The coordinates of the vertices of triangle ABC are A(4, 2), B(6, 7), C(13, 1). Triangle ABC is reflected across y=−x . What are the vertices of triangle A′B′C′ ? Enter your answers in the boxes.

Answer:

10m²

Step-by-step explanation:

A=b×h/2=4×5/2=20/2=10m²

Hope this helps!

Therefore, the common difference of the arithmetic sequence is 1.5.

To find the common difference of an arithmetic sequence, you need to know at least two consecutive terms of the sequence. The common difference is the constant amount by which each term increases or decreases from the previous term.

If you have the first term (a1) and the second term (a2) of an arithmetic sequence, you can find the common difference (d) using the formula:

[tex]d = a_2 - a_1[/tex]

For example, consider the arithmetic sequence: 3, 7, 11, 15, ...

Here, a1 = 3 and a2 = 7. Substituting these values in the formula, we get:

[tex]d = a_2 - a_1 = 7 - 3 = 4[/tex]

So, the common difference of this sequence is 4.

Let the first term of the arithmetic sequence be "a", and let the common difference be "d".

Then the seventh term would be:

[tex]a + 6d = 10.2[/tex]

And the twelfth term would be:

[tex]a + 11d = 17.7[/tex]

Now we have two equations with two variables. We can solve for "a" and "d" using these equations.

First, we can subtract the first equation from the second equation:

[tex](a + 11d) - (a + 6d) = 17.7 - 10.2[/tex]

Simplifying this equation, we get:

[tex]5d = 7.5[/tex]

Dividing both sides by 5, we get:

[tex]d = 1.5[/tex]

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The probability of selecting a blue spool is 14% greater than the probability of selecting an orange spool.

Probability is a branch of mathematics that deals with the study of random events or phenomena. It involves the calculation of the likelihood or chance of an event occurring, based on the available information or data.

Percent is a mathematical concept used to represent a part of a whole as a fraction of 100.

To calculate the probability of selecting a blue spool or an orange spool, we need to first find the total number of spools and the number of blue and orange spools.

The total number of spools is: 8+5+7+10+3+6+4+7 = 50

The number of blue spools is: 10

The number of orange spools is: 3

Therefore, the probability of selecting a blue spool is: 10/50 = 0.2 or 20%

The probability of selecting an orange spool is: 3/50 = 0.06 or 6%

The difference in probability is: 20% - 6% = 14%

Therefore, the probability of selecting a blue spool is 14% greater than the probability of selecting an orange spool.

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The standard deviation of the difference Y - X depends on the standard deviations of both X and Y, and is given by the formula below.

(b) (i) The mean of the difference Y - X is μY - μX, which is 0 since both X and Y have the same mean, μ.

(b) (ii) The standard deviation of the difference Y - X is √(σY^2 + σX^2), where σY and σX are the standard deviations of Y and X, respectively. Assuming that the values of X are independent of the value of Y, we can use the formula for the variance of the difference of two random variables to get:

Var(Y - X) = Var(Y) + Var(X) - 2Cov(Y, X)

where Cov(Y, X) is the covariance between Y and X. Since Y and X have the same mean, we have:

Cov(Y, X) = E[(Y - μ)(X - μ)] = E[(Y - μ)X] - μE[X] = E[(Y - μ)X] - μ^2

where E[] denotes the expected value. Since X and Y are independent, we have:

E[(Y - μ)X] = E[Y - μ]E[X] = 0

Therefore, we get:

Var(Y - X) = Var(Y) + Var(X) = σY^2 + σX^2

Taking the square root of both sides gives us the standard deviation of Y - X:

SD(Y - X) = √(σY^2 + σX^2)

Therefore, the standard deviation of the difference Y - X depends on the standard deviations of both X and Y, and is given by the formula above.

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Therefore, it will cost $8400 to build a floor in the storage house with dimensions 12 feet wide, 10 feet long, and 8 feet high.

Square feet (often abbreviated as sq ft or ft²) is a unit of area commonly used in the United States and other countries that measures the area of a two-dimensional space. One square foot is equal to the area of a square with sides that are each one foot long. For example, a room that measures 10 feet by 12 feet has an area of 120 square feet (10 x 12 = 120). Square feet are commonly used to measure the size of houses, apartments, and commercial spaces, as well as outdoor areas such as yards or gardens.

To calculate the cost of building a floor in the storage house, we need to first determine the area of the floor.

