Polygon ABCD is drawn with vertices at A(1, 5), B(1, 0), C(−1, −1), D(−4, 2). Determine the image vertices of A′ if the preimage is rotated 270° counterclockwise.

A′(−1, −5)
A′(−1, 5)
A′(−5, 1)
A′(5, −1)

Answer:

To solve for the value of z in the equation 6 = 1/2 × z, we can use algebraic manipulation. First, we can multiply both sides of the equation by 2 to eliminate the fraction:

2 × 6 = 2 × (1/2 × z)

Simplifying the right side:

12 = z

Therefore, the value of z is 12.

Step-by-step explanation:

The scale factor used to dilate triangle ABC with vertices at A(−1, −1), B(1, 1), C(0, 1) into triangle A'B'C' with vertices at A′(−3, −3), B′(3, 3), C′(0, 3) is 3.

In mathematics, a scale factor is a number that scales, or multiplies, some quantity. In the context of geometry, the scale factor is the ratio of lengths in a pair of similar geometric figures or the ratio of the areas of two similar geometric figures. When one figure is transformed into another by dilation, the scale factor is the ratio of the lengths of corresponding sides. The scale factor can be greater than 1, less than 1, or equal to 1 (meaning no change in size).

We can determine the scale factor by comparing the lengths of sides of the two triangles.

The length of side AB is,

AB = [tex]\sqrt{[(1 - (-1))^2 + (1 - (-1))^2]}[/tex] = [tex]\sqrt{8}[/tex]

Similarly the length of side A'B' is,

A'B' = [tex]\sqrt{[(3 - (-3))^2 + (3 - (-3))^2]}[/tex] = [tex]\sqrt{72}[/tex]

So the scale factor will be,

A'B' / AB = [tex]\frac{\sqrt{72} }{\sqrt{8} }[/tex] = [tex]\sqrt{9}[/tex] = 3

Therefore, the scale factor used to dilate triangle ABC into triangle A'B'C' is 3.

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Answer:

height = 4 in

base = 5 in

Step-by-step explanation:

The area of a triangle can be found using the equation:

[tex]A = \frac{1}{2} bh[/tex]

where [tex]b[/tex] is the base of the triangle and [tex]h[/tex] is the base.

In order to plug into this equation, we need to use the relationship between the base and height. It is given that the base is 3 inches shorter than twice the height. Converting this to a mathematical equation:

[tex]b = 2h-3[/tex]

Since we are given that the area is 10 inches squared, we can now plug into the area equation to solve for the height (using the quadratic formula):

[tex]10 = \frac{1}{2} (2h-3)(h)\\2h^2 - 3h -20 = 0\\h = 4[/tex]

** We reject the negative solution of -5/2, since the triangle's height cannot be negative.

Now, we can simply plug in this height to solve for the base:

[tex]b = 2(4) - 3\\b = 5[/tex]

The number of cups of vegetable oil used by Colin to make 8 cakes is given by A = 5 1/3 cups

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data,

Let the equation be represented as A

Now, the value of A is

Substituting the values in the equation, we get

Let the number of cups of vegetable oil used by Colin to make 8 cakes be represented as A

Now , the number of cups of vegetable oil used by Colin to make 1 cake is given by = ( 2/3 ) cups of oil

And , number of cups of vegetable oil used by Colin to make 8 cakes A =

A = 8 x number of cups of vegetable oil used by Colin to make 1 cake

On simplifying the equation, we get

[tex]\text{A} = 8 \times \huge \text{(} \dfrac{2}{3} \huge \text{)}= \dfrac{16}{3}[/tex]

[tex]\boxed{\bold{A = 5 \dfrac{1}{3} \ cups}}[/tex]

Therefore, the value of A is 5 1/3 cups

Hence, the number of cups of vegetable oil required is 5 1/3 cups

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Complete question is-

Colin uses 2/3 cup of vegetable oil in each cake that he makes for his father's bakery.

If Colin made 8 cakes, how much oil did Colin use in all?

