if the given triangles are similar find the missing length

To model the given data points, we can use a linear function of the form y = mx + b.

First, we need to find the slope (m) of the line:

m = (y2 - y1) / (x2 - x1)

m = (-6 - (-2)) / (1 - 0)

m = -4/1

m = -4

Now, we can use the slope and one of the points to find the y-intercept (b):

y = mx + b

-2 = (-4)(0) + b

b = -2

Therefore, the linear function that models the given data is:

y = -4x - 2

Geometric growth is a type of exponential growth where a quantity or value increases at a fixed percentage rate over a certain period of time.

Geometric growth is a type of exponential growth where a quantity or value increases at a fixed percentage rate over a certain period of time. This means that the growth rate is proportional to the current size or value of the quantity, resulting in a continuously increasing growth rate.

Geometric growth is commonly observed in natural and social systems, such as population growth, compound interest, and the spread of infectious diseases. It is represented mathematically by an exponential function, where the base of the exponent is greater than one, indicating an increasing rate of growth over time.

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I have solved the question in general, as the given question is incomplete.

The complete question is:

What is geometric growth ?

The coordinates of point C are (17, -1).

let say a line have two points A (x1,y1) and B(x2,y2)

slope of line AB = (y2 - y1) / (x2 - x1)

Now given that  points B, C, and D are collinear, then they lie on the same straight line. This means that the slope of the line passing through any two of the points will be the same as the slope of the line passing through the other two points. We can use this fact to find the value of x.

The slope which is between points B and C is:

slope of line BC = (y2 - y1) / (x2 - x1) = (-1 - 7) / (x - (-1)) = -8 / (x + 1)

The slope which is between points C and D is:

slope of line CD = (y2 - y1) / (x2 - x1) = (8 - (-1)) / (1 - x) = (9) / (1 - x)

Since B, C, and D are collinear, slope of BC = slope of CD. Therefore:

-8/(x+1) = 9/(1-x)

by solving the x, we get:

-8(1 - x) = 9(x + 1)

-8+8x=9x + 9

x = 17

So, the coordinates of point C are (17, -1).

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Explanation:

2 freshmen + 3 sophomores + 2 juniors + 2 seniors = 9 students total.

Let's consider the cases where we have the same number of juniors and seniors. We'll then take the complement of this to get the final answer.

-----------

Case A: There is 1 junior and 1 senior

There are 2 ways to pick a junior and 2 ways to pick a senior. That's 2*2 = 4 ways so far.

Then we have 9-4 = 5 students left to pick from (i.e. 2 freshmen+3 sophomores = 5 students left) and we have 5-2 = 3 seats to fill. Order doesn't matter on the committee since each person has equal rank.

We use the nCr combination formula.

n = 5 students

r = 3 seats to fill

n C r = (n!)/(r!(n-r)!)

5 C 3 = (5!)/(3!*(5-3)!)

5 C 3 = (5!)/(3!*2!)

5 C 3 = (5*4*3!)/(3!*2!)

5 C 3 = (5*4)/(2!)

5 C 3 = (5*4)/(2*1)

5 C 3 = (20)/(2)

5 C 3 = 10

There are 10 ways to fill the remaining 3 seats when we pick from the freshmen and sophomores only.

To recap everything so far:

Therefore, we have 4*10 = 40 different combinations possible for case A. We'll refer to this value later.

-----------

Case B: We pick 2 juniors and 2 seniors

Since there 2 juniors to pick from, and 2 junior seats to fill, there's only 1 way to do this. Likewise, there's only 1 way to pick the 2 seniors to fill the 2 seats.

In total so far there is 1*1 = 1 way to pick the 2 juniors and 2 seniors in any order you like.

Then we have 9-4 = 5 students left that are freshmen or sophomores. This is the number of choices we have for the final 5th seat.

We have 1*5 = 5 ways to have case B happen.

----------

Summary so far:

There are 45 ways to have the same number of juniors as seniors (either 1 of each or 2 of each).

Now we must calculate the number of total combinations possible on this committee. We'll turn to the nCr formula again.

n = 9 students

r = 5 seats

n C r = (n!)/(r!(n-r)!)

9 C 5 = (9!)/(5!*(9-5)!)

9 C 5 = (9!)/(5!*4!)

9 C 5 = (9*8*7*6*5!)/(5!*4!)

9 C 5 = (9*8*7*6)/(4!)

9 C 5 = (9*8*7*6)/(4*3*2*1)

9 C 5 = (3024)/(24)

9 C 5 = 126

There are 126 different five-person committees possible.

Of those 126 committees, 45 of them consist of cases where we have the same number of juniors and seniors.

That must mean there are 126-45 = 81 combinations where we do not have the same number of juniors and seniors. This is where the concept of "complement" comes in.

