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ANTONII [103]
3 years ago
11

What are three consecutive integers whose product is 480 more than their sum?

Mathematics
1 answer:
Natali [406]3 years ago
4 0

Answer:

The three numbers are 7 8 and 9

Step-by-step explanation:

Givens

  • Let the first number be n - 1
  • Let the second number be n
  • Let the third number = n + 1

Equation

(n - 1)(n)(n + 1) - (n-1 + n + n+1) = 480

Solution

Multiply (n - 1) and (n + 1) = (n - 1)*(n + 1) = n^2 - 1

Multiply the second integer by the result of the first and third: n (n^2 - 1)

Add the three integers together: (x - 1) + (n - 1) + n = 3n  Combine these 2 steps

n(n^2 - 1) - 3n = 480 Remove the brackets

n^3 - n - 3n = 480

n^3 - 4n = 480

n^3 - 4n - 480 = 0

Graph

The graph shows that the intercept point is n =8. This is the only way I can see to solve this cubic. There are no other real roots.

Answer

n - 1 = 7

n = 8

n + 1 = 9

Check

Product 7*8*9 = 504

Sum = 7 + 8 + 9 = 24

504 - 24 = 480 Which checks.

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rusak2 [61]

Answer:

7:47

Step-by-step explanation:

Here are two ways of solving this:

The video will be half the time of 15:34, so you need to divide the time 15:34 by 2.

Method 1)

Use the tip. The video is 15 minutes and 34 seconds long.

Convert minutes to seconds: 15 * 60 = 900

Add 34 seconds to the 15 minutes: 900 seconds + 34 seconds = 934 seconds

The video is 934 seconds long.

Divide the total seconds by 2: 934/2 = 467

467 seconds = 420 seconds + 47 seconds = 7 minutes and 47 seconds

Answer: 7:47

Method 2)

Divide the minutes by 2 and divide the seconds by 2.

15 minutes and 34 seconds.

Divide minutes by 2: 15/2 = 7.5

Divide seconds by 2: 34/2 = 17

Now we need to add 7.5 minutes and 34 seconds.

0.5 minutes is half a minute, so it's 30 seconds.

7.5 minutes + 17 seconds =

= 7 minutes + 0.5 minute + 17 seconds

= 7 minutes + 30 seconds + 17 seconds

= 7 minutes + 47 seconds

= 7:47

Answer: 7:47

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What is the distance between (2,-6) and (-4,3)
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Oh okie so cute ☺️ cute lol
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The graph shows the heights, y (in centimeters), of a plant after a certain number of weeks, x. Donna drew the line of best fit
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Using the given linear function of best-fit, the most likely approximate height of the plant after 8 weeks would be of 7.4 centimeters.

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The line of best-fit goes through points (0,1) and (5,5). Point (0,1) means that the y-intercept is of b = 1. The slope is given as follows:

m = (5 - 1)/(5 - 0) = 4/5 = 0.8.

Hence the equation that gives the approximate height after x weeks is:

y = 0.8x + 1.

After 8 weeks, the expected height is:

y = 0.8 x 8 + 1 = 6.4 + 1 = 7.4 centimeters.

More can be learned about linear functions at brainly.com/question/24808124

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Slope of (7, -2) and (2, -6)
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Answer:

it's -8/5 because you subtract y2 from y1 and x2 from x1

Step-by-step explanation:

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