Travis wrote the following equation to model the number of chairs, x, that he is renting for a graduation party 2x - 6 = x + 24

Answer:

A) 3n= 3x1= 3

3n= 3x2= 6

3n= 3x3= 9

3n= 3x4= 12

3n= 3x5= 15

3n= 3x6= 18

3n= 3x7= 21

3n= 3x8= 24

3n= 3x9= 27

3n= 3x10= 30

B)7n= 7x1= 7

7n= 7x2= 14

7n= 7x3= 21

7n= 7x4= 28

7n= 7x5= 35

7n= 7x6= 42

7n= 7x7= 49

7n= 7x8= 56

7n= 7x9= 63

7n= 7x10= 70

C) 6n= 6x1= 6

6n= 6x2= 12

6n= 6x3= 18

6n= 6x4= 24

6n= 6x5= 30

6n= 6x6= 36

6n= 6x7= 42

6n= 6x8= 48

6n= 6x9= 54

6n= 6x10= 60

The perimeter of the given shape as represented in the task content is; 29 cm.

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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Answer:

Step-by-step explanation:

Each term is being multiplied by -0.5

How did I know?

Divide the second term by the first.

-50 divided by 100 = -1/2

Find the last four terms.

-12.5 x -1/2 = 6.25

6.25 x -1/2 = -3.125

-3.125 x -1/2 = 1.5625

1.5625 x -1/2 = -0.78125

Using integration, it is found that the area of the shaded region is of \(240 - \ln{27}\) units squared.

\(A = \int_a^b f(x) - g(x) dx\)

In this problem, the curves are:

\(f(x) = \sqrt[3]{x} = x^{\frac{1}{3}}\)

\(g(x) = \frac{1}{x}\)

The limits of integration are: \(a = 1, b = 27\).

Hence:

\(A = \int_1^{27} \left(x^{\frac{1}{3}} - \frac{1}{x}\right) dx\)

Applying the power properties of integration:

\(A = 3x^{\frac{4}{3}} - \ln{x}|_{x = 1}^{x = 27}\)

Finally, applying the Fundamental Theorem of Calculus:

\(A = 3(27)^{\frac{4}{3}} - \ln{27} - 3(1)^{\frac{4}{3}} + \ln{1}\)

\(A = 240 - \ln{27}\)

The area of the shaded region is of \(240 - \ln{27}\) units squared.

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Answer:

509

Step-by-step explanation:

4581 ÷ 9 = 509

Quotient means to divide

I hope this helps you

The elements using rooster-method:

A){3,4,5,6,7,8,9,10}

B){5,6,7,8,9,10,11,12,13,14}

What is rooster-method?

By listing the items of a set inside brackets, the roster method may be used to display the elements of a set. One of three ways to describe a set is in rooster form. The items of a set are listed in the roster form between curly or following brackets, with commas separating each element. When items repeat in the set, the roster approach actually has an issue. Because the elements do not follow a pattern or have a specific order, it is impossible to describe the elements in roster notation if the set has a significant number of elements or any repeated elements.

A)Set of natural odd numbers greater than 2 but less than 11:

Let us represent the set using symbol O:

O = {3,4,5,6,7,8,9,10}

B){x| x∈ N and 4<x<15}

Given that x is a natural number greater than 4 but less than 15.

X={5,6,7,8,9,10,11,12,13,14}

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The product of two numbers having 0's at the end is calculated by counting the total number of 0's in two numbers. Place the same number of zeros (in both digits) at the end of the product of numbers.

In product of 500 and 6000, there are 2 zeros in 500 and 3 zeros in 6000. So total number of zeros is 2 + 3 = 5.

Evaluate the product of number 5 and 6.

Place five zeros (2 + 3) after the number 30. So product is,

Thus answer is 3000000.

