A certain number is multiplied by 7, and 4 is taken from the product. Finally, the difference is divided by 9, resulting in 5. Find the initial number.

Answer:

32

Step-by-step explanation:

Use the given functions to set up and simplify  f (− 2 ) .

First,

Write the problem as a mathematical expression

Then,

Replace the variable  x  with  − 2  in the expression.

Answer:

The answer is 24

Step-by-step explanation:

You would get this by plugging in -2 for X

2(-2)3(-2)

Then with PEMDA do parenthesis first

So (-4)(-6)

Then multiply the final together and you would get..

24

This is because two negatives equal a positive when multiplying.

The correct statement regarding the transformation is given as follows:

Dilation bu a scale factor of 0.5 about the origin. Then reflect over the x-axis.

The true statements about the dilation are given as follows:

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

For this problem, the coordinates of the dilated line segment are half the coordinates of the original line segment, hence the scale factor is given as follows:

k = 0.5.

The y-coordinate then has the signal exchange, hence the figure is also reflected over the x-axis.

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Answer

y>18−4x

Step-by-step explanation:

Subtract 4 x from both sides of the inequality. y > 18 − 4 x Find the slope and the y-intercept for the boundary line.

Slope: − 4 y-intercept: ( 0 , 18 ) Graph a dashed line, then shade the area above the boundary line since y is greater than 18 − 4 x . y > 18 − 4 x

Answer:

3/2

Step-by-step explanation:

Step-by-step explanation:

\(x + \frac{1}{2} = 2 \\ x = 2 - \frac{1}{2} \\ x = \frac{3}{2} \)

The total distance of the obstacle course can be calculated by finding the distance between each pair of consecutive points and adding them up. The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2).

Using this formula, we can calculate the distances between each pair of consecutive points as follows:

Start to Tire Race: distance = sqrt((-40 - (-40))^2 + (-30 - (-10))^2) = 20 yards

Tire Race to Rope Climb: distance = sqrt((40 - (-40))^2 + (-30 - (-30))^2) = 80 yards

Rope Climb to Monkey Bars: distance = sqrt((40 - 40)^2 + (20 - (-30))^2) = 50 yards

Monkey Bars to Finish: distance = sqrt((10 - 40)^2 + (20 - 20)^2) = 30 yards

Adding up all these distances, we get a total distance of 20 + 80 + 50 + 30 = 180 yards for the obstacle course.

In a case whereby Richard is saving money for a down payment on a car He models his savings plan with the equation y = 200x + 500 based on his current monthly savings rate  y-intercept of linear model represent B. The starting amount in his savings account.

It should be noted that in a  linear equation the y intercept  can be seen as one that is starting point  whereby x is zero, which implkies that starting balance he had is 1000 in the bank.

Therefore, from the  equation y = 200x + 500, the  y-intercept of linear model serves as the starting amount in his savings account.

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Answer:

16

Step-by-step explanation:

First you subtract 12 by 8, which equals 4. The cube root of 4 is 64, 4 x 4 x 4. Now multiply 24 and 2 together to get 48. Subtract 64 by 48 to get 16.

Hope this helps! :DD

Answer:

16 ;)))))))))))))))))

Answer:

D. $30

Step-by-step explanation:

All you have to do is multiply 15 by 2 and you'll get 30.

Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

Answer:

9/f +6

Write 9/f as a fraction.

The value of {x] would be 1.

The point of intersection of the medians is called centroid.

Given is a triangle FGH as shown in the image.

The centroid divides the median in the ratio 2 : 1.

So, we can write -

HM : MT = 2 : 1

(2x + 1/5) : (13x - 2)/10 = 2 : 1

{(2x + 1/5)/(13/10x - 2/10)} = {2/1}

2x + 1/5 = 2(13x/10 - 2/10)

2x + 1/5 = 13x/5 - 2/5

(10x + 1)/5 = (13x - 2)/5

10x + 1 = 13x - 2

3 = 3x

x = 1

Therefore, the value of {x] would be 1.

