The sum of two consecutive even numbers is 214. What are the numbers?​

f(x)=(x+a)/b

or bf(x)=x+a

let f(x)=y

by=x+a

flip x and y

bx=y+a

or y=bx-a

or f^{-1}(x)=bx-a

also g(x) is inverse of f(x)

bx-a=cx-d

so b=c,a=d

again let g(x)=y

y=cx-d

flip x and y

x=cy-d

cy=x+d

y=(x+d)/c

or g^{-1}(x)=(x+d)/c

also f(x) is inverse of g(x)

so (x+a)/b=(x+d)/c

so a=d,b=c

so in either case a=d,b=c

take b=c=1

a=d=2

f(x)=(x+2)/1=x+2

g(x)=1x-2=x-2

so f(x) and g(x) are two parallel lines f(x) with y- intercept=1 and slope 0

g(x) with y-intercept -2 and slope 0

if we take b=c=2,a=d=3

f(x)=(x+3)/2=x/2+3/2

g(x)=2x-3

here f(x) is of slope 1/2 and y-intercept 3/2

g(x) is of slope 2 and y intercept -3

part 3.

f(f(x))=g((x+a)/b)=c[(x+a)/b]-d=(c/b)(x+a)-d

An inverse function or an anti function exists described as a function, which can change into another function. In other words, if any function “f” carries x to y then, the inverse of “f” will carry y to x.

Part 1: f(x) = (x+2) / 3 and g(x) = 3y-2.

Part 2: g(x) = 3x - 2, the inverse.

Part 3: g(f(x)) = x showing that f(x) and g(x) are mutual inverses.

An inverse function in mathematics exists function which "reverses" the another function.

TASK 1

Part 1

Let y = f(x) = (x + a) / b

x = g(y) = by-a = cy-d,

so c = b and d = a.

Let d = a = 2 and c = b = 3

f(x) = (x+2) / 3 and g(x) = 3y-2.

Part 2

y = f(x) = (x+2) / 3

3y = x+2  

x = 3y-2 = g(y)

so g(x) = 3x - 2, the inverse.

Part 3

g(f(x)) = 3

f(x)-2 = 3(x+2)/3-2 = x+2-2 = x,

so g(f(x)) = x showing that f(x) and g(x) exists mutual inverses.

x       -2  -1        0    1     2

f(x)    0    1/3   2/3   1    4/3

g(x)  -8   -5      -2    1      4

Part 4

The graph is given below.

TASK 2

Part 1

(a) Let a=1, b=2, c=3, d=6: [tex]$\sqrt{x}[/tex]+2+3=6 ; [tex]\sqrt{x}[/tex]-6=-5

(b) Let a=-1, b=2, c=3, d=4

(a) Multiply both sides by

[tex]$\sqrt{x}+6: x-36=-5(\sqrt{x}+6)=-5 \sqrt{x}-30[/tex]

[tex]$ x-36+30=-5 \sqrt{x }[/tex]

[tex]$ x-6=-5 \sqrt{x}$[/tex]

Square both sides:

[tex]$x^{2} -12 x+36=25 x ; x^{2} -37 x+36=0=(x-36)(x-1)$[/tex].

Part 2

(a) So x=36 or 1 (apparently).

Substitute x=36 in the original equation: 6+2+3=6, 11=6 is not true.

So x=36 is an extraneous solution.

substitute x=1: 1+2+3=6 is true, so x=1 exists the actual solution.

(b) [tex]$-\sqrt{x}+2+3=4 ;-\sqrt{x}=-1$[/tex]; multiply both sides by -1: [tex]$\sqrt{x}=1$[/tex]; square both sides: x=1.

Substitute x=1 in the original equation: -1+2+3=4 is true.

So x = 1 is the solution.

Part 3

(a) the act of squaring both sides resulted in creating an extraneous solution [tex]$\left((-5)^{2} =25=5^{2} \right)$[/tex].  

(b) the solution was simpler and there was no ambiguity.

To learn more about inverse function

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Answer:

f

and

c

the top is f and front is c

Step-by-step explanation:

f and c

E and C

Step-by-step explanation:

E on the front

C on the top

I hope it helps

Answer:

for which one all ?