A. 5 1/3 cups

B. 7 1/3 cups

C. 8 2/3 cups

D. 16 1/3 cups​

Answer: 22

Step-by-step explanation:

The formula for perimeter of a rectangle is side 1 + side 1 + side 2 + side 2. Side one is 16. This means that 16x2 is 32. Then, you realize there are 44 meters remaining. 44/2=22. The other side is 22.

a. Decision rule: We reject the null hypothesis (μ ≤ 466) and accept the alternative hypothesis (μ > 466) if the test statistic is greater than 1.28 (from the z-table for a one-tailed test at the 0.10 level of significance).

b.The value of the test statistic is 3.75.

A null hypothesis is a statement that suggests there is no significant difference between two sets of data or that any observed difference is due to chance or random sampling error.

The alternative hypothesis is a statement that contradicts the null hypothesis and proposes that there is a significant relationship between two or more variables being studied.

According to the given information:

Dole Pineapple Inc. wants to know if their 466 mL cans of sliced pineapple are being overfilled. They took a random sample of 50 cans and found the average volume to be 467.3 mL, with a known population standard deviation of 0.88 mL.

To determine if the mean volume is greater than 466 mL at a significance level of 0.10, we use a one-tailed test and the following steps:

a. Decision rule: We reject the null hypothesis (μ ≤ 466) and accept the alternative hypothesis (μ > 466) if the test statistic is greater than 1.28 (from the z-table for a one-tailed test at the 0.10 level of significance).

b. Value of the test statistic: Using the formula for the z-test, we find the test statistic to be 3.75.

Since the test statistic (3.75) is greater than the critical value (1.28), we can reject the null hypothesis and conclude that the mean volume is significantly greater than 466 mL.

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a. Decision rule: We reject the null hypothesis (μ ≤ 466) and accept the alternative hypothesis (μ > 466) if the test statistic is greater than 1.28 (from the z-table for a one-tailed test at the 0.10 level of significance).

b.The value of the test statistic is 3.75.

What is Null hypothesis?

A null hypothesis is a statement that suggests there is no significant difference between two sets of data or that any observed difference is due to chance or random sampling error.

The alternative hypothesis is a statement that contradicts the null hypothesis and proposes that there is a significant relationship between two or more variables being studied.

According to the given information:

Dole Pineapple Inc. wants to know if their 466 mL cans of sliced pineapple are being overfilled. They took a random sample of 50 cans and found the average volume to be 467.3 mL, with a known population standard deviation of 0.88 mL.

To determine if the mean volume is greater than 466 mL at a significance level of 0.10, we use a one-tailed test and the following steps:

a. Decision rule: We reject the null hypothesis (μ ≤ 466) and accept the alternative hypothesis (μ > 466) if the test statistic is greater than 1.28 (from the z-table for a one-tailed test at the 0.10 level of significance).

b. Value of the test statistic: Using the formula for the z-test, we find the test statistic to be 3.75.

Since the test statistic (3.75) is greater than the critical value (1.28), we can reject the null hypothesis and conclude that the mean volume is significantly greater than 466 mL.

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Stop using brainly. This whole website has became a big money grab over the last few months and they will remove all your posts and answers unless you pay them money. I've had it happen several times now.

The area of a figure in the shape of a parallelogram is 74.4 m2 . If the height of the parallelogram is 6 m, the length of the parallelogram is 12.4 meters.

A parallelogram is a four-sided plane figure with opposite sides parallel and equal in length. It is a special type of quadrilateral, which is a polygon with four sides.

The opposite sides of a parallelogram are parallel, which means they have the same slope and never intersect. The opposite sides are also equal in length, which means they have the same distance between them.

The adjacent angles of a parallelogram are supplementary, which means they add up to 180 degrees. This property is known as the parallelogram law, which states that the sum of the squares of the diagonals of a parallelogram equals the sum of the squares of its sides.

The area of a parallelogram can be calculated by multiplying the base by the height. The base is one of the parallel sides, and the height is the perpendicular distance between the base and the opposite side.

The area (A) of a parallelogram is given by the formula:

A = base x height

where the base is the length of one of the sides of the parallelogram and the height is the perpendicular distance between the base and the opposite side.

