of the original cylinder's radius and height then solve for the volume and compare
V=πr^2h
The height and radius of the original cylinders were 4 r and 8h
we will find half of that which will be : 2 r and 4 h
Now solve for the volume V=πr^2h
V=π(2)^2* (4)
V=π (4)*(4)
V = π 16
V ≈ 50.26 inches ^3
The volume of the original cylinders was 502.65 in^3 and the volume of the new cylinders is 50.26 in^3... Clearly the volume of the new cylinders is NOT half of the original. Sally is not correct!

Hope this helps :)

7 0

3 years ago

Determine the Rate of Change for this equation.

Lesechka [4]

We are given equation of line 12x-4y+5=18.

We need to find the Rate of Change for this equation.

Please note: Rate of Change is the another name for Slope of an equation.

So, we need to find the slope of the given linear equation.

In order to find the slope(Rate of change) of the equation, we need to solve equation for y and make it in slope-intercept form y=mx+b.

We need isolate it for y on left side.

We have

12x-4y+5=18.

5 is added on left side of the equation.

We need to get rid 5 from left side first.

The reverse operation of addition is subtraction. So, we need to subtract 5 from both sides.

Subtracting 5 from both sides of the equation, we get

12x-4y+5-5=18-5

12x -4y = 13.

Now, we can see, we have 12x on both sides.

We need to get rid 12x from left side now.

Subtracting 12x from both sides, we get

12x-12x -4y = 13-12x

-4y = 13-12x.

-4 is in front of y, we can remove that -4 by dividing both side (each term) by -4.

We get

-4y/-4 = 13/-4-12x/-4.

On simplifying this step, we get

y = - 13/4 + 3x

Now, let us write this equation in slope-intercept form y=mx+b

y= 3x -13/4.

If we compare y= 3x -13/4 and y=mx+b, we can see that coefficents of x are m and 3.

Therefore, m=3.

m represents slope of the equation.

And slope is the another name of Rate of Change.

Therefore, Rate of Change of the given equation is 3.

5 0

4 years ago