-6x+5y=1
Solve for x
Move variable to the right side and change its sign: +5y
-6x=1-5y
Divide both sides of the equation by -6
-6x=1-5y
-6 -6
x=-1/6+5/6y
Substitute the given value of x into the equation 6x+4y=-10
6(-1/6+5/6y)+4y=-10
Solve for y
Distribute 6 through the parenthesis: 6(-1/6+5/6y)
-1+5y+4y=-10
Collect the like terms: 5y+5y
-1+9y=-10
Move constant to the right side and change its sign: -1
9y=-10+1
Calculate the sum or difference: -10+1
9y=-9
Divide both sides of the equation by 9
9y=-9
-9 -9
y=-1
Substitute the given value of y into the simplest equation: 6x+4y=-10
6x+4*(-1)=-10
Any expression multiplied by -1 equals its opposite: 4*(-1)
6x-4=-10
Move constant to right and change sign: -4
6x=-10+4
Calculate sum or difference: -10+4
6x=-6
divide both sides by 6
6x=-6
6 6
x=-1
The solution of the system is the ordered pair (x,y)
(x,y)=(-1,-1)
Check if the given ordered pair is the solution of the system of equations
-6*(-1)+5*(-1)=1
6*(-1)+4*(-1)=-10
Simplify the expression: -6*(-1)+5*(-1)=1
1=1
Simplify the expression: 6*(-1)+4*(-1)=-10
-10=-10
The ordered pair is the solution of the system of equations since both equations are true
(x,y)=(-1,-1)
HOPE THIS HELPS!!!
Answer:
Interior Angle: 165°
Exterior Angle: 15°
Step-by-step explanation:
So first you have to find the sum of all interior angles of a polygon with <u>24 sides</u>. This can be found using the formula:
sum = ( <em>n</em> - 2 ) * 180° where '<em>n</em>' is the number of sides.
When '<em>n</em> = 24' then the sum is:
sum = ( 24 - 2 ) * 180°
Simplify and solve.
sum = 22 * 180°
sum = 3960°
Since there are 24 sides to the polygon, there are 24 interior angles. <u>Assuming that this polygon is equilateral</u>, you can surmise that:
<em>Interior Angle</em> = sum° / <em>n</em> where n is the number of sides,
3960° / 24 = 165° = Interior Angle
Using that information, and combine it with the [Supplementary Angles Theorem] the exterior angle can be found by:
165° + x = 180°
Solve for x.
Answer:
c: g(x) is shifted 3 units to the right and reflected over the x-axis
Answer: Choice B
Simulated probability = 0.533 (approximate)
Simulated probability is larger than theoretical probability
======================================
Explanation:
Getting heads is written shorthand as a "0".
There are 8 copies of "0" in the list out of 15, so 8/15 = 0.533 is the approximate simulated probability.
Compare this to the theoretical probability 1/2 = 0.500 (assuming this is a fair coin)
The simulated probability (0.533) is larger than its theoretical counterpart (0.500)
Answer:
![\sqrt[3]{3140^2\pi}\approx 146.41\ ft^2](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B3140%5E2%5Cpi%7D%5Capprox%20146.41%5C%20ft%5E2)
Step-by-step explanation:
The volume of the cylinder is
where r is the base radius and H is the height.
Since 
and V=1570 cubic feet, then
![1570=\pi r^2\cdot \dfrac{r}{2},\\ \\1570=\dfrac{\pi r^3}{2},\\ \\r^3=\dfrac{3140}{\pi},\\ \\r=\sqrt[3]{\dfrac{3140}{\pi}}\ ft.](https://tex.z-dn.net/?f=1570%3D%5Cpi%20r%5E2%5Ccdot%20%5Cdfrac%7Br%7D%7B2%7D%2C%5C%5C%20%5C%5C1570%3D%5Cdfrac%7B%5Cpi%20r%5E3%7D%7B2%7D%2C%5C%5C%20%5C%5Cr%5E3%3D%5Cdfrac%7B3140%7D%7B%5Cpi%7D%2C%5C%5C%20%5C%5Cr%3D%5Csqrt%5B3%5D%7B%5Cdfrac%7B3140%7D%7B%5Cpi%7D%7D%5C%20ft.)
The area of its bottom floor is
![A_{floor}=\pi r^2=\pi\cdot \left(\sqrt[3]{\dfrac{3140}{\pi}}\right)^2= \sqrt[3]{3140^2\pi}\approx 146.41\ ft^2.](https://tex.z-dn.net/?f=A_%7Bfloor%7D%3D%5Cpi%20r%5E2%3D%5Cpi%5Ccdot%20%5Cleft%28%5Csqrt%5B3%5D%7B%5Cdfrac%7B3140%7D%7B%5Cpi%7D%7D%5Cright%29%5E2%3D%20%5Csqrt%5B3%5D%7B3140%5E2%5Cpi%7D%5Capprox%20146.41%5C%20ft%5E2.)