Answer: 63

Step-by-step explanation:

3(-3)^2 + 2(6)^2 (multiply 3 times -3) & (multiply 2 times 6)

-9^2+12^2 (-9 to the 2nd power and 12 to the 2nd power)

-81+144 (add them up)

=63

The value of the expression is 3a² + 2b² is 69.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

Expression: 3a² + 2b²

Not, put the value of a= -3 and b=6 we get

= 3a² + 2b²

= 3(-3)² + 2(4)²

= 3 x 9 + 2 x 16

= 37 + 32

= 69

Hence, the value of expression is 69.

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Answer:

Step-by-step explanation:

Answer:

y +1 = 3/4(x -1)

Step-by-step explanation:

Answer:

x+7

Step-by-step explanation:

3 + x + 4

Combine like terms

x+ 3+4

x+7

Steps to simplify:

3 + x + 4

~Combine like terms

7 + x

Best of Luck!

The solution to the nonlinear system of equations is (x, y) = (-3, -2) and (x, y) = (1, 6). These points represent the coordinates where the two equations intersect and satisfy both equations simultaneously.

To solve the nonlinear system of equations:

Equation 1: \(y = -x^2 + 7\)

Equation 2: y = 2x + 4

We can equate the right sides of both equations since they both represent y.

\(-x^2 + 7 = 2x + 4\)

To simplify the equation, we can rearrange it to be in the standard quadratic form:

\(x^2 + 2x - 3 = 0\)

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

(x + 3)(x - 1) = 0

From this equation, we get two possible solutions:

x + 3 = 0 => x = -3

x - 1 = 0 => x = 1

Now, we substitute these x-values back into either equation to find the corresponding y-values.

For x = -3:

y = 2(-3) + 4

y = -6 + 4

y = -2

For x = 1:

y = 2(1) + 4

y = 2 + 4

y = 6

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Answer: (0,6)

The y-int is 6

Answer:

-7

Step-by-step explanaton

- (56/8) divide

= -7

Answer:

The function that model the number of bulbs she will plant is g = 5x²

She will plant 320 bulbs in the garden

Step-by-step explanation:

∵ Cindy’s square garden has a side length of x ft

∵ Area of the square = side × side

∴ The area of the garden = x × x

∴ The area of the garden = x² ft²

∵ She will plant 5 tulip bulbs per square foot

→ That means there are 5 tulip bulbs in 1 foot²

∵ The area of the garden is x² ft²

→ Multiply the area of the garden by 5

∴ The number of tulip bulbs in the garden = 5 × x²

∴ The number of tulip bulbs in the garden = 5x²

∵ g represents the number of bulbs she will plant in her garden

∴ g = 5x²

∴ The function that model the number of bulbs she will plant is g = 5x²

∵ The garden has a side length of 8 feet

→ That means the value of x is 8 feet

∴ x = 8

→ Substitute the value of x in the function above

∴ g = 5(8)² = 5(64)

∴ g = 320

∴ She will plant 320 bulbs in the garden

Answer:

80 degrees

Step-by-step explanation:

The sum of the angles of a triangle add to 180 degrees.  Let x be the third angle

37+63+ x = 180

Combine like terms

100 + x = 180

Subtract 100 from each side

100+x-100 = 180-100

x = 80

Answer:

220

Step-by-step explanation:

(63/1.4)+10

=45+10

=55 mph

55*4

=220 miles

The distance traveled by bus after its speed increased by 10 mph is 220 miles.

The distance covered in a unit of time is known as speed.

Given that, the bus can travel 63 miles in 1.4 hours.

The speed of the bus is:

speed = 63/1.4 mph

speed = 45 mph

Now, the speed of the bus is increased by 10 mph, therefore, the new speed is:

45 + 10

= 55 mph

The distance traveled in 4 hours with a speed of 55mph is:

d = 4 ×55 miles

d = 220 miles

Hence, the distance traveled by bus after its speed increased by 10 mph is 220 miles.

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Answer:

Step-by-step explanation:

You want the area and volume ratios when two figures have a similarity ratio of 2 : 7.

