HELP ILL GIVE YOU 50 POINTS IF SOMEONE HELPS ME What is the total area of the figure below?
28 ft
4 ft 6 ft
14 ft
2 11
A. 47 ft2
B. 52 ft2
C. 168 ft2
D. 402 ft2

The transformation rule that describes the rotation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

The rule that describes the transformation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

To understand this, let's apply the transformation rule to each vertex of the original parallelogram ABCD:

Point A (2, 5) becomes A' (-5, 2).

Point B (5, 4) becomes B' (-4, 5).

Point C (5, 2) becomes C' (-2, 5).

Point D (2, 3) becomes D' (-3, 2).

By applying the transformation rule, we observe that the x-coordinate of each point becomes the negative of the original y-coordinate, and the y-coordinate becomes the original x-coordinate.

This transformation is a 90-degree counterclockwise rotation about the origin (0, 0) on the coordinate plane. The image parallelogram A'B'C'D' is obtained by rotating the original parallelogram ABCD by 90 degrees counterclockwise.

Visually, this transformation can be seen as the original parallelogram being rotated around the origin, where the x-axis becomes the y-axis, and the y-axis becomes the negative x-axis.

Therefore, the transformation rule that describes the rotation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

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Required value of f(g(x)), g(f(x)), f(f(x)) are 2x²- 4x + 2 , 2x² -1 and 8x⁴ respectively.

the range of f(g(x)) is [0, ∞), the range of g(f(x)) = = 2x²-1 is [-1,∞) and the range of f(f(x)) is [0, ∞).

What is composition of functions?

Suppose we are given two functions f(x), g(x). We construct a new function h(x) as follows. plug 'x' into g(x) and find its value. then plugin this value into f(x), that is find f(g(x)). Now set h(x) = f(g(x)). This new function h(x) is called the composition of functions f(x) and g(x).

a. f(g(x)) = 2 * (x - 1)² = 2(x² - 2x + 1) = 2x²- 4x + 2 Since fg(x)) is a polynomial its domain is all real numbers. to find the range note that f(g(x)) = 2 * (x - 1) ² . and the range of the square is all non-negative real numbers. So the range of f(g(x)) is [0, ∞).

b. g(f(x)) = (2x²) - 1 =2x² -1.g(f(x)) is a polynomial function, so the domain of g(f(x)) is (-∞, ∞). Note that the range of 2x² is [0, ∞). So the range of g(f(x)) = 2x²-1 is [-1,∞)

c. f(f(x)) = 2 * (2x²)² = 2(4x⁴) = 8x⁴ . Since this is a polynomial function, the domain is (-∞, ∞), and clearly the range is [0, ∞).

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To test whether there is evidence of a linear relationship between the given data (x and y values), we can perform a hypothesis test.

Step 1: State the null hypothesis (H0) and the alternative hypothesis (H1).
H0: There is no linear relationship between x and y (i.e., the correlation coefficient, r, is equal to 0)
H1: There is a linear relationship between x and y (i.e., the correlation coefficient, r, is not equal to 0)
Step 2: Calculate the correlation coefficient, r, using the given data. You can do this using a statistical calculator or software.
Step 3: Determine the critical value for the correlation coefficient at a chosen significance level (e.g., 0.05).
Step 4: Compare the calculated correlation coefficient, r, to the critical value. If |r| is greater than the critical value, reject the null hypothesis (H0) in favor of the alternative hypothesis (H1), indicating evidence of a linear relationship. If |r| is less than or equal to the critical value, fail to reject the null hypothesis (H0), suggesting there is not enough evidence to support a linear relationship.
By following these steps, you can test the hypothesis and determine if there is evidence of a linear relationship between the given data points.

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Thus, the probability are Zero represents the impossibility.

1/2 equals probable and unlikely

1 = event happens.

Because we don't know how something will turn out, we might talk about the probability of one outcome or the potential for several outcomes.

Typically, the likelihood is stated as the proportion of favourable events to all other potential outcomes in the sample space.

The probability of an event is calculated using the formula P(E) = (Number of favourable outcomes) (Sample space).

Given that probability can only be a number between 0 and 1,

The zeroth value is the impossible.

so there is a 50% chance for both likely and unlikely.

