what is the degree measure of f?

Answer:  

32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5

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Explanation:

Let's use Pascal's Triangle

In the row that starts with 1,5,... we have the values 1,5,10,10,5,1

These will be the coefficients of the terms.

Let x = 2a and y = 2b

We want to expand out (x+y)^5

Using pascals triangle, we get the following expansion

(x+y)^5 = 1x^5y^0+5x^4y^1+10x^3y^2+10x^2y^3+5x^1y^4+1x^0y^5

The numbers in bold are the coefficients 1,5,10,10,5,1 found earlier.

Note how the exponents for x start at 5 and count down to 0; while the y exponents start at 0 and count up to 5. For any term, the x and y exponents always add to 5 for the expansion of (x+y)^5. In general, the exponents of any term will add to n for (x+y)^n.

At this point, we plug in x = 2a and y = 2b

Since this will clutter things a bit, I'll do it term by term

So in the end, the expression (2a+2b)^5 expands out to

32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5

The binomial theorem uses the same basic idea, but instead of using Pascal's Triangle to get the coefficients, you'll use the nCr combination formula.

Answer: [tex](2a+2b)^5 =32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5[/tex].

Using Pascal's triangle we get:

[tex](x+y)^5 = 1x^5y^0+5x^4y^1+10x^3y^2+10x^2y^3+5x^1y^4+1x^0y^5[/tex]

Here, x = 2a and y = 2b

So the terms become:

[tex]1x^5y^0 = 1(2a)^5(2b)^0 = 1(32a^5)(1) = 32a^5\\5x^4y^1 = 5(2a)^4(2b)^1 = 5(16a^4)(2b) = 160a^4b\\10x^3y^2 = 10(2a)^3(2b)^2 = 10(8a^3)(4b^2) = 320a^3b^2\\10x^2y^3 = 10(2a)^2(2b)^3 = 10(4a^2)(8b^3) = 320a^2b^3\\5x^1y^4 = 5(2a)^1(2b)^4 = 5(2a)(16b^4) = 160ab^4\\1x^0y^5 = 1(2a)^0(2b)^5 = 1(1)(32b^5) = 32b^5\\[/tex]

Hence: [tex](2a+2b)^5 =32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5[/tex]

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Answer:

c 89+42x+42y

Step-by-step explanation:

On day 1 :

First Machine= 89 stickers

Second Machine= none

On day 2 :

First Machine= ? stickers ( if in 1min = 42stickers

x min=?

( x min/1 min × 42stickers)

=42x stickers.

Second Machine=?stickers ( if in 1min = 42stickers

y min=?

( y min/1 min × 42stickers)

=42y stickers.

Total = 89 + 42x + 42y

Answer:

Step-by-step explanation:

A,because it goes diagonally which (with the fraction) means that the fraction should be equal to the problem

Answer:

A

Step-by-step explanation:

I believe this is the right answer becasue all the other lines and curved (not constant) and the other goes in different directions.

Answer:

D.  7 1/2

Step-by-step explanation:

-3 divided by  (-2/5) = 7 1/2

Answer:

GCF=   2 x 5 x 11 = 110

LCM=   2 x 2 x 5 x 11 = 220

Step-by-step explanation:

Answer:

Circumcenter

Step-by-step explanation:

[tex]y=|x+1|+2[/tex]

also that's a huge blank.

Answer:

88 i believe

Step-by-step explanation:

Answer:

92

Step-by-step explanation:

Angle (x+1) is equal to 92 degrees, and x equals 91. If x equals 91, then (x+1) equals 92. (x+1) and angle y are equal angles, so therefore, you can determine that angle y is equal to 92 degrees.

-I got the question right on the test

Hope this helps!

Answer:500 ft.-65 ft.=435 ft.

Step-by-step explanation:435 ft. is your answer because the change of elevation goes down which means you subtract so I subtracted 500-65=435 feet

Answer:

the slope is 3/4

Step-by-step explanation:

Randomly pick two points

point 1 (0, -1)

point 2 (4, 2)

gradient = (y2-y1)/(x2-x1)

m = (2-(-1))/(4-0)

m = 3/4

A. f(x)=x+2 is a linear function.

Answer:

A

Step-by-step explanation:

A is a linear function because, x^2 would be a parabola, 2^x would also result in a parabola, and |2x| would be a v shape.

Answer:1

Step-by-step explanation:it’s one decimal

Answer:

Solving a system of inequalities is almost like solving a system of equations. Pretend that the inequality signs are equal signs for a moment. Then, solve the system for the two unknown variables just like how you would solve for in a system of equations.

