Let f(x) = (6x³ - 7)³ and g(x) = 6x³ - 7.
Given that f(x) = (h° g)(x), find h(x).
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Answer:

55 minutes

Step-by-step explanation:

sharat's train arrived on time (11.15) but Nitin's was after and 10 mins later it'd be 11.25

Answer:

y = -3

Step-by-step explanation:

-53 = 8y + 4y - 17

combine y terms on right side:

-53 = 12y - 17

add 17 to both sides:

-53 + 17 = 12y - 17 + 17

-36 = 12y

divide both sides by 12:

-36/12 = 12y/12

y = -3

The dimension of the flower garden, which located in the middle of the backyard surrounded by a strip of grass, is 26 m length and 16 m width.

The situation can be depicted on the attached picture.

We need to translate the word problem into algebraic expressions.

Let x be the width of the grass strip.

Let A be the area of the grass strip.

Then,

A = 2 . 22x + 2 . (32 - 2x)x

288 = 2 . 22x + 2 . (32 - 2x)x  (divide by 2)

144 = 22x + x(32 - 2x) (divide by 2)

72 = 11x + x(16 - x)

72 = 27x - x²

x² - 27x + 72 = 0

This is a quadratic equation. One of the methods to solve a quadratic equation is by factorization.

Factorize the left side:

(x - 3) (x - 24) = 0

x = 3  or  x = 24

The length of the flower garden  = 32 - 2x

The width of the flower garden  = 22 - 2x

Substitute x = 3:

The length of the flower garden  = 32 - 2 . 3 = 32 - 6 = 26 m

The width of the flower garden  = 22 - 2 . 3 = 16 m

Note that if we substitute x = 24, it will results in negative values while the dimension is always positive.

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Based on the chemical equations given, the balanced equation would be d. D.

In Chemistry, a balanced equation is one that has the same number of atoms on the left side of the equation, as on the right side of the equation.

The balanced equation is therefore:

2KCIO₃ -->2 KCI + 3 O₂

This is because there are 2 KCI atoms and 6 Oxygen atoms on the left side, and there are also 2 KCI atoms and 6 Oxygen atoms on the right side.

In conclusion, option D is correct.

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Answer:

1/9

Step-by-step explanation:

There is 1/3 gallon of water in a 3 gallon container. The fraction of the container that is filled is  1/9

(1/3 of a gallon divided by 3 gallons equals 1/9)

The length of the rectangle is 10, the width is 2.5 and the perimeter is 25

Let the width of the rectangle be x

The length of rectangle = 2x + 5

The overall length of the outline determines a rectangle's perimeter in two dimensions. We add the lengths of all four corners of a rectangle to find its perimeter. Since the opposite sides of a rectangle are always equal, we must determine the length and width of the rectangle in order to determine its perimeter.

Perimeter = 10 times of width

= 10*x

= 10x

The formula for the perimeter of a rectangle is given:

Perimeter = 2(Length+Breadth)

10x = 2(x + 2x+5)

10x = 2(3x+5)

10x = 6x + 10

4x = 10

x=2.5

Length = 10

Width = 2.5

Perimeter = 25

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The score 3 months ago was 4.130.

What is rate of increase?

Rate of increase is defined the change in rate that describes how one quantity changes in relation to another quantity.

Assume the score 3 months ago was x. This means that the above can be expressed as:

Current score = x × ( 1 + rate) ^ number of months

5.20= x(1+8%)^3

5.20 = x(1.259)

x= 5.20/1.259

x= 4.130

therefore, the score was 4.130

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Answer:

77.5

Step-by-step explanation:

180-25=155

155/2=77.5

Answer:

Step-by-step explanation:

2

Combine multiplied terms into a single fraction

3

Find common denominator

4

Combine fractions with common denominator

5

Multiply the numbers

It would take 35 minutes to drive 1 km at a speed of 1.71 km/h.

Speed is the ratio of distance traveled in a given time.  Speed is given by distance/time.

The time can be computed by dividing distance by speed.

This implies that time is the quotient of distance and speed.

The total distance drove = 1 km

The driving speed = 1.71 km/h

Time = Distance/Speed

= 1/1.71

= 0.58 hours

= 0.58 x 60 seconds

= 35 minutes 5 seconds

Thus, to travel 1 kilometer at the speed of 1/71 kilometers per hour would take 35 minutes.