Answer:

1 orange weighs 5 ounces.

Divide

35÷7 = 5

so, one orange weighs 5 ounces.

Answer:

14

Step-by-step explanation:

Rewrite the equation: 4*4+3-5

Multiply: 16+3-5

Add: 19-5

Subtract: 14

Answer:

Therefore, the length of the hypotenuse of the 45°-45°-90° triangle is 32 centimeters.

Step-by-step explanation:

In a 45°-45°-90° triangle, the two legs are congruent, which means that each leg is equal to the length of the hypotenuse divided by √2.

Let h be the length of the hypotenuse. Then we have:

leg = h/√2

Given that one of the legs is 8√8 centimeters, we can substitute this value into the equation above to solve for h:

8√8 = h/√2

Multiplying both sides by √2, we get:

8√8 x √2 = h

Simplifying, we get:

h = 8√16

h = 8 x 4

h = 32

Therefore, the length of the hypotenuse of the 45°-45°-90° triangle is 32 centimeters.

(b) The difference in sample mean is 0.544 ml. (c) Using StatKey, we find the p-value to be 0.046. (d) It is unlikely that this difference is due to random chance alone.

(a) The null hypothesis is that there is no difference in average brain size between football players with no history of concussions (FBNoConcuss) and football players with a history of concussions (FBConcuss). The alternative hypothesis is that the average brain size is larger in FBNoConcuss than in FBConcuss.

H0: μFBNoConcuss = μFBConcuss

HA: μFBNoConcuss > μFBConcuss

(b) The relevant sample statistic is the difference in sample mean between the two groups.

Therefore, the difference in sample mean is 0.544 ml.

(c) Using StatKey, we find the p-value to be 0.046.

(d) With a p-value of 0.046, which is less than the commonly used significance level of 0.05, we reject the null hypothesis and conclude that there is evidence to suggest that the average brain size is larger in FBNoConcuss than in FBConcuss. It is unlikely that this difference is due to random chance alone.

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Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53.

A loan or investment's principle amount is the sole amount used to compute simple interest. Any interest that has been earned on interest that has accrued over time is not taken into account by simple interest.

Contrarily, compound interest is a sort of interest that takes into account both the original principal and any interest that has accrued over time. As a result, the interest gained during one period is added to the principle for the following month, where it continues to earn interest.

Joni is not correct, because $230 is just the interest she will earn; she will have $430 total.

The compound interest is given by the formula:

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

Substituting the values we have:

[tex]A = 200(1 + 0.05/1)^{(1*3)}\\A = 200(1.05)^3[/tex]

A = 200(1.157625)

A = $231.53

Hence, Joni will have a total balance of $231.53 after 3 years.

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The complete question is:

The answer of the given question based on the histogram is option (a) IQR, because Sunny Town is symmetric and option (b) IQR, because Beach Town is skewed.

Frequency refers to the number of times a particular event or value occurs within a given dataset or sample. In statistics, frequency is often used to describe the distribution of a variable, where a frequency distribution shows the number of observations that fall into each category or interval.

The IQR (interquartile range) should be used for both sets of data to determine the location with the most consistent temperature. The IQR is a measure of spread that is not influenced by extreme values or outliers, which is helpful in comparing the consistency of temperatures in different locations. It is appropriate to use the IQR for Sunny Town because the data is roughly symmetric, and for Beach Town because although it is skewed, the IQR is more robust than the range and is not influenced by outliers.

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Answer: B

Step-by-step explanation:

The ratios are not the same for all values of x and y, we can conclude that x and y are not proportional.

Ratio and proportion are two mathematical concepts that are closely related.

A ratio is a way of comparing two or more quantities by dividing one quantity by another. It expresses the relative size or magnitude of two quantities. Proportion, on the other hand, refers to the equality of two ratios. It states that two ratios are equal. Proportions can be used to solve problems involving unknown quantities.

To determine whether x and y are proportional, we need to check if the ratio of corresponding values of x and y is always the same.

Let's find the ratio of y to x for each corresponding value:

y/x for x=1: 7/1 = 7

y/x for x=2: 8/2 = 4

y/x for x=3: 9/3 = 3

Since the ratios are not the same for all values of x and y, we can conclude that x and y are not proportional.

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Answer:

$104.11

Step-by-step explanation:

To calculate the monthly payment for a loan, we can use the following formula:

Monthly payment = (Pr(1+r)^n) / ((1+r)^n-1)

where:

P = the principal amount (the amount borrowed)

r = the monthly interest rate (annual interest rate divided by 12)

n = the number of payments (total number of years multiplied by 12)

In this case, the principal amount is $3825, the annual interest rate is 15%, and the loan term is 4 years. So we have:

P = $3825

r = 0.15/12 = 0.0125

n = 4*12 = 48

Substituting these values into the formula, we get:

Monthly payment = (38250.0125(1+0.0125)^48) / ((1+0.0125)^48-1)

Monthly payment ≈ $104.11

Therefore, the monthly payment for a $3825 loan at 15% annual interest for 4 years is approximately $104.11.

