Hello!
We can solve for the vertex by completing the square. Begin by factoring out 6 from the equation to simplify the process:
6(x² - 8x) - 54 = 0
To complete the square, we must look at the first two terms (x² - 8x).
Remember that squaring a binomial uses the format a² + 2ab + b². We are already given a² and 2ab², so solve for b:
-8 / 2 = -4. This is the value of b.
We can rewrite this as:
(x - 4)²
However, this produces +16 which much be taken into account. Substitute (x - 4)² into the original equation:
6(x - 4)² - 54 = 0
Multiply 16 by the term in the front and subtract to cancel out this term:
6(x - 4)² - 54 - (6 · 16) = 0
Simplify:
6(x - 4)² - 150 = 0
In this form, the vertex is given as:
a(x - h)² + k, where h = x-coordinate and k = y-coordinate of the vertex.
In this instance, h = 4 and k = -150, so the coordinates of the vertex are:
(4, -150)
Answer:
(5, 0)
Step-by-step explanation:
For the first line, we can isolate x by subtracting 5y on both sides.
x=5-5y.
Now we can use substitution on the second line!
-(5-5y)+6y=-5
= -5+5y+6y=-5
=-5+11y=-5
=11y=0
y=0
We subsitute y for the first line,
x+5(0)=5
x+0=5
x=5
We can check our work by plugging in x and y
5+5(0)=5 ✔
-5+6(0)=-5 ✔
Answer:
-59, -32, 0, 36
Step-by-step explanation:
Answer:
A.
Step-by-step explanation:
The formula for the volume of a cylinder is the formula for the area of the circle, times the height of the cylinder. The formula for the volume of a circle is,
Multiply that by the height to find the formula for the volume of a cylinder,
Where (pi) represents the value (3.1415), (r) represents the radius, and (h) represents the height of the cylinder. Now substitute in the given values, remember, this problem gives the diameter of the cylinder, divide that value by two to find the radius.
(x + 1)(x^2 + 2x - 1) + 2x
x^3 + 2x^2 -x + x^2 + 2x -1 + 2x
x^3 + 3x^2 + 3x -1