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3 years ago

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Identify properties used in each step in rewriting the polynomial expression below: (x + 5) + 3(a + (6x)y) Step 1: (5 + x)+3(a +

(6x)y) Step 2:5 + (x + 3(a + (6x)y) Step 3:5 + (x + 3a + (18x)y) Step 4:5 + (x + 3a +18xy)

1 answer:

8090 [49]3 years ago

5 0

In step 1, the commutative property of addition is used since x + 5 is just equal to 5 + x
In step 2, the associative property of addition is used since x is grouped to the last term.
In step 3, the distributive property of multiplication is used since 3 is multiplied to the terms inside the parenthesis.
In step 4, multiplication is done.

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Nonlinear Systems of Equations

zheka24 [161]

The square root and cube root identities are proved.

According to the statement

we have to find that the use of the square root identity (x − y)2 = x2 − 2xy + y2

And use of cube root identity a3 + b3 = (a + b)(a2 − ab + b2).

So, For this purpose, we know that the

A. Let us assume the two conditions.

So,

2x + 3y = 6 -(1)

4x + 7y = 8 -(2)

Here we use elimination method

So, Multiply 4 with (1) and 2 with (2)

8x + 12y = 24

8x + 14y = 16

Now eliminate x from these equations

-2y = 8

here y is -4.

and the x become

2x + 3y = 6

2x -12 = 6

2x = 18

x = 9.

B. For the use of identity $(x- y)^{2} = x^{2} - 2xy + y^{2}$

Let us assume a number 26 and 28 then fill it in the condition then

$(28- 26)^{2} = 28^{2} - 2(28)(26) + 26^{2}$

Then

$(28- 26)^{2} = 784 - 1456 + 676$

$(28- 26)^{2} = 4$

And we have to prove the cube root identity then

The identity is

$a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2})$

Then let us assume the number 8 and 9 then

$a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2})$

$8^{3} + 9^{3} = (8 + 9)(8^{2} - 8*9 + 9^{2})$

$8^{3} + 9^{3} = (17)(64 - 72 + 81)$

$8^{3} + 9^{3} = (17)(73)$

$8^{3} + 9^{3} = (1241)$

Hence by this way we prove the square and cube root identities.

So, The square root and cube root identities are proved.

Learn more about square root and cube root here

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1 year ago

If the endpoints of `bar(AB)` have the coordinates A(9, 8) and B(-1, -2), what is the midpoint of `bar(AB)`?

alina1380 [7]

To solve this problem you must apply the proccedure shown below:

1. You have the following points given in the problem above:

$A(9,8)\\ B(-1,-2)$

2. To find the midpoint, you must apply the formula that is used for calculate it. This is:

$m=(\frac{x1+x2}{2}, \frac{y1+y2}{2} )$

Where:

$x1=9\\ x2=-1\\ y1=8\\ y2=-2$

3. Now, you must substitute these values into the formula for calculate the midpoint, as following:

$m=(\frac{9+(-1)}{2} ,\frac{8+(-2)}{2} )\\ m=(4,3)$

Therefore, the answer is: $m=(4,3)$

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3 years ago

Candace ate 3 over 4 cup of cereal. The box of cereal states that one serving of cereal is equal to 2 over 3 cup. Which fraction

choli [55]

Answer: Candace ate $\dfrac9{12}$ servings.

Step-by-step explanation:

Given: Candace ate $\dfrac34$ cup of cereal.

The box of cereal states that 1 serving of cereal = $\dfrac23$ cup.

i.e. 1 cup = $\dfrac32$ servings [Multiply $\dfrac32$ both sides]

⇒ $\dfrac{3}{4}$ cup = $\dfrac34\times\dfrac32$ servings

= $\dfrac9{12}$ servings [which is the number of servings she ate]

Hence, Candace ate $\dfrac9{12}$ servings.

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Answer:

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Step-by-step explanation:

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