Step-by-step explanation:

because if so lemme know

[tex](a) {11}^{a} = 1331 \\ = > {11}^{a} = {11}^{3} \\ = > a = 3[/tex]

[tex](b) {2}^{b} = \frac{1}{128} \\ = > {2}^{b} = (\frac{1}{2} ) ^{7} \\ = > {2}^{b} = {2}^{ - 7} \\ = > b = - 7[/tex]

[tex](c) {9}^{c} = 243 \\ = > {3}^{2 \times c} = {3}^{5} \\ = > {3}^{2c} = {3}^{5} \\ = > 2c = 5 \\ = > c = \frac{5}{2} \\ = > c = 2.5[/tex]

[tex](d) {10}^{d} = 0.01 \\ = > {10}^{d} = \frac{1}{100} \\ = > {10}^{d} =( \frac{1}{10} ) ^{2} \\ = > {10}^{d} = {10}^{ - 2} \\ = > d = - 2[/tex]

Hope it helps.

Do comment if you have any query.

Answer:

so subtract -2v to the left side add 5 to the right side so your left with

v = 15

Answer:

15 = v

Step-by-step explanation:

First start by grouping like terms,

=> - 5 - 10 = 2v - 3v

evaluate the LHS and RHS

=> - 15 = - v

Divide through by the coefficient of v, which in this case is - 1

=>

[tex] \frac{ - 15}{ - 1} = v[/tex]

Therefore, 15 = v

Answer:

This is my guess...

"Even today, the need for work is a common reason people move to urban areas."

Step-by-step explanation:

The article talks about technology and how it lead to bigger cities in the past. Because we are reading about prior years, there is no need to talk about the present day.

Answer:

-4, 2    (-4,0) (2,0)

Step-by-step explanation:

factoring in binomials

[tex](x+4)(x-2)=x^{2} +2x-8[/tex]

The zeros:

[tex]x+4=0\\x=0-4\\x_{1} =-4[/tex]

[tex]x-2=0\\x=0+2\\x_{2} =2[/tex]

I hope this help you

Answer:

it is called rectangularization

Step-by-step explanation:

Answer:

68.54 dollars is you answer you would do 63 times .088 and add 63 to your answer

Step-by-step explanation:

Answer:

1,23,098

Step-by-step explanation:

............

[tex] \: \: \: \: \: \: \: \: [/tex]

[tex]m = 2[/tex]

Step-by-step explanation:

[tex]0 = 12 + 2(m - 8)[/tex]

[tex]0 = 12 + 2m - 16[/tex]

[tex]0 = - 4 + 2m[/tex]

[tex] - 2m = - 4[/tex]

[tex] = m = 2[/tex]

[tex] \: \: \: [/tex]

Answer:

m = 2

Step-by-step explanation:

0 = 12 + 2 ( m - 8 )

→ Expand the brackets

0 = 12 + 2m - 16

→ Add 16 to both sides

16 = 12 + 2m

→ Minus 12 from both sides

4 = 2m

→ Divide both sides by 2

2 = m

Answer:

Step-by-step explanation:

Pythagorean theorem: base ² +altitude² = hypotenuse²

1) hypotenuse² = base² + altitude²

          x² = 6² + 3²

               = 36 + 9

               = 45

         x = √45

         x = 6.7 cm

4) base ² +altitude² = hypotenuse²

x ² + 3.7 ² =  4.2 ²

x ² + 13.69 = 17.64

             x ² = 17.64 - 13.69 = 3.95

             x = √3.95

            x = 1.99 cm

10)c ² = a ² + b ²

           = 3 ² +4 ²

         = 9 + 16

  c ² = 25

c = √25 = 5

11) a ² + b ² = c ²

9 ² +b² = 13 ²

81 + b² = 169

     b² = 169 - 81 = 88

b = 9.38

12) a² + b² = c²

12² + b² = 22²

  144 + b² = 484

           b² = 484 - 144 = 340

           b =√340 = 18.44

Answer:

47 is the correct answer.

Step-by-step explanation:

Answer:

47

Step-by-step explanation:

divide 473 by 10

473 divided by 10 = 47

Answer:0.216667

Step-by-step explanation: I figured out how many ft r in a yard the how many seconds r in a mi then went from there.

Answer:

scale factor is 1:4

Step-by-step explanation:

the blue rectangle is 4 times larger than the black one; you can compare coordinates; for example, (4,5) becomes (16,20)

Answer:

Step-by-step explanation:

It isn't an appropriate sample to use to infer the preference of all 7th grade students because they only get the students in one club, a better sampling method would be to get the answer from 25 grade 7 students in other clubs including the art club.

- i'm sorry if this doesn't make any sense

Todd's method of sampling is incorrect because he chose the student from a single club. To make it better he has to choose students from different clubs.

The sampling method is the method of selecting the subset from the set to make a statical inference.

Todd surveyed the 25, 7th-grade students in the art club to determine what movies 7th-grade students prefer.

This method is not an appropriate sample to use infer preference of all 7th-grade students because they only get the students in one club, a better sampling method would get the correct surveyed from 25 grade 7 students in other clubs including the art club.

