6.
CRITICAL THINKING Consider AJKL.
Rotate AJKL 90° clockwise about the origin.
How are the x- and y-coordinates of AJ'K'L'
related to the x- and y-coordinates of AJKL?
a.

Answer:

y=2x+10

Explanation: They start with paying $10 and have to pay and extra $2 for each time at the concession stand.

The calculated value of the force of the resistance is 15.62 N

We can use Newton's Second Law of Motion to solve this problem. The formula is:

F = m*a

where F is the net force, m is the mass of the object, and a is the acceleration.

In this case, the brick is falling through water, so there are two forces acting on it:

The net force is the difference between these two forces:

F_net = F_gravity - F_resistance

The weight of the object is:

F_gravity = m*g

So, we have

F_gravity = 2 kg * 9.81 m/s^2 = 19.62 N

Now we can use the formula for net force to find the force of water resistance:

F_net = F_gravity - F_resistance

F_resistance = F_gravity - F_net

F_resistance = 19.62 N - m*a

This gives

F_resistance = 19.62 N - 2 kg * 2 m/s^2 = 15.62 N

Therefore, the force of water resistance is 15.62 N.

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The value of the variable x for the similar triangles is equal to 25

The triangles BDR and QDC are similar, this implies that the length DC of the smaller triangle is similar to the length DR of the larger triangle

and the length DQ of the smaller triangle is similar to the length DB of the larger triangle

so;

x/(15 + x) = 40/64

64x = 40(15 + x) {cross multiplication}

64x = 600 + 40x

64x - 40x = 600 {subtract 40x from both sides}

24x = 600

x = 600/24

x = 25

Therefore, the value of the variable x for the similar triangles is equal to 25

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The interest that is paid on the loan in 6 years will be $4,200.

The amount of interest that is saved is $2,100.

The simple interest is a linear function of the number of years of the loan, value of the loan and the duration of the loan. The higher either of these values are, the higher the simple interest.

Simple interest = loan x time x interest rate

Simple interest if the loan is paid off after 6 years: $12,500 x 6 x 0.056 = $4,200

Simple interest if the loan is paid off after 3 years: $12,500 x 3 x 0.056 = $2100

Interest saved = $4200 - $2100 = 2100

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The probability of rolling an even number on a single die is 1/2, or 50%. This can be calculated by considering the possible outcomes of rolling the die.

There are six possible outcomes, and three of these are even numbers (2, 4, and 6). Therefore, there is a 3/6, or 1/2, chance of rolling an even number. In terms of probability, this can be expressed as a fraction, percentage, or decimal. As a fraction, the probability of rolling an even number on a single die is 3/6, or 1/2. As a percentage, the probability of rolling an even number on a single die is 50%. As a decimal, the probability of rolling an even number on a single die is 0.5. No matter how it is expressed, the probability of rolling an even number on a single die is 1/2, or 50%. This can be easily remembered by considering that there are six possible outcomes, and three of them are even numbers.

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Answer:

"Undefined slope"

Step-by-step explanation:

The line is vertical on the graph.

Every point on the line has the same x-coordinate.

If the line crosses the x-axis where x=-7, then the

x-coordinate of every point on the line is -7, and the

equation of the line is

                                     x = -7 .

Answer:

147

Step-by-step explanation:

A= h^b b=21*14= 147

Answer: 260 ft^2

Step-by-step explanation:

Find the area of the triangle: 0.5*height*base = 0.5*10*20 = 100 ft^2

Find the area of the rectangle: 20*8 = 160 ft^2

Add them together: 160+100 = 260 ft^2

Try going to the store and they should be surprisingly cheap.

Answer: here it is.

Step-by-step explanation:

The quadratic equation in the given graph can be written in the vertex-form as:

y = -2(x - 1)² + 4

We can see the graph of a quadratic equation. Remember that a quadratic equation with a vertex (h, k) and a leading coefficient a can be written as:

y = a*(x - h)² + k

in the graph we can see that the vertex is (1, 4), replacing that we will get:

y = a*(x - 1)² + 4

In the graph we also can see that the curve passes through the point (0, 2), replacing thesevalues in the equation we will get:

2 = a*(0 - 1)² + 4

2 = a + 4

-2 = a

Then the quadratic is:

y = -2(x - 1)² + 4

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Part A: The actual dimensions of the pool are 10 feet long and 5 feet wide.