In this problem, we are given the area of the parallelogram as 74.4 m² and the height as 6 m. Let the length of the parallelogram be denoted by b. Then, we can use the formula for the area of a parallelogram to write:

74.4 m² = b x 6 m

Solving for b, we get:

b = 74.4 m² / 6 m

b = 12.4 m

Therefore, the length of the parallelogram is 12.4 meters.

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In 1870, the French writer Jules Verne published his novel "Twenty Thousand Leagues Under the Sea", which tells the story of an underwater adventure aboard the submarine Nautilus.

The novel is considered one of Verne's most popular and well-known works, and it has been translated into many languages and adapted into numerous films, TV shows, and stage productions. "Twenty Thousand Leagues Under the Sea" is known for its imaginative portrayal of futuristic technology, such as the advanced submarine Nautilus, and its detailed descriptions of underwater life and exploration.

Therefore, The novel has also been praised for its themes of adventure, exploration, and the relationship between man and nature. It remains a classic in science fiction and adventure literature, and continues to be read and enjoyed by readers around the world.

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The absolute value equation is:

|x - 15| = 0

We want an absolute value equation that only has the solution x = 15.

So we must have something equal to zero (so we avoid the problem with the signs that we can have with other numbers)

So the equation will be something like:

|x - a| = 0

And the solution is 15, so:

|15 - a | = 0

then a = 15

The equation is:

|x - 15| = 0

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well, let's say the regular price is "x", which oddly enough is the 100%, and we know the store is doing a 25% sale, that means the new prices are 100% - 25% = 75%, 75% of the regular price, so when buying item for "$x", the sale price will just be

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{75\% of x}}{\left( \cfrac{75}{100} \right)x}\implies \text{\LARGE 0.75}\cdot x[/tex]

The value of tan(R) is 2/3

What is the trigonometric ratio?

The trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

using tan (θ) = opposite/Adjacent

Here, tan (R) = opposite/Adjacent

Where: opposite side = 14

Adjacent Side = 21

tan (R) = 14/21  = 2/3

tan (R) = 2/3

Hence, the value of tan(R) is 2/3

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The complete question is in the attached figure:

What is tan(R) =?

Make use of Excel, MATLAB, or Python to perform the curve fitting and find the cubic model for the given data.

To find a cubic model for the given data, we can use the method of least squares to fit the data points into a cubic polynomial of the form:

y = ax^3 + bx^2 + cx + d

where y represents the percentage of alternative and nuclear energy use, x represents the year, and a, b, c, and d are the coefficients to be determined.

Given the data points:

(2000, 10.7696)

(2003, 10.6167)

(2005, 10.6213)

(2008, 11.1977)

(2010, 11.7184)

(2011, 11.9921)

(2012, 12.0645)

Make use of Excel, MATLAB, or Python to perform the curve fitting and find the cubic model for the given data.

Once you have the cubic model, you can plug in x = 2016 to predict the alternative energy use for 2016.

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Answer:

-3x² +7x - 18

Step-by-step explanation:

Subtraction of expression:

   Multiply each term of 5x² - x + 7 by (-1)

2x² + 6x - 11 - (5x² - x + 7) = 2x² + 6x - 11 - 5x² + x - 7

Combine like terms. Like terms have same variable with same exponent.

2x² and (-5x²) are like terms. 2x² - 5x² = -3x²

6x and x are like terms. 6x + x = 7x

-11 and (-7) are constants. -11 - 7= -18

                                         = 2x² - 5x² + 6x + x - 11 - 7

                                         = -3x² + 7x - 18

Answer:

5.  x = 60

6.  F' (1, 4)

Step-by-step explanation:

5.  The angles shown are same side exterior angles, so they are supplementary (add to 180)

(x + 85) + 35 = 180

x + 120 = 180

x = 180 - 120 = 60

x = 60

6.  The line x = 1 is a vertical line, passing through the x=axis at (1, 0).  All x coordinates on this line equal 1.

The point F (3,4) is reflected in the line x = 1 at the point F' (1, 4)

