Hello, I need some help with this quadratic equation.

[Anna Barkley]

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!

 

[Deleted member 4993]

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]

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.)

 

[Steven G]

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

 

[JeffM]

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.

[MATH]\text {Let } x = \text {the number of numbers, and }\\ y = \text {mean of the numbers.}[/MATH]Two unknowns requires two equations.

You are told that

[MATH]y = x - 3.[/MATH] And

[MATH]y = \dfrac{70}{x}.[/MATH] WHY?

Now solve.

 

[JOwen56]

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.

 

[HenryTorres]

You're making a mess of things! Answer by demonstrating why, if the mean of x values is x-3 and their total is 70, x2 - 3x - 70 = 0.
Create a formula for the total of the numbers if there are x of them and their mean is x-3, and set it to 70. This will not include the variables you mentioned.

Then, one method for answering the next part is to factor the equation from (a), which is equivalent to (x-7) (x+10)=0.
Solve the x equation that has been factored appropriately. (Make sure your factoring is correct by multiplying it.)

 

[eddy2017]

I will try to answer Dr Peterson request for you.
(x-7) (x+10)=0. Solve the correctly factored equation for x. (Always check your factoring by multiplication.)
first I will simplify both sides of the equation.

X^2+3x−70=0

Then I will factor the left side of equation.

(x−7)(x+10)=0

Now, I will set factors equal to 0.

x−7=0 or x+10=0

x=7 or x=−10
shaking in my boots cos I just sit at the feet of these guys . just practicing factoring and in turn trying to help you modestly.

 

[JeffM]

let me venture this with a lot fear cos i sit at the feet of all these great tutors.
we know that the mean of n numbers is the sum of all divided by n, therefore the mean of x numbers will be....
''<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#x100;</mi><mo>=</mo><mfrac><mrow><msubsup><mo>&#x2211;</mo><mn>1</mn><mi>x</mi></msubsup><mo>=</mo><mn>1</mn><msup><mi>a</mi><mi>i</mi></msup></mrow><mi>x</mi></mfrac><mo>=</mo><mi>x</mi><mo>-</mo><mn>3</mn></math>''

What is all that nonsense supposed to mean?

 

[eddy2017]

What is all that nonsense supposed to mean?

sorry, i tried to do what i posted here in Latex but did not come out. i tried to factor the equation for her, as Doc Peterson suggested.

 

[JeffM]

Eddy This thread is two months old.

The way to invoke LaTeX here is to push the icon that looks like a calculator. But what you wrote does not look like LaTeX to me.

 

[eddy2017]

Tha

Eddy This thread is two months old.

The way to invoke LaTeX here is to push the icon that looks like a calculator. But what you wrote does not look like LaTeX to me.

Thank you Jeff. I did not know it. The thread is thzt old? But i don't see any final answer here.

 

[eddy2017]

Sorry about that. I see now. The poster did not follow thru with it. I didn't check the date.

 

[HallsofIvy]

Oh, heck. I've replied to threads that were 2 YEARS old!