answer:
x = 29
y = 29
z = 61
step-by-step explanation:
all angles in a triangle must equal 180 degrees.
we were already given the angle degree of 61 degrees so we must include that in our formula to determine the degree of y.
the line in the middle already gives us two more angles because they both are 90 degrees for being a perfect quarter turn.
so to figure out y,
we must add 61+90 and then subtract the sum of that from 180.
so, 61+90 = 150 and 180-151 = 29
therefore,
we can conclude that y = 29
now, to determine the degrees of x and z we do the same thing.
we already know one angle equals 90 degrees.
180-90 = 90
that concludes that x and z must have a sum of 90.
if we use our choices,
39+61 = 100 (no)
39+29 = 68 (no)
29+61 = 90 (CORRECT)
29+29 = 28 (no)
<em>therefore, x = 29 and z = 61</em>
<em></em>
<em>so, in total :</em>
<em>x = 29</em>
<em>y = 29</em>
<em>z = 61</em>
<em></em>
<em>hope this helps :)
</em>
<em>-audrey <3
</em>
We are given the following function:
![f(x)=x^2](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2)
We are asked to do the following tranformations:
1. Shift down 5 units and left 77 units.
First, to shift a function down a number "n" of units we follow the next rule:
![h(x)=f(x)-n](https://tex.z-dn.net/?f=h%28x%29%3Df%28x%29-n)
And, to shift a function "m" units to the left we use the following rule:
![h(x)=f(x+m)](https://tex.z-dn.net/?f=h%28x%29%3Df%28x%2Bm%29)
Applying both rules simultaneously we get:
![h(x)=(x+77)^2-5](https://tex.z-dn.net/?f=h%28x%29%3D%28x%2B77%29%5E2-5)
2. Reflect about the y-axis.
The rule to reflect a function about the y-axis is the following:
![r(x)=h(-x)](https://tex.z-dn.net/?f=r%28x%29%3Dh%28-x%29)
The means that we will change "x" for "-x" in the function we are going to reflect. Applying the rule we get:
![r(x)=(-x+77)^2-5](https://tex.z-dn.net/?f=r%28x%29%3D%28-x%2B77%29%5E2-5)
3. Compress vertically by a factor of 2.
To compress a function vertically by a factor "m" we multiply the entire function by 1/m, like this:
![g(x)=\frac{1}{m}r(x)](https://tex.z-dn.net/?f=g%28x%29%3D%5Cfrac%7B1%7D%7Bm%7Dr%28x%29)
Applying the rule we get:
![g(x)=\frac{1}{2}((-x+77)^2-5)](https://tex.z-dn.net/?f=g%28x%29%3D%5Cfrac%7B1%7D%7B2%7D%28%28-x%2B77%29%5E2-5%29)
And thus we get to the final function.
Answer:
12x-15
Step-by-step explanation:
A triangle has 3 sides
An equilateral triangle has 3 sides that are all the same length
The perimeter of a triangle is
P = s1+s2+s3
P = 4x-4 + 4x-5+4x-5
Combine like terms
P = 12x -15
Answer:
Pfffft only one. I went to California
Step-by-step explanation:
Answer:
x = 3 or x = 2 or x = -1 or x = -5
Step-by-step explanation:
Solve for x:
((x - 3) (x - 2) (x + 1) (x + 5))/x = 0
Multiply both sides by x:
(x - 3) (x - 2) (x + 1) (x + 5) = 0
Split into four equations:
x - 3 = 0 or x - 2 = 0 or x + 1 = 0 or x + 5 = 0
Add 3 to both sides:
x = 3 or x - 2 = 0 or x + 1 = 0 or x + 5 = 0
Add 2 to both sides:
x = 3 or x = 2 or x + 1 = 0 or x + 5 = 0
Subtract 1 from both sides:
x = 3 or x = 2 or x = -1 or x + 5 = 0
Subtract 5 from both sides:
Answer: x = 3 or x = 2 or x = -1 or x = -5