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The answer will de 10 bacterias

Answer: 1024

Step-by-step explanation: Since there's only 1 bacteria at first, we can just do 2^x. x being the amount of time divided by the amount of time between each time it doubles. Since the bacteria doubles every 2 seconds, and 20/2 = 10 we get 2^10 which is 1024.

a) Value of Expression 1 is 29.833.

b) After inserting the parentheses the expression is (5+4) * 2 + 6 -2 * 2 - 1.

The order of operations to solve in expression 1 is:

First parenthesis, then multiplication and division, and then addition and subtraction.

So, the expression is:

6 × 7 - 3 ÷ 2 × 9 + 4 ÷ 3

First, solve division and then multiplication:

= 42 - 1.5 × 9 + 1.34

= 42 - 13.5 + 1.34

= 29.84

b) Because the parenthesis is the initial action, so insert it in 5+4 which provides the following result:

(5 + 4) × 2 + 6 - 2 × 2 - 1

First, calculate the parenthesis, then the multiplication and division, and finally perform addition and subtraction:

= (9) × 2 + 6 - 4 - 1

= 18 + 6 - 4 - 1

= 19

The final value is 19.

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Answer:

x = 58°

y = 74°

z = 106°

w = 42°

Step-by-step explanation:

  Finding the value of unknown variables:

  x + 32° = 90°

           x  = 90 - 32

          [tex]\sf \boxed{\bf x = 58^\circ}[/tex]

  x + y + 48 = 180  {Angle sum property of triangle}

 58 + y + 48 = 180

         y + 106 = 180

                  y = 180 - 106

                  [tex]\sf \boxed{\bf y = 74\°}[/tex]

y + z = 180  {Linear pair}

74 + z = 180

       z = 180 - 74

     [tex]\sf \boxed{\bf z = 106\°}[/tex]

32 +z + w = 180 {Angle sum property of triangle}

32 + 106 +w = 180

       138 + w = 180

                w = 180 - 138

              [tex]\sf \boxed{\bf w = 42\°}[/tex]

The total area of the figure is; 32 millimeters sq.

The area of a parallelogram is the product of the base and the height of the figure.

The area of a parallelogram = Base x Height

We have been given that a parallelogram has a base is 6 millimeters and a height is 4 millimeters

The area of a parallelogram = Base x Height

= 6 x 4

Area = 24 millimeters sq.

Similarly, The area of the triangle = 1/2 x b x h

= 1/2 x 8 x 2

= 8 millimeters sq.

The total area of the figure is;

Total = area of the triangle + area of a parallelogram

Total = 24 + 8 = 32

Hence, the total area of the figure is; 32 millimeters sq.

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Answer:

30.24%

Step-by-step explanation:

Each time you lose x%, you end up with 1 - 0.01x.

For example, if you lose 10% of an amount, you end up with 1 - 0.01(10), or 0.9 times the original amount.

Let's say you started with x.

You lost 10%. Now you have 0.9x.

Then you lost 20% of the remaining amount. Now you have 0.8(0.9x).

Then you lost 30% of the remaining amount. Now you have 0.7(0.8)(0.9x).

Finally you lost 40% of the remaining amount. Now you have 0.6(0.7)(0.8)(0.9x).

The final amount you have is

0.6(0.7)(0.8)(0.9x) = 0.3024x = 30.24% of x

Answer: 30.24%

In serving punch to guests at the party, Vinny can fill 9 guests' cups to the top based on this unit rate.

The unit rate is the ratio of a variable to another.

The whole number here is the total gallons of punch available to serve the guests.

The unit rate is the volume that each guest's cup can hold or contain.

This implies that the ratio is 5/64: 3/4

The total number of gallons of punch = 3/4 or 0.75 gallons.

The volume or capacity of each guest's cup = 5/64 gallons or 0.078125.

The number of guests' cups to fill to the brim = 9.6 cups (0.75/0.078125)

= 9 guests' cups.

Thus, Vinny can fill 9 guests' cups to the brim, using the given ratio or unit rate.

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Step-by-step explanation:

First is

5(1-1)+10= 5×0+10= 0+10 = 10

2nd is

5(2-1)+10=5× 1+10= 5+10=15

3rd= 5(3-1)+10= 5×2+10=10+10=20

4th=5(4-1)+10=5×3+10=15+10=25

I hope it will be helpful for you.

