Find g(x), where g(x) is the translation 2 units down of f(x)=x2.Write your answer in the form a(x–h)2+k, where a, h, and k are integers.

Answer:

The polynomial in factored form is:

P(x) = (x-10)(x+1)(x+1)

or, we can write it in expanded form as:

P(x) = x^3 - 8x^2 - 11x + 40.

Step-by-step explanation:

If the x-intercepts are at (10,0) and (-1,0), then the polynomial must have factors of (x-10) and (x+1). If the y-intercept is at (0,-40), then the constant term must be -40.

To satisfy the given requirements, we can write the polynomial as:

P(x) = (x-10)(x+1)(x-a)

where a is a constant that we need to determine. To find a, we can use the fact that the leading coefficient is 1.

Expanding the expression above, we get:

P(x) = (x^2 - 9x - 10)(x-a)

= x^3 - ax^2 - 9x^2 + 9ax - 10x + 10a

= x^3 - (a+9)x^2 + (9a-10)x + 10a

Since the leading coefficient is 1, we know that the coefficient of x^3 is 1. Therefore, we must have:

1 = 1*(-a-9)*(9a-10)

Simplifying and solving for a, we get:

a = -1

Therefore, the polynomial in factored form is:

P(x) = (x-10)(x+1)(x+1)

or, we can write it in expanded form as:

P(x) = x^3 - 8x^2 - 11x + 40.

The transformation is a reflection over the x-axis.

On the given graph we can see two triangles, one is pointing up and the other one is pointing down, from that we clearly can see that we hade a kind of reflection.

Now, the distance between the base of the top triangle and the x-axis is 4 units.

The distance between the top side of the bottom triangle and the x-axis is aslo 4 units.

Then the reflection is over the x-axis.

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The Slope of the line is 1.

The slope of a line is a numerical value that shows the stiffness or direction of the line. The formula used to find the Slope of the line is given by  

Where (x₁, y₁) and (x₂, y₂) are pairs of points that pass through the line.

Here we have

The pair of points (-6, -5) and (-4, -3)

By using the formula,

The slope of the line = [ y₂ - y₁] / [ x₂ - x₁]

= [ -3 - (-5) ] / [ -4 - (-6) ]

= [ -3 + 5 ]/ [ -4 + 6 ]

= [ 2/2] = 1

Therefore

The Slope of the line is 1.

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Answer:

230

Step-by-step explanation:

trying to find (in this case, 46.0), P is the percentage (20%), and B is the whole amount we're looking for. We can write this equation as:

46.0 = 0.20B

To solve for B, we can divide both sides by 0.20:

B = 46.0 / 0.20

B = 230

Therefore, 20% of 230 is 46.0.

The requried, Liam is 24 blocks away from his house.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,
A graph is shown, Liam left his house and drove to the store. He stopped and went inside. From there, he drove in the same direction until he got to the bank. He stopped and went inside the bank. Then he drove home. The graph below shows the number of blocks away from home Liam is x minutes after he left his house until he got back home.

In order to calculate Liam's distance after x = 15 minutes. Draw a perpendicular at x = 15 that intersects the curve. Since the line intersects the curve at y = 24. This implies that Liam is 24 blocks away from his house.

Thus, the requried Liam is 24 blocks away form his house.

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The standard deviations of the data are different.

The formula used to calculate the standard deviation of data is given by

x - mean of the data and n = number of observations

Here we have

(a) 4, 5, 11, 13, 13, 14

Mean of the data = [4 + 5 + 11 + 13 + 13 + 14 ]/6 = 60/6 = 10

On calculating deviations

=> ∑(x[tex]_{i}[/tex] - x)² = 96

=> √[ ∑(x[tex]_{i}[/tex] - x)²/n ] = √[ 96/ 6 ] = 4    

(b) 5, 7, 10, 10, 13, 15

Since the mean of the data is equal for all  

On calculating deviations

=> ∑(x[tex]_{i}[/tex] - x)² = 68

=> √[ ∑(x[tex]_{i}[/tex] - x)² /n ] = √[ 68/ 6 ] = 3.36

(c) 3, 10, 11, 11, 12, 13

On calculating deviations

=> ∑(x[tex]_{i}[/tex] - x)² = 64

=> √[ ∑(x[tex]_{i}[/tex] - x)² /n ] = √[ 64/ 6 ] = 3.26  

Therefore,

The standard deviations of the data are different.

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Thus, the archery set's discounted price is $61.10.

A reduction from the normal or list price. providing clients with a 10% discount. purchasing discounted tickets. (2): a proportionate reduction from an account of debt, typically provided in exchange for cash or quick payment.

