-2y + 8
348
117
7
21in.
Step-by-step explanation:
This is a good bit of work but lets do it.
Starting with 1 :
We need to distribute :
-2(y-4)
To do this we need to multiply the outside of the ( ) by the inside, one by one.
So :
-2(y-4)
We do :
-2 × y
and
-2 × -4 (Negative multiplied by a negative is a positive.)
to get
-2y + 8
Now #2
We need to evaluate an algebraic expression by taking what we know and plugging it in and then solving.
So we know :
a = 4
b = 6
And our equation is :
6a + 3b²
So we can plug in our a = 4 and the b = 6 to get rid of the numbers.
If we do this we now get :
(6 x 4) + (3 x 6)²
Now we can solve :
(6 x 4) + (3 x 6)²
24 + 18²
24 + 324
=
348
Moving onto 3 :
We have to find a percent. How I like to start these is actually find what 5% is in this whole and the multiply to get our answer.
So what we know is the whole is 180. And we need to find 65%
So what I want to do is find 5% of 180. I first want to find out how many 5%'s go into 100%. To do this we can simply do 100 / 5 to get 20.
So 5% can go into 100% 20 times.
So in this case all we need to do is take our whole (180) and divide it by the amount 5 can go into 100 for the % (20).
So:
180 / 20
=
9
So now we know 5% of 180 is 9.
But we need to find 65%. So basically all we need to do is find how many times 5% go into 65% and then multiply that by 9 (How much 5% is).
To find how many times 5 goes into 65 we can divide.
65/5
=
13
So we take 13 and multiply by the value of 5 (9)
13 x 9
=
117
And that is it, 65% of 180 is 117
4 is very very simple.
Basically absolute value is literally how far a number is from 0.
So we need to find how far away 7 is from 0.
You can do most likely do it in your head but literally all you need to do is write the number in positive form. Cause depending on the -/+ of the number you will always add or subtract by itself to get to 0. And an absolute value will always be a positive value. So we just take that info and find that the absolute value of :
|-7 | = 7
And onto the last one is the area of a triangle.
To find this lets first go over the formula of a triangle :
A = B x H x 1/2
or in full terms
Area = base x height x 1/2
So basically what we first need to do is find the base and the height and the multiply the two together.
Base = 6in.
Height = 7in.
6 x 7
=
42
Now that we have this we need to multiply by 1/2. Which may be confusing but this is literally the same as dividing by 2. We are essentially splitting the number in half.
So:
42 x 1/2
or
42/2
=
21in.
And that is it! That is your final answer for that.
I hope all of these help!
If you have any questions or are confused feel free to comment or message me.
