Answer:
![m\widehat{VU}=120^{\circ}](https://tex.z-dn.net/?f=m%5Cwidehat%7BVU%7D%3D120%5E%7B%5Ccirc%7D)
Step-by-step explanation:
The angle
forms arc
. The measure of this arc is twice the measure of angle
, since
is a point on the circle. Since
forms an arc
, we can set up the following equation:
.
Since arc TU represents half of a circle and there are 360 degrees in a circle, we can substitute the following values and solve for the measure of arc VU:
![\\2\cdot 30^{\circ}+\widehat{VU}=180^{\circ},\\60^{\circ}+\widehat{VU}=180^{\circ},\\m\widehat{VU}=\boxed{120^{\circ}}](https://tex.z-dn.net/?f=%5C%5C2%5Ccdot%2030%5E%7B%5Ccirc%7D%2B%5Cwidehat%7BVU%7D%3D180%5E%7B%5Ccirc%7D%2C%5C%5C60%5E%7B%5Ccirc%7D%2B%5Cwidehat%7BVU%7D%3D180%5E%7B%5Ccirc%7D%2C%5C%5Cm%5Cwidehat%7BVU%7D%3D%5Cboxed%7B120%5E%7B%5Ccirc%7D%7D)
Answer:
Step-by-step explanation:
This is a proportion question.
change 2.6 to a decimal. 2/6 = 1/3 = 0.3333333
change 3/5 to a decimal 3/5 = 0.6
3.3333 / 2.6 = x / 4 Cross multiply
4*3.33333 = 2.6x Combine the left.
13.33333= 2.6x Divide by 2.6
13.3333/2.6 = x
x = 5.128 spoons of syrup.
SF stands for either Science Fiction or San Fransico
X=-b/2a is the formula for finding the axis of symmetry
So x= -30/2(5)
X=-30/10
X=-3
Because the axis of symmetry is -3, we know where to place our line, and we also know that the parabola is open downwards, which means that the vertex will be maximum. To find the vertex, plug in your values with the axis of symmetry as a midway point. Plug that in for x and so you should have the following:
F(x)
Y(f(x) and y variables are interchangeable) =5(-3)^2-30(-3)+49
Solve for y(f(x))
5(-3)^2-30(-3)+49
(-3)^2=3^2
3^2*5+30*3+49
Multiply
3^2*5+90+49
Add numbers
3^2*5+139
9*5=45
45+139=184
Y=184
So, your vertex would be
(-3,184) and it would be maximum. From there you can plug in the rest of your table of values.