What steps transform the graph of y=x 2 to y=−2(x−1) 2 +5?

The total amount of money in the account at the end of 5 years, compounded monthly, is $2,329.48.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

To find the total amount of money in the account, we can use the formula for compound interest:

A = \(P*(1 + r/n)^{(n*t)}\)

where:

A is the total amount of money in the account

P is the principal or initial amount of money in the account

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time period in years

In this case, P = $2,000, r = 0.03 (since 3% is equivalent to 0.03), n = 12 (since the interest is compounded monthly), and t = 5.

So, plugging in the values, we get:

A = \(2000*(1 + 0.03/12)^{(125)}\)

A = \(2000(1.0025)^{60}\)

A = $2,329.48 (rounded to the nearest cent)

Therefore, the total amount of money in the account at the end of 5 years, compounded monthly, is $2,329.48.

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The profanity filter refused my answer.

Please find it in the txt file.

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Answer:

I like yo cut gggggggggggg

The square root function involves the square root symbol √ which is  mostly read as "square root of", the rule says that the square root of a number 'x' is a number 'y' such that y² = x.

We know that the square root of a number can be either positive or negative, but while defining the square root function, we restrict its range to be the set of all positive real numbers and hence making all square roots possible to be positive.

If the range for the square root of a number is set to be positive as well as negative it wont be a function that is why there is a restriction to the range of this set allowing only positive real numbers.

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Answer:

my x = ⅓

Step-by-step explanation:

\(6 + 3x = 7 \\ 3x = 7 - 6 \\ 3x = 1 \\ x = \frac{1}{3} \)

The final coordinate of the vertices after the transformation is F"(0, -1), G"(10, 5), H"(14, 15) and I"(4, -11)

If the resulting coordinate is centered at (12, -1), we will simply subtract the center from the resulting coordinate to get the final position of the rhombus. The final coordinates will be as shown:

F'' = (12-12, -2+1) = (0, -1)

G'' = (22-12, -6+1) = (10, -5)

H'' = (26-12, -16+1) = (14, -15)

I" = (16-12, -12+1) = (4, -11)

Therefore final coordinate of the vertices after the transformation is F"(0, -1), G"(10, 5), H"(14, 15) and I"(4, -11)

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Sarah uses 10 bottles of water to make juice, and each bottle holds 1/5 L of water. To find the total amount of water Sarah used, we multiply the number of bottles by the amount of water in each bottle. Therefore, Sarah used a total of 2 liters of water to make juice.

Given that each bottle holds 1/5 L of water, we can calculate the total amount of water used by multiplying the amount of water per bottle by the number of bottles.

Amount of water per bottle = 1/5 L

Number of bottles = 10

To find the total amount of water, we multiply:

Total water = (Amount of water per bottle) x (Number of bottles)

              = (1/5 L) x (10 bottles)

              = 2 L

Therefore, Sarah used a total of 2 liters of water to make juice.

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Answer:

Below.

Step-by-step explanation:

In Δ ABC m < B = 180 - (50+70) = 60 degrees.

in Δ DEF m < D = 180- ( 60 + 70) = 50 degrees.

BC = DE  ( both are 10 cm).

m < A = m < F  ( both 70 and directly opposite BC and DE)

m < C = m < D (corresponding angles and both = 50 degree)

Therefore, Δ's ABC and DEF are congruent by AAS.

Answer:

325

Step-by-step explanation:

500×.35=175

500-175=325

To find the area of a triangle given the angle C = 70°30' and sides a = 10 and b = 24, we can use the formula A = (1/2)ab sin(C). After substituting the values, the area of the triangle is approximately X square units.

To calculate the area of a triangle, we can use the formula A = (1/2)ab sin(C), where a and b are the lengths of two sides of the triangle, and C is the angle between them.

In this case, we are given that angle C is 70°30' (or 70.5°), and sides a and b are 10 and 24 units respectively.

We can now substitute the given values into the formula to find the area:

A = (1/2)(10)(24) sin(70.5°).

Using a calculator, we can evaluate the sin(70.5°) to get a decimal value.

Finally, we multiply the decimal value by (1/2)(10)(24) to obtain the area of the triangle.

