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3 years ago

Apply the distributive property to create an equivalent expression. 1/5(15+10k)

Mathematics

2 answers:

lara [203]3 years ago

7 0

3 + 2k

This is because multiplying by 1/5 is like dividing each term by 5

horrorfan [7]3 years ago

7 0

Answer: Equivalent expression is 3+2k.

Step-by-step explanation:

Since we have given that

$\dfrac{1}{5}(15+10k)$

As we have to use "Distributive property":

$a\times (b+c)=a\times b+a\times c$

So, it becomes

$\dfrac{1}{5}(15+10k)\\\\=\dfrac{1}{5}\times 15+\dfrac{1}{5}\times 10k\\\\=\dfrac{15}{5}+\dfrac{10k}{5}\\\\=3+2k$

Hence, equivalent expression is 3+2k.

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Free points to y'all. 1+1+1*0

DiKsa [7]

I think it’s probably 12

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3 years ago

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Mark has 17 coins that are dimes and quarters. The total value of the coins is $2.45. How many dimes does mark have?

seropon [69]

Answer: 12 dimes and 5 quarters

Step-by-step explanation: Let's start this problem by setting up a chart so we can organize our information that we're given in this problem.

Down the left side, we'll have our different types of coins. In this case dimes and quarters. Across the top we'll have our formula which is shown below.

Number of coins · value of each coin = total value

Now let's fill out our chart.

For number of dimes and quarters, we know that mark has a total of 17 dimes and quarters but we don't know how many of each he has. In fact, that's what the problem is asking.

So if we represent our number of dimes as x, we can call our number of quarters 17 - x.

The value of each dime is 10¢ and the value of each quarter is 25¢.

Our total value based on our formula is going to come from the first column times the second column. So the total value of our dimes is x times 10 or 10x and the total value of our quarters is 17 - x times 25 or 25 (17 - x).

Our goal in this problem will be to find x because x represents our number of dimes and the problem asks how many dimes does he have. If we know the number of dimes, we can easily find the number of dimes and we'll have our answer. However, we need an equation in order to find x.

It's important to understand that he information in this equation will always come from the last column of your chart, the total value column. So what do we know about the total value of our dimes and the total value of our quarters?

Well we know that the total value of all of our coins is $2.45. So if we add the total value of our dimes + the total value of our quarters, that should equal $2.45. So below the chart I added an additional box and I put 245 in it. Notice that I wrote 245 in terms of cents because our value of dimes and value of quarters is also written in terms of cents and we need to be constient.

So here's our equation.

10x + 25 (17 - x) = 245.

If we solve this, we get x = 12.

Going back up into our chart, remember that x represents our number of dimes so Mark has 12 dimes. To get his number of quarters, we take 17 - x which is 17 - 12 or 5 quarters and that's our answer.

I have also attached the chart that I have made below.

7 0

3 years ago

Evaluate the function f(x)=x^2+6x+2 at the given values of the independent variable and simplify.

____ [38]

Answer:

a) 18

b)x^2+10x+18

c)x^2 -6x+2

Step-by-step explanation:

This is a case of plugging in the value into f(x).

a) f(-8)= -8^2 + 6(-8) +2

f(-8)= 64 + (-48) +2

f(-8)=64 + (-46)

f(-8)=18

b) f(x+2)= (x+2)^2+6(x+2)+2

So here I'll take a break to explain what's going on, because x+2 is a binomial meaning two terms and it is being squared I have to multiply the whole thing by itself. Meaning: (x+2) x (x+2), this is also known as foiling!! and for the next part its distributing 6 into x and 2.

f(x+2)= x^2+4x+4+6x+12+2

I'll reorder it

f(x+2)= x^2+4x+6x+12+2+4

f(x+2)= x^2+10x+18

c) f(-x)= -x^2+6(-x) +2

f(-x)= x^2 -6x+2

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2 years ago

Please use the figure below to solve for both x and y

kkurt [141]

Answer:

x=10°

y = 12°

Step-by-step explanation:

<TSV = 5x + 4x = 90°

=> 9x = 90°

Divide by 9,

x = 10°

<RSU = 10y + 10° + 5x = 180°

=> 10y + 10° + 5*10° = 180°

=> 10y + 10° + 50° = 180°

=> 10y + 60° = 180°

Subtract 60° on both sides,

10y = 180° - 60° = 120°

Divide by 10,

y = 120° / 10 = 12°

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3 years ago

How many times can 27 go into 192

lutik1710 [3]

It can go into 192 7.1 times

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3 years ago

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