Answer:

a. The circumference of the base is 2πr, where r is the radius of the cylinder. Therefore, the circumference of the base is:

2π(10) = 20π

So the circumference of the base is 20π.

b. The area of the base is πr^2, where r is the radius of the cylinder. Therefore, the area of the base is:

π(10)^2 = 100π

So the area of the base is 100π.

c. The lateral area of the cylinder is given by the formula 2πrh, where r is the radius of the cylinder and h is the height (or length) of the cylinder. Therefore, the lateral area of the cylinder is:

2π(10)(2) = 40π

So the lateral area of the cylinder is 40π.

d. The total surface area of the cylinder is the sum of the lateral area and the areas of the two bases. The area of each base is πr^2, which we already calculated to be 100π. Therefore, the total surface area of the cylinder is:

2(100π) + 40π = 240π

So the total surface area of the cylinder is 240π.

e. The volume of the cylinder is given by the formula πr^2h, where r is the radius of the cylinder and h is the height (or length) of the cylinder. Therefore, the volume of the cylinder is:

π(10)^2(2) = 200π

So the volume of the cylinder is 200π.

Answer: 205.031(nearest thousandth)

or 205.03125

Step-by-step explanation:

Answer: 337.5.

Step-by-step explanation:

Answer:

337.5

Step-by-step explanation:

The ordered pairs for the equation y = -7x + 8 are (0, 8), (1, 1), and (-1, 15).

To find ordered pairs for the equation y = -7x + 8, we can substitute different values of x and solve for y.

Let's choose three values of x:

When x = 0, y = -7(0) + 8 = 8. So one ordered pair is (0, 8).

When x = 1, y = -7(1) + 8 = 1. So another ordered pair is (1, 1).

When x = -1, y = -7(-1) + 8 = 15. So another ordered pair is (-1, 15).

Therefore, the ordered pairs  are (0, 8), (1, 1), and (-1, 15).

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The answers to both the subparts using the confidence interval are shown:
(A) His population's mean finishing time for the 100-meter event has a 99% confidence interval of (12.8081,15.5919).

(B) The right choice is Option B, which is Option II which is narrower.

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval.

Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.

The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.

So, let X represent the amount of time (in seconds) needed to complete a 100-meter race with Tom.

His population's mean 100-meter race finishing time falls within a 99% confidence interval of 12.8081 and 15.5919.

x = 14.2

s²= 0.9867

s= 0.9933

t α2, n-1 = 3.7074

The margin of error= 1.3919

lower bound= 12.8081

upper bound= 15.5919

Therefore, the answers to both the subparts using the confidence interval are shown:
(A) His population's mean finishing time for the 100-meter event has a 99% confidence interval of (12.8081,15.5919).

(B) The right choice is Option B, which is Option II which is narrower.

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Correct question:

Tom is preparing for a 100 meters race competition. During his practice last week, a sample of seven 100

meters races is reviewed, and the finishing times (in seconds) were as below:

13.4

15.6

13.1

14.5

14.2

13.3

15.3

It is reasonable to assume his finishing times are normally distributed.

(a) Construct a 99% confidence interval estimate of his population mean finishing time of 100 meters race.

(b) If the confidence interval estimate of his population mean finishing time of 100 meters is constructed at 95% instead of 99%, would the new confidence interval be (I) wider, (II) narrower, or (III) the same as the interval constructed at part (a)? (Just state your answer, no calculation is needed in part (b))

Therefore, the first Leap year after 2000 that the number of deer reaches 150 is 2000.1, or 2000 and 1/10 of a year.

If you sum up all the days on a calendar from January to December, there are 365 in a regular year. But about every four years, February has 29 days rather than 28. Therefore, a year has 366 days. There is a term for it: a leap year.

We must find x in the equation D=150 in order to determine the year that the number of deer exceeds 150 for the first time after 2000.

150=200+100sin(2πx)

Subtracting 200 from both sides, we get:

-50 = 100sin(2πx)

Dividing both sides by 100, we get:

-0.5 = sin(2πx)

To find the value of x that satisfies this equation, we can take the inverse sine of both sides:

sin⁻¹(-0.5) = 2πx

Using a calculator, we find that sin⁻¹(-0.5) = -π/6.