Rounding the result to one decimal place gives us the final answer for the area of the triangle in square units.

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Answer:

2x + 50 is the area

so now find the area of the not shaded region

which is 2x + 2

subtract that from the answer

2x + 50 - 2x + 2

52

2(-2) + 1 + (-2) = 3(-2 - 2) + 7

-4 + 1 -2 = 3(-4) + 7

-3 - 2 = -12 + 7

-5 = -5

Yes

Answer:

6th

Step-by-step explanation:

the chart says not, 7th has majority

Answer:

If it doubles every 8 hours then

population = initial population * 2 ^ (hours / 8)

********************************************---------

after 26 hours

population increases by a factor of

2 ^ (26 / 8) = 9.51365692

************************************************--------

after 1 week, or 168 hours

population increases by a factor of

2 ^ (168 / 8) = 2 ^ 21 = 2,097,152

Answer:

alternate interior angles

Step-by-step explanation:

Answer:

C. Alternate interior angles

Step-by-step explanation:

they're on the inside but of opposite sides of line RK

The evaluated value of the expression (-1) x (-2) x (-3) x (-4) x (-5) is 120.

To evaluate the expression (-1) x (-2) x (-3) x (-4) x (-5), we can simplify the multiplication of negative numbers using the rules of multiplication.

When multiplying negative numbers, we follow the rule that states "a negative multiplied by a negative equals a positive." Applying this rule to the given expression:

(-1) x (-2) x (-3) x (-4) x (-5) = 1 x 2 x 3 x 4 x 5

Multiplying the positive integers together, we get:

1 x 2 x 3 x 4 x 5 = 120

The evaluated value of the expression (-1) x (-2) x (-3) x (-4) x (-5) is 120.

In simpler terms, multiplying five negative numbers together results in a positive value. In this case, the product of -1, -2, -3, -4, and -5 is 120. This illustrates the concept that when an odd number of negative factors are multiplied, the result is negative, but when an even number of negative factors are multiplied, the result is positive.

It's worth noting that the expression can be further simplified by removing the negative signs altogether, resulting in 1 x 2 x 3 x 4 x 5 = 120.

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Answer:

-3

Step-by-step explanation:

slope formula is y2-y1 over x2-x1

if we plug in the values and solve, that gets you -3.

Answer:

-3

Explanation:

1-(-2) divided by 3-4

Answer:

m∠JKM = 63°

m∠MKL = 27°

Step-by-step explanation:

Since ∠JKL is a right angle. This means that by summing up both m∠JKM and m∠MKL will result in the same as ∠JKL figure. Thus, m∠JKM + m∠MKL = m∠JKL which is 90° by a right angle definition.

\(\displaystyle{\left(12x+3\right)+\left(6x-3\right) = 90}\)

Solve the equation for x:

\(\displaystyle{12x+3+6x-3 = 90}\\\\\displaystyle{18x=90}\\\\\displaystyle{x=5}\)

We know that x = 5. Next, we are going to substitute x = 5 in m∠JKM and m∠MKL. Thus,

m∠JKM = 12(5) + 3 = 60 - 3 = 63°

m∠MKL = 6(5) - 3 = 30 - 3 = 27°

88.89 m³ of water will fill the Larger swimming pool.

The volume of a rectangular prism is given by V = lwh, where l is the length, w is the width, and h is the height. In this case, we have a pool that is in the shape of a rectangular prism and is filled with 15 m³ of water. Let's call the length of this pool "L", the width "W", and the height "H".

Then, we can write the equation:

V = LWHNow, we are told that there is a similar pool that has dimensions that are increased by a scale factor of 4/3. This means that the new length of the pool is (4/3)L, the new width is (4/3)W, and the new height is (4/3)H. We want to find out what volume of water will fill the larger swimming pool.

Let's call the volume of the larger swimming pool V', then we can write: V' = (4/3)L(4/3)W(4/3)H = (64/27)LWH

So, we can see that the volume of the larger swimming pool is (64/27) times the volume of the original swimming pool. To find out how much water will fill the larger swimming pool,

we need to multiply the volume of the larger swimming pool by the density of water. The density of water is approximately 1000 kg/m³ or 1 g/cm³, so we can use either of these values to convert the volume from cubic meters to kilograms or cubic centimeters to grams.