The area of the floor is simply the product of the length and width of the storage house. Therefore:

[tex]Area of floor = Length * Width = 12 ft *10 ft = 120 sq ft[/tex]

To calculate the cost of building the floor, we can multiply the area of the floor by the cost per square foot:

Cost of building floor = Area of floor × Cost per square foot

[tex]Cost of building floor = 120 sq ft * $70/sq ft = $8400[/tex]

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Answer:

The pages that will be favored for the search terms Chevrolet AND Corvette are Pages that include Chevrolet Corvette.

Step-by-step explanation:

I hope it helps:)

Answer:

  a) sin(β) = 7/6 is false for any β

  b) angle β is not a real angle

Step-by-step explanation:

You want to use the Sine Law to show that a triangle with sides of lengths 6 and 10 and a smallest angle of 44.5° is impossible.

The Sine Law tells you side lengths are proportional to the sines of their opposite angles.

  sin(β)/10 = sin(44.5°)/6

  sin(β) = 10(0.7)/6

  sin(β) = 7/6

The angle β does not exist. The maximum value of the sine function is 1. There are no angles for which the sine is greater than 1.

The triangle is impossible because angle β cannot exist.

In effect, the angle 44.5° is too large, or side 10 is too long, or side 6 is too short for the figure to be a triangle.

__

Additional comment

In the realm of complex numbers, β ≈ π/2 -0.569618i radians, about (90 -32.64i)°. You cannot draw this complex angle with your real pencil.

a) For any, sin(β) = 1.17 is false.

b) Angle (β) is not a true angle.

In the branch of mathematics known as trigonometry, the relationships between the sides and angles of triangles are examined.

It involves the study of trigonometric functions like sine, cosine, tangent, cotangent, secant, and cosecant that describe the connections between the sides and angles of a right triangle.

(a) Using the Sine Law, we have:

sin(β)/10 = sin(44.5°)/6

Multiplying both sides by 10, we get:

sin(β) = (10/6)sin(44.5°)

sin(β) = 1.17

However, this is impossible since the sine of an angle can never be greater than 1. Therefore, there is no value of β that satisfies the equation, and we cannot find the value of B.

(b) The fact that the sine of β is greater than 1 means that there is no angle whose sine is equal to that value.

Therefore, there is no possible angle for β that can satisfy the given conditions of the triangle.

This means that the triangle is impossible and cannot exist with the given side lengths and angle measures.

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Where the daily growth factor is 1.15 and the starting height in inches is 7.

a. Given by, the function that calculates the height of the beanstalk in relation to the time since Gregory planted it.

[tex]f(t) = 7(1.15)^t[/tex]

where the daily growth factor is 1.15 and the starting height in inches is 7.

B). The following ratios can be calculated using the formula from section (a):

f(1)/f(0) = (71.15¹)/(71.15⁰) = 1.15

f(2)/f(1) = (71.15²)/(71.15¹ = 1.15

f(1)/f(1) = (71.15¹)/(71.15¹) = 1

[tex]f(9.56)/f(8.56) = (71.15^{9.56})/(71.15^{8.56})[/tex] ≈ 1.15

[tex]f(8.56)/f(8.55) = (71.15^{8.56})/(71.15^{8.55})[/tex] ≈ 1.15

c. For the any value of z, we have:

[tex]f(z+1)/f(z) = (71.15^{(z+1)})/(71.15^z)[/tex] = 1.15

and

[tex]f(z)/f(z-1) = (71.15^z)/(71.15^{(z-1)})[/tex] = 1.15

For question 6:

a. As a increases throughout the function's domain, f(z) [Select an answer]

Since the base of the exponential function is less than 1 (0.69 < 1), as x increases, f(x) will approach 0.

b. The 1-unit growth factor of f is

The 1-unit growth factor for f is 0.69, since f(x+1)/f(x) = 0.69.

c. The -unit growth factor of f is

The 1/2-unit growth factor for f is (0.69)¹/₂, since f(x+1/2)/f(x) = (0.69)¹/₂.

d. The 6-unit growth factor of f is

The 6-unit growth factor for f is (0.69)⁶, since f(x+6)/f(x) = (0.69)⁶.

e. The 6-unit percent change of  f is

The 6-unit percent change for f is ((0.69)^6 - 1) * 100%, which is approximately -38.77%.

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The area of the 2 by 2 unit square is 4 square units.

Assuming that the shape being referred to is a square with sides of length 2 units as shown in the figure, the area can be calculated as follows:

Area of a square = (side length)^2

In this case, the side length is 2 units, so we can substitute this value into the formula:

Area = (2 units)^2 = 4 square units

Therefore, the area of the 2 by 2 unit square is 4 square units.