If 1, the event must take place.

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Answer:

I believe it is 14.

Step-by-step explanation:

Answer: The value of x is 14°

Step-by-step explanation:

Since line m is parallel to n, then then the two given angles will have the same measures. Meaning that 136 degrees has to equation (9x+10).

Set them to equal each other and solve for x.

9x + 10 = 136

    - 10      -10

  9x  = 126

x=  14

Therefore, in either partial derivatives, we have u = 0 or v = 0.

The given information implies that two vectors u and v satisfy:

u * v = 0, where * denotes the dot product between vectors.

u X v = 0, where X denotes the cross product between vectors.

From the first equation, we know that the angle between u and v is either 90 degrees or 270 degrees. That is, u and v are orthogonal (perpendicular) to each other.

From the second equation, we know that the magnitude of the cross product u X v is equal to the product of the magnitudes of u and v multiplied by the sine of the angle between them. Since u and v are orthogonal, the angle between them is either 90 degrees or 270 degrees, which means that the sine of the angle is either 1 or -1. Therefore, we have:

|u X v| = |u| * |v| * sin(θ)

= 0

Since the magnitudes of u and v are non-negative, it follows that sin(θ) must be zero. This can only happen if the angle between u and v is either 0 degrees (i.e., u and v are parallel) or 180 degrees (i.e., u and v are anti-parallel).

In the case where u and v are parallel, we have:

u * v = |u| * |v| * cos(θ)

= |u|²

= 0

This implies that |u| = 0, which means that u = 0.

In the case where u and v are anti-parallel, we have:

u * v = |u| * |v| * cos(θ)

= -|u|²

= 0

This again implies that |u| = 0, which means that u = 0.

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The value 159 pounds is equal to 72.12 kilograms. The kilogram (kg) is a unit of mass, used for measuring weight.

It's worth noting that the kilogram is defined as the mass of a particular cylinder of platinum-iridium alloy kept at the International Bureau of Weights and Measures, while the pound is based on the historical use of a pound of wrought iron as a unit of mass. In everyday usage, however, the kilogram is often preferred for its use in scientific research and international trade.

This can be calculated by dividing 159 by 2.20462.

= 159/ 2.20462

= 72.12 kg

So, 159 pounds is equal to 72.12 kilograms.

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The dimensions of the rectangular poster are 9 inches by 22 inches.

Let's assume the width of the rectangular poster is x inches.

According to the given information, the length of the poster is 4 more inches than two times its width. So, the length can be expressed as 2x + 4 inches.

The formula for the area of a rectangle is length × width. In this case, the area is given as 198 square inches.

Therefore, we have the equation:

(2x + 4) × x = 198

Expanding the equation:

\(2x^2 + 4x = 198\)

Rearranging the equation to standard quadratic form:

\(2x^2 + 4x - 198 = 0\)

To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

x = (-b ± √\((b^2 - 4ac\))) / (2a)

Plugging in the values:

x = (-4 ± √\((4^2 - 4(2)(-198)))\) / (2(2))

x = (-4 ± √(16 + 1584)) / 4

x = (-4 ± √1600) / 4

x = (-4 ± 40) / 4

Simplifying:

x = (-4 + 40) / 4 = 9

x = (-4 - 40) / 4 = -11

Since we are dealing with dimensions, the width cannot be negative. Therefore, the width of the poster is 9 inches.

Substituting the value of x back into the length equation:

Length = 2x + 4 = 2(9) + 4 = 18 + 4 = 22 inches

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Answer:

48

Step-by-step explanation:

there are 16 cups in a gallon therefore you would multiply 16 times the number of gallons she uses which is 3 so 16 times 3 or you could do 16+16+16 which both would get you 48 so she would need 48 cups to make 3 gallons. hope this helps have a good rest of your night :)❤

Answer:

(10, 17)

Step-by-step explanation:

It might be easier to explain with a picture or drawing, but I am new to this, so I would try using words.

Assuming the fruit market is on that straight line from Tia's home to Lei's, So we look at both address (coordinates)

From Tia to Lei, x coordinate is from 4 to 12, that's increased by 8, divide by 4, one step is 2.

y coordinate is from 8 to 20, an increase of 12, divide by 4 again, one step is 3.

