y
20
16
12
8
4
D
G
G
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4 8 12 16 20
Find the coordinates of each point in the original figure
D() E() F() G(__)
Find the coordinates of each point in the resulting image
D'(__) E (__) F'(__) G'(__)
What scale factor did we multiply the coordinates of the original preimage by in order to get the
coordinates of the resulting image?

To find a power series representation for the function \(\(f(x) = 5 + x\),\) we can start by expanding the function using the binomial series.

Using the binomial series expansion, we have:

\(\[f(x) = 5 + x = 5 + \sum_{n=0}^{\infty} \binom{1}{n} x^n\]\)

Since the binomial coefficient \(\(\binom{1}{n}\)\) simplifies to 1 for all \(\(n\),\) we can rewrite the series as:

\(\[f(x) = 5 + \sum_{n=0}^{\infty} x^n\]\)

The series \(\(\sum_{n=0}^{\infty} x^n\)\) is a geometric series with a common ratio of \(\(x\)\). The formula for the sum of an infinite geometric series is:

\(\[S = \frac{a}{1 - r}\]\)

where \(\(a\)\) is the first term and \(\(r\)\) is the common ratio. In this case, \(\(a = 1\)\) and \(\(r = x\).\)

Thus, we have:

\(\[f(x) = 5 + \frac{1}{1 - x}\]\)

Therefore, the power series representation for the function \(\(f(x) = 5 + x\) is \(f(x) = 5 + \sum_{n=0}^{\infty} x^n\)\) and its interval of convergence is \(\((-1, 1)\) (excluding the endpoints).\)

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Answer:

Step-by-step explanation:

If x represents one day of sales and x=12, then we can substitute that value into the equation to find the total number of pencils sold:

y = 160x

y = 160(12)

y = 1920

So the supply store sold a total of 1920 pencils on the day when x=12.

For a balloon mortgage, the monthly payments are usually lower, but there is a final "balloon" payment due at the end of the term.

a. Property Taxes:

The assessed value of the building is $500,000, and the property tax rate is 2.415%. To calculate the property taxes, we multiply the assessed value by the tax rate:

Property taxes = Assessed value * Tax rate

Property taxes = $500,000 * 2.415% (convert percentage to decimal)

Property taxes = $500,000 * 0.02415

Property taxes = $12,075

Therefore, the property taxes on the assessed value of the building will be $12,075.

b. Monthly Mortgage Payment:

To calculate the monthly mortgage payment, we need to consider the loan amount, interest rate, and loan term. The down payment is 20%, so the loan amount will be 80% of the market value of the building:

Loan amount = Market value * (1 - Down payment percentage)

Loan amount = $457,350 * (1 - 20%) (convert percentage to decimal)

Loan amount = $457,350 * 0.8

Loan amount = $365,880

We can now use this loan amount, along with the mortgage interest rate and loan term, to calculate the monthly payment using the formula for a fixed-rate mortgage:

Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Total number of months))

The monthly interest rate is the annual interest rate divided by 12, and the total number of months is the loan term multiplied by 12.

Annual interest rate = 4.55% (convert percentage to decimal)

Monthly interest rate = 4.55% / 12

Loan term = 30 years

Total number of months = 30 * 12

Now, let's calculate the monthly payment:

Monthly payment = ($365,880 * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Total number of months))

c. Total Interest Paid:

To calculate the total interest paid over the life of the loan, we multiply the monthly payment by the total number of months and subtract the loan amount:

Total interest paid = (Monthly payment * Total number of months) - Loan amount

d. Closing Costs:

The closing costs can vary, but a common range is between 2% and 5% of the purchase price. To calculate the range for closing costs, we'll use these percentages:

Minimum closing costs = Purchase price * 2%

Maximum closing costs = Purchase price * 5%

e. Balloon Mortgage Payment:

For a balloon mortgage, the monthly payments are usually lower, but there is a final "balloon" payment due at the end of the term. To calculate the monthly payment for the balloon mortgage, we'll use the loan amount, interest rate, and loan term:

Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Total number of months))

Now, let's calculate the monthly payment for the balloon mortgage.

