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2 years ago

7

(a-3b)^5 expand the binomial please

1 answer:

sergij07 [2.7K]2 years ago

6 0

Expand the binomial:
( a - 3 b ) ^5 =
= a^5 - 5 * a^4 * ( 3 b ) + 10 * a^3 ( 3 b ) ^2 - 10 * a^2 ( 3 b)^3 + 5 *a*( 3 b ) ^4 -
- ( 3 b )^5 =
= a^5 - 15 a^4 b + 90 a^3 b^2 - 270 a^2 b^3 + 405 a b^4 - 243 b^5

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Write the quadratic function in vertex form.<br><br> y = x2 - 2x + 5

Jlenok [28]

Vertex form formula: y = a(x-h)^2 +k, with vertex (h,k)
There are multiple ways to find the vertex. One way is to find the roots and then find the x value exactly in between them, because this parabola is symmetrical.

0 = (x - 3)(x + 2), so x = 3 and -2. The point directly in the middle is x = 1/2 = h

To find the y value of the vertex, plug in 1/2 to the equation.

(1/2)^2 - 2(1/2) + 5 = 4.25 = k

y = (x - 0.5)^2 + 4.25

4 0

3 years ago

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The ratio of M & M’s to raisins in a bag of trail mix is 3:5. If there are 36 M & M’s, how many raisins are there?

Iteru [2.4K]

The correct answer is 60 raisins. To get this answer you will write a proportion of M & Ms to raisins and create and equivalent ratio using the number 36.

After you have the proportion set up, you will use cross products to solve for the number of raisins.

You can also use equivalent ratios to find the number of raisins.

Both of these strategies are shown in the attached picture.

4 0

2 years ago

Which function has a vertex on the y-axis? f(x) = (x – 2)2 f(x) = x(x + 2) f(x) = (x – 2)(x + 2) f(x) = (x + 1)(x – 2)

strojnjashka [21]

we know that

If the vertex is on the y-axis, then the x-coordinate of the vertex is equal to zero

we are going to verify the vertex of each one of the functions to determine the solution

Remember that

The equation in vertex form of a vertical parabola is equal to

$y=a(x-h)^{2} +k$

where

(h,k) is the vertex

if $a>0$ -------> the parabola open upward (vertex is a minimum)

if $a$ -------> the parabola open downward (vertex is a maximun)

<u>case A)</u> $f(x)=(x-2)^{2}$

This is a vertical parabola open upward

the vertex is the point $(2,0)$

therefore

The function $f(x)=(x-2)^{2}$ does not have a vertex on the y-axis

<u>case B)</u> $f(x)=x(x+2)$

$f(x)=x(x+2)=x^{2}+2x$

convert to vertex form

Complete the square. Remember to balance the equation by adding the same constants to each side.

$f(x)+1=x^{2}+2x+1$

Rewrite as perfect squares

$f(x)+1=(x+1)^{2}$

$f(x)=(x+1)^{2}-1$

the vertex is the point $(-1,-1)$

therefore

The function $f(x)=x(x+2)$ does not have a vertex on the y-axis

<u>case C)</u> $f(x)=(x-2)(x+2)$

$f(x)=(x-2)(x+2)=x^{2}-2^{2}$

$f(x)=x^{2}-4$

the vertex is the point $(0,-4)$

The x-coordinate of the vertex is equal to zero

therefore

The function $f(x)=(x-2)(x+2)$ has a vertex on the y-axis

<u>case D)</u> $f(x)=(x+1)(x-2)$

$f(x)=(x+1)(x-2)\\ \\f(x)= x^{2}-2x+x-2 \\ \\f(x)= x^{2} -x-2$

convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)+2= x^{2} -x$

Complete the square. Remember to balance the equation by adding the same constants to each side.

$f(x)+2+0.25= x^{2} -x+0.25$

$f(x)+2.25= x^{2} -x+0.25$

Rewrite as perfect squares

$f(x)+2.25= (x-0.50)^{2}$

$f(x)=(x-0.50)^{2}-2.25$

the vertex is the point $(0.5,-2.25)$

therefore

The function $f(x)=(x+1)(x-2)$ does not have a vertex on the y-axis

<u>the answer is</u>

$f(x)=(x-2)(x+2)$

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2 years ago

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1. Use a ratio box to solve this problem. Tammy saved nickels and

Mice21 [21]

Answer:

245

Step-by-step explanation:

let 'c' = total coins

2/7 = 70/c

2c = 490

c = 245

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2 years ago

Pls help? :( brainliest if correct

brilliants [131]

Answer:

Option C is the Correct Answer

6 0

2 years ago

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