Polygon DEFG has coordinates D(2, 5), E(3, 1), F(4, 6), and G(6, 6). If the polygon is translated 3 units to the left, what are the coordinates of F'?

( , )

The length of the midsegment of trapezoid is 24 units.

An open, flat figure with four successive sides and one pair of parallel sides is termed to as a trapezoid or trapezium.

The parallel and non-parallel sides of a trapezium are called as the bases and the legs, respectively. A trapezium may also have parallel legs. The parallel sides can be slanted, vertical, or horizontal.

The altitude is the evaluation of the angle perpendicular to the parallel sides.

Now in the given question,

a = 15

b = 23

length of mid segment EF,

[tex]l=\frac{a+b}{2} \\\\l=\frac{15+23}{2} \\\\l=\frac{48}{2} \\\\l=24[/tex]

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Answer: To find the monthly rent during the 11th year, we need to calculate the total increase in rent over the course of 10 years and then add that to the original monthly rent of $900.

The total increase in rent over 10 years is $120 per year * 10 years = $1200.

So, the monthly rent during the 11th year would be $900 + $1200 = $2100.

Therefore, the monthly rent during the 11th year would be $2100.

Step-by-step explanation:

Answer:

9.968

Step-by-step explanation:

[tex]c^2=a^2+b^2 -2ab*cos(C)[/tex]

and more generally, a side squared of a triangle is equal to the other two sides squared then added, minus double the product of the other two sides and the cosine of the opposite angle, generally denoted as the capital letter of the side. (c is the side, C is the opposite angle)

in this case the other two sides are 7 and 10, so we can say that a=7, b=10 if  it helps understand this a bit more, but "a" and "b" really just represent the other two sides.

the opposite angle is: [tex]\frac{5\pi}{13}[/tex] and the unknown is "a", but we can just express it as "c" for the sake of simplicity. Now plugging in all the known values we get the following equation:

[tex]c^2=7^2+10^2-2(7)(10)cos(\frac{5\pi}{13})\\\\c^2=49+100-140cos(\frac{5\pi}{13})\\\\c^2=149-140cos(\frac{5\pi}{13})[/tex]

Now from here we can just use a calculator to approximate the cosine, but make sure it's in radian mode! otherwise your answer may be incorrect as degrees are different than radians.

[tex]c^2=149-140(0.3546)\\\\c^2=149-49.64468\\\\c^2=99.355315814\\\\c=\sqrt{99.355315814}\\\\c=9.96771367035\\\\c\approx 9.968[/tex]

So the side is approximately 9.968 units in length.

Answer:

2787

Step-by-step explanation:

add them all together

9.19% of the total is made up of Green.

The percentage formula is dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Number of green cars = 120

Number of green planes = 250

Number of green trains = 500

Total = 870

Now,

The total number of all colors of the car, plane, and train.

= 870 + 1250 + 820 + 800 + 990 + 4730

= 9460

Now,

The percentage of green cars, planes, and trains.

= 870/9460 x 100

= 9.19%

Thus,

9.19% of the total is made up of Green.

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Answer:

Step-by-step explanation:

Here's a step-by-step explanation of the reflections:

Point R is located at (1, 1) on the coordinate plane.

Reflection over the y-axis: This reflection changes the sign of the x-coordinate. In other words, if the point (x, y) is reflected over the y-axis, the reflected point will be ( -x, y). So, for point R at (1, 1), the reflection over the y-axis creates R' at (-1, 1).

Reflection over the x-axis: This reflection changes the sign of the y-coordinate. In other words, if the point (x, y) is reflected over the x-axis, the reflected point will be (x, -y). So, for point R' at (-1, 1), the reflection over the x-axis creates R'' at (-1, -1).

So the final location of R'' is at the ordered pair (-1, -1).

