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4 years ago

Expand and simplify 2(5x+4)+3(2x-1)

Mathematics

1 answer:

stepladder [879]4 years ago

8 0

2(5x+4)+3(2x-1)

Use the distributive property for both sets of parenthesis:

2(5x+4) = 2*5x + 2*4 = 10x+8

3(2x-1) = 3*2x - 3*1 = 6x-3

Now you have:

10x+8 + 6x-3

Now combine like terms:

10x + 6x = 16x

8-3 = 5

The final answer is 16x+5

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Nicki has 30 pencils. for every green pencil, she has 5 purple pencils. how many pencils of of each color could she have

Hatshy [7]

Answer:

Step-by-step explanation:

(1) P = 5G

(2) G + P = 30

Substituting (1) into (2) gives:

G + 5G = 30

6G = 30

G =5

So there are 5 green pencils.

Now using that in (1) gives us P = 5 x 5 = 25

So there are 5 green pencils and 25 purple pencils.

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3 years ago

A playground is being designed where children can interact with their friends in certain combinations. If there is 1 child, ther

mariarad [96]

<h2>Answer:</h2>

Recursive equation for the pattern followed is given by,

$a_{n}=a_{n-1}+(n-1)^{2}$

<h2>Step-by-step explanation:</h2>

In the question,

The number of interaction for 1 child = 0

Number of interactions for 2 children = 1

Number of interactions for 3 children = 5

Number of interaction for 4 children = 14

So,

We need to find out the pattern for the recursive equation for the given conditions.

So,

We see that,

$a_{1}=0\\a_{2}=1\\a_{3}=5\\a_{4}=14\\$

Therefore, on checking, we observe that,

$a_{n}=a_{n-1}+(n-1)^{2}$

On checking the equation at the given values of 'n' of, 1, 2, 3 and 4.

At,

n = 1

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{1}=a_{1-1}+(1-1)^{2}\\a_{1}=0+0=0\\a_{1}=0$

which is true.

At,

n = 2

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{2}=a_{2-1}+(2-1)^{2}\\a_{2}=a_{1}+1\\a_{2}=1$

Which is also true.

At,

n = 3

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{3}=a_{3-1}+(3-1)^{2}\\a_{3}=a_{2}+4\\a_{3}=5$

Which is true.

At,

n = 4

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{4}=a_{4-1}+(4-1)^{2}\\a_{4}=a_{3}+9\\a_{4}=14$

This is also true at the given value of 'n'.

Therefore, the recursive equation for the pattern followed is given by,

$a_{n}=a_{n-1}+(n-1)^{2}$

3 0

3 years ago

What is the slope intercept equation for this line?

adell [148]

Answer:

Option 3. y = 2x + 3

Step-by-step explanation:

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3 years ago

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shepuryov [24]

Answer:

Step-by-step explanation:

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3 years ago

-6(2+n) is greater than 72

Hitman42 [59]

Answer:

n > -14

Step-by-step explanation:

Firstly, you use the distributive property;

-12 - 6n > 72

Then, since 12 is negative, you add 12 to both sides;

-12 - 6n > 72

+12 +12

-6n > 84

Then you divide both sides by -6 to get n > -14.

Shoot, hold on; this is an edit; did you mean that 72 is greater than -6(2 + n) or did you accidentally flip the sign in the picture? Hopefully I did what you needed.

5 0

3 years ago

Read 2 more answers