Find the inverse of the function Y=(X -4) cubed

Answer: 4^3 = 64

Step-by-step explanation:

Formula is [tex]a^c=b[/tex]

[tex]4^3=64[/tex]

Answer:

[tex]{4}^{3} = 64 \\ [/tex]

Step-by-step explanation:

[tex] log_{a}(c) = b \\ {a}^{b} = c[/tex]

Use the formula.

[tex] log_{4}(64) = 3[/tex]

[tex] {4}^{3} = 64[/tex]

hope this helps

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good luck! have a nice day!

Answer:

The answer is 7 meters

Step-by-step explanation:

Its 7 meters because if you divide the area by the width you would get the length (49 divided by 7 = 7)

Answer:

A

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

m(x) = 2(x + 4)² - 8 ← is in vertex form

with vertex = (- 4, - 8 ) → A

Step-by-step explanation:

U2=ar

U2=17.5

U3=ar^2

U3=122.5

U3/U2=122.5/17.5

ar^2/ar=7

r=7

17.5=ar

17.5=7a

a=2.5

x+28 / 5 = 7

Multiply both sides by 5:

x +28 = 35

Subtract 28 from both sides:

x = 7

Answer:

a) 10,500 big cats

b) 13,401 big cats

c) 33 years

Step-by-step explanation:

Hi, to answer this question we have to apply an exponential growth function:  

A = P (1 + r) t  

Where:  

p = original population  

r = growing rate (decimal form; 5/100= 0.05)

t= years  

A = population after t years  

Replacing with the values given:  

a) At 2005, 1 year passed since 2004 (t=1)

A = 10,000 (1+ 0.05)^1

A = 10,500 big cats

b)

At 2010, 6 years passed since 2004 (2010-2004= 6)

A = 10,000 (1+ 0.05)^6

A = 13,401 big cats

c)

50,000 < 10,000 (1+ 0.05)^t

Solving for t:

50,000/10,000 < 1.05^t

5 < 1.05^t

log 5 < log 1.05^t

log 5 < t ( log 1.05)

log 5 / log 1.05 < t

32.9 years < t

33 years  = t

Feel free to ask for more if needed or if you did not understand something.  

Answer: 4 inches by 6 inches or 8 inches by 3 inches.

Step-by-step explanation:

The area of a rectangle is A = W*L

where L is the width and L is the lenght.

Now, the original rectangle has a measure of 8 in by 6 in.

if 8in is the lenght and 6 in is the width.

We want to divide only one of those measures in equal parts, such that when we take the product of the end results is equal to 24 in.

If we divide the lenght by half (so both parts will have the same width as this did not change), we now have that the lenght is 8in/2 = 4in and the width is 6in.

Now the area is 4in*6in = 24in, which is the area that we where looking for.

We also could cut the width in half, and get the dimensions 8 inches by 3 inches.

a

26<a<28

Step-by-step explanation:

The class interval of age in year is 2

so, 2 is the class interval

Answer:

Mean: 58

Median: 59

Mode: 59

Step-by-step explanation:

34, 59, 59, 67, 71

Mean: 34 + 59 + 59 + 67 + 71 = 290/5 = 58

Median: 59

Mode: 59

Answer:

mean 58

median 59

mode 59

Step-by-step explanation:

67, 59, 34, 71, 59

The mean is the sum divided by the number of numbers

(67+ 59+ 34+ 71+ 59)/ 5 = 290/5 = 58

The median is the middle number  when the numbers are written from smallest to largest

34,   59, 59, 64, 71

The middle number is 59

The median is 59

The mode is the number that appears most often

The number 59 appears twice

59 is the mode

Answer:

The area of the triange is 20 feet. beacause the area of the rectangel is 40 feet.

Step-by-step explanation:

Answer:

7.698 m

Step-by-step explanation:

From the question,

Faisal's distance to the flagpole = 30 m

angle of elevation of its top = 12.4°

angle of depression of its bottom = 2.1°

Thus, the height of the flagpole is divided into two parts. Let the upper part be represented by x and the lower part by y.