Answer:

Cost $50.63

Step-by-step explanation:

To calculate the cost, we need to find out how many gallons of gasoline the car will consume in 450 miles. We can use the formula:

Gallons = Total miles / Miles per gallon

Gallons = 450 miles / 24 miles per gallon

Gallons = 18.75

Next, we multiply the number of gallons by the cost per gallon to get the total cost:

Total cost = Gallons * Cost per gallon

Total cost = 18.75 gallons * $2.70 per gallon

Total cost = $50.63

So, it will cost $50.63 to drive 450 miles when gasoline costs $2.70 per gallon and your car gets 24 miles per gallon.

Answer: The present value of an annuity due with a monthly payment of $300 at 6% interest compounded monthly for 10 years can be calculated using the formula:

PV = PMT * [ (1 - (1 + r)^-n) / r ] * (1 + r)

where:

PMT = $300 (the monthly payment)

r = 0.06/12 (the monthly interest rate)

n = 10*12 (the number of periods over 10 years, with 12 months in a year)

Plugging in the values into the formula, we get:

PV = $300 * [ (1 - (1 + 0.06/12)^-n) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * [ (1 - (1 + 0.06/12)^-(10*12)) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * [ (1 - 1.06^-120) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * [ (1 - 0.379362539) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * [ (0.620637561) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * 10.34300138

PV = $31,029.

So the present value of the annuity due is $31,029. This means that if you were to invest $31,029 today, you would receive a monthly payment of $300 for 10 years at 6% interest compounded monthly.

Step-by-step explanation:

The positive coterminal angle less than 360° is, 55°

Angles with the same initial and terminal sides but a multiple of 360° degree difference are known as coterminal angles (or a full rotation). In other words, you can create an angle that is coterminal with the original angle by taking it and adding or subtracting 360 degrees (or any multiple of 360 degrees).

To find a positive angle that is coterminal with -1025°,

we can add or subtract any multiple of 360° until we get an angle between 0° and 360°.

Adding 1080° (which is 3 revolutions of 360°) to -1,025° gives us:

= -1,025° + 1080°

=   55°

Since this angle is less than 360°,

Therefore, a positive angle less than 360° that is coterminal with -1025° is 55°.

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This curve symbolizes the curve of indifference. Those combinations of quantities that the customer considers to be of equal value are connected by a curve on a graph whose axes reflect amounts of two commodities.

It dislikes all product combinations that offer the same level of enjoyment to the consumer. Because each combination provides the same level of enjoyment, the buyer Favours them all equally. The indifference curve therefore gets its name.

An indifference curve is a graphic representation of a collection of products that give consumers comparable levels of satisfaction, leading to their indifference. A consumer or person is indifferent between the two products at every point on the indifference curve because they provide the same kind of benefit.

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The values of the operations between the two functions are, respectively:

In this problem we find the representations of two functions, each on one Cartesian plane: f(r), h(r). Based on that information we can determine the result of operations between functions, which are defined below:

Addition

(f + h)(x) = f(x) + h(x)

Subtraction

(f - h)(x) = f(x) - h(x)

Multiplication  

(f · h)(x) = f(x) · h(x)

Division

(f / h)(x) = f(x) / h(x)

Now we proceed to determine each operation:

(f + h)(5) = f(5) + h(5) = 3 + 4 = 7

(h - f)(2) = h(2) - f(2) = 1 - 1 = 0

(f · h)(3) = f(3) · h(3) = 4 · 0 = 0

(h / f)(0) = h(0) / f(0) = 3 / 5

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The solution for x in the triangle is x = 51.98 units

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Using trigonometric ratio:

sin 38° = 32/x  (Sine = opposite/hypotenuse)

x = 32/sin 38°

x = 51.98 units

Therefore, the solution is x = 51.98 units

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The length of CD can be found to be 7. 21 units .

The length of CD can be found by using the distance formula which is :

= √ [ ( x ₂ - x ₁ ) ² + ( y ₂ - y ₁ ) ² ]

Given the points, ( 3, - 2 ) and ( 7, - 8 ).

The length of CD is :

= √ [ ( 7 - 3 ) ² + ( - 8 - (- 2 ) ) ² ]

= 7. 21

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The number of times it is not land on the blue color sector is 7-1 = 6

A probability is defined as the ratio to the number of required outcomes to the total number of outcomes of an event.

