Hello, I need some help with this quadratic equation.

Anna Barkley

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Apr 5, 2021
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I'm a bit confused when it comes to number 3.
Is 3 a) supposed to be (x-7) (x+10)?

Also, I'm thinking that b's solution is the answer to (x-7) (x+10).

Help is greatly appreciated, thank you!
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Subhotosh Khan

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I'm a bit confused when it comes to number 3.
Is 3 a) supposed to be (x-7) (x+10)?

Also, I'm thinking that b's solution is the answer to (x-7) (x+10).

Help is greatly appreciated, thank you!
View attachment 26231
Please share your work for part (a). Did you derive the equation shown? Please share work.

What did you mean by:

".....b's solution is the answer to (x-7) (x+10)"

Can you restate it another way? "(x-7) (x+10)" is a statement - does not have an "answer".
 

Dr.Peterson

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Nov 12, 2017
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11,107
I'm a bit confused when it comes to number 3.
Is 3 a) supposed to be (x-7) (x+10)?

Also, I'm thinking that b's solution is the answer to (x-7) (x+10).

Help is greatly appreciated, thank you!
View attachment 26231
You're getting things out of order.

The way to answer (a) is to show why, if the mean of x numbers is x-3, and their sum is 70, then x^2 - 3x - 70 = 0. To do that, write an expression for the sum of the numbers if there are x of them and their mean is x-3, and set that equal to 70. This will not involve the factors you wrote.

Then, one way to answer (b) is to factor the equation from (a), which turns out to be similar to (x-7) (x+10)=0. Solve the correctly factored equation for x. (Always check your factoring by multiplication.)
 

Jomo

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Dec 30, 2014
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(the sum of all the numbers)/x = x-3.
Then 3a is NOT (x-7) (x+10). It is not even an equation!
 

JeffM

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Sep 14, 2012
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6,181
First off do you see that x numbers must mean that x is a positive number.

Assign letters to the numbers you do not know.

\(\displaystyle \text {Let } x = \text {the number of numbers, and }\\
y = \text {mean of the numbers.}\)
Two unknowns requires two equations.

You are told that

\(\displaystyle y = x - 3.\) And

\(\displaystyle y = \dfrac{70}{x}.\) WHY?

Now solve.
 

JOwen56

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Feb 5, 2021
Messages
10
It may help the mean of x numbers is the arithmetic mean, otherwise known as the average. And their total is 70 means that when you add those numbers together that you are finding the average of, you get 70.
 
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