From the triangle of the upper part (elevation), we have;

tan 12.4° = [tex]\frac{x}{30}[/tex]

x = 30 × tan 12.4°

 = 30 × 0.2199

 = 6.597 m

From the triangle of the lower part (depression), we have;

tan 2.1° = [tex]\frac{y}{30}[/tex]

y = 30 × tan 2.1°

  = 30 × 0.0367

  = 1.101 m

The height of the flagpole = x + y

                                           = 6.597 + 1.101

                                           = 7.698 m

The height of the flagpole is 7.698 m.

Answer:

Correct option: third one

f(x) = 86(1.02)7x; grows approximately at a rate of 2% daily

Step-by-step explanation:

We can rewrite the equation using the model:

P = Po * (1 + r/n) ^ (nt)

Where P is the final value, Po is the inicial value, r is the rate, t is the time and n is the relation of the rate and the time (in our case, the rate is weekly and the time will be in days, so n = 7)

With P = f(x), Po = 86, r = 0.18 and t = x, we have:

f(x) = 86 * (1 + 0.18/7) ^ (7x)

f(x) = 86 * (1.02) ^ (7x)

So the daily rate of growth is approximately 2%

Correct option: third one

Answer:

xy-xz+yz-yx+zx-zy hoped this helped a little

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

x (y-z)+y (z-x) +z ( x-y)​

Simplify the bracket

xy -xz + yz - yx + zx - zy

combine the like terms

xy - yx -xz + zx + yz - zy

= 0

Answer:

Yeo wsp

60g onions

40g carrots

1 tablespoon of oil

200 g tomatoes

.4 L vegetable stock

Step-by-step explanation:

You just divide everything by 3

Answer: The solution is   (0,2)

Step-by-step explanation:

2x +3y = 6      We will solve the  equations using the elimination method

-5x +2y= 4     but first we need to eliminate one of the variables and we will multiply the first equation by 5 and multiply the second equation by 2 to eliminate the x variable.

5(2x + 3y) =6(5)     new equation  :  10x  +15y = 30

2(-5x + 2y) = 4(2)   new equation   ;   -10x +4y =8    

Now we have to new equations so we will eliminate the x term by adding

10x  +15y = 30

 -10x +4y =8    

       19y = 38  divide both sides by 19.

  y= 2     Now using the solution for y plot it  into one of the new equations and solve for x

10x + 15(2) = 30

10x  + 30  =  30

        -30       -30

10x = 0

x= 0

Answer:

15: 1, 3, 5, 15

20x: 1, 2, 4, 5, 10, 20, x

Step-by-step explanation:

Answer:

mph or miles per hour

Step-by-step explanation:

The required equation is, y = 4 + x.

Hence, The correct answer would be an option (A).

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Now, Jayne stopped for gas before embarking on a road trip.

There were already 4 gallons of gas in the tank.

Hence, As per the question, the required equation would be as:

⇒ y = 4 + x

Thus, This equation relates the total amount of gasoline in the tank, y, to the number of gallons that she put in the tank, x. The total amount of gasoline in the tank, y, is equal to the number of gallons that she put in the tank, x, plus the 4 gallons that were already in the tank.

Learn more about the equation here:

brainly.com/question/10413253

#SPJ7

Answer:

He made 42 cookies and 30 brownies.

Step-by-step explanation:

Let c = number of cookies

Let b = number of brownies

"He made 12 more cookies than brownies."

The number of cookies is 12 more than the number of brownies.

c = b + 12

"He sold cookies for $1.50 and brownies for $2."

The money he made from selling cookies was 1.5c.

The money he made from selling brownies was 2b.

The total sales were $123

1.5c + 2b = 123

We have a system of equations.

c = b + 12

1.5c + 2b = 123

Substitute c of the second equation with b + 12

1.5(b + 12) + 2b = 123

1.5b + 18 + 2b = 123

3.5b = 105

b = 30

c = b + 12

c = 30 + 12

c = 42

He made 42 cookies and 30 brownies.

Answer:

16 + 6pi

Step-by-step explanation:

We have a square and 3 semicircles

The area of the square is

A = s^2 and the side length is 4

A = 4^2 = 16

The radius of the semi circle is 2

The area of a semicircle is

1/2 pi r^2

1/2 pi (2)^2 = 2pi

We have 3 of them

3 *2pi = 6pi

Add the areas together

16 + 6pi

Answer:

(6π + 16) cm²

Step-by-step explanation:

The composite shape can be cut into 4 shapes.