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Answer:

  θ ∈ {π/4, π/2, 3π/4, 5π/4, 3π/2, 7π/4}

Step-by-step explanation:

You want the solutions to sin(2θ)sin(θ)=cos(θ) on [0, 2π).

We can use the identity for sin(2θ) to write the equation in terms of sine and cosine.

  (2sin(θ)cos(θ))·sin(θ) = cos(θ) . . . . replace sin(2θ)

  2sin(θ)²cos(θ) - cos(θ) = 0 . . . . . . . subtract cos(θ)

  cos(θ)(2 sin(θ)² -1) = 0

The zero product rule tells you a product will be zero only when one or more factors is zero. The zeros of the factors are ...

  cos(θ) = 0   ⇒   θ = π/2, 3π/2

  2sin(θ)² -1 = 0   ⇒   sin(θ) = ±√(1/2)   ⇒   θ = π/4, 3π/4, 5π/4, 7π/4

The solutions are θ ∈ {π/4, π/2, 3π/4, 5π/4, 3π/2, 7π/4}.

__

Additional comment

The solutions are the x-intercepts of the graph of sin(2θ)sin(θ) -cos(θ), the values of x where this expression is zero. A graphing calculator finds them nicely.

Answer:

a. To find the number of diagonals in an n-sided polygon, we need to count the number of pairs of vertices that can be connected by a diagonal, while excluding the sides of the polygon. Any pair of vertices that are adjacent or separated by only one vertex are already connected by a side of the polygon, so we need to consider pairs of vertices that are separated by at least two vertices.

We can choose two vertices out of n vertices in the polygon in nC2 ways. However, any pair of vertices that are separated by only one vertex defines a side of the polygon, so we need to subtract n from this count to exclude the n sides of the polygon. Therefore, the number of diagonals in an n-sided polygon is:

nC2 - n = (n * (n-1))/2 - n = (n^2 - 3n)/2

b. The above expression gives the number of diagonals for any polygon, not just a convex one. However, for a convex polygon, any pair of vertices separated by only one vertex defines a side of the polygon, so we need to exclude these diagonals as well.

For an n-sided convex polygon, there are n sides and n vertices, so we have to exclude n diagonals (one diagonal for each vertex). Therefore, the number of diagonals in an n-sided convex polygon is:

(n^2 - 3n)/2 - n = (n^2 - 5n)/2

Step-by-step explanation:

The image coordinates of N'M'O' are (−9, −2), (−6, −1), and (−9, −5).

To translate the preimage 5 units to the left, we need to subtract 5 from the x-coordinates of all three vertices.

So the new coordinates of N', M', and O' will be:

N'((-4)-5, (-2)) = (−9, −2)

M'((-1)-5, (-1)) = (−6, −1)

O'((-4)-5, (-5)) = (−9, −5)

Therefore, the image coordinates of N'M'O' are (−9, −2), (−6, −1), and (−9, −5).

So the correct answer is N′(−9, −2), M′(−6, −1), O′(−9, −5).

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Step-by-step explanation:

If Debbie saves $900 each summer for four summers, she will have saved a total of:

$900 x 4 = $3600

Her parents have agreed to pay half the tuition, which is $8,500 / 2 = $4250.

Therefore, Debbie will need to come up with the remaining amount:

$8,500 - $4,250 = $4,250

Since Debbie will have saved $3,600 from her summer job, she will need an additional:

$4,250 - $3,600 = $650

Debbie will need $650 more to afford her first year's tuition.

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The answer is: f has a local maximum at x = 2 and a local minimum at x = 4.

A local minimum is a point on the graph of a function where the function takes on its smallest value in some small interval around the point. More formally, a point (x,y) is a local minimum if there exists some open interval (a,b) containing x such that for all values of x in (a,b), y is greater than or equal to f(x). Visually, a local minimum is a "valley" on the graph of the function where the function is lower than all nearby points, but may still be higher than points farther away.

In the given question,

(a)

The curve labeled y = f'(x) represents the derivative of a function f(x). Since f'(x) is positive when f(x) is increasing and negative when f(x) is decreasing, we can use the sign of f'(x) to determine the intervals of increase and decrease of f(x).

From the given information, we can sketch the graph of f'(x) as follows:

Based on this graph, we can see that f(x) is increasing on the intervals: [0, 1) and (3, 5).

Similarly, f(x) is decreasing on the intervals: (1, 3) and (5, 6).