The initial cost of the soccer jersey must be multiplied by (100% - 20%) = 80%, or 0.8, to determine the sale price after a 20% discount.

$85.75 x 0.8 = $68.60; Sale Price =Original Price multiplied by (1 - Discount)

Hence, the soccer jersey's retail price is $68.60.

We can apply the formula to get the tennis racket's original cost after just a 55% reduction and a $49.05 sale price:

Original Cost = Discounted Cost (1 - Discount)

Original Price = $49.05 / (1 - 55%) = $49.05 / 0.45 = $109.00

Hence, the tennis racket's original cost is $99.00.

The following formula can be used to determine the discount % for the archer set with just an original cost of $94.00 as well as a sale of $61.10:

Discount = (Original Price - Sale Price) / Original Price x 100%

Discount = ($94.00 - $61.10) / $94.00 x 100% = 35%

Hence, the archery set has a 35% discount.

The following equation can be used to determine the retail price of a archery kit with a 35% reduction and an original cost of $94.00:

Sale Price =Original Price multiplied by (1 - Discount)

Sale Price = $94.00 x (1 - 35%) = $61.10

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The percentage representation of T as part of S + T as required is; 40 percent.

As evident in the task content;

S is 150% of T.

S = 150/100 × T

S = 1.5T.

Therefore, expressing T as a percentage of S + T as required is as follows;

= (T / (S + T)) × 100%

substitute S = 1.5T into the equation

= T / (T + 1.5T) × 100%

= (1/2.5) × 100%

= 0.4 × 100%

= 40%.

Ultimately, the variable T is 40 percent of S + T.

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Here are the possible outcomes of randomly drawing two marbles from the bag:

O, G

O, B

G, O

G, B

B, O

B, G

There are six possible outcomes in total, each with an equal chance of occurring. Therefore, the theoretical probability of drawing an orange marble and a green marble from the bag is 1/6 or approximately 0.167.

The length of the guy wire to the nearest foot would be = 10 ft.

The relationship between the tower, guy wire and pole forms the shape of a right angle triangle.

The distance from the stake to the pole (opposite) =a = 5 ft

The distance from the pole to the tower (adjacent) =b= 9ft

The length of the guy wire= c = X

Using the Pythagorean formula:

c² = a² + b²

c² = 5² + 9²

c² = 25+81

c² = 106

C = √106

C= 10 ft ( to the nearest foot)

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Complete question:

A guy wire runs from the top of a cell tower to a metal stake in the ground. Sophie places a 7 ft tall pole to support the guy wire. After placing the pole, Sophie measures the distance from the stake to the pole to be 5 ft. She then measures the distance from the pole to the tower to be 9 ft. Find the length of the guy wire, to the nearest foot.

The amount that Fatima will pay each month for the student loan of $15,000 for 10 years at 8.25% interest is $183.98.

The monthly payment can be computed using an online finance calculator below.

The monthly payment shows the periodic amount that the borrower repays the financier to settle the student loan, including accumulated interest.

N (# of periods) = 120 months (10 years x 12)

I/Y (Interest per year) = 8.25%

PV (Present Value) = $15,000

FV (Future Value) = $0

Results:

Monthly payment (PMT) = $-183.98

Sum of all periodic payments = $-22,077.47

Total Interest = $7,077.47

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Answer:33 1/3

Step-by-step explanation:

Answer: 33.35

Step-by-step explanation:

6 2/3 is 6.67 in decimal form. 6.67 x 5 = 33.35

So, the answer is 33.35

I hope this helps!

Answer:The quotient of 8,426 divided by 82 can be found using long division or a calculator. When rounded to the nearest hundredth, the quotient is:

102.85

Therefore, the answer is 102.85.

Step-by-step explanation:

The correct statement regarding the sign of the function is given as follows:

A. The function is negative when x < 0.

We have to look at the graph of the function relative to the x-axis, as follows:

Hence the sign of the function for this problem is given as follows:

Meaning that option A is the correct option.

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Answer:

200

Step-by-step explanation:

300=150%

300/3=100

150/3=50

100x2=200

50x2=100

100%=200

Tom's total annual tax for the following year, assuming the tax table remains the same, is R325,287.17.

To calculate Tom's tax for the following year, we need to first calculate his current monthly PAYE (Pay As You Earn) deduction. We can use the current tax table to do this.