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Answer:

f(n) = 2 × \(3^{n-1}\)

Step-by-step explanation:

In order to write an explicit rule for a geometric function, you need to know the common ratio; you can find the common ratio by dividing two consecutive terms:

6 ÷ 2 = 3, 18 ÷ 6 = 3, 54 ÷ 18 = 3, etc..

Now you know the common ratio is 3. At this point you can write your explicit function following the rule f(n) = [1st term] × [common ratio]^(n-1):

f(n) = 2 × 3^(n-1)

Answer:

4) 24

Step-by-step explanation:

Diagonals of a rectangle are congruent and bisect each other.

AE = x + 2

BD = 4x - 16

2AE = BD

2(x + 2) = 4x - 16

2x + 4 = 4x - 16

20 = 2x

x = 10

AC = BD = 4x - 16 = 4(10) - 16 = 40 - 16 = 24

Answer: 4) 24

Considering exponential functions, it is found that:

6.

12. The number of hits 3 weeks from now will be of 27,348, hence option B is correct.

An exponential function is modeled according to the rule given next:

\(y = ab^x\)

The parameters of the exponential function are defined as follows:

For item 6, considering the points (0,10) and (1,7.5), the parameters are given as follows:

For item 12, the initial amount and the rate of change are given as follows:

a = 34,000, b = 1 - 0.07 = 0.93.

Hence the number of hits x weeks from now is modeled according to the following function:

\(h(x) = 34000(0.93)^x\)

After 3 weeks, x = 3, hence the number of hits will be of:

\(h(3) = 34000(0.93)^3 = 27348\)

Meaning that option B is correct.

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Simplifying the fraction, we get:

Pr(A|B) = 1/36

We are given that Pr(A and B) = 1/216. Now let's calculate Pr(B):

Pr(B) = Pr(first die shows a 6) = 1/6

Now we can substitute these values into the formula:

Pr(A|B) = (1/216) / (1/6)

To divide fractions, we multiply the numerator by the reciprocal of the denominator:

Pr(A|B) = (1/216) * (6/1) = 6/216

Simplifying the fraction, we get:

Pr(A|B) = 1/36

Therefore, the answer is (a) 1/36.

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Answer:

\(x=6+3\sqrt{2}\) is the size of the square

Step-by-step explanation:

Let the side of the square cut from the cardboard be “x”

Size of the square base = \(12 -2x\), height of the box = x

Volume of square box = Area * height = \((12-2x)^2 * x\)

Differentiating the above equation and equating it to zero, we get –  

d/dx \(((12-2x)^2 * x)\)

d/dx\({(144 + 4x^2 -48x)*x}\)= d/dx \((144x + 4x^3 -48x^2)\)

d/dx \((144x + 4x^3 -48x^2) = 0\)

\(144+8x^2-96X= 0\\18 +X^2-12X = 0\)

On solving above equation, we get –  

\(x=6+3\sqrt{2} \\ x=6-3\sqrt{2}\)

Answer:

-4

Step-by-step explanation:

If you look on the x axis (Horizontal) the line hits the graph at -4

Answer:

The second option will cost her less than the first one.

Step-by-step explanation:

In order to solve this problem we will create two functions to represent the cost of the car in function of the miles drove by her.

For the first option we have:

\(cost_1(x) = 0.5*x\)

For the second option we have:

\(cost_2(x) = 5000 + 0.1*x\)

Since she intends to drive it for 10,000 miles per year for 6 years, then the total mileage she intends to drive her car is 60,000 miles. Applying this to the formula of each car and we have:

\(cost_1(60000) = 0.5*60000 = 30000\)

\(cost_2(60000) = 5000 + 60000*0.1 = 11000\)

The second option will cost her less than the first one.