The fruit market is at 3/4 distance, so 3 steps, on both x and y coordinates.

x: 4+6 = 10

y: 8+9=17

The fruit market is at point (10,17)

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The point (x,y) which divides the segment AB with endpoints at A(x₁,y₁) and B(x₂,y₂) in ratio m:n has cordinates

\(x= \dfrac{nx_1+nx_2}{m+n}\)

\(y= \dfrac{ny_1+ny_2}{m+n}\)

Tia is at P(4, 8) and Lei is at Q(12, 20).

The fruit market (F) is three-fourths the distance from Tia’s home to Lei's home, then PM : PQ = 3:4 or PM : MQ = 3:1

So,

\(x= \dfrac{1.4+3.12}{3+1} = \dfrac{4+36}{4} = \dfrac{40}{4} = 10 \\y= \dfrac{1.8+3.20}{3+1} = \dfrac{8+60}{4} = \dfrac{68}{4} = 17\)

Hence, the fruit market is at point (10,17) which means it is placed at the corner of 10th Street and 17th Avenue.

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Jane has 12 coins and Jim has 29 coins.

We know that this is a word problem and the first thing that we have to do is to form the equation from the problem that have been given to us here. This is what we shall now proceed to do below.

Let the number of coins that Jane has be x

Number of coins that Jim has = 5 + 2x

Total number of coins = 41

Thus we have that;

x + 5 + 2x = 41

3x + 5 = 41

3x = 41 - 5

3x = 36

x = 12

This implies that Jane has 12 coins and Jim has 5 + 2(12) = 29 coins

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Answer:

Step-by-step explanation:

According to vertical angles theorem, when two lines intersect the opposite angles are equal and adjacent angles are supplementary.

A) Find the value of x:

B) Find the measure of angle 2:

C) Angles 2 and 3 are supplementary so their sum is 180°.

Answer:

A.  x = 18

B.  m∠2 = 68°

C.  m∠2 = 112°

Step-by-step explanation:

Given:

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Therefore:

\(\implies \angle 2 = \angle 4\)

\(\implies 4x-4= x+50\)

\(\implies 4x-4-x= x+50-x\)

\(\implies 3x-4= 50\)

\(\implies 3x-4+4= 50+4\)

\(\implies 3x=54\)

\(\implies 3x\div 3=54 \div 3\)

\(\implies x=18\)

To find the measure of ∠2, substitute the found value of x into the given expression for ∠2:

\(\implies m\angle 2 =(4x-4)^{\circ}\)

\(\implies m\angle 2 =[4(18)-4]^{\circ}\)

\(\implies m\angle 2 =(72-4)^{\circ}\)

\(\implies m\angle 2 =68^{\circ}\)

Angles on a straight line sum to 180°:

\(\implies m\angle 2 +m\angle 3=180^{\circ}\)

\(\implies 68 ^{\circ}+m\angle 3=180^{\circ}\)

\(\implies m\angle 3=180^{\circ}-68 ^{\circ}\)

\(\implies m\angle 3=112 ^{\circ}\)

Answer:

The homeowner’s insurance company will pay for the damages after the homeowner pays the deductible of $1,175 for each claim. Therefore, the amount that the homeowner’s insurance company will pay for the damages is $42,500 - $1,175 = $41,325.

I hope that helps! (´▽`ʃ♡ƪ)

Step-by-step explanation:

After solving, the reaminder is 1 if x^3-2x^2+X+1 is divided by x-1.

In the given question we have to find the remainder if x^3-2x^2+X+1 is divided by x-1.

The given equation is x^3-2x^2+X+1.

We have to divide this equation by x-1 to find the remainder.

To find the remainder we firstly find the value of x from x-1. Then we put the value of x in the given equation then we can easily find the remainder.

Putting the x-1 equla to zero, so

x=1

Now putting the value of x in the given equation.

=x^3-2x^2+X+1

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

=1-2+1+1

=1

Hence, the remainder is 1 if x^3-2x^2+X+1 is divided by x-1.

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The graph shows the relationship between the number of students who attend a homecoming dance and the amount of money raised. The graph is a straight line with a slope of $10, passing through the point (0, $80) and another point on the line. The fixed cost for decorations is $80, which is a constant cost that does not depend on the number of students attending the dance. For each additional student that attends the dance, the amount of money raised will increase by $10.