-π/6 = 2πx

Solving for x, we get:

x = -1/12

Since x is the number of years since 2000, we need to add 1/12 to find the first year after 2000 that the number of deer reaches 150:

2000 + 1/12 ≈ 2000.1

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Answer:

x > 3

Step-by-step explanation:

−8 + x/3 > -7

x/3 > 1

x > 3

We can't simplify anymore, so the answer is x > 3

The finance charge for Antoni Gaudi's bedroom set purchase is $731.08.

An installment refers to a sum of money that is paid back in parts over a period of time, typically with interest.

A loan is a financial agreement between a lender and a borrower, in which the lender provides the borrower with a specific amount of money or assets, which the borrower agrees to pay back with interest over a predetermined period of time. Loans can be used for a variety of purposes, such as purchasing a home, starting a business, or paying for education.

Based on the given information, the bedroom set sells for $2,650, and the financing requires a 15% down payment, which is $397.50 ($2,650 x 0.15).

Therefore, the amount financed is $2,252.50 ($2,650 - $397.50).

To calculate the finance charge, we need to know the total amount of payments Antoni Gaudi will make over the 42-month period. Each monthly payment can be calculated using the following formula:

Monthly Payment = (Amount Financed x (APR/12)) / (1 - (1 + APR/12)^-n)

Where:

APR is the annual percentage rate (12% in this case)

n is the total number of payments (42 in this case)

Plugging in the values, we get:

Monthly Payment = ($2,252.50 x (0.12/12)) / (1 - (1 + 0.12/12)^-42)

= $70.99 (rounded to the nearest cent)

Therefore, the total amount of payments Antoni Gaudi will make over the 42-month period is $2,983.58 ($70.99 x 42).

The finance charge can be calculated as follows:

Finance Charge = Total Payments - Amount Financed

= $2,983.58 - $2,252.50

= $731.08

Therefore, the finance charge for Antoni Gaudi's bedroom set purchase is $731.08.

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We can classify the polynomial as a "trinomial" with a degree of 3.

The given polynomial is:

9x^3 + 4x^2 - 7

The degree of a polynomial is the highest power of the variable present in the polynomial. In this case, the degree of the polynomial is 3, because the highest power of x in the polynomial is 3.

The number of terms in a polynomial is the number of individual expressions added or subtracted together. In this case, the polynomial has three terms: 9x^3, 4x^2, and -7.

Therefore, we can classify the polynomial as a "trinomial" with a degree of 3.

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Becky would have to invest 43,478 to be able to take the 200,000. The solution has been obtained by using the simple interest.

What is simple interest?

Simple interest is the cost of borrowing that is determined by utilising only the original principle and a constant interest rate.

We are given the following information:

Amount = 200,000

Interest rate = 9%

Time = 40 years

Let the principal be x.

So, we get

⇒ Amount = Principal + Interest

⇒ 200,000 = x + (9% of x) * 40

⇒ 200,000 = x + 0.09x * 40

⇒ 200,000 = x + 3.6x

⇒ 200,000 = 4.6x

⇒ x = 43,478

Hence, Becky would have to invest 43,478 to be able to take the 200,000.

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The median of the data set is: 95.5

What is median?

median is the number at the middle of the given data.

To find the median of the data set {102, 74, 86, 74, 96, 95, 103, 102}, we first need to arrange the values in order from lowest to highest:

74, 74, 86, 95, 96, 102, 102, 103

Since the data set has an even number of values, the median is the mean of the two middle values. In this case, the two middle values are 95 and 96.

Therefore, the median of the data set is: (95 + 96) / 2 = 95.5

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Step-by-step explanation:

y = x and y = 4

(x + y)²

(4 + 4)² = (8)² = 64

Answer:

24

Step-by-step explanation:

The formula for area of any triangle is (length * width) * 1/2. This makes the angle of 90 degrees irrelevant.

6 x 8 = 48

48 / 2 = 24