The ratio of areas is the square of the similarity ratio:

  2² : 7² = 4 : 49

The ratio of volumes is the cube of the similarity ratio:

  2³ : 7³ = 8 : 343

__

Additional comment

It can help to think about the units of area and volume. For linear dimensions in inches, area dimensions are in square inches, and volume dimensions are cubic inches. Any ratio of inches will be squared when those inch dimensions are used for area, and will be cubed when volume is computed.

  side length of a square or cube: smaller: 2", larger: 7"

  area of the square: smaller: 2² in², larger: 7² in² or 4 in² and 49 in²

  volume of the cube: smaller: 2³ in³, larger: 7³ in³ or 8 in³ and 343 in³

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Answer:

1/4

Step-by-step explanation:

First you add all of the marbles in the bag which is 16 marbles.  The fraction of red marbles to the total would be 4/16.  In the simplest form that is 1/4. You can also just do 4 divide by 16 which gives you 0.25 and in decimal form that is 1/4.

Answer:

Propaganda: ideas or statements spread to promote one side's views and present an opposing side negatively.

Front: the front lines where combat between opposing armies occurs.

Free enterprise system: an economic system characterized by private or corporate ownership of capital goods.

Allied Forces: the military alliance of the USA, Britain, France, and other countries during WWII.

Axis Powers: Germany, Italy, Japan.

It will take 150 minutes for the two containers to have the same amount of water.

To find the number of minutes it will take for the two containers to have the same amount of water, we need to use the following formula:

m = |A - B| / (a - b)

where m is the number of minutes, A is the initial amount of water in Container A, B is the initial amount of water in Container B, a is the rate at which water is being added to Container A, and b is the rate at which water is being drained from Container B.

In this case, the initial amount of water in Container A is 300 liters, the initial amount of water in Container B is 900 liters, the rate at which water is being added to Container A is 6 liters per minute, and the rate at which water is being drained from Container B is 2 liters per minute. Substituting these values into the formula, we get:

m = |300 - 900| / (6 - 2)

m = |-600| / 4

m = 600 / 4

m = 150 minutes

Therefore, it will take 150 minutes for the two containers to have the same amount of water.

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Answer: B = 15 kph or 15 kph

step by step

(b-5)*10=(b+5)*5

10b-50=5b+25

5b=75

b=15 kph in still water

Among the mean, mode, and median, the unique one is the b. mode.

The mode is the data value that occurs many times more than other data values.

Unlike the mean that shows the average value of all the data values, the mode occurs more.  While we compute the mean by dividing the total data value by the number of data items, the mode is not computed but found as the most frequent data value.

Similarly, the median can be computed when two values occur as the middle values.

Thus, among the three measures of central tendency, the mean, the median, and the mode, the mode is the most unique since it is not computed.

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Choice D is correct

Every point on circle is equidistant from the point at its centre and that fixed distance = radius of that circle.

Let y be the expression you want to differentiate:

\(y=\log_7(5-3x) \implies 7^y=5-3x\)

Now,

\(7^y=e^{\ln(7^y)}=e^{y\ln(7)}\)

Use the chain rule to differentiate both sides with respect to x :

\(\ln(7)e^{y\ln(7)}\dfrac{\mathrm dy}{\mathrm dx}=-3\)

Solve for dy/dx :

\(\ln(7)7^y\dfrac{\mathrm dy}{\mathrm dx}=-3\)

\(\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac3{\ln(7)7^y}\)

\(\dfrac{\mathrm dy}{\mathrm dx}=\boxed{-\dfrac3{\ln(7)(5-3x)}}\)

start by using the definition of slope

what this means is that for every change of 3 in the x axis, there is only going to be a change of 1 in the y axis.

if we make this graph it should look something like this.

The implicit derivative is given as follows:

dx/dt(x = 4)  = 1/12.

The function in this problem is given as follows:

y = 3x² + 1.

The implicit derivative, relative to the variable t, is given as follows:

dy/dt = 6x dx/dt.

(the derivative of the constant 1 is of zero).

The parameters for this problem are given as follows:

x = 4, dy/dt = 2.

Hence the derivative is obtained as follows:

2 = 6(4) dx/dt

dx/dt = 2/24

dx/dt = 1/12.

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