For simplicity, we will use the density of water in kg/m³. The volume of larger swimming pool = (64/27)LWH Volume of water needed to fill a larger swimming pool = (64/27)LWH × 1000 kg/m³= (64000/27)LWH kg= (2400/27) m³ = 88.89 m³

Therefore, 88.89 m³ of water will fill the larger swimming pool.

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Answer:

Jeffery walked 1.13 miles in total.

Step-by-step explanation:

1/3 and 4/5. To solve this problem, we need to find a common denomonator.

3 and 5

LCM = 15

1/3* 5/5

5/15

4/5 * 3/3

12/15

5/15 + 12/15 = 17/15

= 1.13

Answer:73 ft

Step-by-step explanation:

Answer:

(120 + 12.5pi) ft^2

Step-by-step explanation:

10ft x 12 ft = 120ft^2

10ft/2 = 5 ft (Radius)

Area of semi circle:

\(\frac{\pi r^{2} }{2} = \frac{\pi 5^{2} }{2} = 12.5\pi ft^{2}\)

Area = (120 + 12.5pi) ft^2

Answer:

Michelle < Staci < Kelly < Kyle

Kyle is the greatest distance from work, while Michelle is the closest to work.

Step-by-Step Explanation:

1 kilometer = 0.62137119 mile(s)

4.5 miles = 0.62137119 × 4.5 = 2.79617036 kilometers

4,200 meters = 4.2 kilometers

670,000 centimeters = 6.7 kilometers

So,

Michelle = 2.8 kilometers (rounded up)

Kelly = 5.6 kilometers

Staci = 4.2 kilometers

Kyle = 6.7 kilometers

So,

Michelle < Staci < Kelly < Kyle

Kyle is the greatest distance from work, while Michelle is the closest to work.

Hope this helps! ^^

Answer:

The answer is 0 a commonly used angle

Step-by-step explanation:

The quantity of data segments that the transmitting machine is allowed to send without receiving an acknowledgement for them is called the "window size" or "sending window."

The window size represents the number of data segments that can be transmitted consecutively without waiting for individual acknowledgments from the receiving machine. It is a mechanism used in many communication protocols to optimize data transmission efficiency.

By allowing the transmitting machine to send multiple data segments before waiting for acknowledgments, the window size helps reduce the overhead associated with frequent acknowledgments and allows for better utilization of network resources. Once the transmitting machine reaches the window size limit, it will typically pause and wait for the corresponding acknowledgments before continuing to send additional data segments.

The window size can be dynamically adjusted based on network conditions and the available buffer space at the receiving end to ensure efficient and reliable data transmission.

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In the first month's payment for a $180,000 mortgage with a 5.5 percent, 30-year loan, a portion will go towards the principal. The exact amount can be determined using an amortization schedule.

To calculate how much of the first month's payment goes towards the principal, we can follow these steps:

Step 1: Determine the monthly interest rate: Divide the annual interest rate by 12 to obtain the monthly interest rate. In this case, 5.5 percent divided by 12 equals 0.004583 (approx).

Step 2: Calculate the monthly payment: Use a loan payment formula or a mortgage calculator to determine the monthly payment amount. For a $180,000 mortgage with a 30-year loan term and a 5.5 percent interest rate, the monthly payment would be approximately $1,019.32 (approx).

Step 3: Create an amortization schedule: An amortization schedule shows the breakdown of each monthly payment, indicating the amount allocated to interest and principal. Using the loan details, create an amortization schedule or use an online tool to generate one.

Step 4: Locate the first month on the schedule: Find the first month's entry on the amortization schedule to determine the amount allocated to principal. This amount will vary depending on the specific terms of the loan. Locate the principal portion of the payment, which represents the reduction of the loan balance.

By following these steps and referencing the amortization schedule, you can determine the exact amount of the first month's payment that goes towards the principal of the $180,000 mortgage.

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Answer:

13.2 gallons

Step-by-step explanation:

286/260 *12 = 13.2

Answer:

about 13.2 gallons

Step-by-step explanation:

Easy way to calculate.