Therefore, the answer is:

f is increasing on the intervals [0, 1) and (3, 5).

f is decreasing on the intervals (1, 3) and (5, 6).

(b)

From the given graph, we can see that f(x) has a local maximum at x = 2 and a local minimum at x = 4.

Therefore, the answer is: f has a local maximum at x = 2 and a local minimum at x = 4.

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The midline of the function is the horizontal line: y = -0.9

What is Graph ?

A graph is a visual representation of data or a mathematical function that shows the relationship between different variables. Graphs can take many forms, but some common types of graphs include line graphs, bar graphs, scatter plots, and pie charts.

The midline of a trigonometric function is the horizontal line that is equidistant from the maximum and minimum points of the function. For a sine or cosine function, the midline is given by the equation:

y = a

where a is the vertical displacement of the graph (i.e., the distance between the horizontal axis and the center of the graph).

In this case, the function has a minimum point at (2, -0.9) and an amplitude of 3. The amplitude is the distance between the maximum and minimum points of the function, which is equal to half the distance between the maximum and minimum y-values. Therefore, the maximum y-value is:

y_max = -0.9 + 3 = 2.1

Similarly, the minimum y-value is:

y_min = -0.9 - 3 = -3.9

The center of the graph is the average of the maximum and minimum y-values, which is:

a = (y_max + y_min) ÷ 2

a = (2.1 - 3.9)÷ 2

a = -0.9

Therefore, the midline of the function is the horizontal line: y = -0.9

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If Julian and two of his friends are going to share 1/4 of a pizza, then they will be sharing the pizza equally among three people. To find out how much each person will get, you need to divide the 1/4 of the pizza by 3, which gives:

1/4 ÷ 3 = 1/4 × 1/3 = 1/12

So each person will get 1/12 of the pizza.

The five number summary, based on the given box plot would be:

Minimum value is the left-most point or the left end of the left whisker of the box plot. In the box plot, the minimum value is 1. Q1 is the left edge of the box. It represents the value below which 25% of the data falls.

Median is the line inside the box that divides it into two parts. It represents the value below which 50% of the data falls, or the 50th percentile. The median is 7. Q3 is the right edge of the box. It represents the value below which 75% of the data falls. In your given summary, Q3 is 9.

Maximum value is the right-most point or the right end of the right whisker of the box plot.

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Answer:

Step-by-step explanation:

Solution:

A four-digit number 4ab5 is divisible by 55. Then the value of b - a is 1.

The volume of the rectangular prism is 210cm³.

A rectangular prism is a three-dimensional solid shape that has six rectangular faces. Each face of the prism is a rectangle, and the opposite faces are congruent and parallel. The rectangular prism is also known as a rectangular cuboid or a rectangular parallelepiped. The rectangular prism has eight vertices (corners), twelve edges, and six faces. It is a special case of a parallelepiped, which is a three-dimensional solid with six parallelogram faces.

The surface area of the rectangular prism is:

Surface Area = 2(lw + lh +  wh)

Surface Area = 2(7cm x 6cm) + 2(7cm x 5cm) + 2(6cm x 5cm)

Surface Area = 84cm² + 70cm² + 60cm²

Surface Area = 214cm²

Hence, the rectangular prism has a 214 cm² surface area.

We must multiply the rectangular prism's length, width, and height in order to get its volume.

The volume of the rectangular prism is:

Volume = lwh

Volume = 7cm x 6cm x 5cm

Volume = 210cm³

Hence, the rectangular prism has a 210 cm³ volume.

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The x-intercepts are (4,0)(5,0) of the following graph.

In the context of a graph, an x-intercept is a point where a curve or line crosses the x-axis. It is the point at which the value of y is zero. In other words, the x-intercept is the value of x when the function or equation crosses the x-axis.

To find the x-intercepts of a function, you can set y equal to zero and solve for x. The resulting values of x will be the x-intercepts.

In the context of a graph, a y-intercept is a point where a curve or line crosses the y-axis. It is the point at which the value of x is zero. In other words, the y-intercept is the value of y when the function or equation crosses the y-axis.

To find the y-intercept of a function, you can set x equal to zero and solve for y. The resulting value of y will be the y-intercept.

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Answer: Sorry meant to send this*

Step-by-step explanation:

an employee's overtime rate is 1.5 times their regular rate, but this can vary depending on the company and jurisdiction. Once the overtime rate is known

what is regular rate?

Regular rate refers to the standard hourly wage that an employee receives for their regular, non-overtime work. This is the base rate of pay that an employer agrees to pay an employee for their normal working hours

In the given question,

In order to determine how much Ashley made in overtime, we would need to know her overtime rate and the number of overtime hours she worked. Without this information, it is not possible to calculate the amount she earned in overtime.

