Ask question

Ask question

All categories

3 years ago

9

The sum of three numbers is 83. The first number is 8 more than the second. The third number is 3 times the second. What are the

numbers?

1 answer:

Brut [27]3 years ago

6 0

Answer:

23, 15 and 45

Step-by-step explanation:

a+b+c = 83

a = b + 8

c = 3*b

(b+8) + b + 3*b = 83

5*b + 8 = 83

5*b = 75

b = 15

a = b + 8 = 15 + 8 = 23

c = 3*b = 3*15 = 45

Verification

a+b+c = 23 + 15 + 45 = 83; correct

You might be interested in

A wooden log 10 meters long is leaning against a vertical wall with its other end on the ground. The top end of the log is slidi

Andre45 [30]

Answer:

Step-by-step explanation:

This is a related rates problem from calculus using implicit differentiation. The main equation is Pythagorean's Theorem. Basically, what we are looking for is $\frac{dx}{dt}$ when y = 6 and $\frac{dy}{dt}=-2$ .

The equation for Pythagorean's Theorem is

$x^2+y^2=c^2$ where x and y are the legs and c is the hypotenuse. The length of the hypotenuse is 10, so when we find the derivative of this function with respect to time, and using implicit differentiation, we get:

$2x\frac{dx}{dt}+2y\frac{dy}{dt}=0$ and divide everything by 2 to simplify:

$x\frac{dx}{dt}+y\frac{dy}{dt}=0$ . Looking at that equation, it looks like we need a value for x, y, $\frac{dx}{dt}$ and $\frac{dy}{dt}$ .

Since we are looking for $\frac{dx}{dt}$ , that can be our only unknown and everything else has to have a value. So what do we know?

If we construct a right triangle with 10 as the hypotenuse and use 6 for y, we can solve for x (which is the only unknown we have, actually). Using Pythagorean's Theorem to solve for x:

$x^2+6^2=10^2$ and

$x^2+36=100$ and

$x^2=64$ so

x = 8.

NOW we can fill in the derivative and solve for $\frac{dx}{dt}$ .

Remember the derivative is

$x\frac{dx}{dt}+y\frac{dy}{dt}=0$ so

$8\frac{dx}{dt}+6(-2)=0$ and

$8\frac{dx}{dt}-12=0$ and

$8\frac{dx}{dt}=12$ so

$\frac{dx}{dt}=\frac{12}{8}=\frac{6}{4}=\frac{3}{2}=1.5 m/sec$

7 0

3 years ago

Diego wants to buy a new TV. The TV costs $649.99 right now. She has a coupon for 20% off any

Vlad [161]

Answer:

$519.00

Step-by-step explanation:

The 20% off coupon takes $130.00 off the original price of the TV.

$649.99

- $130.00 =

$519.00

6 0

3 years ago

14 pies eaten in 2 minutes what the rate

NeTakaya

Rate : every minute 7 pies are eaten 7:1

7 0

4 years ago

Read 2 more answers

25 POINTS! WILL GIVE BRAINLIEST!

iVinArrow [24]

Answer:

I think the answer is A.

Step-by-step explanation:

A minute is 60 seconds so you would have to see how many times 5 sec and 6 sec goes into 1 minute in order to find out how many times they pass each other in 1 minute.

-I hope this helps!-

-Good luck!-

-Please mark as brainliest!-

-Please let me know if I got it correct or incorrect!-

5 0

3 years ago

Find the value of y.

Bas_tet [7]

Step-by-step explanations

explanation is in the image above hope this helps please mark me brainiest

8 0

2 years ago

Read 2 more answers