Answer:
No solution.
Step-by-step explanation:
So we have the system of equations:
![x=5-2y\\4y=15-2x](https://tex.z-dn.net/?f=x%3D5-2y%5C%5C4y%3D15-2x)
We can solve this by substitution. Substitute the first equation into the second. Thus:
![4y=15-2(5-2y)](https://tex.z-dn.net/?f=4y%3D15-2%285-2y%29)
Distribute the right:
![4y=15-10+4y](https://tex.z-dn.net/?f=4y%3D15-10%2B4y)
Subtract 4y from both sides:
![0=15-10](https://tex.z-dn.net/?f=0%3D15-10)
Subtract the right:
![0=5](https://tex.z-dn.net/?f=0%3D5)
As you can see, this statement is not true. In other words, the system of equations have no solution (likely because the lines are parallel).
And we're done!
Answer:
v = 7
is the value for which
x = (-21 - √301)/10
is a solution to the quadratic equation
5x² + 21x + v = 0
Step-by-step explanation:
Given that
x = (-21 - √301)/10 .....................(1)
is a root of the quadratic equation
5x² + 21x + v = 0 ........................(2)
We want to find the value of v foe which the equation is true.
Consider the quadratic formula
x = [-b ± √(b² - 4av)]/2a ..................(3)
Comparing (3) with (2), notice that
b = 21
2a = 10
=> a = 10/2 = 5
and
b² - 4av = 301
=> 21² - 4(5)v = 301
-20v = 301 - 441
-20v = -140
v = -140/(-20)
v = 7
That is a = 5, b = 21, and v = 7
The equation is then
5x² + 21x + 7 = 0
Answer:
The volume of the kiosk is 72 m³.
Step-by-step explanation:
The volume of the kiosk is given by the sum of the volume of a cylinder (
) and the volume of a cone (
):
![V = V_{cy} + V_{c} = \pi r^{2}h_{cy} + \frac{1}{3}\pi r^{2}h_{c}](https://tex.z-dn.net/?f=%20V%20%3D%20V_%7Bcy%7D%20%2B%20V_%7Bc%7D%20%3D%20%5Cpi%20r%5E%7B2%7Dh_%7Bcy%7D%20%2B%20%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E%7B2%7Dh_%7Bc%7D%20)
Where:
r: is the radius of the cylinder and the cone = d/2 = 5/2 = 2.5 m
d: is the diameter = 5 m
: is the height of the cylinder = 3 m
: is the height of the cone = 2 m
Hence, the volume is:
![V = \pi (2.5 m)^{2}(3 m + \frac{1}{3}*2 m) = 72 m^{3}](https://tex.z-dn.net/?f=%20V%20%3D%20%5Cpi%20%282.5%20m%29%5E%7B2%7D%283%20m%20%2B%20%5Cfrac%7B1%7D%7B3%7D%2A2%20m%29%20%3D%2072%20m%5E%7B3%7D%20)
Therefore, the volume of the kiosk is 72 m³.
I hope it helps you!
Answer: 12/100
Step-by-step explanation:
You multiply 25 4 times to get to 100
You need to then multiply the 3 4 times.
Answer:
Step-by-step explanation:
2.7 is the answer just took the test