12 gallons divided by 260 miles

Take that answer and multiply it by 286.

The postfix expression of "7+5-3*2(6*7)/4" is "7 5 + 3 2 * 6 7 * 2 * - 4 /". Evaluating the postfix expression gives the result of the expression. The prefix expression for the given infix expression is "/ - + 7 5 * 3 * 2 ( * 6 7 ) 4".

To convert the infix expression "7+5-3*2(6*7)/4" into postfix expression, we follow the rules of operator precedence and associativity. The postfix expression is obtained by placing operators after their operands.

The postfix expression for the given infix expression is:

"7 5 + 3 2 * 6 7 * 2 * - 4 /"

To evaluate the postfix expression, we use a stack data structure. We scan the postfix expression from left to right and perform the corresponding operations.

Starting with an empty stack, we encounter the operands "7" and "5". We push them onto the stack. Then we encounter the operator "+", so we pop the last two operands from the stack (5 and 7), perform the addition operation (7 + 5 = 12), and push the result back onto the stack.

We continue this process for the remaining operators and operands in the postfix expression. Finally, after evaluating the entire expression, the result left on the stack is the final answer.

To convert the infix expression into prefix expression, we follow similar rules but scan the expression from right to left. The prefix expression is obtained by placing operators before their operands.

The prefix expression for the given infix expression is:

"/ - + 7 5 * 3 * 2 ( * 6 7 ) 4"

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Answer:

width = 14 feet

Step-by-step explanation:

the 7 part of the ratio relates to the length of the garden , then

24.5 feet ÷ 7 = 3.5 feet ← value of one part of the ratio , so

width = 4 × 3.5 feet = 14 feet

Answer:

34.6 units

Step-by-step explanation:

Given data

A (-5, -5), B (3, 4)

distance is

\(d= \sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)\\\\d= \sqrt((3 +5)^2 + (4 +5)^2)\\\\d= \sqrt((8)^2 + (9)^2)\\\\d= \sqrt(64 +81)\\\\d= \sqrt(145)\\\\d= 12.04\)

B (3, 4), C (3, -5)

\(d= \sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)\\\\d= \sqrt((3 -3)^2 + (-5-4)^2)\\\\d= \sqrt((0)^2 + (-9)^2)\\\\d= \sqrt(0 +81)\\\\d= \sqrt(81)\\\\d= 9\)

C (3, -5), A (-5, -5)

\(d= \sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)\\\\d= \sqrt((-5 -3)^2 + (-5-5)^2)\\\\d= \sqrt((-8)^2 + (-10)^2)\\\\d= \sqrt(64 +100)\\\\d= \sqrt(164)\\\\d= 12.80\)

Hence the perimeter

= 12.80+9+12.80

=34.6 units

The length and width of a similar rectangular screen are 132.5 meters and 25.5 meters, respectively.

Let's assume the width of the rectangular screen to be "w" meters.

According to the given information, the length of the screen is 10 meters more than 5 times its width, which can be expressed as

Length = 5w + 10

The viewable area of the screen is given as 8,400 square meters. We know that the formula for the area of a rectangle is

Area = Length x Width

Substituting the values from the given information, we get

8,400 = (5w + 10) x w

Expanding the right-hand side, we get

8,400 = 5w² + 10w

Rearranging the terms, we get a quadratic equation in standard form

5w² + 10w - 8,400 = 0

We can solve this quadratic equation by factoring or by using the quadratic formula. I'll use the latter method here:

w = [-b ± sqrt(b² - 4ac)] / 2a

where a = 5, b = 10, and c = -8,400. Substituting these values, we get:

w = [-10 ± sqrt(10² - 4(5)(-8,400))] / 2(5)

w = [-10 ± sqrt(70,100)] / 10

w = [-10 ± 265] / 10

Taking only the positive solution, we get

w = (255) / 10 = 25.5

Therefore, the width of the rectangular screen is 25.5 meters.

Now we can find the length by using the formula

Length = 5w + 10

Substituting the value of w, we get

Length = 5(25.5) + 10 = 132.5

Therefore, the length of the rectangular screen is 132.5 meters.

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