Answer:
Its the last one: a translation 2 units right and 4 units down.
Step-by-step explanation:
To get from point E (1,3) to E' (3-1) you add 2 units to the x coordinate since the x-axis goes from left to right and moving to the right means its positive and then you subtract 4 from the y coordinate since the y axis is going up and down and when you move -4 points you move down 4 points. You do this to every other point get the new figure.
We can only solve it is equal to something
if we assume that it eausl zero, then if we factor it we can assume the factors eqal zero
xy=0, then assume x and y=0
so what we do is if we have
ax^2+bx+c
we factor a and take the factors closest together
then place them with the x
then factor c and chose the closest ones
then try them and see if it works
so if we had
6x^2+20x+16
6=2 times 3
(2x+ )(3x+ )
we know that they are both + because the middle terms is positive and the end terms is positive
16=4 times 4
(2x+4)(3x+4)=6x^2+12x+8x+16=6x^2+20x+16
th easy way to check is we know that teh end terms will be right since we made them that way
to check the middle terms
if we have
(ax+b)(cx+d)
to check what the middle term is we do
bcx+dax
and see if that equals the middle term
so
2. 6x^2+20x+16
6=2 times 3
(2x+ )(3x+ )
we know that they are both + because the middle terms is positive and the end terms is positive
16=4 times 4
(2x+4)(3x+4)=6x^2+12x+8x+16=6x^2+20x+16
facored is (2x+4)(3x+4)=0
2x+4=0
x=-2
3x+4=0
x=-4/3
3. 5x^2+21x+4
5=1 times 5 prime is nice since we only have 1 option
(x+ )(5x+ )
we know they are both pluss since middle and end term is positive
4=2 times 2
(x+2)(5x+2)
(2 times 5x)+(x times 2)=10x+2x=12x, we need 21 so this wrong
change end term
(x+4)(5x+1)
(4 times 5x)+(1 times x)=20x+x=21x correct
factore form
(x+4)(5x+1)=0
x+4=0
x=-4
5x+1=0
x=-1/5
4.
-7x^2+59x-24
-7=-1 and 7 or -7 and 1
we pick -1 and 7 since we want the middle term to be positive
(7x- )(-x+)
signs are differenc since end term is negaive
-24=8 and -3
(7x-3)(-x+8)
(7x times 8)+(-3 times -x)=56x+3x=59x
correct
(7x-3)(-x+8)=0
7x-3=0
x=3/7
-x+8=0
x=8
OK, so I am getting tired of this so I will just do the rest in factored form isnce you probably shoud have figured out how to do it from the previous examples
5. (x-3)(3x-5)
6. (x-1)(2x+13)
7. (x-2)(3x+8)
8. 2x^2+17x-20 cannot be factored but 2x^2+18x-20 can maybe typing mistake
9. (x+3)(11x-8)
answers:
2.(2x+4)(3x+4)
3.(x+4)(5x+1)
4.(7x-3)(-x+8)
5. (x-3)(3x-5)
6. (x-1)(2x+13)
7. (x-2)(3x+8)
8. 2x^2+17x-20 cannot be factored but 2x^2+18x-20 can maybe typing mistake
9. (x+3)(11x-8)
Step 1: Pick any two points
The points are represented as (x1,y1), (x2,y2).
where x1= -4, y1= -8, x2= 0, y2= 4
Step 2: Write out the formula of the equation to use
![\frac{y-y_1}{x-x_1}=\text{ }\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cfrac%7By-y_1%7D%7Bx-x_1%7D%3D%5Ctext%7B%20%7D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Step 3: Substituting the values and to get the equation
![\begin{gathered} \frac{y-(-8)_{}}{x-(-4)}=\text{ }\frac{4-(-8)}{0-(-4)} \\ \frac{y+8}{x+4}=\frac{4+8}{0+4} \\ \frac{y+8}{x+4}=\text{ }\frac{12}{4} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7By-%28-8%29_%7B%7D%7D%7Bx-%28-4%29%7D%3D%5Ctext%7B%20%7D%5Cfrac%7B4-%28-8%29%7D%7B0-%28-4%29%7D%20%5C%5C%20%5Cfrac%7By%2B8%7D%7Bx%2B4%7D%3D%5Cfrac%7B4%2B8%7D%7B0%2B4%7D%20%5C%5C%20%5Cfrac%7By%2B8%7D%7Bx%2B4%7D%3D%5Ctext%7B%20%7D%5Cfrac%7B12%7D%7B4%7D%20%5Cend%7Bgathered%7D)
![\begin{gathered} \frac{y+8}{x+4}=\text{ 3} \\ \text{Cross multiply} \\ y+8=\text{ 3(x+4)} \\ y+8=\text{ 3x+12} \\ \text{Collect like terms} \\ y=\text{ 3x+12-8} \\ y=\text{ 3x + 4} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7By%2B8%7D%7Bx%2B4%7D%3D%5Ctext%7B%203%7D%20%5C%5C%20%5Ctext%7BCross%20multiply%7D%20%5C%5C%20y%2B8%3D%5Ctext%7B%203%28x%2B4%29%7D%20%5C%5C%20y%2B8%3D%5Ctext%7B%203x%2B12%7D%20%5C%5C%20%5Ctext%7BCollect%20like%20terms%7D%20%5C%5C%20y%3D%5Ctext%7B%203x%2B12-8%7D%20%5C%5C%20y%3D%5Ctext%7B%203x%20%2B%204%7D%20%5Cend%7Bgathered%7D)
The equation that represents the graph is y= 3x+4.
Option A is the correct answer.
Answer:
This type of data is called Box and Whisker plots
Step-by-step explanation:
This type of data tells you the range of the data as well as the inner quartile range as it shows the minimum, maximum, median, and Q1 and Q3.
Let’s see, so x=6
The equations should be written out as
2(10) = 8(4) - 2(6)
The x is replaced by 6, since in this problem x equals 6, and thenceforth are the same. When solved:
20 = 32 - 12
Which means:
20 = 20
Which is correct.