MATHEMATICS MIDDLE SCHOOL

What is the inverse of the function f(x) = 4x + 8?o h(x) = -x-2
Tt it
h(x) =
X-
to the
O
h
(x) =
x + 2

Answers

Answer 1
Answer:

eplace f(x) with y

swtich x and y

solve for y

replace y with f⁻¹(x)

f(x)=4x+8

y=4x+8

x=4y+8

x-8=4y

1/4x-2=y

y=1/4x-2

f⁻¹(x)=1/4x-2

none of the above

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You want to put $4,000 in a simple interest account. It has a 2.5% annual interest rate. How long will it take you to earn $500 in interest?

Answers

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Find the coordinates of the stationary points on each curve(in each equation).1.y=x^2+2x

2.y=4x^3+3x^2+2

3.y=2x+3+8/x

4.y=x^3-9x^2-21x+11

5.y=9x^2/3-2x+5

Please provide full working out, thanks.

Answers

1)
y=x²+2x

we have to calculate the first derived

y´=2x+2

we equal to "0" the first derived and find out the value of "X"
2x+2=0
x=-2/2=-1

we have to calculate de second derived
y´´=2>0  ⇒we have a minimun at x=-1

we calculate y
y=(-1)²+2(-1)=1-2=-1

Answer: we have a minimum at (-1,-1)

2)
y=4x³+3x²+2
we have to calculate the first derived

y´=12x²+6x

we equalize to "0" the first derived and find out the value of "X"
12x²+6x=0
6x(2x+1)=0

6x=0      ⇒x=0
2x+1=0  ⇒x=-1/2


we have to calculate de second derived
y´´=24x+6

y``(0)=24(0)+6=6  >0    ⇒we have a minimun at x=0
y``(-1/2)=24(-1/2)+6=-12+6=-6  ⇒we have a maximum at x=-1/2

we calculate y
if x=0, y=2
if x=-1/2;    y=4(-1/2)³+3(-1/2)²+2=9/4.

we have to equalize the second derived to "0" and find out the value of "x"
24x+6=0
x=-6/24=-1/4; in x=-1/4 we have an inflection point.

y=4(-1/4)³+3(-1/4)²+2=31/16

Answer: we have a minimum at (0,2), a maximum at (-1/2, 9/4) and a inflection point at (-1/4,  31/16).

3.
y=2x+3+8/x
y=(2x²+3x+8)/ x

we have to calculate the first derived

y´= [(4x+3)x-(2x²+3x+8)] / x²=(4x²+3x-2x²-3x-8) / x²=(2x²-8)/x²

we equal to "0" the first derived and find out the value of "X"
(2x²-8) / x²=0
2x²-8=0
x=⁺₋2

we have to calculate de second derived
y´´=[(4x)x²-2x(2x²-8)] / x⁴=(4x³-4x³+16x)/x⁴)=16/x³
y``(-2)=16/(-2)³=-2>0   ⇒ at x=-2 exist a maximum
y´´(2)=16/(2)³=2<0    ⇒ at x=2 exist a minimum
 

we calculate y
y(-2)=-4+3-4=-5
y(2)=4+3+4=11

Answer: we have a maximum at (-2,-5 ) and a minimun at (2,11)

4)
y=x³-9x²-21x+11

we have to calculate the first derived

y´=3x²-18x-21

we equal to "0" the first derived and find out the value of "X"
3x²-18x-21=0
x²-6x-7=0
x=[6⁺₋√(36+28)]/2=(6⁺₋8)/2
x₁=-1
x₂=7

we have to calculate de second derived
y´´=6x-18
y``(-1)=-6-18=-24<0  ⇒at x=-1 exist a maximum
y´´(7)=42-18=24>0  ⇒ at x=7 exist a minimum.

we calculate y
y(-1)=-1-9+21+11=22
y(7)=343-441-147+11=-234

We equalize the second derive to 0, and find out the value of "x"
6x-18=0
x=3 in x=3 exist an inflection point

y=27-81-63+11=-106
Answer: we have a minimum at (7,-234), a maximum at (-1,22) and an inflection point at (3,-106).

5)
y=9x²/³-2x+5

we have to calculate the first derived

y´=6x⁻¹/³-2

we equal to "0" the first derived and find out the value of "X"
6x⁻¹/³-2=0
x⁻¹/³=1/3
x¹/³=3
x=27


we have to calculate de second derived
y´´=-2x^(-4/3)
y´´(27)=-0.024<0  ⇒ at x=27 exist a maximum
we calculate y
y=32

Answer: we have a maximum at (27,32)

Alex, Ralph, Bella, and Doug live on Division Street, which divides Bigville from Smallville, Ralph lives across the street from Alex. Bella lived next door to Doug.

You can walk from Doug's house to Ralph's without crossing the street.

Bella lives in Smallville.

Who lives in Bigville?

Answers

Alex lives in bigville

Answer:

No one lives in Bigville nor Smallville.

Explanation:

They . all live on Division Street which SEPERATES Bigville from Smallville. So, they're living in between Bigville and Smallville.

What is 54 3/11 as a decimal

Answers

the answer is 54.27. Hope I was halpful 

The surface area of a square pyramid is 85 square meters. The base length is 5 meters. What is the slant height?

Answers

35 that what i think it is hope it helps you

Answer:

6

Step-by-step explanation:

if this is on bigideas ch 9.2 I did it and got it right

there are 150 sheep in a flock 34% of them are white what is the total number of white sheep in the flock?

Answers

150 (total) × 34 (percent) = 5,100

5,100 ÷ 100 (total percent you can have) = 51

51 sheep are white.

51. 34
150. 100
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