Which are properties of rotations? Check all that apply.
1 Rotations are always counterclockwise.
2 Rotations preserve size.
3 Rotations of 360° map a figure to itself.
4 Lines connecting corresponding points on the pre-image and image are parallel.
5 Lines connecting corresponding points on the pre-image and image have equal length.
6 Lines connecting the center of rotation to the pre-image and the corresponding point on the image have equal length.

Answer:

Te plant was 228.29 centimeters tall.

Step-by-step explanation:

To find the size of the plant 14 days (2 weeks ago), we will use a formula called "exponential growth."

[tex]A=P(1+r)^{t}[/tex]

where

A=accumulated amount.

P=initial ammount

r=rate

t=elapsed time.

replacing the values ​​we have

A=452 centimeters

P=variable to find

r=5% = 0.05

t=2 weeks= 14 days

So, we substitute the values ​​in the equation

[tex]452=P(1+0.05)^{14}[/tex]

Then, we clear the variable P

[tex]P=\frac{452}{1.05^{14} }[/tex]

and perform the operations

[tex]P=\frac{452}{1.979931} =228.29centimeters[/tex]

In this exercise we have to perform the parameterization of the given function and we will have:

[tex]\int\limits_C {f} \, dr = f(1, 2)-f(-1, 2)= 2/3[/tex]

In there is some scalar function [tex]f(x, y)[/tex] such that:

[tex]\nabla f(x,y) = f(x, y) = x^2i+y^2j[/tex]

Then we want to find [tex]f[/tex] such that:

[tex]f'(x)= x^2= f(x,y) = \frac{x^3}{3} + g(y)\\f'(y)= y^2= f(x,y)= \frac{y^3}{3} + C\\f(x, y)= \frac{x^3}{3} +\frac{y^3}{3} + C[/tex]

So the vector filed [tex]f(x, y)[/tex] is conservative, which means the fundamental theorem applies; the line integral of [tex]f[/tex] along any path [tex]C[/tex] parameterized by some vector-valued function [tex]r(t)[/tex] over [tex]a\leq t\leq b[/tex] is given by:

[tex]\int\limits_C {f} \, dr\\\int\limits^t=a_t=b {f(r(t))} \, dt= f(r(b))-f(r(a))[/tex]

In the case:

[tex]\int\limits_C {f} \, dr = f(1, 2)-f(-1, 2)= 2/3[/tex]

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This problem requires calculation in multivariable calculus. Function f = ∇f when f(x, y) = x³/3 + y³/3. To calculate the line integral of ∇f · dr over the curve c, take the difference between the end and start points of the scalar function.

The subject for this calculation is multivariable calculus, dealing with operations such as the gradient (∇) and line integrals.

According to the given function f(x, y) in part (a), it can be seen that f = ∇f for f(x, y) = x³/3 + y³/3. The vector field of this function is conservative since it corresponds to the gradient of a scalar function.

For part (b), you will need to calculate the line integral of ∇f · dr over the curve c, which is y = 2x² from (-1, 2) to (1, 2). The result of this will be the difference between the end and start points of the scalar function: f(1, 2) - f(-1, 2).

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The double integral of the function f(x, y) = x over the rectangle defined by [1, 6] and [4, 5] is calculated through an iterated integral to be 17.5.

The problem asks to find double integral of the function f(x, y) = x over the rectangle R defined by the interval [1, 6] for x and [4, 5] for y. To find this, we perform an iterated integral. The integral is setup as follows:

∬Rf(x,y)dA = ∫ from 1 to 6 ∫ from 4 to 5 x dy dx

We first integrate with respect to y which gives us: xy| from 4 to 5 = x(5) - x(4) = x.

Then, we integrate this result with respect to x which gives us: 0.5x²| from 1 to 6 = 0.5(6^2) - 0.5(1^2) = 17.5

So, ∬Rf(x,y)dA equals to 17.5

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The approximate cost per square foot for the tiles is $3.22 when rounded to the nearest cent.

To calculate the price per square foot of tiles, divide the total cost of the tiles by the total number of square feet. The total cost given is $40.21, and the total area is 12 1/2 square feet.

First, convert the mixed number to an improper fraction. 12 1/2 is the same as 25/2 square feet. Now, to find the cost per square foot, perform the following division:

Price per square foot = Total cost / Total area in square feet

Price per square foot = $40.21 / (25/2 square feet)

Multiply by the reciprocal:

Price per square foot = $40.21 / 1 x 2 / 25

Price per square foot = $40.21 x 2 / 25

Price per square foot = $80.42 / 25

Price per square foot = $3.2168

Therefore, the approximate cost per square foot for the tiles is $3.22 when rounded to the nearest cent.