More about the sample method link is given below.

https://brainly.com/question/15125943

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Answer:

12 feet 9 inches

Step-by-step explanation:

There are 3 feet in a yard, and 12 inches in a foot. Multiply those together and you get 36 inches in a yard.

2 yards × 36 inches/yard = 72 inches

2 feet × 12 inches/foot = 24 inches

72 inches + 24 inches = 96 inches

------------

7 yards × 36 inches/yard = 252 inches

252 inches + 9 inches = 261 inches

==============

Add those together:

96 inches + 261 inches = 357 inches

Then to convert to feet again, you need to divide by 12 and find the remainder. I prefer to do it with a calculator like this, but you can do it however you prefer:

357 ÷ 12 = 29.75 feet (round down)

12 × 29 = 348 inches in 12 feet

Then find the remainder:

357 - 348 = 9 inches

12 feet 9 inches

The volume of the box is the amount of space in it.

The dimension of the postcard is:

[tex]\mathbf{Length = 10}[/tex]

[tex]\mathbf{Width = 18}[/tex]

Let x represents the length of the cut.

So, the dimension of the box is:

[tex]\mathbf{Length = 10 -2x}[/tex]

[tex]\mathbf{Width = 18 -2x}[/tex]

[tex]\mathbf{Height = x}[/tex]

(a) The function that represents the volume of the box

This is calculated as:

[tex]\mathbf{V(x) = Length \times Width \times Height}[/tex]

So, we have:

[tex]\mathbf{V(x) = (10 - 2x) \times (18 - 2x) \times x}[/tex]

Expand

[tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]

Hence, the volume function is: [tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]

(b) The dimension that maximizes the volume

We have:

[tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]

Differentiate

[tex]\mathbf{V'(x) = 180- 112x + 12x^2}[/tex]

Set to 0

[tex]\mathbf{180- 112x + 12x^2 = 0}[/tex]

Using a calculator, we have:

[tex]\mathbf{x = 7.3,2.1}[/tex]

The value x = 7.3 is greater than the dimension of the box.

So, we have:

[tex]\mathbf{x = 2.1}[/tex]

Recall that:

[tex]\mathbf{Length = 10 -2x}[/tex]

[tex]\mathbf{Width = 18 -2x}[/tex]

[tex]\mathbf{Height = x}[/tex]

So, we have:

[tex]\mathbf{Length = 10 -2 \times 2.1 = 5.8}[/tex]

[tex]\mathbf{Width = 18 -2 \times 2.1 = 13.8}[/tex]

[tex]\mathbf{Height = 2.1}[/tex]

Hence, the dimension that maximizes the volume is 5.8 by 13.8 by 2.1

(c) The maximum volume

This is calculated as the product of the dimension of the box

So, we have:

[tex]\mathbf{Volume = 5.8 \times 13.8 \times 2.1}[/tex]

[tex]\mathbf{Volume = 168.1}[/tex]

Hence, the maximum volume of the box is 168.1 cubic inches

Read more about volumes at:

https://brainly.com/question/17056191

Answer:

Step-by-step explanation:

I thought of a 2 digit number. The digits of my number are different:  [XY]

Then I'm lost. Does "The unit digit of my number is the tens digit raised third power" mean that the X is raised to the third power?:

X^3

But then we need more information.  X could be 1, 2,3, or 4.  At 5 it becomes a three digit number.  All of the other option result in a two digit number with different digits, so all seem possible.  I don't know how to answer this without more information.

Answer:

-1

Step-by-step explanation:

Using the formula to find gradient or slope:

m = (y2 - y1)/ (x2 - x1)

Using any two points from the graph: (-2, 0) (0, -2)

Substitute this into the equation to get the answer of -1.

Answer:

B.97

Step-by-step explanation:

Heyy so angle ADC and DAB are supp to one another, thus

83 + DAB = 180 --> subtracting

DAB =97. B

Hope that made sense :)

Step-by-step explanation:

check the attached file

Answer:

for the first one the answer is 65.94 and for the second one its 50.27

Step-by-step explanation:

to find circumference from diameter(the half) you just multiply your diameter by pie(3.14). To find the circumference from the radius(the line on second circle), you just do 2 x pie(3.14) x R(which in this case is 8) and that will give you your answer

No because for 5x10, you just add 10 5 times for 50. For 5x5x5, you multiply 5x5 and get 25 then multiply it again with the other 5 and get 125.

Answer:

No

Step-by-step explanation:

No, because 5 × 5 × 5 = 25 × 5 and that does not equal 10×5.

Answer:

15%

Step-by-step explanation:

24/160 = 0.15

0.15*100 = 15