Answer:

y = 10x - 80

Therefore your answer is B, hope this helps! :)

Based on the number of birdhouses that Felipe has to build in the holiday season, the meters of wood that Felipe needs would be 23 ⁵/₈ meters

First, find out the number of birdhouses Felipe needs to make:

= Normal number of birdhouses x Increase in holiday season

= 12 x 4¹/₂

= 54 birdhouses

The meters of wood he needs are:

= Number of birdhouses to be made / Number of bird houses he usually makes x Meters of wood needed for birdhouses Felipe usually makes

= 54 / 12 x 5¹/₄

= 23 ⁵/₈ meters

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the independent variable is the one that's squared, namely the "x", that means that the parabola is a vertically opening parabola, so its axis of symmetry will simply be the equation of the vertical line that passes through the vertex, hmmm what's its vertex anyway?

\(\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-1}x^2\stackrel{\stackrel{b}{\downarrow }}{+12}x\stackrel{\stackrel{c}{\downarrow }}{-38} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)\)

\(\left(-\cfrac{ 12}{2(-1)}~~~~ ,~~~~ -38-\cfrac{ (12)^2}{4(-1)}\right) \implies \left( - \cfrac{ 12 }{ -2 }~~,~~-38 - \cfrac{ 144 }{ -4 } \right) \\\\\\ (6~~,~~-38+36)\implies (\stackrel{x}{6}~~,~~-2)~\hfill \stackrel{\textit{axis of symmetry}}{x=6}\)

Check the picture below.

Using the Empirical Rule, it is found that 99.7% of the values lie between 76 and 88.

It states that, for a normally distributed random variable:

In this problem, we have that:

99.7% of the values lie within 3 standard deviations of the mean, hence between:

\(82 - 3(2) = 76\)

\(82 + 3(2) = 88\)

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Answer: A

Step-by-step explanation:

We know the y intercept is -6 so the first point will be  (0,-6)   and we also know that the slope is  2/1  so after plotting (0.-6) you will have to go up by two and  1 unit to the right.  

Answer:

The answer is A!

Step-by-step explanation:

I just did it and it is right! Have an absolutaly amazing day! :) :) :) :)

Answer:

It can either be 4 or 5

Step-by-step explanation:

It is because of how 4x5 is equal to 9 so they are both sides.

The correct answer is option C. The domain is {10, 3, -7}, and the range is {2, -9, 1, -7}.

The domain of a relation refers to the set of all possible input values or x-coordinates, while the range represents the set of all possible output values or y-coordinates. Given the points in the relation ((10, 2), (-7, 1), (3, -9), (3, -7)), we can determine the domain and range.
Looking at the x-coordinates of the given points, we have 10, -7, and 3. Therefore, the domain is {10, 3, -7}.
Considering the y-coordinates, we have 2, 1, -9, and -7. Hence, the range is {2, -9, 1, -7}.
Thus, option C is the correct answer with the domain as {10, 3, -7} and the range as {2, -9, 1, -7}.

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Answer:

\(x = \sqrt{ {28.46}^{2} - {27}^{2} } = \sqrt{80.9716} = 9.00\)

The sum of infinite geometric series is

\(25 - 10 + 4 - \frac{8}{5}\)

is \(\frac{125}{7}\)

What is geometric series?

The series where the ratio between the consecutive terms of the series are same is called geometric series.

The sum of infinite geometric series is

\(25 - 10 + 4 - \frac{8}{5}\)

Here

common ratio (r) = \(-\frac{10}{25} = -\frac{2}{5}\)

Here r lies between -1 and 1

So the given geometric series converges

First term is 25

Sum =

\(\frac{25}{1 -(-\frac{2}{5})}\\\\\frac{25}{\frac{5+2}{5}}\\\\\frac{25}{\frac{7}{5}}\\\\\frac{25 \times 5}{7}\\\\\frac{125}{7}\)

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The graph representing the given function g(x) = 45 + 9x is as drawn in the attachment.