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Answer:

The  AILP for management to decide  how many classes should be scheduled for each subject daily is

The objective function is mathematically represented as

       \(M  =  P_c  *  a  + P_w  *  b\)

=>    \(M  = 720  a  + 300  b\)

Now the first constraints to this functions is

     \(t_c  *  x  + t_w * y  \le t_a\)

=>  \( 7.5  x  + 3 y  \le 56\)

Another constraints to this function is

     \(k  x  +  u  y  \le  N\)

=>    \(6  x  +  2  y  \le  100\)

Here x and  y are the number of classes    

Step-by-step explanation:

From the question we are told that

   The time required for each ITC class is  \(t_c  = 7.5 \ hours\)

   The profit of each ITC class is  \(P_c  =  \$ 720\)

   The time require for  CWP  class is  \(t_w  =  3 \  hours\)

    The profit for   CWP  class is  \(P_w  =  \$ 300\)

   The total time available  is \(t_a  =  56 \  hours / day\)

   the maximum number of trainee that can be accommodated in a daily basis is   \(N  =  100\)

   The class size limit for  ITC  is  \(k  =6\)

    The class size limit for CWP is  \(u  =12\)

Generally the aim of Hi-Tech is to maximize profit

So the objective function will be a function that maximizes profit

Generally the objective function is mathematically represented as

       \(M  =  P_c  *  a  + P_w  *  b\)

=>    \(M  = 720  a  + 300  b\)

Now the constraints to this functions are

     \(t_c  *  x  + t_w * y  \le t_a\)

=>  \( 7.5  x  + 3 y  \le 56\)

Another constraints to this function is

     \(k  x  +  u  y  \le  N\)

=>    \(6  x  +  2  y  \le  100\)

Here x and  y are the number of classes

Answer:

17 and 18

Step-by-step explanation:

divide 35 by 2 and u get 17.5, this is in between 17 and 18 so that's why they are they consecutive numbers.

Answer:

384

Step-by-step explanation:

You multiply 16 by 24 and that equals 384. Good luck and have a great day!

campers = y and counselors = x, 1 counselor to 5 campers

Function graph that has y- intercept of 3 is g(x) = 3\((\frac{1}{4}) ^{x}\).

y- intercept will be 3 when we will put value of x = 0 and y will be 3 that graph will have y intercept 3

A) h(x) = 5\((2)^{x}\)

when x = 0

Any number with zero power is always 1

h(x) = 5

B) h(x) = 5\((0.5)^{x}\) + 0.5

when x = 0

h(x) = 5 + 0.5

h(x) = 5.5

C) g(x) = 3\((\frac{1}{4}) ^{x}\)

when x = 0

g(x) = 3

Here we get y intercept as 3.

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Answer:

D. (17,-1)

Step-by-step explanation:

We'll start by canceling out x. To do so, multiple the first equation by -1

-1( x - 2y)=( 19 )(-1)

This gives us:

-x +2y = -19

x + 3y = 14

Add the equations together:

→ 5y = -15

→ y = -1

Plug in y = -1 into an equation:

→ x + 3(-1) = 14

→ x - 3 = 14

→ x = 17

(17,-1)

Hope this helps!

The order of the matrices of each product is given as follows:

AB is nonexistent, BA is nonexistent.

Multiplication of matrices is applied multiplying the rows of the first matrix by the columns of the second matrix, and hence the number of columns of the first matrix must be equal to the number of rows of the second matrix.

For the product AB, we have that:

Hence the product is nonexistent.

For the product BA, we have that:

Hence the product is nonexistent.

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Answer:

8.38744e+160

Step-by-step explanation:

Answer:

You will have saved $69,612 after five years.

Step-by-step explanation:

This can be calculated using the for formula for calculating the future value of a growing annuity as follows:

FV = C * (((1 + r)^n - (1 + g)^n) / (r - g)) ……………………………………… (1)

Where;

FW = future value or amount you will have saved after five years = ?

