(3x+8) (4x+10) what is the length

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Answer 1

Answer: 12x^2+62x+80
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The gross salary was increased twice during the year. First by 8%, then again by 10%.Its final amount was 10,098. Calculate the amount of the original gross salary.

Answers

Answer:

$8,500

Step-by-step explanation:

Let the original gross salary be "X" dollars.

First, it was increased by 8%, which can be calculated as 1.08 times the original salary:

1.08 * X

Then, this new amount was increased by 10%, which can be calculated as 1.10 times the previous amount:

1.10 * (1.08 * X)

The final amount is given as $10,098:

1.10 * 1.08 * X = 10,098

Now, solve for X:

1.188 * X = 10,098

Divide both sides by 1.188 to find X:

X = 10,098 / 1.188

X ≈ 8,500

So, the original gross salary was approximately $8,500.

a ball is dropped from a height of 100 inches the ball bounces, each time reaching a lower and lower height. the height of each bounce is 75% of the previous bounce what height will the ball reach after bouncing four time? how many bounces does it take for the ball to reach a heigh of less than one inch?

Answers

After the 'n'th bounce, the ball returns to a maximum height of

   (100) times (0.75)^n .

-- After 4 bounces, the maximum height is (100) (0.75)^4 = 31.64 inches.

-- To look for the maximum height of 1 inch,    (100) (0.75)^x = 1

Let's take the log of each side: log(100) + x log(0.75) = 0

Subtract log(100) from each side: x log(0.75) = -log(100)

Divide each side by log(0.75) :     x = -log(100) / log(0.75).

log(100) = 2 . So ... x = -2 / log(0.75) = -2 / -0.124939 = 16.00785

So the ball returns to a slim hair more than 1 inch high on the 16th bounce,
and returns to definitely less than 1 inch high on the 17th bounce.

If a+b = 10 and ab= 16 . Find the value of a^2 - ab + b^2