Typically, an employee's overtime rate is 1.5 times their regular rate, but this can vary depending on the company and jurisdiction. Once the overtime rate is known, we could multiply the overtime rate by the number of overtime hours worked to determine the amount earned in overtime.

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The true statement would be: The theoretical probability of landing on 11 is 12.5% while the experimental probability of landing on 11 is 30%

Experimental probability is a type of probability that is based on actual experimental results or data. It is the ratio of the number of times an event occurs to the total number of trials or experiments conducted.

For example, if you were to toss a coin 100 times and record the number of times it lands on heads, the experimental probability of the coin landing on heads would be the number of times it landed on heads divided by the total number of coin tosses (100 in this case). If the coin landed on heads 45 times out of 100, then the experimental probability of the coin landing on heads would be 45/100 or 0.45.

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The percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The total number of water bottles the company manufactured in February, March, and April.

In February, the company manufactured 4,100 water bottles. In March, the company manufactured 7% more water bottles than in February, which is 7/100 * 4,100 = 287 water bottles.

Therefore, the total number of water bottles the company manufactured in March is 4,100 + 287 = 4,387 water bottles. In April, the company manufactured 500 more water bottles than in March, which is 4,387 + 500 = 4,887 water bottles.

This is calculated as (4,887 - 4,100) / 4,100 = 0.195 or 19.5%.

Therefore, the percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

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The simplified expression is 84/125.

An expression is a combination of numbers, variables, and mathematical symbols that represent a mathematical relationship or formula. Expressions can be simple or complex and can include operations such as addition, subtraction, multiplication, and division, as well as exponents, radicals, and functions.

In the given question,

To simplify the expression 5x1 + 6x1/10 + 7x1/100 + 2x1/1,000, we can start by converting all the fractions to have a common denominator of 1,000. This gives:

5x1 + 6x100/1,000 + 7x10/1,000 + 2x1/1,000

Next, we can add the terms that have the same denominator:

(6x100 + 7x10 + 2x1)/1,000

Simplifying the numerator, we get:

(600 + 70 + 2)/1,000

Adding the terms in the numerator, we get:

672/1,000

Simplifying the fraction, we can divide both the numerator and denominator by the greatest common factor, which is 8:

84/125

Therefore, the simplified expression is 84/125.

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Answer:

$24.5

Step-by-step explanation:

Given info:

Kaitlin bought 6 games which are $3.30 each and 1 DVD which cost $4.70

Now to find out the cost of all 6 games multiply 6 by the cost of each one, $3.30

$3.30*6 = $19.8

Now add the price of the DVD to it to find the total price

19.8+ 4.70= $24.5

So thus, the total cost of Kaitlin's items was $24.5

Answer:Quadrant 1

Only in Quadrant 1, the both y and x-axis is positive. So (10, 15) is in quadrant 1.

The given function is not one-to-one.

To determine whether the function y = 2(x+1)²-4 is one-to-one, we need to check whether each unique value of x produces a unique value of y.

Let's begin by assuming that two different values of x, say x1 and x2, produce the same value of y, i.e., y(x1) = y(x2).

Then we have:

2(x1+1)²-4 = 2(x2+1)²-4

Simplifying this equation, we get:

(x1+1)² = (x2+1)²

Taking the square root of both sides, we get:

x1+1 = ±(x2+1)

We can now solve for x1 in terms of x2 as follows:

x1 = -(x2+1)±1

Since there are two possible values for x1 corresponding to a given value of x2, the function is not one-to-one.

Therefore, the given function is not one-to-one.

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Using trigonometric functions, we can find the value of the angles as:

Sinθ = 3/5

Cosθ = 4/5

Tanθ = 3/4

Six basic trigonometric operations are used in trigonometry. These operations are described by trigonometric ratios. The six basic trigonometric functions are the sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function. The foundation for trigonometric identities and functions is the ratio of the sides of a right-angled triangle. The sine, cosine, tangent, secant, and cotangent values are computed for the perpendicular side, hypotenuse, and base of a right triangle using trigonometric formulas.

Here as per the question,

Opposite side of the angle = 3 units.

Adjacent side of the angle = 4 units.

Hypotenuse of the triangle = 5 units.

Sinθ = opposite side/ hypotenuse

= 3/5

Cosθ = adjacent side/ hypotenuse

= 4/5

Tanθ = opposite side/adjacent side

= 3/4

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