The approximate price per square foot is $3.22.

To find the price per square foot, divide the total cost by the total square footage. In this case, the cost is $40.21 and the square footage is 12 1/2 square feet.

1. Cost per square foot = Total cost / Total square footage

2. Cost per square foot = $40.21 / 12.5 sq ft ≈ $3.22/sq ft

1. Convert 12 1/2 square feet to a decimal: 12.5 sq ft.

2. Divide the total cost by the total square footage: $40.21 / 12.5 sq ft ≈ $3.22/sq ft.

To calculate the cost per square foot, you need to divide the total cost by the total square footage. In this case, the total cost is $40.21, and the total square footage is 12 1/2 square feet. First, convert 12 1/2 square feet to a decimal, which is 12.5 sq ft. Then, divide the total cost by the total square footage:

Cost per square foot = $40.21 / 12.5 sq ft ≈ $3.22/sq ft.

Therefore, the approximate price per square foot is $3.22.

complete question

A box contains 12 1/2 square feet of tiles and costs $40.21 what is the approximate price per square foot

Answer:

Parameter

Step-by-step explanation:

The given lines Y=(3/5)x -3 and 5y =3x-10 are examples of linear equations which, when solved, are found to be parallel due to their identical slope.

The lines given in the question are in the format y = mx + b, where 'm' is the slope and 'b' is the y-intercept. The equations are Y=(3/5)x -3 and 5y =3x-10. By comparing the coefficients, the slope of the first line is 3/5 and the y-intercept is -3. For the second equation, we first need to convert it into the 'y = mx + b' form. Dividing every term by 5 gives us y = (3/5)x - 2. Therefore, the slope of the second line is also 3/5 and the y-intercept is -2. Since both lines have the same slope, they are parallel lines.

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Answer:

3540.00

Step-by-step explanation:

The decimal 0.8333 is equivalent to the fraction 2/3.

To convert the decimal 0.8333 to a fraction, follow these steps:

Step 1: Let x be the decimal value:

x = 0.8333

Step 2: Multiply both sides of the equation by 10000 to remove the decimal:

10000x = 8333.3

Step 3: Subtract x from both sides of the equation:

10000x - x = 8333.3 - 0.8333

9999x = 8332.4667

Step 4: Divide both sides of the equation by 9999 to isolate x:

x = 8332.4667 / 9999

Divide both the numerator and the denominator by their greatest common divisor, which is 3333:

x = (8332.4667 ÷ 3333) / (9999 ÷ 3333)

x = (2.49995) / 3

Now, the fraction as a whole number over the denominator:

x = 2 / 3

Therefore, the fraction is 2/3.

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To convert 2.2 liters to cups, multiply by 4.22675. Rounded, it's approximately 9 cups. So, option C) [tex]$9$[/tex] cups is correct.

To find out how many cups 2.2 liters is equivalent to, we'll first convert liters to cups.

1 liter is approximately equal to 4.22675 cups.

So, to find out how many cups are equivalent to 2.2 liters:

[tex]\[ \text{Number of cups} = 2.2 \, \text{liters} \times 4.22675 \, \text{cups/liter} \][/tex]

[tex]\[ \text{Number of cups} \approx 9.29885 \, \text{cups} \][/tex]

Rounded to the nearest whole number, 2.2 liters of water is approximately equivalent to 9 cups. Therefore, the correct answer is:

C) [tex]$9$[/tex] cups

The correct question is:

Mary is 19 years old. She drinks the recommended intake of 2.2 liters of water and other beverages a day. About how many cups is this equivalent to?

A) 3 cups

B) 6 cups

C) 9 cups

D) 12 cups

The only value of x where f(x) = 0 can be determined by looking at the function's behavior near the x-axis and using the Intermediate Value Theorem. In this case, the potential x value is -9.

The one and only value of x where f(x) = 0 is the point of the function that intersects the x-axis. Since the function is continuous, it must cross the x-axis at this point due to the Intermediate Value Theorem.

To determine the possible value of x, we look at the given function values at x = -10 and x = -8 and identify where the function changes sign from negative to positive. The value of x where this sign change happens is the possible x value.

From the provided choices, the only value that would make this sign change possible is -9. Therefore, -9 could be the value of x where f(x) = 0.

Answer:

paralell lines, i think.

Step-by-step explanation:

The average speed of Mami on all surfaces is 10.64 km/hr.

Average is the mid value of two different higher and lower values. The average can be determined by taking the sum of all data and then dividing it by the number of data or the total value divided by the total no. of values.