You paid the total amount of $1257 at the end of 5 years.

Let us assume that c represents the cost per month.

So, c = $20.95

and let t represents the total number of months.

We know that there are 12 months in a year.

so, the number of months in 5 years would be:

12 × 5 = 60

So, t = 60 months

Using unitary method the total amount paid at the end of five years :

s = c × t

s = 20.95 × 60

s = $1257

Therefore, the total amount is $1257

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There is no alternate exterior angle corresponding to ∠8. ∠3 ∠4 ∠5 ∠6 are not an alternate exterior angle to ∠8

We know that alternate exterior angles are the pair of angles on the outer side of the two parallel lines but on the opposite side of the transversal,

here, we have,

We have been given a geometrical figure as shown in the image.

Now we know that a pair of alternate exterior angles exist for a pair of parallel lines.

Hence, there is no alternate exterior angle corresponding to ∠8.

Therefore, there is no alternate exterior angle corresponding to ∠8.

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Answer:

12.9cm

Step-by-step explanation:

Trapeziums QRVW and QRSP are similar because they share the same side 5.5 cm and their angles are corresponding to each other.

We can express the ratios of sides in both trapeziums to find WV.

Since side 5.5 is the same in each trapezium,

[tex]\frac{5.5}{WV}=\frac{5.5}{12.9}[/tex]

Thus, WV = 12.9cm

Hope this helps:)

Answer:(0,-1).

Step-by-step explanation:

As the diagonals of a parallelogram bisect each other, the midpoint of AC is the same as the midpoint of BD. Therefore, the fourth vertex D is (0,-1).

Answer:

To graph the function f(x) = 2sin(x) - 2 by hand, we can use the following steps:

Step 1: Find the amplitude

The amplitude of the function is the absolute value of the coefficient of the sine function, which is 2 in this case. Therefore, the amplitude is 2.

Step 2: Find the period

The period of the function is given by the formula 2π/b, where b is the coefficient of x in the sine function. In this case, b = 1, so the period is 2π/1 = 2π.

Step 3: Find the midline

The midline is the horizontal line that the graph oscillates around. For the sine function, the midline is the y-value of the function when there is no vertical shift. In this case, the midline is y = -2.

Step 4: Find the y-intercept

The y-intercept is the value of the function when x = 0. Plugging in x = 0, we get f(0) = 2sin(0) - 2 = -2. Therefore, the y-intercept is -2.

Step 5: Sketch the graph

Based on the amplitude, period, midline, and y-intercept we just found, we can sketch the graph of the function as follows:

- The graph oscillates between y = 2 and y = -6, with a midline at y = -2.

- The graph starts at (0, -2), then goes up to (π/2, 0), down to (π, -2), down further to (3π/2, -4), and back up to (2π, -2).

- The graph is symmetric about the midline.

Therefore, the information about the function is:

Amplitude: 2 (The distance from the midline to the maximum or minimum of the graph is 2.)

Period: 2π (The graph completes one full cycle over a horizontal distance of 2π.)

Midline: y = -2 (The horizontal line that the graph oscillates around.)

y-intercept: -2 (The value of the function when x = 0.)

The probability of selecting a striped marble, not replacing it, then selecting a black marble is 4/15.

The probability of selecting a striped marble on the first draw is 6/10, since there are 6 striped marbles out of a total of 10 marbles in the bag.

After the first marble is drawn, it is not replaced, so there are now 9 marbles left in the bag. Out of these, there are 4 solid marbles and 5 striped marbles. Therefore, the probability of selecting a black marble on the second draw is 4/9.

To find the probability of both of these events occurring together, we multiply the probabilities

P(striped, then black) = P(striped) × P(black | striped not replaced)

P(striped, then black) = (6/10) × (4/9)

P(striped, then black) = 24/90

P(striped, then black) = 4/15

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The given question is incomplete, the complete question is:

There are 10 marbles in a bag (4 solid, 6 striped) .what is the probability of selecting a striped marble, not replacing it, then selecting a black marble?