Part B: the cost of the cover for the pool would be $15.00.

Dimension is a measure of a physical property of an object, such as its length, breadth, height, or mass.

Part A: The actual dimensions of the pool can be determined by using the given scale. To do this, we need to convert the given measurements in inches to feet. We can do this by dividing the given measurements in inches by the scale, which is 2 inches equals 7 feet.

The actual length of the pool is 20 ÷ 2 = 10 feet.

The actual width of the pool is 10 ÷ 2 = 5 feet.

Therefore, the actual dimensions of the pool are 10 feet long and 5 feet wide.

Part B: To calculate how much it would cost to buy a cover for the pool, we need to determine the area of the pool. We can do this by multiplying the length by the width of the pool.

Area = length x width

Area = 10 ft x 5 ft

Area = 50 ft²

Therefore, the cost of the cover for the pool would be

$0.30 x 50 ft² = $15.00.

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Question :

The blueprint of a pool has a scale of 2 inches equals 7 feet. The scale drawing is shown below. the length is 20 and the width is 10

Part A What are the actual dimensions of the pool? Blueprint: 10 in. Actual: ft Blueprint: 20 in. Actual: ft

Part B How much would it cost to buy a cover for the pool that costs $0.30 per square foot?

Answer: no they wouldn't be similar

Step-by-step explanation: if x=60 if triangle 1 then the third angle would be (180-(58+60)) =180-118=62
if we decide to calculate the third angle in triangle 2 we will have 180-(50+58) = 180-108=72

therefore not all angles in 1 are similar to angles in 2 so the triangles aren't similar

Algebraic expressions are useful for solving different and complex equations in mathematics, as well as for modelling real-life situations such as revenue, cost, inference, etc

The algebraic expression is: [tex]6x - 9[/tex].

To represent the sentence as an algebraic expression, we can follow these steps: Identify the variable. In this case, “a number” is x. Identify the operation. In this case, “less than” means subtraction and “times” means multiplication.

An algebraic expression is an expression that contains variables, constants and mathematical operations. Algebraic expressions are useful because they can help us solve different and complex equations.

For example, if you want to calculate the area of a rectangle with length x and width y, you can use the algebraic expression xy to represent the area.

Write the expression using the order of operations. In this case, we need to multiply six by x first, then subtract nine from the result.

Therefore, The algebraic expression is: [tex]6x - 9[/tex]

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Answer:

To calculate the payback period (PBP) for this project, we need to determine how long it will take for the initial cash outlay of $40,000 to be recovered from the after-tax cash flows.

Year 1 cash flow = $10,000

Year 2 cash flow = $12,000

Year 3 cash flow = $15,000

Year 4 cash flow = $10,000

Year 5 cash flow = $7,000

Total cash inflows for year 1 and year 2 = $10,000 + $12,000 = $22,000

Total cash inflows for year 3 = $15,000

Total cash inflows for year 4 = $10,000

Total cash inflows for year 5 = $7,000

Cumulative cash inflows for year 1 and year 2 = $22,000

Cumulative cash inflows for year 3 = $37,000

Cumulative cash inflows for year 4 = $47,000

Cumulative cash inflows for year 5 = $54,000

It can be seen that the cumulative cash inflows reach the initial cash outlay of $40,000 after year 2, and therefore the payback period for this project is 2 years. Since the payback period is less than the maximum PBP of 3.5 years set by management, this project can be considered acceptable.

So, Hodgman Honest should recommend that Basket Wonders should accept this project as it has a payback period of only 2 years, which is less than the maximum PBP of 3.5 years set by management.

Therefore , the solution of the given problem of percentage comes out to be the firm expects that each warranty it sells will be worth $1.41.

In statistics, "a%" is used to refer to a figure or number that is expressed as a percentage of 100. Additionally rare are the forms that "pct," "pct," or "pc". It is typically represented by the symbol "%," though. Additionally, there are not any indicators and the proportion of each item to the overall amount is flat. Since percentages typically add up to 100, they are essentially integers. Either the expression "fraction" or the symbol for percentage (%) .

