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1 year ago

Find the sum of 10 x 2 + 7 x + 6 10x 2 +7x+6 and 6 x + 5 6x+5.

Mathematics

1 answer:

dusya [7]1 year ago

8 0

The sum of the given expression expressed as a quadratic equation is 10x^2 + 13x + 11

<h3>Sum of expressions</h3>

Expressions are equations separated by mathematical signs. This expressions are known to contains certain unknowns

Given the following expression

10x^2 +7x+6 and 6x + 5

We are to take the sum of both expression to have:

f(x) = 10x^2 +7x+6 + 6x + 5

Collect the like terms

f(x) = 10x^2 + 7x + 6x + 6 + 5

f(x) = 10x^2 + 13x + 11

Hence the sum of the given expression expressed as a quadratic equation is 10x^2 + 13x + 11

Learn more on sum of functions here: brainly.com/question/11602229

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3 years ago

Michael's bank contains only nickels, dimes, and quarters. There are 57 coins in all, valued at $4.55. The number of nickels is

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Answer:

10 dimes.

Step-by-step explanation:

Let n represent number of nickels, d represent number of dimes and q represent number of quarters.

We have been given that there are 57 coins in all. We can represent this information in an equation as:

$n+d+q=57...(1)$

We are also told that the value of all coins is $4.55. We can represent this information in an equation as:

$0.05n+0.10d+0.25q=4.55...(2)$

The number of nickels is 7 short of being three times the sum of the number of dimes and quarters together. We can represent this information in an equation as:

$n+7=3(d+q)...(3)$

From equation (1), we will get:

$d+q=57-n$

Substituting this value in equation (3), we will get:

$n+7=3(57-n)$

$n+7=171-3n$

$n+3n+7-7=171-7-3n+3n$

$4n=164$

$\frac{4n}{4}=\frac{164}{4}$

$n=41$

Therefore, there are 41 nickels in the bank.

$d+q=57-n...(1)$

$d+q=57-41...(1)$

$d+q=16...(1)$

$q=16-d...(1)$

Upon substituting equation (1) and value of n in equation (2), we will get:

$0.05(41)+0.10d+0.25(16-d)=4.55$

$2.05+0.10d+4-0.25d=4.55$

$6.05-0.15d=4.55$

$6.05-6.05-0.15d=4.55-6.05$

$-0.15d=-1.5$

$\frac{-0.15d}{-0.15}=\frac{-1.5}{-0.15}$

$d=10$

Therefore, there are 10 dimes in the bank.

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