C = first deposit = $1,000

r = periodic monthly interest rate of = 0.4%, or 0.004

g = growth rate of contribution = 0.1%, or 0.001

n = number of months = 5 years * 12 = 60

Substituting all the values into equation (1), we have:

FV = $1,000 * (((1 + 0.004)^60 - (1 + 0.001)^60) / (0.004 - 0.001))

FV = $1,000 * 69.612001854052

FV = $69,612.00

Therefore, you will have saved $69,612 after five years.

The area of the Region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

To find the area of the region bounded by y = √x, y = 2-x², and y = -√2x, we need to graph the equations and determine the points of intersection. Then we can integrate to find the area.

Firstly, we'll graph the equations and find the points of intersection:

y = √xy = 2-x²y = -√2xGraph of y = √x, y = 2-x², and y = -√2xWe need to solve for the points of intersection, so we'll set the equations equal to each other and solve for x:√x = 2-x²√x + x² - 2 = 0Let's substitute u = x² + 1:√x + u - 3 = 0√x = 3 - u

(Note: Since we squared both sides, we have to check if the solution is valid.)u = -2x²u + x² + 1 = 0 (substituting back in for u

)Factoring gives us:u = (1, -2)We can then solve for x and y:x = ±1, y = 1y = 2 - 1 = 1, x = 0y = -√2x = -√2, x = 2y = 0, x = 0Graph of y = √x, y = 2-x², and y = -√2x with points of intersection to find the area, we need to integrate.

The area is bounded by the x-values -1 to 2, so we'll integrate with respect to x:$$\int_{-1}^0 (2 - x^2) - \sqrt{x} \ dx + \int_0^1 \sqrt{x} - \sqrt{2x} \ dx$$

We can then simplify and integrate:$$\left[\frac{2x^3}{3} - \frac{2x^{5/2}}{5/2} + \frac{4}{3}x^{3/2}\right]_{-1}^0 + \left[\frac{2x^{3/2}}{3} - \frac{4x^{3/2}}{3}\right]_0^1$$$$= \frac{4}{3} + \frac{4}{3} - \frac{4}{15} + \frac{4}{3} - \frac{4}{3}$$$$= \frac{32}{15}$$

Therefore, the area of the region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

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Given:

(A)

Solve:

The probability of a prime number or a number greater than 3 coming up is given as follows:

5/6.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

When a dice is thrown, there are six possible outcomes, ranging from 1 to 6, and the desired outcomes are given as follows:

Hence the probability is given as follows:

5/6.

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The range of g is bounded between 1 - 2M and 1, but it may not include all values in that interval, depending on the range of f.

The range of function g depends on the range of the function f.

Let's start by assuming that we know the range of f.

If the range of f is Rf, then the range of -2f is the set {-2y | y ∈ Rf}, which is just the set of all numbers that can be obtained by multiplying an element of Rf by -2.

Finally, we add 1 to each of these values to get the range of g. Therefore, the range of g is:

Rg = {1 - 2y | y ∈ Rf}

In other words, the range of g is obtained by taking the range of f, multiplying each element by -2, and adding 1 to each result.

If we don't know the range of f, we can still say something about the range of g. Specifically, we know that g(x) can never be greater than 1 (since the largest value that -2f(x) can take is 0, and adding 1 to 0 gives us 1), and g(x) can never be less than 1 - 2M, where M is the largest possible value that f(x) can take on. In other words, the range of g is bounded between 1 - 2M and 1, but it may not include all values in that interval, depending on the range of f.

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The two answers for w are around -13.3 and 10.3, however the negative answer. As a result, the pathway should be 2.55 feet wide.

A two-dimensional surface's size or extend is measured in mathematics using the concept of area. Usually, it is expressed in square units like square inches or square meters. A shape's area can be determined by multiplying its length by its breadth or by applying the appropriate formula. For instance, the formula A = lw can be used to determine the area of a rectangle, where A stands for the area, l for the length, and w for the width. The formula A = r2, where A is the area and r is the radius of the circle, can be used to determine the area of a circle.

given

Let's begin by calculating the pool's area, which is 18 feet by 7 feet, or 126 square feet.

Let's name the walkway's width "w" (in feet). The pool and walkway's combined width will be 18 feet + 2 widths, and their combined length will be 7 feet + 2 widths (widths).

