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schepotkina [342]
3 years ago
12

Find two consecutive even integers such that the square of the second, decreased by twice the first is 52

Mathematics
1 answer:
Fiesta28 [93]3 years ago
8 0

Let the first integer be x. So, the next even number is x+2

Let's translate the formula: the square of the second is (x+2)^2, twice the first is 2x. So, the equation is

(x+2)^2 - 2x = 52

Expand the square to get

x^2+4x+4-2x = 52 \iff x^2+2x+4 = 52 \iff x^2+2x - 48 = 0

The solutions to this equations are

x = -8,\quad x = 6

So, the possible consecutive even numbers are

-8\text{ and } -6\quad\text{or}\quad 6\text{ and } 8

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Solve for a.<br><br> 5a - 2 = 23<br> a = ?
snow_tiger [21]
5a - 2 = 23.

First, take 5a - 2 = 23 and add 2 to each side

5a - 2 = 23
     +2    +2
5a = 25

now, divide each side by 5

5a = 25
/5      /5

a = 5
3 0
3 years ago
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Molly opened a savings account with a one‐time deposit of $100 that will be left in the account for at least 5 years. The saving
Anettt [7]

The amount of interest Molly will earn after 5 years on a deposit of \$100 compounded annually over 5 years is \$27.63

First, we need to find the future value of her investment, then we subtract the original deposit from it to get the amount of interest she will get at the end of 5 years.

The future value of an investment that is compounded annually is given by

A=P(1+r)^t

where

A=\text{Amount of money in Molly's account after 5 years}\\P=\text{Molly's initial deposit into her account}=\$500\\r=\text{The annual interest rate as a decimal}=0.05\\t=\text{The time the money is invested (in years)}=5

Substituting the available values into the formula and solving

A=100(1+0.05)^5=100(1.05)^5 \approx \$ 127.63

The interest Molly will earn after 5 years is

A-P=\$127.63-\$100=\$27.63

Therefore, the amount of interest Molly will earn after 5 years on a deposit of \$100 compounded annually over 5 years is \$27.63

Learn more about compound interest here: brainly.com/question/21270833

8 0
3 years ago
See attached picture ​
lions [1.4K]

Answer:

ok i see it

Step-by-step explanation:

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3 years ago
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Simora [160]
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8 0
3 years ago
How do I solve this using the Pythagorean theorem​
charle [14.2K]

Answer:

x=3

Step-by-step explanation:

First would need to convert the radical into a number.

And since if you have a perfect square of a radical it goes outside the square root sign, you would take the 3 and square it to make 9 and then take the 2 inside the square root sign and multiply so you have the square root of 18|

Since we have \sqrt{18} as the Leg c we would need to square it, squaring a square root sign would just cause them to be cancelled out and you being left with 18, afterwards find the square of 3, which is 9

18-9=9

square root of 9 = 3

3 0
3 years ago
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