What is the inverse of the function f(x) =1/4x – 12?

Answer:

YES

Step-by-step explanation:

YESSSSSSSSSSSSSSSSS IS THE ANSWER i think :))

Answer:yes they are all correct

Step-by-step explanation:

Put in a calculator 2^0=1

And 2^1=2

Remember the exponents tell you how many times you multiply the base number to itself

Hope that helps

Answer:

-3, -3

Step-by-step explanation:

The coordinates of point B on line AC is (6/7, -30/7).

Given that, A(6, -6), C(-6,-2) and AB= 3/4 AC.

The section formula is P(x, y)[tex]=(\frac{mx_{2} +nx_{1}}{m+n}, \frac{my_{2} +ny_{1}}{m+n} )[/tex].

Now, AB= 3/4 AC⇒AB:AC=3:4

P(x,y)[tex]=(\frac{3(-6)+4(6)}{3+4}, \frac{3(-2) +4(-6)}{3+4} )[/tex]

=(6/7, -30/7)

Therefore, the coordinates of point B on line AC is (6/7, -30/7).

To learn more about the coordinates visit:

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Answer:

3, 4, 81

Step-by-step explanation:

plz thank

The value of a is 3, value of b is 4 and value of c is 81.

To understand more, check below explanation.

The exponential identity is,

                       [tex]\frac{a^{m} }{a^{n} } =a^{m-n}[/tex]

We have to solve,  [tex]\frac{3^{8} }{3^{4} }[/tex]

              [tex]\frac{3^{8} }{3^{4} } =3^{8-4} \\\\\frac{3^{8} }{3^{4} } =3^{4} \\\\\frac{3^{8} }{3^{4} } =3*3*3*3=81[/tex]

Hence, the value of a is 3, value of b is 4 and value of c is 81.

Learn more about the exponential expression here:

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Answer:

1:    Y=0.8x+72         =         x=1.25y−90

2: 20x+32y=43          =          x= -8/5y + 43/20

First question steps:

Solved for x

Step 1: Flip the equation.

Step 2: Add -72 to both sides.

Step 3: Divide both sides by 0.8.

Second question steps:

Step 1: Add -32y to both sides.

Step 2: Divide both sides by 20.

Answer:

1:    Y=0.8x+72         =         x=1.25y−90

2: 20x+32y=43          =          x= -8/5y + 43/20

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Hope this helps.

Answer:

D) [tex]Y = 1.03(2.93^x)[/tex]

Step-by-step explanation:

To Find the exponential regression equation that fits these data, we substitute the value of x into the equation and see if it produces the value of y.

x: 1 2 3 4 5 6

y: 3 8 27 85 240 570

A. Y = 2.93([tex]1.03^x[/tex])

Substituting x = 1 to get

Y = 2.93(1.03) ≅ 3

Substituting x = 2 to get

Y = 2.93([tex]1.03^2[/tex]) ≅ 3.1

Option A is wrong

B. Y = 38.73x² – 168.58x + 158.1

Substituting x = 1 to get:

Y = 38.73(1)² – 168.58(1) + 158.1 = 28.25

Therefore option B is wrong

C. Y = [tex]102.54^x - 203.4[/tex]

Substituting x = 1 to get:

Y = 102.54 – 203.4 = -100.86

D) [tex]Y = 1.03(2.93^x)[/tex]

Substituting x = 1 to get:

[tex]Y = 1.03(2.93^1)=3[/tex]

Substituting x = 2 to get:

[tex]Y = 1.03(2.93^2)=8.84[/tex]

Substituting x = 3 to get:

[tex]Y = 1.03(2.93^3)=25.9[/tex]

Option D is the closest, it is the correct option

Answer:

6

Step-by-step explanation:

[tex]f(6)=-6 \\\\g(5)=-5\\\\4\cdot f(6)-6\cdot g(5)=\\\\-24+30=\\\\6[/tex]

Hope this helps!