As a result, the pool's and walkway's area can be stated as follows:

672 square feet are equal to (18 feet + 2w) * (7 feet + 2w)

By extending this phrase, we get:

\(126 + 36w + 14w + 4w^2 = 672\)

By condensing and rearrangeing, we obtain:

\(4w^2 + 50w - 546 = 0\)

The two answers for w are around -13.3 and 10.3, however the negative answer should be disregarded because the width cannot be negative. As a result, the pathway should be 2.55 feet wide.

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Given the equations a × b = 5742 × 6368, a × c = 5748 × 6362, and c × b = 5738 × 6372, we need to determine the relationship between the three variables a, b, and c.

By comparing the given equations, we notice that the numbers on the right-hand side of each equation are very close to each other, differing only by small amounts. This suggests that a, b, and c are approximately equal.Since a × b, a × c, and c × b involve the same numbers with slight variations, we can conclude that a, b, and c are all very close in value.

Therefore, the inequality we can infer from this information is a ≈ b ≈ c, indicating that a, b, and c are approximately equal.

In simple terms, based on the given equations, it suggests that the values of a, b, and c are very similar or approximately equal to each other.

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The expression using only positive exponents is 1/(5¹² * 32³ * 9¹⁵)

Given that

5-12 * 32-3 * 9-15

Express properly

So, we have

5⁻¹² * 32⁻³ * 9⁻¹⁵

By using the definition of negative exponents, we have

1/5¹² * 1/32³ * 1/9¹⁵

By using the rules of exponents to simplify, we have

1/(5¹² * 32³ * 9¹⁵)

So, the solution is 1/(5¹² * 32³ * 9¹⁵)

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Answer:

  D. Square

Step-by-step explanation:

You want the best name for the quadrilateral with vertices (-3, 0), (-3, -3), (0, -3), and (0, 0).

A graph of the points is shown in the attachment. We notice the vertices are aligned with the grid, so the corner angles are all right angles.

The differences of x-coordinates and y-coordinates are both 3, so the side lengths of this rectangle are all 3 units.

The figure is all of a rectangle, rhombus, and square.

The most specific name for the figure is Square.

__

Additional comment

A trapezoid has one pair of parallel sides. This figure has two pairs of parallel sides, so is not a trapezoid.

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Answer:

Step-by-step explanation:

$2.12 - $1.65 = $0.47
$0.47 x 65 = $30.55 profit.

This is an exercise in the formula to calculate the profits obtained from the sale of a product, it is an essential tool in the management of any business. By knowing the profits obtained from the sale of a product, business owners and managers can make informed decisions and adjust their business strategies to maximize their profitability.

Profit is calculated by subtracting the total costs of production from the total revenue earned from the sale of a product. Total production costs include not only the direct costs associated with manufacturing the product, but also indirect costs, such as advertising and marketing costs, the cost of packaging materials, and other overhead.

The total income obtained from the sale of a product is the product of the number of units sold by the sale price per unit. It is important to remember that the selling price per unit must be sufficient to cover both the direct and indirect costs of production, and to provide a reasonable profit.

Once the profit earned from the sale of a product has been calculated, business owners and managers can use this information to improve their profitability. If profits are low, they might consider lowering production costs, raising the selling price, or finding ways to sell more units. On the other hand, if profits are high, they might consider increasing their investment in advertising and marketing to attract more customers and expand their business.

In addition, profit calculation can also help business owners and managers assess the feasibility of launching a new product or expanding into new markets. By calculating total production costs and potential total revenue, they can determine if the new product or market is profitable and make informed decisions about whether to proceed with the launch or expansion.

The total cost of making the handles is the product of the number of handles times the cost per unit:

Total cost = 65 potholders × $1.65/potholder = $107.25

The total revenue from selling the handles is the product of the number of handles times the selling price per unit:

Total revenue = 65 potholders x $2.12/potholder = $137.8

Elmo's profit is the difference between total revenue and total cost:

Profit = Total Revenue - Total Cost

Profit = $137.8 - $107.25 = $30.55

Profit = $30.55