k(x) = 6x - 12
k(x) = 18
substitute:
6x - 12 = 18 <em> |+12</em>
6x = 30 <em> |:6</em>
<h3>x = 5</h3>
Answer:
The perimeter of the triangle is 40.
Step-by-step explanation:
Pythagorean Theorem: If x and y are the leg lengths of a right triangle, then r = √(x^2 + y^2) is the length of the hypotenuse. Alternatively, x^2 + y^2 = r^2.
The side lengths 2x, 4x - 1 and 4x + 1 are already arranged in ascending order. Thus, (2x^)2 + (4x - 1)^2 = (4x + 1).
Performing the indicated operations, we get:
4x^2 + 16x^2 - 8x + 1 = 16x^2 + 8x + 1. Simplify this first by combining like terms:
20x^2 - 16x = 16x^2, or
4x^2 - 16x = 0, or
4x(x - 4) = 0. Thus, x = 0 (which makes no sense here) or x = 4.
The perimeter of the rectangle is the sum of the three sides 2x, 4x - 1 and 4x + 1. Substituting 4 for x, we get
P = 8 + 16 - 1 + 16 + 1, or 40.
The perimeter of the triangle is 40.
<h2>
Hello!</h2>
We have to remember that absolute value functions have the following form:
![f(x)=|x|\left \{ {{x,if}x\geq0 \atop {-x,if}x](https://tex.z-dn.net/?f=f%28x%29%3D%7Cx%7C%5Cleft%20%5C%7B%20%7B%7Bx%2Cif%7Dx%5Cgeq0%20%5Catop%20%7B-x%2Cif%7Dx%3C0%7D%20%5Cright.)
It means that there is a positive and a negative slope lines,
Let's find the information that we need to graph a absolute value function:
First:
Finding the y-intercept,
![f(0)=2(0)+2=2](https://tex.z-dn.net/?f=f%280%29%3D2%280%29%2B2%3D2)
So, the y-intercept is (0,2)
Second:
Finding the two lines intercepts,
if x ≥ 0
![y=2*(x)+2=2x+2](https://tex.z-dn.net/?f=y%3D2%2A%28x%29%2B2%3D2x%2B2)
if x< 0
![y=2*(-x)+2=-2x+2](https://tex.z-dn.net/?f=y%3D2%2A%28-x%29%2B2%3D-2x%2B2)
Therefore,
If
, we have that:
![-2x+2=2x+2\\2-2=2x+2x\\0=4x\\x=0](https://tex.z-dn.net/?f=-2x%2B2%3D2x%2B2%5C%5C2-2%3D2x%2B2x%5C%5C0%3D4x%5C%5Cx%3D0)
![f(0)=-2(0)+2=2\\y=2](https://tex.z-dn.net/?f=f%280%29%3D-2%280%29%2B2%3D2%5C%5Cy%3D2)
So, both lines intercepts at (0,2).
Answer
$212
Step-by-step explanation:
to get this answer, you must find what 6% of 200 is, which can be calculated using this little equation here
percentage/100 x original price = sales tax
6/100 x 200= 0.06 x 200= 12
this gives you the sales tax, or the amount of money that was added onto the original price, all that's left to do is to add, so original price + sales tax
200+12= $212