Tom's gross salary is R25,780.25 per month, and he is 45 years old, so according to the 2021/2022 tax table for individuals under 65 years old, his monthly PAYE deduction is:

= R1,458.75 + 25% of the amount over R14,958

= R4,569.96

Tom argues that his PAYE will increase by R593.09 for the following year. This means that his expected monthly PAYE deduction for the following year is:

= R4,569.96 + R593.09

= R5,163.05

Tom's salary for the following year will increase by 8.5%, so his new gross salary will be:

= R25,780.25 + (8.5% x R25,780.25)

= R27,959.83

Tom's pension fund contribution remains the same at 7.5% of his gross salary:

= R27,959.83 x 7.5%

= R2,097.49

His charity organization contribution increases by R50.00 per month:

= R50.00 x 12

= R600.00

Assuming the tax table remains the same as the previous year, Tom's new monthly PAYE deduction is:

= R1,577.98 + 26% of the amount over R17,708

= R5,502.86

To calculate Tom's total annual tax, we need to subtract his annual PAYE deduction from his gross salary and then add back his pension and charity contributions:

Total annual tax = (R27,959.83 x 12) - (R5,502.86 x 12) + R2,097.49 + R600.00

Total annual tax = R325,287.17.

Full question "Tom is 45 years old. He earns a gross salary of R25,780.25 per month.. Tom argues that his PAYE for the following year will increase by R593.09. The following year Tom's salary increases by 8.5%. How much tax will Tom pay per year, if he still contributes only 7.5% of his gross salary to a pension fund but increases his contribution to the charity organization by further R50.00 a month? Calculate as if the tax table for the following year remains the same."​

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Answer:

To set up this problem, you have to begin with Newton's second law, F = ma. There are two forces acting on this mass, gravity and air resistance. The force of gravity is constant and equal to -mg, where g = 9.8 m/s^2 and m is the given mass.

Step-by-step explanation:

Answer:

the velocity of the mass when it hits the ground is approximately 58.4 m/s.

Step-by-step explanation:

We can solve this problem using the equations of motion for a particle under constant acceleration. The acceleration of the particle is the sum of the gravitational acceleration and the air resistance force, which is given by 5v:

a = -g + 5v/m

where g is the acceleration due to gravity (9.8 m/s^2) and m is the mass of the particle (50 kg).

Using the initial conditions, we can find the velocity of the particle as a function of time. At t=0 (when the particle is shot from the cannon), the initial velocity is 10 m/s, and the initial position is 100 m above the ground. Therefore, we have:

v(0) = 10 m/s

y(0) = 100 m

Using the equation of motion for the position of the particle, we have:

y = y(0) + v(0)t + (1/2)at^2

where y is the position of the particle as a function of time t.

Solving for t when the particle hits the ground (y=0), we get:

0 = 100 + 10t + (1/2)(-g+5v/m)t^2

Simplifying, we get a quadratic equation in t:

-gt^2/2 + (5v/m)t + 100 = 0

Solving for t using the quadratic formula, we get:

t = (-b ± sqrt(b^2 - 4ac))/2a

where a = -g/2, b = 5v/m, and c = 100. Using the positive solution (since we're interested in the time it takes for the particle to hit the ground), we get:

t = (-5v/m + sqrt((5v/m)^2 + 4g100))/(-g)

Simplifying, we get:

t = (-5v/m + sqrt((5v/m)^2 + 3920))/(-4.9)

Now we can use the equation of motion for the velocity of the particle to find the velocity when it hits the ground:

v = v(0) + at

Substituting the time t we just found and solving for v, we get:

v = 10 + (-g + 5v/m)t

Substituting the value of t we just found and solving for v, we get:

v = 10 + (-g + 5v/m)(-5v/m + sqrt((5v/m)^2 + 3920))/4.9

Simplifying and solving for v, we get:

v ≈ 58.4 m/s

Therefore, the velocity of the mass when it hits the ground is approximately 58.4 m/s.

Answer:

Step-by-step explanation:

I got you

So,

The perimeter of a square is the sum of the lengths of all its sides, and since a square has all sides equal, we can find the length of one side by dividing the perimeter by 4:

32 cm ÷ 4 = 8 cm

Therefore, each side of the square measures 8 centimeters. To find the area of the square, we can use the formula:

Area = side length x side length

So, the area of the square is:

Area = 8 cm x 8 cm = 64 square centimeters

Therefore, the area of the square with a perimeter of 32 centimeters is 64 square centimeters.

The IQ score given the mean and the standard deviation, can be found to be 105. 25.

To find the indicated IQ score corresponding to a right tail area of 0.3694, we can use a standard normal distribution table or calculator. Using a calculator, we can find that the z-score corresponding to a right tail area of 0.3694 is approximately 0.35.