Answer:

Point B

Step-by-step explanation:

-2 represents the X-value (horizontal line, or the one going sideways), and 5 represents the Y-value (vertical line, the one going up and down), so if you look, you'd find that point B is correct.

hope this helps!

ibrahim

Answer:

y = f(x-2) + 1

Step-by-step explanation:

The original functions looks like f(x) = |x|

For the new function the vertex has shifted -2 left (x) and up +1 (y)

So

y = f(x-2) + 1

Answer:

The cost for one pound would be 3.8

Step-by-step explanation:

if you do 19divided by 5 you get 3.8

HUNTER X HUNTER

wrong ANIME gtg

Answer: C

Step-by-step explanation:

12 %- 2 = -6

hope this helps :)

Answer:

8

Step-by-step explanation:

\( |15 - 23| = | - 8| = 8\)

Shawn’s science class takes 1 and half hour.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Shawn’s science class starts at 11:25 a. M.

It ends at 12:45 p. M.

Now, to find the How long is Shawn’s science class we have to find the time difference as

= 12: 45 pm - 11: 25 am

So, From 11:25 am to 12:25 pm it is one hour and additional of 30 minutes or half an hour.

This, the class is 1 and half hour long.

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Based on the given inequality of y≥ x - 1, the graph that matches it best is C. Graph A.

When graphing an inequality with the "greater or equal" and "less or equal" signs, the line will be a steady line as shown by graphs A and B.

If y is the larger or equal variable, the shaded area will be to the left of the line.

The inequality is y≥ x - 1 which means that the line should be steady and the shading should be on the left of the line. Graph A is therefore the correct graph.

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Step-by-step explanation:

Total yards =    11+11    +   31+31 = 84 yards

84 yd * $9/yd =  $ 756 total

Answer:

0.3 cups

Step-by-step explanation:

divide 6 by 20

The area of parallelogram with "one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches" is 60√3 inch².

A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus. A parallelogram is a geometric shape with sides that are parallel to one another in two dimensions. It is a type of polygon with four sides (also known as a quadrilateral) in which each parallel pair of sides is the same length.

Here,

A parallelogram has adjacent angles that add up to 180 degrees.

Since one angle of parallelogram is 120°.

240+2x=360

2x=120

x=60

The other will be 60°

The area of parallelogram= lh

l=15 inch

h=b(sin 60°)

=8*√3/2

h=4√3 inch

area of parallelogram= 15*4√3

= 60√3 inch²

The parallelogram's area is 60√3 inch² when "one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches."

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Store #1 has the better price amount , as the price per dozen eggs is $1.44, whereas Store #2 is $1.29 per dozen eggs.

Store #1 has the better price, as the price per dozen eggs is $1.44, whereas Store #2 is $1.29 per dozen eggs. To compare the prices, we need to calculate the cost per dozen eggs for each store. To do this, we divide the cost by the number of eggs. For Store #1, the cost per dozen eggs is $1.44 divided by 12, which is $0.12. For Store #2, the cost per dozen eggs is $4.68 divided by 36, which is $0.13. Therefore, Store #1 has the better price, as it is cheaper than Store #2. By comparing prices, we can find the best deal for our money. It is important to compare prices to get the best value for our money, as it can help us save money in the long run. Additionally, by comparing prices, we can make sure we are getting the highest quality product at the best price.

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Answer:

120 degrees

Step-by-step explanation:

vertical angle of isoceles = 180 - 2(base angles) = 180 - 2(30) = 120

Answer:

isosceles triangle means both angle or sides equal so in this way

unknown angle + 30 + 30 = 180°

unknown angle+60=180

so unknown angle=120°

which is vertical angle

\(-\frac{8}{5}\) = -1.6

\(-9\frac{3}{8}\) = -11.625

\(-\frac{9}{11}\) = -0.81818...

\(6\frac{7}{27}\) = 2.4814

Answer:

5 : 2 : 3

Step-by-step explanation:

Total sweets = 50

Sweet types:

Jellies = 25

Fizzy cola = 10

Number of boiled sweets = 50 - (25 + 10) = 15

Ratio of :

Jellies : Fizzy cola : boiled sweets

25 : 10 : 15

Divide through by 5

Jellies : Fizzy cola : boiled sweets

5 : 2 : 3

The following is the null and alternate hypothesis:

H₀ = u = 40.1

H₁ = u < 40.1

The null hypothesis should read as follows if we want to test the assertion that the average workweek has decreased:

The claim that there is a decrease in the typical work week should be made in the alternative hypothesis. The genuine mean is smaller than 40.1 can be used to express this.

