Answer:
528
Step-by-step explanation:
(80:100)*660 =
(80*660):100 =
52800:100 = 528
Now we have: 80 percent of 660 = 528
The next numbers are 32 and -64 the pattern multiplies by -2
6 + m/4 = 3 (subtract 6 from both sides)
m/4 = -3 (multiply both sides by 4)
m = -12
Can plug in to original equation to check work:
6 - 12/4 = 3
6 - 3 = 3
3 = 3
The answer m = -12 checks out
Answer:
1. x=8 is the line of symmetry for f(x) = -4(x − 8)2 + 3
2. x=-2 is the line of symmetry of g(x) = 3x2 + 12x + 15
3. x=3 is the line of symmetry of h(x), shown in the graph.
Step-by-step explanation:
To find the line of symmetry of a vertical parabola (second degree polynomial), find the value of x that sets the squared term to zero. This is a vertical line passing through the vertex of the second degree function.
1. f(x) = -4(x − 8)2 + 3
setting x=8 will give f(8) = 3, so x=8 is the line of symmetry
2. g(x) = 3x2 + 12x + 15
here, we need to complete the squares,
g(x) = 3x2 + 12x + 15
g(x) = 3(x^2+4x+5)
g(x) = 3(x^2 + 2(2x) +4 +1)
g(x) = 3((x+2)^2 +1)
So setting x=-2 will anihilate or cancel the squared term, therefore
x= -2 is the line of symmetry.
3. the curven shown in graph,
we see that the vertex is at x=3, so x=3 is the line of symmetry.
see the attached figure with the letters
1) find m(x) in the interval A,BA (0,100) B(50,40) -------------- > p=(y2-y1(/(x2-x1)=(40-100)/(50-0)=-6/5
m=px+b---------- > 100=(-6/5)*0 +b------------- > b=100
mAB=(-6/5)x+100
2) find m(x) in the interval B,CB(50,40) C(100,100) -------------- > p=(y2-y1(/(x2-x1)=(100-40)/(100-50)=6/5
m=px+b---------- > 40=(6/5)*50 +b------------- > b=-20
mBC=(6/5)x-20
3)
find n(x) in the interval A,BA (0,0) B(50,60) -------------- > p=(y2-y1(/(x2-x1)=(60)/(50)=6/5
n=px+b---------- > 0=(6/5)*0 +b------------- > b=0
nAB=(6/5)x
4) find n(x) in the interval B,CB(50,60) C(100,90) -------------- > p=(y2-y1(/(x2-x1)=(90-60)/(100-50)=3/5
n=px+b---------- > 60=(3/5)*50 +b------------- > b=30
nBC=(3/5)x+30
5) find h(x) = n(m(x)) in the interval A,B
mAB=(-6/5)x+100
nAB=(6/5)x
then
n(m(x))=(6/5)*[(-6/5)x+100]=(-36/25)x+120
h(x)=(-36/25)x+120
find <span>h'(x)
</span>h'(x)=-36/25=-1.44
6) find h(x) = n(m(x)) in the interval B,C
mBC=(6/5)x-20
nBC=(3/5)x+30
then
n(m(x))=(3/5)*[(6/5)x-20]+30 =(18/25)x-12+30=(18/25)x+18
h(x)=(18/25)x+18
find h'(x)
h'(x)=18/25=0.72
for the interval (A,B) h'(x)=-1.44
for the interval (B,C) h'(x)= 0.72
<span> h'(x) = 1.44 ------------ > not exist</span>