Once we have the z-score, we can use the formula z = (x - μ) / σ to solve for the IQ score :

0.35 = (x - 100) / 15

Solving for x, we get:

x = 0.35 x 15 + 100

= 105.25

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Answer:

best of my knowledge hope its right -4

Step-by-step explanation:

Answer:Hence, there are 1200 1200 1200 stiches per minute.

Step-by-step explanation:

Answer:

(w^4 - 81)(y^4)

Step-by-step explanation:

The following conclusions can be made regarding the given graph -

A proportional relationship between two variables {x} and {y} means that if {x} increases, then {y} increases with it proportionally.

Given is the graph of a straight line as shown in the image.

Only one single graph of a straight line is given. We cannot compare it, so we will analyze its meaning itself.

        {m} = (0 - 2.4)/(0.8 - 0)

        {m} = -2.4/0.8

        {m} = - 3

Therefore, the following conclusions can be made regarding the given graph -

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The answer is A. x y 2 4 3 6 4 9 for the given values.

What is proportional relationship ?

A proportional relationship is a type of relationship between two quantities, where the ratio of one quantity to the other remains constant. In other words, as one quantity increases or decreases, the other quantity changes in a way that maintains the same ratio between them.

For example, if we have a proportional relationship between

The table that shows a proportional relationship between x and y is A.

In a proportional relationship, the ratio of y to x remains constant. We can check this ratio for each table:

A. For x=2, y=4, so y/x=2. For x=3, y=6, so y/x=2. For x=4, y=9, so y/x=2. The ratio of y to x remains constant at 2.

B. For x=3, y=4, so y/x=4/3. For x=9, y=16, so y/x=16/9. For x=15, y=20, so y/x=4/3. The ratio of y to x is not constant.

C. For x=4, y=12, so y/x=3. For x=5, y=15, so y/x=3. For x=6, y=18, so y/x=3. The ratio of y to x remains constant at 3.

D. For x=1, y=4, so y/x=4. For x=2, y=8, so y/x=4. For x=3, y=15, so y/x=5. The ratio of y to x is not constant.

Therefore, the answer is A. x y 2 4 3 6 4 9 for the given values.

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A_n = A_n-1 + 2 represents the recursive formula.

A recursive formula is a formula or equation that describes a sequence or function in terms of itself. In other words, the formula for a given term or value depends on the formula for one or more previous terms or values.

For example, the Fibonacci sequence is a sequence of numbers in which each term is the sum of the two preceding terms: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...

This sequence can be described recursively using the following formula:

F(n) = F(n-1) + F(n-2)

where F(n) is the nth term of the sequence, F(n-1) is the (n-1)th term, and F(n-2) is the (n-2)th term.

Another example of a recursive formula is the factorial function, which is defined for non-negative integers n as:

n! = n * (n-1)!

This formula states that the factorial of n is equal to n multiplied by the factorial of (n-1). This recursive definition can be used to compute the factorial of any non-negative integer.

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So the balloon payment six years from now will be approximately $24,612.09.

(P, R, and T) / 100 is the SI unit.

In this case, SI stands for Straightforward Interest. P is the initial investment or loan amount, and R is the interest rate.

To find the amount of the balloon payment six years from now, we can use the formula for the present value of a series of payments:

PV = PMT x (1 - (1 + r/n)^(-nt)) / (r/n)

where PV is the present value of the payments, PMT is the monthly payment, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the total number of years for the loan.

In this case, we have:

PMT = $1,300 (paid for 5 years)

r = 0.05 (5% APR)

n = 12 (monthly compounding)

t = 6 (total loan term, including the first year with no payments)

To calculate the present value of the payments, we first need to find the present value of the $93,500 loan, one year from now, when the payments begin. This is equivalent to finding the future value of the loan now, and then discounting it back one year using the interest rate.

The future value of the loan after one year is:

FV = $93,500 x (1 + r)¹ = $98,175.00

The present value of this future amount, discounted back one year at an interest rate of 5%, is:

PV = $98,175.00 / (1 + r)¹ = $93,500.

So the present value of the loan one year from now, when the payments begin, is approximately $93,500.

Using this present value as the principal amount for the remaining 5 years of payments, we can calculate the balloon payment using the present value formula above:

PV = PMT x (1 - (1 + r/n)^(-nt)) / (r/n)

PV = $1,300 x (1 - (1 + 0.05/12)⁻⁶⁰) / (0.05/12)

PV = $68,887.91

Therefore, the balloon payment six years from now will be the remaining principal on the loan after five years of payments, which is:

Balloon payment = $93,500 - $68,887.91 = $24,612.09.

So the balloon payment six years from now will be approximately $24,612.09.

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Answer:

Step-by-step explanation:

its 1

Answer:

Step-by-step explanation:

caca