The spinner is divided into 7 sectors, in which each sector is equal in size.

Among 7 sectors two of of them are blue in color.

We have to calculate that how many times the spinner not landing on the blue color sector.

For that we have to calculate the possible outcome for the blue color sector for 1 spin.

For 1 spin , the number of possible outcomes = 7.

Number of required outcomes = 2.

Probability of number of spins on blue sector for 1 spin = 2/7.

Probability of number of spins on blue sector for 7 spin = 7*(2/7) = 2.

Standard deviation = [tex]\sqrt{\frac{2}{7} *\frac{5}{7} }[/tex]= 0.4518.≅0.452.

Standard error=root(7)*0.452= 1.19≅1.2

Expected value =2-1.2 = 0.8 ≅1

Therefore the expected value is 1.

Number of times it will land on the blue color sector is 1.

Hence, the number of times it is not land on the blue color sector is 7-1 = 6.

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Answer:

784 R 13

Hope this helps!

Step-by-step explanation:

Answer:

Of the shapes you mentioned (circle, square, triangle, rectangle), the only one that has only one line of symmetry is the triangle. All other shapes have multiple lines of symmetry.

Step-by-step explanation:

The function type of the graph with asymptotes, x = 2, and y = 0  is a rational polynomial, where the degree of the numerator is less than the degree of the denominator, and (x - 2) is a factor of the denominator, which is a function of the form;

[tex]f(x) = \frac{1}{(x - 2)}[/tex]

An asymptote is a line to which the output value of a function approaches as the input value becomes very large approaches infinity.

The function type represented by the graph is a polynomial function that has an horizontal asymptote of y = 0, and a vertical asymptote of x = 2

A function has a vertical asymptote at the location at which the denominator approaches zero.

The vertical asymptote of x = 2 , indicates that the denominator approaches zero when x = 2, therefore, (x - 2) is a factor of the denominator

A function has an horizontal asymptote which is the value the function approaches as the input value approaches infinity.

Therefore, the horizontal asymptote of y = 0, indicates that the the degree of the numerator is less than the degree of the denominator

The function type in the question is therefore;

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Answer: Let's say there are a total of 100 students at the middle school. Then, 5 parts out of 7 are playing basketball and 2 parts out of 7 are playing soccer. The percent of students playing soccer can be calculated as follows:

(2/7) * 100 = 28.57% (rounded to the nearest percent)

So, approximately 28.57% of the students at the middle school play soccer.

Step-by-step explanation:

A student would have to score approximately 0.84 standard deviations above the mean to be publicly recognized.

The dispersion of asset prices from their average price, or market volatility, can be calculated with the use of standard deviation. A large standard deviation indicates a dangerous investment when prices move erratically. Low standard deviation indicates stable prices, which lowers the risk associated with investments.

The remaining 79 percent of pupils are not recognised if just the top 21% of students receive public recognition. Since a normal distribution is assumed, the conventional normal distribution and its corresponding z-scores can be used to provide the solution.

The percentage of scores that are higher than a certain z-score is shown by the area under the standard normal distribution to its right. Finding the z-score that represents the top 21% of scores is equivalent to locating the z-score that represents the bottom 79% of scores. By using a calculator or a table of the ordinary normal distribution, we can determine that the z-score for the bottom 79 percent of scores is roughly 0.84.

In order to be officially acknowledged, a student would need to get a score that is roughly 0.84 standard deviations above the mean.

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The numerical value of x in the given right triangle is 20.14.

The figure in the image is right-triangle.

To find the value of x, we use trigonometric ratio.

Sine = Opposite / Hypotenuse

Plug in the values and solve for x.

sin( 32° ) = x / 38

x = sin( 32° ) × 38

x = 0.529919 × 38

x = 20.14

Therefore, the value of x is 20.14.

Option C) 20.14 is the correct answer.

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Answer:

Step-by-step explanation:

To find the two diameters that separate the top 3% and the bottom 3% of the bolts produced in the machine shop, we need to find the lower and upper bounds of the interval that contains the middle 94% of the data. This can be done using the standard normal distribution and the z-score.

