Multiply the variable k times 4 would give you 4k.
Then cross multiply 14x8 = 112
Therefore, you would have 4k = 112.
Divide 112 by 4 to get your answer!
The equation y = -x^2+6x+5 is really the equation y = -1x^2+6x+5. It is in the form y = ax^2 + bx + c where
a = -1
b = 6
c = 5
We will use 'a' and 'b' in the formula below
h = -b/(2a)
h = -6/(2*(-1))
h = -6/(-2)
h = 3
The h refers to the x coordinate of the vertex. Since we know the x coordinate of the vertex (is 3), we can use it to find the y coordinate of the vertex
Simply plug x = 3 into the original equation
y = -x^2 + 6x + 5
y = -(3)^2 + 6(3) + 5
y = -(9) + 6(3) + 5
y = -9+18+5
y = 14
This is the k value, so k = 14.
In summary so far, we have a = -1, h = 3 and k = 14. Plug all this into the vertex form below
y = a(x-h)^2 + k
y = -1(x-3)^2 + 14
y = -(x-3)^2 + 14
Therefore the vertex form equation is y = -(x-3)^2 + 14
So when x = 3, the paired y value is y = 14. The point (x,y) = (3,14) is a point on the parabola. This point is either the highest or lowest point.
How can we figure out if it's the highest or lowest point? By looking at the value of 'a'. Notice how a = -1 and this is less than zero. In other words, a < 0
Since a < 0, this means the parabola opens downward forming a "frown" so to speak. That's one way to remember it: negative 'a' leads to sad face.
Anyways, this parabola opening downward means that the vertex is the highest point.
So (3,14) is the vertex
The maximum is y = 14.
Answer:
5/3 x + 4 = 2/3 x Multiplying both sides by 3
5 x + 12 = 2 x
3x = -12
x = -4
Step-by-step explanation:
Answer:
15°C
Step-by-step explanation:
Use the following formula to convert Fahrenheit to Celsius:
![C=\frac{5}{9}(F-32)](https://tex.z-dn.net/?f=C%3D%5Cfrac%7B5%7D%7B9%7D%28F-32%29)
Substitute the value for the variable and solve for C.
![C=\frac{5}{9}(59-32)\\C=\frac{5}{9}(27)\\C=15](https://tex.z-dn.net/?f=C%3D%5Cfrac%7B5%7D%7B9%7D%2859-32%29%5C%5CC%3D%5Cfrac%7B5%7D%7B9%7D%2827%29%5C%5CC%3D15)
Therefore, 59°F is equivalent to 15°C.
Answer:
![v=s-u+t](https://tex.z-dn.net/?f=v%3Ds-u%2Bt)
Step-by-step explanation:
Hi there!
![s=u-t+v](https://tex.z-dn.net/?f=s%3Du-t%2Bv)
Our goal is to isolate <em>v</em> on one side of the equal sign.
Subtract <em>u</em> from both sides:
![s-u=u-t+v-u\\s-u=-t+v](https://tex.z-dn.net/?f=s-u%3Du-t%2Bv-u%5C%5Cs-u%3D-t%2Bv)
Add <em>t</em> to both sides to isolate <em>v</em>:
![s-u+t=-t+v+t\\s-u+t=v\\v=s-u+t](https://tex.z-dn.net/?f=s-u%2Bt%3D-t%2Bv%2Bt%5C%5Cs-u%2Bt%3Dv%5C%5Cv%3Ds-u%2Bt)
I hope this helps!