Answer:

3x2x2x3

Step-by-step explanation:

3x2x2x3= 36

I hope that was helpful!

My pleasure to help!!

When a point is reflected across the x-axis, the x-coordinate remains unchanged, but the y-coordinate is assumed to be the additive inverse. Point (x, yreflection )'s across the x-axis is (x, -y).  A point's reflection over the y axis is shown. The reflection rule over the y axis is (x,y)(x,y).

A coordinate plane is a two-dimensional plane formed by two number lines intersecting. One of these number lines is a horizontal number line known as the x-axis, and the other is a vertical number line known as the y-axis.

1) Determine the absolute value of x1(y2-y3) + x2(y3-y1) + x3(y1-y2).

2) The area of the triangle is calculated by dividing this value by two.

3) Use our area of a triangle with coordinates calculator to confirm this result.

The coordinate plane can be used to draw lines and points. This system allows us to visually describe algebraic relationships, as well as create and interpret algebraic concepts.

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Answer:

Positive, so the answer would be y=4/2 or 2. y=2x-4

Step-by-step explanation:

Slope formula y=mx+b

The mx is the rise/ over run

The b is the y-intercept

You can check in the end by checking so to see if the rise over the run is correct

Also, you can check the b by looking at the y-intercept, which is -4

Hope this helps!

Answer:

3.94*10^7

Step-by-step explanation:

Answer:

3.94 * 10^7

Step-by-step explanation:

:]

The percentage of members that voted is 70%.

The art club had an election to select a president. 42 out of the 60 members of the art club voted in the election.

Therefore, the percentage of the members that voted can be calculated as follows;

percentage that voted = number of people that voted / total number members × 100

Therefore,

number of people that voted = 42

total number members = 60

Hence,

percentage that voted = 42 / 60 ×100

percentage that voted = 4200 / 60

Therefore,

percentage that voted = 70%

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The range of the function is 1

As seen by the graph in the following figure

As can be seen, x's value falls between

nonetheless, y is equal to 1 for all values of x.

This holds true regardless of x's value.

Consequently, the function's range is 1.

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Answer:

$390,000

Explanation

To do this, we will use the compound interest formula;

A = P(1+r)^t

P = 275000

rate r = 6%

Time t = 30years

Substitute

A = 275000(1+0.06)^30

A = 275000(1.06)^30

A = 275000(5.7435)

A = 1,579,460.07

For the rate of 5%

A = 275000(1+0.05)^30

A = 275000(1.05)^30

A = 275000(4.3219)

A = 1,188,534.15

Takeing their difference;

Difference = 1,579,460.07-1,188,534.15

Difference =390,925.92

Hence the approximate difference in his ending balance of the actual rate is 5% instead of six ​is about $390,000

Answer:

The range is 28

The variance is 90.855

The mean is 56.36

The median is 53

The sample standard deviation is 9.532

Step-by-step explanation:

Answer:

b Adding 4 to the parent function shifts the function up four units.

Step-by-step explanation:

The original function is y(x) = 2^x

Adding four is y(x) = 2^x + 4

We've simply told y to take whatever value is generated for x and add four to it.

So the new value for the same x would have 4 added to y:  (x,y+4),

Point (1,2) would shift to point (1,6).

Adding four to the parent function will shift the entire graph up by 4.  See ate attached graph.

Step-by-step explanation:

any ordered pair is a solution, if we can use its coordinates in the equation, and the equation stays true.

for x - 3y = 6

1. (3, -1)

3 - 3×-1 = 6

3 + 3 = 6

6 = 6

true, this is a solution.

2. (0, 2)

0 - 3×2 = 6

-6 = 6

false, this is not a solution.

3. (3, 1)

3 - 3×1 = 6

3 - 3 = 6

0 = 6

false, this is not a solution.

SOLUTION

Step 1 : We need to recognize the value of x in 5 places means 5 x

and the value of 1 in 6 times means 6,

so we have that: 5 x + 6 = 1 .

Step 2 : We need the linear equation: 5 x + 6 = 1

collecting like terms, we have that:

5 x = 1 - 6

5 x = - 5

Divide both sides by 5 , we have that:

x = - 1

CONCLUSION : The value of x = -1 ( OPTION B )

Answer:

The larger number is 68 and the small number is 25

Step-by-step explanation:

Large number y

small number is x

y=2x+18

x+y=93