First, we'll find the z-score that corresponds to the lower bound. To do this, we'll use the formula:

z = (x - μ) / σ

where x is the lower bound, μ is the mean of the data (6.48 mm), and σ is the standard deviation of the data (0.06 mm). We want to find the value of x such that the area to the left of x is equal to 3%:

z = (x - 6.48) / 0.06

z = -2.33

Next, we'll use the z-score to find the value of x (the lower bound). We'll use the standard normal distribution table to look up the value of -2.33 and find that it corresponds to a cumulative probability of 0.01. So, the lower bound is such that 1% of the data is less than or equal to this value. To find the value of x, we'll use the formula:

x = μ + zσ

x = 6.48 + (-2.33) * 0.06

x = 6.32

So, the lower bound of the interval that contains the middle 94% of the data is 6.32 millimeters. This is the diameter that separates the bottom 3% of the bolts from the rest.

Next, we'll find the upper bound in a similar way. To do this, we'll use the formula:

z = (x - μ) / σ

where x is the upper bound, μ is the mean of the data (6.48 mm), and σ is the standard deviation of the data (0.06 mm). We want to find the value of x such that the area to the left of x is equal to 97%:

z = (x - 6.48) / 0.06

z = 2.33

Using the standard normal distribution table, we find that the value of 2.33 corresponds to a cumulative probability of 0.99. So, the upper bound is such that 99% of the data is less than or equal to this value. To find the value of x, we'll use the formula:

x = μ + zσ

x = 6.48 + 2.33 * 0.06

x = 6.64

So, the upper bound of the interval that contains the middle 94% of the data is 6.64 millimeters. This is the diameter that separates the top 3% of the bolts from the rest.

Therefore, the two diameters that separate the top 3% and the bottom 3% of the bolts produced in the machine shop are 6.32 millimeters and 6.64 millimeters, rounded to the nearest hundredth.

The boolean expression that evaluates to True if "x is non-negative and y is negative" is: (x >= 0) ∧ (y < 0).

A boolean expression is a logical expression that evaluates to either true or false. Boolean expressions can be composed of one or more boolean operators, such as AND, OR, and NOT, and can involve one or more variables.

We need to find boolean expression for: "x is non-negative and y is negative", then output is true.

The boolean expression is:

(x >= 0) ∧ (y < 0), or (x>=0) AND (y<0)

In this expression, the ∧ symbol represents the logical AND operator. The expression (x >= 0) checks if x is greater than or equal to 0 (i.e. non-negative), and the expression (y < 0) checks if y is less than 0 (i.e. negative).

If both conditions are true, the overall expression evaluates to true, indicating that x is non-negative and y is negative.

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Answer:

2+1=3, 7+8=15, 0+1=1, 8+7=15, 2+9=11, 1+3=4, 2+0=0, 4+5=9, 3+4=7

Given that there are 26 red cards in the deck of 52 cards, the probability of obtaining a red card on any given draw is 26/52 = 1/2.

The probability of the complimentary event—the probability that no red cards are drawn in the first three draws—can be used to determine the likelihood that a red card will be pulled at least once by the third draw.

Particular that there are 26 non-red (black) cards in the 52-card deck, there is a 50% chance that no red cards will be drawn on any given draw.

As a result, the likelihood that none of the three draws will result in a red card is:

(1/2) x (1/2) x (1/2) = 1/8

The likelihood of drawing a red card at least once by the third draw is the counterpart of this probability.

1 - 1/8 = 7/8

Therefore, by the third draw, there is a 7/8 chance of drawing a red card at least once, or 0.88 rounded to two decimal places.

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Answer:

Step-by-step explanation:

To find the perimeter of a right-angled triangle when only the length of the hypotenuse is known, you'll need to use the Pythagorean theorem. Here's a step-by-step explanation:

Step 1: Understand the Pythagorean theorem

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b):

c^2 = a^2 + b^2

Step 2: Substitute the known length of the hypotenuse

Let's say the length of the hypotenuse is "h". Substitute "h" for "c" in the Pythagorean theorem:

h^2 = a^2 + b^2

Step 3: Solve for one of the unknown sides

To find the perimeter of the triangle, we need to know the lengths of both sides "a" and "b". To do this, we need to solve for one of the unknown sides. Let's solve for "a".