Step-by-step explanation:

[tex]r = \sqrt{ \frac{ax - p}{q + bx} } \\ {r}^{2} = \frac{ax - p}{q + bx} [/tex]

r² (q + bx) = ax - p

qr² + bxr² = ax - p

qr² + p = ax - bxr²

qr² + p = x (a - br²)

[tex]x = \frac{q {r}^{2} + p}{a - b {r}^{2} } [/tex]

Answer:

[tex]\displaystyle x=\frac{-P-\math{R}^2Q}{\math{R}^2b-a}[/tex]

Step-by-step explanation:

[tex]R=\sqrt{\frac{ax-P}{Q+bx}}[/tex]

[tex]\mathrm{Square\:both\:sides}[/tex]

[tex]R^2=\left(\sqrt{\frac{ax-P}{Q+bx}}\right)^2[/tex]

[tex]R^2=\frac{ax-P}{Q+bx}[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}Q+bx[/tex]

[tex]\math{R}^2\left(Q+bx\right)=\frac{ax-P}{Q+bx}\left(Q+bx\right)[/tex]

[tex]\math{R}^2\left(Q+bx\right)=ax-P[/tex]

[tex]\math{R}^2Q+\math{R}^2bx=ax-P[/tex]

[tex]\mathrm{Subtract\:}\math{R}^2Q\mathrm{\:from\:both\:sides}[/tex]

[tex]\math{R}^2Q+\math{R}^2bx-\math{R}^2Q=ax-P-\math{R}^2Q[/tex]

[tex]\math{R}^2bx=ax-P-\math{R}^2Q[/tex]

[tex]\mathrm{Subtract\:}ax\mathrm{\:from\:both\:sides}[/tex]

[tex]\math{R}^2bx-ax=ax-P-\math{R}^2Q-ax[/tex]

[tex]\math{R}^2bx-ax=-P-\math{R}^2Q[/tex]

[tex]\mathrm{Factor}\:\math{R}^2bx-ax[/tex]

[tex]x\left(\math{R}^2b-a\right)=-P-\math{R}^2Q[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}\math{R}^2b-a[/tex]

[tex]\frac{x\left(\math{R}^2b-a\right)}{\math{R}^2b-a}=-\frac{P}{\math{R}^2b-a}-\frac{\math{R}^2Q}{\math{R}^2b-a}[/tex]

[tex]x=\frac{-P-\math{R}^2Q}{\math{R}^2b-a}[/tex]

Answer:

A graph using y=mx+b would include a positive or negative line (slope) and a y-intercept. If there is a y-intercept between 1 & infinity then the line will not start on the origin. y=mx+b doesnt have to include a y-intercept though. It can include a y-intecept of 0. This would mean that the line would start on the origin. y=mx+b will ALWAYS be a straight line.

Step-by-step explanation:

Hope this helps :)

no. of squares=90

no. of toothpicks=(89*3)+4

=271

rule of patern = 4+3+3...

no. of toothpicks=1000

no. of squares= (996÷3)+1

= 333

Answer:

Total volume = (145/3)π in³

Step-by-step explanation:

First find the volume of the entire cylinder.  The correct formula to use here is:

V = πr²h, where r is the radius and h is the height.  Here, with the radius being 5/2 inches and the height being 8 inches, the cylinder volume is

V = π(2.5 in)²(8 in) = 50π in³

Next find the volume of the conical shape:  V = (1/3)π(2.5 in)²(0.8 in)

The desired volume is equal to the volume of the entire cylinder LESS the volume of the cone:

π(2.5 in)²(8 in) = 50π in³  LESS  (1/3)π(2.5 in)²(0.8 in), which simplifies as follows:

Total volume =

50 π in³ -  (1/3)π(2.5 in)²(0.8 in), or

(2.5 in)²π[8 in - 0.8/3 in] =  π(6.25 in²)(8 in - 8/30 in) = π( 6.25 in²)(116/15 in), or

Total volume = (145/3)π in³

Answer:

x = 28

y = 32

Step-by-step explanation:

3

4

(x−12)=12

(

3

4

)(x)+(

3

4

)(−12)=12(Distribute)

3

4

x+−9=12

3

4

x−9=12

Step 2: Add 9 to both sides.

3

4

x−9+9=12+9

3

4

x=21

Step 3: Multiply both sides by 4/3.

(

4

3

)*(

3

4

x)=(

4

3

)*(21)

x=28

Answer:

x=28

3

4

y−12+12=12+12

3

4

y=24

Step 2: Multiply both sides by 4/3.