Here,

The price to substitute each item is $200. The anticipated price for each component is thus:

Expected cost per product equals Replacement cost x Failure Probability

=> Cost per product anticipated = 0.008 x $200

=>  Expected price per item is $1.60.

So, the following is the anticipated value of each warranty sold:

Expected worth of the warranty = Failure rate x (Replacement cost - Cost of warranty)

=>   Expected guarantee value = 0.008 * ($200 - $22 - $1.60).

=>  Expected guarantee value = 0.008 * $176.40

=>  Expected warranty worth is $1.41

As a result, the firm expects that each warranty it sells will be worth $1.41.

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Step-by-step explanation:

Quadrilateral Sum Theorem. The total sum of the interior angles of a quadrilateral is 360°. A quadrilateral is formed by joining four non-collinear points. A quadrilateral has four sides, four vertices and four angles. Therefore, that is the Quadrilateral Sum Theorem.

The mass of the individual can be up to 87.27 kg for the hot-weather training strategy to be appropriate.

Given that the training strategy is appropriate for a BSA less than 2.0, we need to find the maximum mass (M) for the individual with a height (H) of 165 cm. The equation for BSA is:

BSA = √(H x M) / 3600

We can rearrange the equation to solve for M:

M = (BSA^2 x 3600) / H

Since we want the maximum mass for a BSA less than 2.0, we can use BSA = 2.0 as the upper limit:

M = (2.0^2 x 3600) / 165

M = (4 x 3600) / 165

M = 87.27 kg

The above question is in response to the full question as seen in the image;

A sports medicine specialist determines that a hot-weather training strategy is appropriate for a 165 cm tall individual whose BSA is less

than 2.0. To the nearest hundredth, what can the mass of the individual be for the training strategy to be appropriate?

The equation for BSA is BSA = √(H x M)/3600

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Answer:

The given expression is:

3x + 2 / (x + 1)(x² + x + 2)

To simplify this expression, we need to factor the denominator first:

x² + x + 2 = (x + 2)(x + 1)

So the expression becomes:

3x + 2 / (x + 1)(x + 2)(x + 1)

Next, we can use partial fraction decomposition to express the expression in terms of simpler fractions. Let's assume:

3x + 2 / (x + 1)(x + 2)(x + 1) = A/(x + 1) + B/(x + 2) + C/(x + 1)²

Multiplying both sides by the common denominator, we get:

3x + 2 = A(x + 2)(x + 1) + B(x + 1)² + C(x + 2)(x + 1)

Expanding the right side, we get:

3x + 2 = Ax² + 3Ax + 2A + Bx² + 2Bx + B + Cx² + 3Cx + 2C

Combining like terms, we get:

3x + 2 = (A + B + C)x² + (3A + 2B + 3C)x + (2A + B + 2C)

Since this equation holds for all values of x, the coefficients of each power of x must be equal on both sides. We can equate the coefficients of x², x, and the constant term to get a system of three equations for A, B, and C:

A + B + C = 0

3A + 2B + 3C = 3

2A + B + 2C = 2

Solving this system, we get:

A = 2/3

B = -1/3

C = -1/3

Substituting these values back into the partial fraction decomposition equation, we get:

3x + 2 / (x + 1)(x² + x + 2) = 2/3/(x + 1) - 1/3/(x + 2) - 1/3/(x + 1)²

Therefore, the simplified expression is:

3x + 2 / (x + 1)(x² + x + 2) = 2/3/(x + 1) - 1/3/(x + 2) - 1/3/(x + 1)²

Answer:

3. 216 cm^3

4a. A = 5 ft, B = 4 ft.

4b. 88 ft^3

Step-by-step explanation:

3. Separate into two rectangular prisms:

Volume of first one: 4cm*2cm*3cm = 24cm^3

Volume of second one: 4cm*12cm*4cm = 192cm^3

Add them together: 24 + 192 = 216cm^3

4a.

Length A = 8-3 = 5ft.

Width B = 8-4 = 4ft.

