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-3(-4) = √144

If angle BAC = 120º then the perimeter of triangle ABC is 6 units.

Heyy! In scenarios like this, the \(a\) coefficient isn't \(1\), so I would either factor it using decomposition or use the quadratic formula.

here's a article on decomposition (https://tentotwelvemath.com/fmp-10/factors-and-products/factoring-a-trinomial-using-decomposition/)

here's a article on the quadratic formula (https://www.purplemath.com/modules/quadform.htm)

Hoped that helped! 

AnxiousLlama

We can find the roots, which you can check later, I use the quadratic formula and find the roots, 

$x = -31/4 - sqrt(969)/4$

$x = 2/(31 + sqrt(969))$

We know that the standard form of a quadratic is $(x - r_1)(x-r_2)$ solve it from here

We can setup an equation:

Let \(x\) be Austin's age. 

We can make this equation: \(x -3 = \frac{1}{3} * (x+15)\) , which simplifies to \(x=12\). 

Austin is 12 years old. 

Hope this helps! 

AnxiousLlama

Sparklingwater2  is almost correct.    

To get 2 you have to have 1,1   what you have done is perfect.

But to get 6 you have to have a 1 and a 6.  OR  a 6 and a 1.   Your answer for that bit will need to be doubled.

etc

I have done it and I also checked that my probabilities add to 1.  (And they do)  

This is a problem where you have to have the formula in mind to work backwards and solve the problem.

Basically, we know that the area of a triangle is:

A = 1/2 * B * H

Where we have to solve for B.

So, we can input the numbers we already have into the equation:

33.6 = 1/2 * 4 * B

And then we just use simple algebra to solve it.

33.6 = 2 * B

(Divide by two)

16.8 = B

So, the length of the base of the triangle is 16.8 inches.

Btw, which time zone r u in?

I understand, I will be posting more on here, thank you!

Thanks so much for the explanation and references, it really helps! :)

thx :)

So 2/3

Sorry, I missed 70

Here is my answer, based on what I see in the question:

Because Aaron works two times as fast as Michael, and he can finish a job in 1 hour, it stands to reason that if they were both working at the same pace, they would finish it in 30 minutes.

But, that isn't the question. The question states that Michael works 2 times slower than Aaron, so if only Aaron were working than it would take 1 hour and if both were working (but at the same pace) it would take 30 minutes.

Therefore, we have to choose the number in the middle, because we need to acknowledge the fact that Michael works 2 times slower.

Because of this, my answer would be 45 minutes.

Hope this helps :)

Because 1/3 of the spinner would be 1/3 of 12, we just have to computate that and find out which color takes up the amount of space that we get.

1/3 * 12 = 4

Because we got 4 as our answer, the color that covers 1/3 of the spinner would cover 4 sections.

This means that the color would be Indigo Blue

first find out how many there are:

1/2 x 32 + 5 = 16 + 5 = 21

21 = how many are not plain

32-21=11.

There are 11 plain popcorn balls. this means that the chance of choosing a plain is $\boxed{\dfrac{11}{32}}$

64/15=4 r 4

so he has to do it one extra time. so the answer is $\boxed{5}$

22x3/4=16 1/2

11x1/2=5 1/2

5 1/2+16 1/2=22

22x6.13=$\boxed{\$134.86}$

Hello!

You can graph it out with desmos. https://www.desmos.com

x intercepts are when y = 0, when y = 0, the x coordinates are -4 and 1. 

y intercepts are when x = 0, which is 4. 

https://www.varsitytutors.com/hotmath/hotmath_help/topics/axis-of-symmetry-of-a-parabola

Try to see if you can find the vertex and axis by yourself. :))

You can also see by graphing it in desmos. 

=^._.^=