(

4

3

)*(

3

4

y)=(

4

3

)*(24)

y=32

Answer:

x = 28

y = 32

Step-by-step explanation:

Equation 1:

First, we will distribute the 3/4 to everything in the parentheses like this:

[tex]\frac{3x}{4} - \frac{36}{4} = 12[/tex]

We can simplify the 36/4 down like this:

[tex]\frac{3x}{4} - 9 = 12[/tex]

We can add the 9 to the other side:

[tex]\frac{3x}{4} = 21[/tex]

Then multiply the 4 to the other side

[tex]3x = 84[/tex]

Finally, we can divide by 3

[tex]x = 28[/tex]

Equation 2:

We can add 12 to the other side:

[tex]\frac{3y}{4} = 24[/tex]

Then multiply 24 by the 4

[tex]3y = 96[/tex]

Then divide by 3

[tex]y = 32[/tex]

Answer:

4.104

Step-by-step explanation:

Volume of any prism = Area of cross section x height.

so, volume = 0.6 x 1.9 x 3.6 = 4.104

Answer:

a) 72

b) 1/72

c) 1/36

Step-by-step explanation:

a) number of ways she can choose route= 3C1 = 3

   number of ways she can choose parking lots= 4C1 = 4

number of ways she can choose entrances= 3C1 = 3  

number of ways she can choose elevators= 2C1 = 2

number of ways she can go to office= number of ways she can choose route×number of ways she can choose parking lots×number of ways she can choose entrances×number of ways she can choose elevators

      number of ways she can go to office= 3×4×3×2

                                                                      = 72

b) Probability of morning side= number of morning side/ total number of routes=  1/3

probabiltiy of Parking lot A=  number of parking lot A/ total number of parking lot= 1/4

probability of south entrance= number of south entrance/ total number of entrances=  1/3

probablity of elevator 1=  number of elevator 1/ total number of elevator= 1/2

combine probability= 1/3× 1/4×1/3×1/2 = 1/72

c) Probability of Industrial Avenue= number of industrial avenue/ total number of avenue= 1/3

Probability of parking lot D= number of parking lot D/ total number of parking lot after deducting number of parking lots A and B = 1/2

Probability of north entrance= number of north entrance/ total number of entrance= 1/3

probablity of elevator 2= number of elevator 2/ total number of elevator

                                      = 1/2

combine probability= 1/3 × 1/2 × 1/3 ×1/2

                                  = 1/36

Answer:

Speed = 410 miles/hour

Step-by-step explanation:

Speed = Distance / Time

Distance = 1640 miles, Time = 4 hours

Speed = 1640/4

Speed = 410 miles/hour

Answer:

-2

-1

Step-by-step explanation:

The y-intercept is the point on the y-axis intersected by the graph.

y-intercept is -2

The x-intercept is the point on the x-axis intersected by the graph.

x-intercept is -1

Answer:

see below

Step-by-step explanation:

The x intercept is where it crosses the x axis

It crosses at x = -1

(-1,0)

The y intercept is where it crosses the y axis

It crosses at y = -2

(0,-2)

Answer:

Sabemos que:

[tex]MH(x, y) = \frac{2xy}{x+y}[/tex]

y tenemos que:

[tex]MH (a,4) = \frac{2*a*4}{a+4} = \frac{8*a}{a+4} = 6[/tex]

Con esto podemos encontrar el valor de a:

8*a/(a+ 4) = 6

8*a = 6*(a + 4) = 6*a + 24

8a - 6a = 24

2a = 24

a = 24/2 = 12.

Tambien sabemos que:

[tex]MH(8,b) = \frac{2*8*b}{8+b} =\frac{16*b}{8+b} = 12[/tex]

Y de ahí podemos despejar b:

(16*b)/(b + 8) = 12

16*b = 12*(b + 8) = 12b + 96

16b - 12b = 96

4b = 96

b = 96/4 = 24

Entonces tenemos a = 12 y b = 24, y el MH de a y b es:

MH(12,24) = 2*12*24/(12 + 24) = 24*24/36 = 16

Answer:

9b-8

Step-by-step explanation:

6b+5b-2b-8

11b-2b-8

9b-8

Answer:

22.360679775

Step-by-step explanation:

i used a calulator on the web

Answer:

±10 sqrt(5)

Step-by-step explanation:

sqrt(500)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(100*5)

sqrt(100) sqrt(5)

±10 * sqrt(5)

235.5 units^2 or 75π

Here is why:

The formula for the surface area of a cone is...

[tex]SA=\pi r^2+\pi rl[/tex]

Since you didn't specify if you wanted an exact or approximate answer, I will be doing both. The lateral height is l, so I'm going to assume the height you gave is the lateral height. We can now plug everything in.