We are given the equation of line as;

g(x) = 45 + 9x

Where;

x represents the number of hours studied.

g(x) represents the test score

Thus, to plot this graph, we need to input some x values and find their corresponding g(x) values

At x = -10;

g(x) = 45 + 9(-10)

g(x) = -45

At x = -1;

g(x) = 45 + 9(-1)

g(x) = 35

At x = 0;

g(x) = 45 + 9(0)

g(x) = 45

At x = 1;

g(x) = 45 + 9(1)

g(x) = 54

At x = 2;

g(x) = 45 + 9(2)

g(x) = 63

At x = 3;

g(x) = 45 + 9(3)

g(x) = 72

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Therefore, the mean of the number of tests is 5 and the variance is 4 for finding the first fracture in the beam rather than in the weld.

a) To calculate the probability that the first fracture in the beam occurs on the third test of weld strength, we can use the geometric probability formula.

The probability of the first fracture occurring in the beam is 20%, which can be expressed as 0.2. The probability of not fracturing in the beam in the first two tests is (1 - 0.2)^2 = 0.64. The probability of fracturing in the beam on the third test, given that it has not occurred in the first two tests, is 0.2.

Therefore, the probability that the first fracture in the beam occurs on the third test is 0.64 * 0.2 = 0.128, or 12.8%.

b) The number of tests to find the first fracture in the beam follows a geometric distribution. The mean of a geometric distribution is given by 1/p, where p is the probability of success (fracture in the beam).

In this case, p = 0.2 (probability of fracturing in the beam). Therefore, the mean of the number of tests to find the first fracture in the beam is 1/0.2 = 5 tests.

The variance of a geometric distribution is given by (1 - p) / (p^2). In this case, the variance is (1 - 0.2) / (0.2^2) = 4.

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the magnitude of the force vector is approximately 470.41 N, and the x component of the force vector is approximately 357.98 N.

(a) The magnitude of the force vector can be found using the given information. The y component of the force is given as 311 N, and we can calculate the magnitude using trigonometry. The magnitude of the force vector can be determined by dividing the y component by the sine of the angle. Therefore, the magnitude is given by:

Magnitude = y component / sin(angle) = 311 N / sin(41.5°)

Magnitude = y component / sin(angle)

Magnitude = 311 N / sin(41.5°)

Magnitude ≈ 470.41 N

(b) To find the x component of the force vector, we can use the magnitude and the angle. The x component can be determined using trigonometry by multiplying the magnitude by the cosine of the angle. Therefore, the x component is given by:

x component = magnitude * cos(angle)

x component = magnitude * cos(angle)

x component = 470.41 N * cos(41.5°)

x component ≈ 357.98 N

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The monthly payment is obtained with the following equation:

\(A = 6960\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)

In which:

The monthly payment formula is defined as follows:

\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)

In which:

For this problem, the lone parameter given is P = 6960, hence the equation is:

\(A = 6960\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)

In which:

The problem is incomplete, hence the formula used to obtain the monthly payment was presented.

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There are 73,701 different 6-card hands (from a standard deck) with at least 3 kings.

To calculate the number of 6-card hands with at least 3 K's, the problem can be divided into:

Case 1:

Exactly 3 Kings

There are 4 ways to choose 3 kings to put in the hand, then there are 48 cards left to choose the remaining 3 cards (because we used 3 cards in a 52-card deck). Therefore, the number of 6-card hands with exactly 3 kings is:

4 * (48 choose 3) = 4 * 17,296 = 69,184

Case 2:

Exactly 4 Kings

There are 4 ways to choose 4 kings to put in the hand, then there are 48 cards left to choose the remaining 2 cards. Therefore, the number of 6-card hands with exactly 4 kings is:

4 * (48 choose 2) = 4 * 1.128 = 4.512

Case 3:

Exactly 5 kings

There are 4 ways to choose the 5 kings in the hand, then there is only one card left to choose from (because we used 5 of the 52 cards in the deck of cards). Therefore, the number of 6-card hands with exactly 5 kings is:

4*1=4

Case 4:

6 cards are king

There is only one way to choose all 6 cards as king.

Therefore, the total number of 6-card hands with at least 3 kings is:

69,184 + 4,512 + 4 + 1 = 73.701

So there are 73,701 different 6-card hands with at least 3 kings.  

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