4b. Separate into two rectangular prisms:

Volume of first one: 2ft*3ft*4ft = 24ft^3

Volume of second one: 8ft*4ft*2ft = 64ft^3

Add them together: 24 + 64 = 88ft^3

Answer:

Step-by-step explanation:

To calculate the equal monthly payments under this loan, we can use the formula for the present value of an annuity due, since the payments are due at the end of each period. The present value of the equal monthly payments can then be set equal to the loan amount of R250,000, and we can solve for the payment amount.

First, we need to calculate the present value factor for an annuity due with 12 payments per year over a four-year period, using a nominal annual rate of 6%.

PVIFA(due) = (1 - (1 + r/n)^(-nt))/((r/n)(1 + r/n))

Where:

r = nominal annual rate = 6%

n = number of compounding periods per year = 12

t = number of years = 4

PVIFA(due) = (1 - (1 + 0.06/12)^(-12*4))/((0.06/12)(1 + 0.06/12)) = 43.232

Next, we can use the formula for the present value of an annuity due to calculate the equal monthly payments:

PMT = PV / PVIFA(due)

Where:

PV = present value of the loan = R250,000

PMT = 250000 / 43.232 = R5,785.97

Therefore, your equal monthly payments will be R5,785.97. At the end of the four-year period, you will also need to make a final balloon payment of R50,000 to fully pay off the loan.

Answer:

31000 - y = x

Step-by-step explanation:

Solve for x

[tex]12000\times5=9500+9500+10000+x+y[/tex]

Add and multiply the integers

[tex]60000=29000+x+y[/tex]

Subtract 29000 on both sides

[tex]31000=x+y[/tex]

Subtract y on both sides

[tex]31000-y=x[/tex]

It will take around 3.72 months to pay off the credit card debt.

The formula for APR is:

A = P * [tex](1 + r/n)^{nt}[/tex]

In which,

A = amount after compounding.

P = balance amount

r = rate of interest.

n = number of time compounded.

Initial balance: $30,000.

Payments per month = $200.

Expenses = $100

Balance amount = 30,000 - 12 *(200 - 100)

Balance amount = $28800

So, time taken for paying off credit card debt.

30,000 = 28800  [tex](1 + 0.24/1)^{1*t}[/tex]

[tex](1.24)^{t}[/tex] = 30,000 / 28800

[tex](1.24)^{t}[/tex] = 1.04

Solve by using logarithmic function.

t = ln (1.04) / 1.24

t = 0.31  year

t = 3.72 months

Thus, it will take around 3.72 months to pay off the credit card debt.

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The correct equation relating the volume of mulch purchased (v) and the total cost of the purchase (c) is: c = 33v + 720

The total cost formula is used to combine the variable and fixed costs of providing goods to determine a total.

The cost of the mulch depends on the volume purchased, so the equation relating the volume of mulch purchased (v) and the cost of the purchase (c) is:

c = 33v

The cost for 5 yards of edge material is $60, so the cost for 60 yards of edge material is:

60/5 x 60 = $720

Therefore, the total cost of the purchase is the sum of the cost of the mulch and the cost of the edge material:

total cost = cost of mulch + cost of edge material

c = 33v + 720

So the correct equation relating the volume of mulch purchased (v) and the total cost of the purchase (c) is: c = 33v + 720

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The family actually lost purchasing power due to the combination of the wage increase and inflation, as their budget did not keep pace with rising prices.

We need to calculate the inflation-adjusted increase in their wages.

First, we can find the amount of the wage increase by multiplying the original budget by the percentage increase:

Wage increase = $22,300 x 0.03 = $669

Next, we need to adjust for inflation. We can do this by finding the inflation rate as a decimal (5.6% = 0.056) and subtracting it from 1 to get the inflation-adjustment factor:

Inflation-adjustment factor = 1 - 0.056 = 0.944

Finally, we can calculate the inflation-adjusted wage increase by multiplying the wage increase by the inflation-adjustment factor:

Inflation-adjusted wage increase = $669 x 0.944 = $631.08

Therefore, the family's net gain in purchasing power is:

Net gain = Inflation-adjusted wage increase - Original budget

Net gain = $631.08 - $22,300

Net gain = -$21,668.92

So the family actually lost purchasing power due to the combination of the wage increase and inflation, as their budget did not keep pace with rising prices.

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The  X, Y, and Z values ​​are 84, 90, and 90, respectively. To answer this question, we need to understand the meaning of the words "median", "mean" and "range".

