The vertex form of
where:
We have:
substitute:
The vertex form of f(x):
The value of minimum is equal k.
Therefore:
When graph crosses y-axis, x=0
<span>-2x+2y=4
</span><span>-2*0+2y=4
2y=4
y=2
x=0, y=2,
so point is (0,2).</span>
Measure of the smaller angle is 75°
Step-by-step explanation:
- Step 1: Sum of supplementary angles is 180°. Given ratio of angles is 5:7.
Let angles be 5x and 7x.
⇒ 5x + 7x = 180
⇒ 12x = 180
⇒ x = 15
- Step 2: Calculate smaller angle which is 5x
⇒5x = 5 15 = 75°
Answer: The required equation is
Step-by-step explanation: We are given to write the following statement as an equation :
"The sum of one-third of a number, one-half of a number and twice the number is thirty-four".
Let the number be represented by x.
Then, one-third of the number is one-half of the number is and twice the number is
Therefore, as an equation, the given statement is written as:
Thus, the required equation is
No
There is not a common factor