All categories

4 years ago

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

Mathematics

1 answer:

Natali [406]4 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.

You might be interested in

How do you know if a graph is a linear function

Furkat [3]

Answer:

You know a graph is a linear function when the equation is in the format of y=mx+b

<u>mx is the slope</u>

<u>b is the y-intercept</u>

6 0

3 years ago

Suppose we want to express the point (2,3) in R2 as the solution space of a linear system of equations. (a) What is the smallest

kow [346]

Answer:

Step-by-step explanation:

Smallest number of equations required are:

$N=2(forR^2)$

Let equations are

$2x+3y=13\\7x+y=17$

Yes we can add one more equation

We can add infinite such equations so that solution remains same.

General form of such equations are called inconsistent equations

6 0

4 years ago

Paige was playing a trivia game where you gained points for correct answers and lost points for incorrect answers. At the start

victus00 [196]

Givens

Start = S = - 700

# Correct = C = 8

Value Correct = VC = 400

# Incorrect =I = 9

Value Incorrect =VI = - 600

Equation

Score = S + C*VC + I*VI Substitute

Solve

Score = -700 + 8*400 + 9(-600)

Score = -700 + 3200 - 5400

Score = - 700 - 2200

Score = - 2900 <<<<< Answer

5 0

3 years ago

4a. In a book store, for every 9 books sold, 13 magazines were sold. If they had a 572 sales, how many of the sales were for boo

topjm [15]

Answer:

234 books.

Step-by-step explanation:

You need to set up a proportion. Be careful to note what it looks like and the explanation that follows.

9 books 13 magazines

======= = ===========

x 572 - x Cross multiply

What you want is the number of book sales from the proportion.

However all you have is the ratio of books to magazines. So you have to set up the total sales to magazines, which is a bit awkward. 572 - x is the number of magazine sales.

9*(572 - x) = 13x Remove the brackets on the left.

5148- 9x = 13x Add 9x to both sides.

5148 = 13x + 9x Transpose and add the right.

22x = 5148 Divide by 22

x = 5148/22

x = 234

234 books were sold.

5 0

3 years ago

How do you begin to solve x^3-3x^2 > x-3?

aliya0001 [1]

For any polynomial, first check to see if it factors. Then you can set each factor equal to zero.
$x^3 -3x^2 -x+3 \ \textgreater \ 0 \\ \\ x^2 (x-3) - (x-3) \ \textgreater \ 0 \\ \\ (x^2 -1)(x-3) \ \textgreater \ 0 \\ \\ (x-1)(x+1)(x-3) \ \textgreater \ 0$

The three zeros are -1,1,3

Next plug in values in each interval between zeros to test whether its greater than 0.

Try x values: -2,0,2,4

x = -2 yields a negative result, the interval x< -1 is Not a solution.

x = 0 yields a positive result, the interval -1
x = 2 yields a negative result, the interval 1
x = 4 yields a positive result, the interval x>3 IS a solution

4 0

3 years ago