Given a runner in 24 hours named Mami can run 255.303 kilometers on all surfaces.

∴ Her average speed is (255.303/24) km/hr.

= 10.64 km/hr.

∴ Her average speed is 10.64 km/hr all surfaces.

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Answer:

T = 13.9 + 12.85 + 14.82 + 12.74

Step-by-step explanation:

Great question, it is always good to ask away and get rid of any doubts that you may be having.

Based on the information in the question, the total time for the relay would be calculated by simply adding each of the four-relay members time during the 100 meter run. Therefore the expression would be

T = 13.9 + 12.85 + 14.82 + 12.74

T = 54.31 seconds.

If we decided to solve for the Total time (T) it would add up to 54.31 seconds for the relay time. But since the question did not ask for the total but just the expression. Then the answer is the expression above.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Carlene needs to sell 400 more T-shirts at $20.50 each to reach her goal of raising more than $8,900, after already raising $700.

The question asks us to determine how many more T-shirts, designated as x, Carlene needs to sell to reach her fundraising goal of more than $8,900, given that each T-shirt costs $20.50 and she has already raised $700. To solve for x, we can set up the following equation:

Total goal - Amount already raised = Amount still needed

$8,900 - $700 = $8,200

Next, we divide the amount still needed by the price per T-shirt to find out how many T-shirts need to be sold:

x = Amount still needed / Price per T-shirt

x = $8,200 / $20.50

x = 400

Carlene needs to sell 400 more T-shirts to reach her goal.

Final answer:

The 200 samples available for distribution will last for 8 hours at a consumption rate of 25 samples per hour.

Explanation:

The health food producer has 200 samples to distribute (250 total minus 50 for display), and if consumers take samples at a rate of 25 every hour, you would divide the 200 samples by the rate of 25 samples per hour to calculate how long the samples will last.

200 samples ÷ 25 samples/hour = 8 hours.

Therefore, the samples available for distribution at the mall will last for 8 hours before they run out, assuming the rate of consumption is constant at 25 samples per hour.

Answer:

Option 1 is correct.

Step-by-step explanation:

The given polynomial is

[tex]f(x)=20x^4+x^3+8x^2+x-12[/tex]

we have to find  all the rational roots of the polynomial f(x)

The Rational Root Theorem states that the all possible roots of a polynomial are in the form of a rational number i.e in the form of [tex]\frac{p}{q}[/tex]

where p is a factor of constant term and q is the factor of coefficient of leading term.

In the given polynomial the constant is -12 and the leading coefficient is 20.

[tex]\text{All possible factor of -12 are }\pm1,\pm2, \pm3, \pm4,\pm6,\pm12[/tex]

[tex]\text{All possible factor of 20 are }\pm1,\pm2,\pm4,\pm5,\pm10,\pm20[/tex]

So, the all possible rational roots of the given polynomial are,

[tex]\pm1,\pm2, \pm3, \pm4,\pm6,\pm12,\pm\frac{1}{2},\pm\frac{3}{2},\pm\frac{1}{4},\pm\frac{3}{4},\pm\frac{1}{10},\pm\frac{1}{5},\pm\frac{3}{5},\pm\frac{3}{10},\pm\frac{2}{5},\pm\frac{6}{5},\pm\frac{1}{20},\pm\frac{3}{20},\pm\frac{4}{5},\pm\frac{12}{5}[/tex]

Now, the rational roots of polynomial satisfy the given polynomial

[tex]f(-\frac{4}{5})=20(-\frac{4}{5})^4+(-\frac{4}{5})^3+8(-\frac{4}{5})^2-\frac{4}{5}-12=\frac{256}{625}\times 20-\frac{64}{125}+\frac{128}{125}-\frac{4}{5}-12[/tex]

[tex]=\frac{1024}{125}-\frac{64}{125}+\frac{128}{25}-\frac{4}{5}-12[/tex]

[tex]=\frac{960}{125}+\frac{128}{25}-\frac{4}{5}-12=12-12=0[/tex]

Hence, rational root.

[tex]f(\frac{3}{4})=20(\frac{3}{4})^4+(\frac{3}{4})^3+8(\frac{3}{4})^2+\frac{3}{4}-12=\frac{405}{64}+\frac{27}{64}+\frac{9}{2}+\frac{3}{4}-12=0[/tex]

rational root

[tex]f(1)=20(1)^4+(1)^3+8(1)^2+1-12=20+1+8-11=18\neq 0[/tex]

not a rational root.

hence, option 1 is correct

Answer:

The first option

Step-by-step explanation:

Right on edg:)