Square root both sides of the equation:

√(h^2) = √(a^2 + b^2)

h = √(a^2 + b^2)

Square both sides of the equation:

h^2 = a^2 + b^2

Step 4: Use the Pythagorean theorem to find the other unknown side

Now that we have an expression for "a", we can use the Pythagorean theorem again to find "b":

h^2 = a^2 + b^2

Substitute the expression for "a" that we found in Step 3 into the equation:

h^2 = (√(a^2 + b^2))^2 + b^2

h^2 = a^2 + b^2 + b^2

h^2 = 2 * b^2 + a^2

h^2 - a^2 = 2 * b^2

b^2 = (h^2 - a^2) / 2

Take the square root of both sides:

b = √((h^2 - a^2) / 2)

Step 5: Calculate the perimeter

The perimeter of the triangle is the sum of the lengths of all three sides, so we can now calculate the perimeter using the lengths of "a" and "b" that we found in Steps 3 and 4:

P = a + b + h

Step 6: Conclusion

Therefore, the perimeter of the right-angled triangle can be found by first using the Pythagorean theorem to find the lengths of two of the sides, and then adding up the lengths of all three sides to find the perimeter.

Answer:

D

Step-by-step explanation:

why the panic ? you only need to compare the tiles with the actual terms in the equations and add them up.

x²

-x²

-x -x

x x x x (clearly that means 4x)

-1 -1 -1

1 1

so, we see it is D.

Answer:

4 cups of fruit sorbet.

Step-by-step explanation:

There are 128 cups in 1 gallon. So, 1 gallon of fruit sorbet is equal to 128 cups.

Therefore, each person will receive 128 cups / 32 people = 4 cups of fruit sorbet.

The solution is, each person get 4 cups of fruit sorbet.

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

given that,

Hugo is serving fruit sorbet at his party.

He has 1 gallon of fruit sorbet to serve to 32 friends .

now. we get,

There are 128 cups in 1 gallon.

So, 1 gallon of fruit sorbet is equal to 128 cups.

so, we have,

Therefore, each person will receive 128 cups / 32 people = 4 cups of fruit sorbet.

If each person receives the same amount,

then, each person will receive 4 cups of fruit sorbet.

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Answer:

1,3 or 4,2

Step-by-step explanation:

The measure of angle 1 is given as follows:

m < 1 = 42º.

To obtain the measure of angle 1 in the kite, we must consider that the consecutive angles are complementary, that is, the sum of their measures is of 90º.

Relative to angle 1, we have that:

m < 4 + m < 1 = 90º.

For the bottom left triangle, the internal angle measures are given as follows:

Considering that the sum of the measures of the internal angles of a triangle is of 180º, the measure of angle 4 is obtained as follows:

m < 4 + 42 + 90 = 180

m < 4 = 58º.

Then the measure of angle 1 is obtained as follows:

m < 1 = 90 - 58

m < 1 = 42º.

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Answer:

smaller value = 4yd

larger value = 8yd

Step-by-step explanation:

Let's call the garden's width and length W and L respectively.

The area of the garden is 36yd². We can write this mathematically as W*L=36

If 26yd is enough fencing to perfectly enclose the garden, then this must be the garden's perimeter. Written mathematically, this is 2W+2L=26. We can simplify this by dividing each term by two to get W+L=13

If W and L multiply to get 36, they must be both a factor pair of 36. The factor pairs of 36 (the pairs of numbers which multiply to get 36) are '1 and 36', '2 and 18', '3 and 12', '4 and 9', and '6 and 6'.

W and L must also add to 13, and the only factor pairs of 36 which add to 13 are '4 and 9' so these are our dimensions.

Answer:

smaller value = 4yd

larger value = 8yd

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