First of all, we need to know what is the vertex means which is the maximum or minimum point of a parabola and the formula will be:
x=-b/2a
Where b and a from
f(x)=ax^2+bx+c
So do find which function has a vertex of origin. Let's find the vertex of all the function that we had:
f(x)=(x+4)^2
f(x)=(x+4)(x+4)
f(x)=x^2+8x+16
x=-b/2a
x=-8/2(1)
x=-8/2
x=-4
Not the right answer because the vertex needs to be origin which is x=0
f(x)=x(x-4)
f(x)=x^2-4x
x=-b/2a
x=-(-4)/2(2)
x=4/4
x=1
Not the right answer
f(x)=(x-4)(x+4)
f(x)=x^2-16
x=-0/2(1)
x=0
Yay! This is the right answer. As a result, f(x)=(x-4)(x+4) is your final answer. Hope it help!
Answer:
m<AFE = 128°.
Step-by-step explanation:
<u>Step 1: Find the value of x</u>
<em>Angle EFD + Angle DFC = Angle EFC</em>
5x + 6 + 19x - 15 = 17x + 19
24x - 9 = 17x + 19
7x = 28
x = 4
<u>Step 2: Find all angles</u>
<em>Angle AFB=Angle EFD= 5x + 6</em>
5(4) + 6 = 26°
Angle DFC = 19x - 15
19(4) - 15 = 61°
<u>Step 3: Find angle AFE</u>
<em>Line BD is a straight line and all angles on a straight line are equal to 180°.</em>
<em>Angle AFB + Angle AFE + Angle EFD = 180°</em>
26 + BFC + 26 = 180°
BFC = 180 - 52
BFC = 128°
<em>Therefore, m<AFE is equal to 128°.</em>
!!
Answer:
0 < k < 2
Step-by-step explanation:
<u>In the first quadrant both of x and y get positive values, so </u>
<u>And replacing x with 2k in the second equation:</u>
- 3x + 2y = 12
- 3*2k + 2y = 12
- 2y= 12 - 6k
- y = 6 - 3k
<u>Since y > 0:</u>
<u>Combining both k > 0 and k < 2, we get:</u>
The error rate has decreased after changing the painting process.
<u>Step-by-step explanation:</u>
Abdulla knows that 20 percent of the parts have an error in their painting. After suggesting changes in painting process, he wants to know whether the error rate has changed.
Number of parts in the random sample=400400400
Number of parts that had an error=606060
We have to determine what percentage of 400400400 is 606060
After changing the painting process 0.15% of parts have error.
The previous percentage was 20.Hence the error rate has clearly changed.