3 equal semi-circles and 1 square.

The square has a side length of 2 + 2 = 4cm.

The radius of the semi-circle is 2 cm.

The area of the square is:

4 × 4 = 16 cm²

The area of the semi-circle is:

2²π × 1/2

= (2π) cm²

There are 3 equal semi-circles, so multiply the area by 3.

2π × 3 = (6π) cm²

Add the areas of the 4 shapes.

16 cm² + (6π) cm²

= (6π + 16) cm²

The total area of the composite shape is (6π + 16) cm².

Answer:

150%

Step-by-step explanation:

25-10= 15

15/10 = 1.5

1.5 = 150%

Answer:

C

Step-by-step explanation:

Because in N(8)>2.N(5) there is 2 times N(5) in front of it. In the example N(g) means the numbers of students whose grade on the exam was g. so in this case N(8) means the numbers of students whose grade on the exam was 8 and N(5) means the numbers of students whose grade on the exam was 5. So when you turn this equation into words  it means The numbers of students whose grade was 8 is more than twice the number of students whose grade was 5.

Answer:

y = (-3/2)x - 4

Step-by-step explanation:

Recall that a line perpendicular to a given line has a slope which is the negative reciprocal of the given line.  The given line can be re-written as  -3y  = -2x + 13, or

y = (2/3)x - 13/3

and so the slope of a line perpendicular to this given line is -3/2.

Then the desired equation, in point-slope form, is

y - 5 = (-3/2)(x + 6)  (This is in point-slope form.)

Alternatively,

2y - 10 = -3(x + 6) = -3x - 18, or

2y = 10 - 3x - 18, or

2y = -3x - 8, or y = (-3/2)x - 4  (This is in slope-intercept form.)

Answer: 3 units up

Step-by-step explanation:

Answer: Id say b

Step-by-step explanation: a would be too high and a bit too detailed. Whereas c and d will be inaccurate.

Answer:

A. Twelve thousand

Step-by-step explanation:

cant specify my sources but please hit thank it would make my day :)

Answer:

36

Step-by-step explanation:

This is a 30, 60 90 triangle, which means that there is a ration for calculating each side.

Answer:

1.) 300 - 5w = 150

2.) 30 weeks

Step-by-step explanation:

w = weeks on the diet

if every week he's on the diet, that means that the weeks * 5 is how many pounds he loses. If he's on the diet one week then he loses 5 pounds. 2 weeks then 10 pounds... etc. But because he's losing punds the value is negative

He starts at 300 pounds so the y-intercept (starting value) would be 300

Finally, because he's looking to get to 150 pounds, that is the final value you're solving for

So this is your firat equation:

300 - 5w = 150

Then we are looking for when two different eqaution have the same value.

Your equation is: 60 + 7w

Her equation is: 120 + 5w

Your final equation is 60 + 7w = 120 + 5w

Solve for this by getting w on one side, and your plain old variable-less value on the other. Do this by subtracting 5w from each side, as well as 60.

Your equation is now 2w = 60

Then divide the whole equation by 2, and you get w = 30

Answer:

7

Step-by-step explanation:

!..........................

Step-by-step explanation:

[tex](1\frac{1}{3} )(1\frac{1}{2} )(1\frac{1}{5} )\\(\frac{4}{3} )(\frac{3}{2} )(\frac{6}{5} )\\(\frac{2}{1} )(\frac{1}{1} )(\frac{6}{5} )\\\frac{12}{5}[/tex]

In the second step I made them all into simple fractions, just because that's easier.

In the third step I did a bit of cancelling to simplify everything as much as possible.

Answer:

[tex]\frac{12}{5}[/tex]

Answer:

28/36 or 7/9

Step-by-step explanation:

there are 36 possible answers

4 of them equal 5 (1+4, 2+3, 3+2, 4+1)

4 of them equal 9 (3+6, 4+5, 5+4, 6+3)

8-36 = 28