lokiisnotdead

Hi guest!
 

This problem was a bit confusing for me - is "Ben and Daniel first met two years ago." extraneous information? It seems like it to me...

Well anyways, let's start.

We know that

\(B=20+D\) (since Ben is 20 years older than Daniel)

\(B-3=3D-3\) (since 3 years ago, Ben was thrice Daniel's age)

Now all we have to do it plug it in. 

\(B=20+D\)

\(B=3D\)

\(20+D=3D\)

\(D=10\)

\(D+3= \text{his age now}\)

Daniel is now 13.

Hi guest!

\( 3ab - 12a + 7b + \underline{~~~~}\)

So let's start off by noticing the signs. Since all the signs are positive except for -12a, that means that \(a\) has to be multiplied with a negative number. 

This is what we have so far: \((\text{_}a+\text{_})(\text{_}b-\text{_})\) (I'm using the blank spaces to represent numbers we don't know yet)

Now, we see that there is a \(7b\) term. What do we have to multiply \(b\) by to get \(7b\)? It's \(7\). So we can put \(7\) in the blank on the right of \(a\).

Now we have: \((\text{_}a+7)(\text{_}b-\text{_})\)

We also know that there is a \(3ab\) term. Since there is  \(-12a\) term, we have to multiply \(a\) by 3 since -12a is divisible by 3.

Now we have: \((3a+7)(\text{_}b-\text{_})\)

The only term we have to deal with is the \(-12a\) term. What do we have to multiply \(3a\) by to get \(-12a\)?  It's \(4\)! So we can put the 4 on the blank.

Now we have: \((3a+7)(b-4)\)

All we have to do now is multiply it all out!

3a*b=3ab

3a*4=-12a

7*b=7b

7*-4=-28

Adding all the terms together, we see that the quadratic is: \(3ab-12a+7b-28\)

So the blank is \(\boxed{-28}\)

I hope this helped you, guest!
If you have any questions, don't hesitate to ask!

:)

Hi guest!

hmmm that wasn't right.... :(

g(x)'s vertex is (-4,-5). 

So, the \(g(x)=(x+4)^2-5\).

Here's a good image that explains how I got the answer.

I hope this helped you!

:)

Hi guest!
 

We can start off by multiplying the pairs together:

1*1=1

1*-4i=-4i

2i*1=2i

2i*-4i=\(-8i^2\). We know that i^2 = -1. So -8i^2 = -8*-1=8

Now, let's add these all together.

1-4i+2i+8 = 9-2i.

I hope this helped you!

:)

Hi guest!

We know that the smaller triangle is a 30-60-90 triangle. Since the bottom side of that triangle is 1, we know that the hypotenuse of the smaller triangle is 2. 

Now, we can look at the bigger triangle. We can see that the bigger triangle is also a 30-60-90 triangle since one of its angles is 90-30=60. Since we already know that the shorter leg of the bigger triangle is 2, that means x=2(2). 

Therefore, x=4.

I hope this helped you!

:)

a number is divisible by 9 is you can add all the digits up and that number is divisible by 9. 

So, we can make the equation 3+2A+1= x (x has to be a multiple of 9)

We can't make x=9 because then A would have to be a decimal.

So, let's make x=18.

3+2A+1=18

4+2A=18

2A=14

A=7

I hope this helped you, guest!

:)

hmmm shadlow I think its 468/13 because x+4x+8x=13x.