Median is the middle number of a set of numbers - it is the number in the middle when the numbers are ordered from smallest to largest.

Since the median is 90, this means that Y (the mean number) is 90. Since the average is 92, this means that the sum of the three numbers is 276 (92 x 3). The interval is 6, which means that the difference between the largest number and the smallest number is 6.

To solve for X and Z, we can use the equation X Y Z = 276. We know that Y is 90, so we can plug 90 into Y:

X 90 Z = 276

Then we can  subtract 90 from both sides to find the value of X and Z:

X Z = 186

Since the range of the three numbers is 6, this means that X and Z must be 6 plus. The only two numbers that differ by six and add up to 186 are 84 and 90.

Therefore the  X, Y, and Z values ​​are 84, 90, and 90, respectively.

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Answer: yes correct i love math

Step-by-step explanation:

This is a contradiction, so our original assumption that g(x) = f(x) must be false. Therefore, the solution is not true algebraically.

What are functions ?

In mathematics, a function is a rule that maps each element in a set (the domain) to a unique element in another set (the range). It is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions are commonly represented using function notation, where the symbol "f" is used to represent the function, and the input value is placed inside parentheses. For example, if the function takes the input "x" and returns the output "y"

According to the question:
To prove algebraically that g(x) = f(x), we need to show that the expressions for g(x) and f(x) are equivalent for all values of x. That is, we need to show that:

2x²+3x-1 = x²-3

We can start by simplifying both sides of the equation:

2x²+3x-1 - (x²-3) = 0

Simplifying the left side, we get:

2x²+3x-1 - x²+3 = x²+3x+2

Now we can simplify the right side:

x²+3x+2 = (x+1)(x+2)

Substituting this expression back into the equation, we get:

2x²+3x-1 - x²+3 = (x+1)(x+2)

Simplifying the left side again, we get:

x²+3x-4 = (x+1)(x-4)

Now we have:

(x+1)(x-4) = (x+1)(x+2)

We can cancel out the factor of (x+1) from both sides, since it is not equal to zero for any value of x:

x-4 = x+2

Subtracting x from both sides, we get:

-4 = 2

This is a contradiction, so our original assumption that g(x) = f(x) must be false. Therefore, the solution is not true algebraically.

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The probability that John's drive to work will take between 36 and 40 minutes is 0.3413.

Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. Probability is used in many areas of life, such as gambling, finance, and science. It is also used to make decisions in everyday life, such as estimating the likelihood of rain or the chance of winning a bet.

Using the normal distribution, the probability of John's drive taking between 36 and 40 minutes can be calculated using the standard normal distribution table. The formula for calculating the probability is: P(x<X<y) = P(y) - P(x).

For the given problem, the lower boundary is 36 minutes and the upper boundary is 40 minutes. Using the standard normal distribution table, the probability of John's drive taking between 36 and 40 minutes can be calculated by subtracting the probability of 36 minutes from the probability of 40 minutes. This gives us a probability of 0.3413.

Therefore, the probability that John's drive to work will take between 36 and 40 minutes is 0.3413.

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The probability that John's drive to work will take between 36 and 40 minutes is 0.3829.

Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. Probability is used in many areas of life, such as gambling, finance, and science. It is also used to make decisions in everyday life, such as estimating the likelihood of rain or the chance of winning a bet.

The probability that John's drive to work will take between 36 and 40 minutes can be calculated using a normal distribution table. The mean of the distribution is µ = 38 minutes, and the standard deviation is σ = 5 minutes.

To calculate the probability, we need to convert the given range (36 minutes to 40 minutes) into standard normal scores. This is done by subtracting the mean (µ = 38 minutes) from the lower bound (36 minutes) and then dividing by the standard deviation (σ = 5 minutes). The result is a standard normal score of -0.4. The same calculation is carried out for the upper bound (40 minutes) and the result is a standard normal score of 0.4.

Using a normal distribution table, we can then determine the probability that John's drive to work will take between 36 and 40 minutes. This probability is equal to the area under the normal curve between the two standard normal scores of -0.4 and 0.4. The result is a probability of 0.3829.

Therefore, the probability that John's drive to work will take between 36 and 40 minutes is 0.3829.

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