Answer: You can comment if this is wrong but I don't know what an area model is entirely I might just I don't remember

|\ |\

| \ | \

|  \|  \

|___\|___\

1/4  1/5

Step-by-step explanation:

1. Draw a rectangular area model with two sections.

2. Label the left section with 1/4 and the right section with 1/5.

3. Divide the left section into 4 equal parts by drawing lines horizontally and vertically

4. Divide the right section into 5 equal parts by drawing lines horizontally and vertically.

5. Count the number of parts in the left section (4 parts) and the number of parts in the right section (5 parts).

6. Multiply the parts in the left section by the parts in the right section, which gives 4 x 5 =20.

7. The answer is 20/4 = 5.

Answer:

-7/9

Step-by-step explanation:

its not a complete change to 1 but it is very close to being a 1

the orthogonal projection of a point P onto a line L can be expressed as: projection  L(P) = ((P . u) ×u)·

Orthogonal projection is a mathematical operation that involves projecting a vector or point onto another vector or line in a way that the projection is perpendicular (or orthogonal) to the vector or line.

In mathematical notation, the orthogonal projection of a point P onto a line L can be expressed as:

projection L(P) = ((P . u) × u)

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Answer:Red

Step-by-step explanation:

Answer:

Step-by-step explanation:

5 blue out of 15 chips

An equation is formed of two equal expressions. The maximum height reached by a rocket, to the nearest tenth of a foot is 1542.82 feet.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

To find the maximum height through which the rocket will reach, we need to differentiate the given function, therefore, we can write,

y=-16x²+173x+140

dy/dx = -16(2x)+173

Substitute the value of dy/dx as 0, to get the value of x,

0 = -32x + 173

173 = 32x

x =5.406

Substitute the value of x in the equation to get the maximum height,

y=-16x²+173x+140

y=-16(5.406²) +173(5.406) +140

y= 467.59 + 935.23 + 140

= 1542.82 feet.

Hence, the maximum height reached by the rocket, to the nearest tenth of a foot is 1542.82 feet.

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the measure of angle V is approximately 21.87 degrees. To find the measure of angle V, we need to use the fact that the sum of the angles in a triangle is 180 degrees. Therefore, we can write:

m∠V + m∠W + m∠X = 180

where angle X is the third angle in the triangle formed by V, W, and X. We know that m∠W is (3x+4) degrees, and we can see that angle X is adjacent to angle V, so we can use the fact that the sum of adjacent angles is equal to the total angle to write:

m∠V + m∠X = (2x+2) degrees

Now we can substitute this expression for m∠X into the first equation to eliminate m∠X:

m∠V + (2x+2 - m∠V) + (3x+4) = 180

Simplifying and solving for x, we get:

5x + 6 = 180

5x = 174

x = 34.8

Now we can substitute this value of x back into our expression for m∠V + m∠X to find m∠V:

m∠V + (2(34.8)+2 - m∠V) = 71.6

Simplifying and solving for m∠V, we get:

3m∠V = 65.6

m∠V = 21.87 (rounded to two decimal places)

Therefore, the measure of angle V is approximately 21.87 degrees.

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In order to be within a 1% margin of error at a 95% confidence level, the candidate would need to survey 9604 people in the community. The size of the sample is 9604.

We have a political candidate who wants a 1% margin of error at a 95% confidence level. To find the size of the sample, we use the formula given below;

n = [ Z (α/2) / E ]²

Where,

n = the sample size required

Z (α/2) = the value obtained from the standard normal distribution for the given level of confidence

E = the margin of error

Here, α = 1 - 0.95 = 0.05

Z (α/2) = Z (0.025), is the z-value corresponding to 0.025 in the normal distribution table. It is found to be 1.96.

Now, substituting the given values in the formula,

n = (1.96² * 0.5 * 0.5) / 0.01² ⇒ 9604

Hence, the sample size required for the poll is 9604.

However, this is not feasible, as it would be very expensive and time-consuming. Therefore, we will round the answer to the nearest whole number as we are looking for a practical solution. Thus, the candidate would need to survey 9604 people in the community (rounded to the nearest whole number).

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In addition, the image's y-coordinate would be , this indicates that we must raise the point by  to align it with the y-axis. Hence, D  is the right response.

Option A moves the point 4 units horizontally and 8 units vertically, but does not move it onto the y-axis.

Option B moves the point -4 units horizontally and 8 units vertically, but does not move it onto the y-axis.

Option C moves the point horizontally by 8 units and vertically by 4 units, but it does not move it to the y-axis.

Option D moves the point 8 units horizontally and -4 units vertically. When we apply this transformation to an x-axis point, its y-coordinate remains unchanged, so the point's image is on the y-axis. As a result, option D is the correct translation:

(x, y) → (x+8, y-4)

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Answer:

The correct responses are:

A) S(10)=S(5) means that there were the same number of students in 2010 as in 2005.

E) S(0) = 2,000 means that there were no students in the year 2000.

B and D are not plausible statements because they imply that there is an inverse relationship between t and S(t), meaning that the number of students decreases as t increases. Also, C is incorrect as it implies that there were fewer students in 2015 than there were in 2010, which contradicts the nature of the situation.