[tex]SA=(3.14*5*5)+(3.14*5*10)[/tex]

[tex]SA=78.5+157[/tex]

[tex]SA=[/tex]

235.5

Now that we have the approximate answer, we will find the exact answer or the answer in pi.

[tex]SA=(\pi *5*5)+(\pi *5*10)[/tex]

[tex]SA=25\pi +50\pi[/tex]

[tex]SA=[/tex]

75π

~

The approximate answer for the surface area of the cone is 235.5 units^2 and the answer in terms of pi is 75π.

Answer:

x = 2, y = - 4

Step-by-step explanation

5x-y=14

x+3y= - 10

x = - 10 - 3y

5(- 10 - 3y) - y = 14

- 50 - 15y - y = 14

-16y = 64

y = - 4

x = -10 - 3y = - 10 - 3*(- 4) = - 10 + 12 = 2

x = 2

Answer:

a. x = 1.2, b. A = 32.1°

Step-by-step explanation:

1.41²-.75²=x²

a. x = 1.2

sin A = 0.75/1.41

b. A = 32.1°

Answer:

x= -3

Step-by-step explanation:

12x-8x = -20+8

4x = -12

x= -12/4

x = -3

Steps:

Step 1: Subtract 8x from both sides.

12x−8−8x=8x−20−8x

4x−8=−20

Step 2: Add 8 to both sides.

4x−8+8=−20+8

4x=−12

Step 3: Divide both sides by 4.

4x/4   =    −12/4

Answer: x=−3

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Hope this helps.

Answer:

16:24 is the answer

Hope it helps:)

Step-by-step explanation:

The initial number of cards were

1x:1x

(Equal red cards and black cards)

So, total of 48 and..

24 red cards

24 black cards

Now, since 8 red cards are removed we have,

24-8= 16 red cards

and 24 black cards

So the ratio of red to black is--

16:24

= 2:3 ( i divided both with 8 to simplify )

Pack 48                          48/2 =24

Red= 24                      24/24 : 24 / 24

Black = 24                            1:1

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

Pack 48                        48/2 = 24    

Red= 16                     24 / 16 : 24 / 24

Black= 24                    1,5 : 1

There's 1,5 black cards for each red card

Answer:

Barlow School has the greater number of boys by  178.

Answer:

Barlow school by 178

Step-by-step explanation:

→ First let's work out the number of boys at Barlow school

[tex]\frac{4}{9}[/tex]  of  [tex]873[/tex]  [tex]=[/tex]  [tex](873/9)*4[/tex]  [tex]=[/tex]  [tex]388[/tex]

→ There is 388 boys in Barlow school. Now let's work out the number of boys at Willow school. Since we know that  [tex]\frac{2}{3}[/tex]  of the school is girls, it must mean that the remaining part must be boys so the fraction of boys at Willow school is  [tex]\frac{1}{3}[/tex]

[tex]\frac{1}{3}[/tex]  of  [tex]630[/tex]  [tex]=[/tex]   [tex](630/3)*1[/tex]  [tex]=[/tex] 210

→ The question specifies to say which school has a greater number of boys and we can see Barlow school has more boys and the question says by how many so we take away the totals so 388 - 210 = 178

[tex]answer \\ = (4.5 , 1.5) \\ please \: see \: the \: attached \: picture \\ for \: full \: solution \\ hope \: it \: helps[/tex]

Answer:

D

Step-by-step explanation:

Let's say we're translating the origin, (0, 0) left 6 units and up 4 units. We would get ( -6, 4), which is (x - 6, y + 4), which is D

Answer:

Speed in km/hr = 518.4 km/hr

Step-by-step explanation:

Speed = 144 m/s

To convert m/s to km/her, you just need to multiply it by 3.6

Speed in km/hr = 144 × 3.6

Speed in km/hr = 518.4 km/hr

Answer:

518.40km/h

Step-by-step explanation:

144m/s

it means that in 1 sec it does 144m

we are searching how many km it does in 1 hour

1 hour = 60*60=3600 sec

so in 3600 sec (= 1 hour) it does 144*3600 m

and 1 km = 1 000m

so in 1 hour it does 144*3600/1000 = 144*3.6 = 518.40

the speed of the car is 518.40km/hr

hope this helps

Answer:

54 is the answer

Step-by-step explanation:

5+(8x5)+72/8

5+40+9

54