But, there's a catch. If you divide both sides of the inequality by a negative number, you have to flip the inequality sign. For example, if you are trying to solve the inequality -x > 4 you would have to divide both sides of the equation by -1. We would get x < -4 (see how I switched the inequality sign from > to <).

Once you find the values of x and y (they will be an inequality), graph the solutions.

Answer:

(-3,1)

Step-by-step explanation:

(x,y)---->(x,-y)

(-3,-1)--->(-3,1)

Answer:

1. -9.  2.i cant see what all the options are but the slope is y= 1/2x -3

Step-by-step explanation:

Hope this helps :)

Answer:

1/2, 1/4

Step-by-step explanation:

Let the numbers be x and y.

Given, x=2y

1/x + 1/y = 6

plug in x=2y ,

1/2y+1/y = 6

Taking common denominator ,

(1+2)/2y = 6

2y = 3/6 = 1/2 => y=1/4

x = 2y = 2* 1/4 = 1/2

So, the numbers are 1/2 and 1/4

Answer:

I think 27 is the answer

Answer:

C= 66°

B= 74°

A= 35°

Step-by-step explanation:

sorry I don't have much time to explain- but I hope this answer helps

Answer:

y = 3.5x

Step-by-step explanation:

y=mx+b. given the points (0,0) and (2,7), you solve using y2-y1 / x2-x1 to find slope. This equals 7/2 which = 3.5. Then just put it into equation form of y=mx+b. But, our b is 0 so your equation just becomes y=3.5x

Answer:

Step-by-step explanation:

9.

a1=-35

d=a2-a1=-28-(-35)=7

a35=a1+(35-1)7

=-35+34×7

=-35+238

=203

Answer:

13÷10 5/6

7/8÷3 1/16

how many 1 3/5 inch books can fit on a

14 1/2 inch long book self

Step-by-step explanation:

Answer:

the missing angle is 45

180-135=45

Answer:

Negative Slope.

-7/5

Step-by-step explanation:

Decreasing from left to right.

x = 3- -2 = 5

y = -2 - 5 = -7

y = -7/5x + 11/5

Answer:

7/-5

Step-by-step explanation:

Answer: b.

Step-by-step explanation:

Answer:

<1 and <8 are alternate exterior angles

<4 and <6 and same said interior angles

<3 and <6 are alternate interior angles

Step-by-step explanation:

The correct options are 1) ∠ 1 and ∠ 8 are alternate exterior angles, 2) ∠ 4 and ∠ 6 are same side interior angles, 4) ∠ 2 and ∠ 8 are corresponding angles and 5) ∠ 3 and ∠ 6 are alternate interior angles, this is true.

The amount of space between two straight lines that have a common end point is called angle. Two angles can be related if certain conditions are met.

Given that, lines m and n are intersected by a transversal l, making angles 1, 2, 3, 4, 5, 6, 7 and 8

∠ 1 and ∠ 8 are alternate exterior angles, this is true.

∠ 4 and ∠ 6 are same side interior angles, this is true.

∠ 5 and ∠ 7 are vertical angles, no this is not true because these are making a linear pair angles.

∠ 2 and ∠ 8 are corresponding angles, this is true.

∠ 3 and ∠ 6 are alternate interior angles, this is true.

Hence, the correct options are 1, 2, 4, and 5

Learn more about angle relationships, click;

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Answer:

The maximum height of the rocket is 256 feet

Step-by-step explanation:

The vertex form of the quadratic function f(x) = ax² + bx + c is

f(x) = a(x - h)² + k, where

Let us use these rules to solve the question

∵ h(t) = -16t² + 128t

→ Compare it by the form of the quadratic function above

∴ a = -16 and b = 128

∵ a < 0

∴ The vertex (h, k) is a maximum point

∴ The maximum height of the rocket is the value of k

→ Use the rule of h above to find it

∵ h = [tex]\frac{-128}{2(-16)}[/tex] = [tex]\frac{-128}{-32}[/tex]

∴ h = 4

→ Substitute x in the equation by the value of h to find k

∵ k = h(h)

∴ k = -16(4)² + 128(4)

∴ k = -256 + 512

∴ K = 256

∴ The maximum height of the rocket is 256 feet

Answer:

-10

Step-by-step explanation:

If the equation is 2 x 3+4 x 2-3 x 2- 6(x)=  .  Than the equation would turn into  2 x 3+4 x 2-3 x 2- 6(3) which equals -10.