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Hunter-Best [27]
3 years ago
14

Six students are working to simplify the expression shown.

Mathematics
1 answer:
krok68 [10]3 years ago
6 0

<u>Equivalent and Fully Simplified:</u>

8+7x+4y

<u>Equivalent and not fully simplified:</u>

8+12x-5x+4y

15+7x+4y-7

<u>Note Equivalent:</u>

15-7x-4y

8+17x+4y

8+11y

Step-by-step explanation:

Given expression is:

15+12x-5x+4y-7

We will simplify the expression one by one

8+12x-5x+4y

8+7x+4y

Now we can categorize the expressions in boxes given below

<u>Equivalent and Fully Simplified:</u>

8+7x+4y

<u>Equivalent and not fully simplified:</u>

8+12x-5x+4y

15+7x+4y-7

<u>Note Equivalent:</u>

15-7x-4y

8+17x+4y

8+11y

Keywords: Expressions, simplification

Learn more about expressions at:

  • brainly.com/question/2131336
  • brainly.com/question/2150928

#LearnwithBrainly

<u></u>

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Given f(x) = x² - 10x + 22, what is the range of f?
adoni [48]

Answer:

[-3, ∞)

Step-by-step explanation:

There are many ways to find the range but I will use the method I find the easiest.

First, find the derivative of the function.

f(x) = x² - 10x + 22

f'(x) = 2x - 10

Once you find the derivative, set the derivative equal to 0.

2x - 10 = 0

Solve for x.

2x = 10

x = 5

Great, you have the x value but we need the y value. To find it, plug the x value of 5 back into the original equation.

f(x) = x² - 10x + 22

f(5) = 5² - 10(5) + 22

      = 25 - 50 +22

      = -3

Since the function is that of a parabola, the value of x is the vertex and the y values continue going up to ∞.

This means the range is : [-3, ∞)

Another easy way is just graphing the function and then looking at the range. (I attached a graph of the function below).

Hope this helped!

6 0
3 years ago
En red socks and ten blue socks are all mixed up in a dresser drawer. The 20 socks are exactly alike except for their colour. Th
Gennadij [26K]

Answer:

3 socks

Step-by-step explanation:

Given that, there are 10 red socks and 10 blue socks which are mixed up in the dresser drawer.

The socks are identical except the color.

We need to find out, the minimum number of socks to be taken out from the dark room so that there is at least a pair of matching socks comes out of the drawer.

Let us consider the cases:

First Two socks pulled out of the drawer.

Case 1: Both are red or both are blue.

In this case, the matching pair is ready.

But there can be other case as well.

Case 2:

One red and one blue color taken out.

Now, when we pull the third, there will be either red or blue.

That will make a pair.

Therefore, to cover up all the cases and to be certain to get a matching pair out of the drawer, <em>at least 3 socks must be taken out</em>.

So, the answer is:

We need to take out at least 3 socks.

5 0
3 years ago
What is 7/10 - 1/10 in its simplest form
Elenna [48]
3/5 cause you get the lowest common denominator
4 0
2 years ago
Read 2 more answers
13y-{-14y+[9y-(-8y+17)]}
Lesechka [4]

Answer:

Step-by-step explanation:

6 0
2 years ago
What are the answers to the questions below?
Tcecarenko [31]

Answer:

You have to follow PEMDAS or parenthesis, exponents, multiplication, division, addition, and subtraction. It's an order to solve equations. I listed the steps and the answers for you below :) I have throughly checked them so they should be correct! yw :D

Step-by-step explanation:

1. 5x + 4x - 6x = 24

9x - 6x = 24

3x = 24

24/3 = 8

<u><em>x = 8</em></u>

2. 8y + 5 - 4y + 1 = 46

8y - 4y = 4y

5 + 1 = 6

4y + 6 = 46

4y = 46 - 6

4y = 40

40/4 = 10

<u><em>y = 10</em></u>

<u><em></em></u>

3. 33 = 5 ( x + 8 ) + 3

33 =  5x + 40 + 3 <em>(because we distributed)</em>

33 = 5x + 43

5x + 43 = 33<em> (just rewriting it to make it easier)</em>

5x = 33 - 43

5x = -10

-10/5 = -2

<em><u>so x = - 2</u></em>

4. 2m + 3 ( m - 8 ) = 1

2m + 3m - 24 = 1

<em>we got 3m - 24 because we distributed the 3</em>

5m - 24 = 1

5m = 25

25/5 = 5

<em><u>m = 5</u></em>

<em><u /></em>

5. p + p - 2p + 4p = - 48

2p - 2p + 4p = - 48

4p = - 48

- 48 / 4 = - 12

<u><em>p = - 12</em></u>

<u><em></em></u>

6. 2 ( y + 5 ) + 3y = 25

2y + 10 + 3y = 25

5y + 10 = 25

5y = 25 - 10

5y = 15

15/5 = 3

<u><em>y = 3</em></u>

7. 1/4 h + 3/4 h + 1/2 h + 2 = 5

1/4 h + 3/4 h + 1/2 = 3/2 h

3/2 h + 2 = 5

3/2 h = 5 - 2

3/2 h = 3

<u><em>h = 2</em></u>

<u><em></em></u>

8. 60 = 4 ( k + 3 ) + 2 ( k - 3 )

60 = 4k + 12 + 2k - 6

4k + 12 + 2k - 6 = 60

6k + 6 = 60

6k = 60 - 6

6k = 54

<u><em>k = 9 </em></u>

<u><em></em></u>

9. - 2 ( d + 1.4 ) - 1.8 = 20.6

-2d + - 2.8 - 1.8 = 20.6

-2d - 2.8 = 22.4

-2d = 25.2

<u><em>d = - 12.6 </em></u>

<u><em></em></u>

10. 8 - 2 ( w + 4 ) = 10

8 + - 2 w + - 8 = 10

-2w + 9 + - 8 = 10

-2w = 10

10 / -2 = -5

<u><em>w = -5</em></u>

4 0
2 years ago
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