The null hypothesis should assert that the average work week has not been significantly reduced, which is the opposite of the alternative. This can be expressed mathematically as 40.1 as the genuine mean.

Therefore, The alternative and null hypothesis are then:

H₀ = u = 40.1

H₁ = u < 40.1

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Given differential equation isdr/ dθ + r = 50 cos θ ........................... (1)This is a Bernoulli's differential equation. It can be converted into linear differential equation by using the substitution r = u^(-1)The differential equation becomes- u^(-2) du/dθ + u^(-1) = 50

cos θu^(-2) du/dθ - u^(-1) = -50 cos θThis is a linear differential equation which can be solved using integrating factor as follows Multiplying both sides by integrating factor   \(u^(-2) exp (-θ)d/dθ (u^(-1) exp (-θ)) =\)

\(-50 cos θ exp (-θ)d/dθ (u^(-1) exp (-θ)) = -50 cos θ exp (-θ)\) Integrating both sides

u^(-1) exp (-θ) = 50 sin θ + C1 Multiplying both sides by ru = r/r

\(= (1/u)So,r = 1/(50 sin θ + C1)\)This is the required solution.  The expression using r as variable is:r = 1/(50 sin θ + C1)

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The annual premiums for the following $250,000 Sun-Belt life insurance policies are:

The annual premiums for the following $250,000 Sun-Belt life insurance policies are as follows:

a. A 10-year life insurance policy purchased by a 30-year-old male would cost $36 x 12 = $432 per year.

b. A 20-year term policy for a 40-year-old female would cost $60 x 12 = $720 per year.

c. A 10-year term life insurance policy for a 40-year-old male would cost $51 x 12 = $612 per year.

d. A 20-year term life insurance policy for a 50-year-old female would cost $x x 12 = $12x per year.

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A rhombus is a quadrilateral that has four sides of equal length. A rhombus also has two diagonals, which are perpendicular bisectors of each other. This formula is given as follows: Perimeter = 4 × a, where a is the length of each side of the rhombus.

To find the perimeter of a rhombus using diagonals, follow these steps:

Step 1: Obtain the length of each diagonal of the rhombus.

Step 2: Use the length of the diagonals to find the length of each side.

Step 3: Add the length of each side to find the perimeter of the rhombus.

The perimeter is the sum of all the sides of a figure. To get the perimeter of a rhombus using diagonals, the length of each diagonal has to be found first. The formula for finding the length of each side of a rhombus is:  where the diagonal is the measure of the diagonal of the rhombus.

To find the perimeter of a rhombus, add the length of all the sides of the rhombus. This formula is given as follows: Perimeter = 4 × a, where a is the length of each side of the rhombus.

Therefore, the perimeter of a rhombus using diagonals can be found by following the above procedure and then using the formula to add all the sides of the rhombus.

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The trinomial 3x²+7x-12x-34-2x²+10 simplifies to x² - 5x - 24, which factors into (x + 3) (x - 8).

Alice was provided with the trinomial 3x²+7x-12x-34-2x²+10. To simplify the trinomial, Alice will need to group the like terms and combine them. Here's how to do it:

3x² - 2x² = x²7x - 12x = -5xNow, the trinomial becomes:x² - 5x - 24To factorize the trinomial, Alice can use different methods such as factoring by grouping, completing the square, quadratic formula, or graphing.

Here's how to factorize the trinomial by grouping:x² - 5x - 24 = (x + 3) (x - 8)Therefore, Alice can check her answer by expanding the factored expression.

When she expands (x + 3) (x - 8), she should get the original trinomial:x² - 5x - 24 = x(x - 8) + 3(x - 8) = (x + 3) (x - 8).Alice can also use the quadratic formula to solve the trinomial.

Here's how:Given the trinomial ax² + bx + c, where a = 1, b = -5, and c = -24The quadratic formula is:x = [-b ± √(b² - 4ac)] / 2aSubstituting the values of a, b, and c:x = [5 ± √(5² - 4(1)(-24))] / 2x = [5 ± √(121)] / 2x = [5 ± 11] / 2x = 8 or x = -3

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