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vagabundo [1.1K]
2 years ago
14

If $(ax+b)(2x+3)=20x^2+44x+21$, where $a$ and $b$ are two distinct integers, what is the value of the sum $a+b$?

Mathematics
1 answer:
sladkih [1.3K]2 years ago
6 0

Answer: 17

Step-by-step explanation:

Given: (ax+b)(2x+3)=20x^2+44x+21, where a and b are two distinct integers.

First simplify left hand side as

(ax+b)(2x+3)=ax\cdot \:2x+ax\cdot \:3+b\cdot \:2x+b\cdot \:3\\\\=2axx+3ax+2bx+3b\\\\=2ax^2+(3a+2b)x+3b

Then comparing left side and right side

2ax^2+(3a+2b)x+3b=20x^2+44x+21

we get 2a = 20 (coefficient of x^2) , and 3b = 21  (constant term)

⇒ a= 10 and b= 7

Then, a+b= 10+7=17

Hence, the value of sum a+b is 17.

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3 years ago
Sarah began the week with $2.60 in her lunch account. She deposited $20 on Monday, and then spent $4.75 each day that week for l
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The balance in her lunch account at the end of the day on Friday is -$1.15.

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The balance at the end of the week will be the result of adding up the initial balance with the amount deposited on Monday minus the total amount spent that week.

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3 years ago
The formula for compound interest is:
sveta [45]

Answer:

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Step-by-step explanation:

Given the following data;

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To find the future value, we would use the compound interest formula;

A = P(1 + \frac{r}{n})^{nt}

Where;

A is the future value.

P is the principal or starting amount.

r is annual interest rate.

n is the number of times the interest is compounded in a year.

t is the number of years for the compound interest.

Substituting into the equation, we have;

A = 500(1 + \frac{0.05}{365})^{365*5}

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3 years ago
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