If the measure of arc EF=47 and the measure of angle ACD=55, determine the measure of angle ECF. I really need help with this, t
hank you!!
1 answer:
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Answer:
"complete the square" to put in vertex form
Step-by-step explanation:
It may be helpful to consider the square of a binomial:
(x +a)² = x² +2ax +a²
The expression x² +x +1 is in the standard form of the expression on the right above. Comparing the coefficients of x, we see ...
2a = 1
a = 1/2
That means we can write ...
(x +1/2)² = x² +x +1/4
But we need x² +x +1, so we need to add 3/4 to the binomial square in order to make the expressions equal:
_____
Another way to consider this is ...
x² +bx +c
= x² +2(b/2)x +(b/2)² +c -(b/2)² . . . . . . rewrite bx, add and subtract (b/2)²*
= (x +b/2)² +(c -(b/2)²)
for b=1, c=1, this becomes ...
x² +x +1 = (x +1/2)² +(1 -(1/2)²)
= (x +1/2)² +3/4
_____
* This process, "rewrite bx, add and subtract (b/2)²," is called "completing the square"—especially when written as (x-h)² +k, a parabola with vertex (h, k).
Answer:
Step-by-step explanation:
The formula one would use for finding the volume of a rectangular prism is as follows:
- Volume = length × width × height ,
With this in mind, let's plug in the given variables in the question for this formula.
?
- We don't know the height, but that's just fine. We will plug in all our values and isolate
.
- I'm leaving in units just because I want to show that units aren't just for show. They can be used when in doubt of how to go about your math.
- Notice, that the units on the left side cancel out, leaving only the unit
left next to the solution. In the same way, the units on the right side cancel out too, leaving only
If involving units only confuses you, like it does for me, you can remove them like so, you just need to know what units your solution uses instead of being able to come to the proper units by using math.