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Given WX is tangent to OS at point V, the statements that must be true include:

A. m∠TVX =m∠TVX

C. m∠TVW = m∠TSV

D. m∠TUV =m∠TVW

In mathematics, a tangent is a line that touches a curve at exactly one point, without intersecting it at that point. The tangent line at a point on a curve represents the slope of the curve at that point. The concept of tangent is important in calculus, where it is used to calculate derivatives of functions.

TUV = 1/2MTU = TVW

TUV = TVW

Also, MTV = TSV = 2TVW

TVW = TSV

The correct options are A, C and D.

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Answer

Hi!, if you need help right away, chat with a tutor!

Step-by-step explanation:

Answer:

(a) width = 71 ft; (b) length = 77 ft

Step-by-step explanation:

(a) The formula for area of a rectangle is

A = lw, where

Because we're already given the area and length, we can find the width by plugging everything into the formula and solve for width, w:

6319 = 89w

71 ft = w

(b) The formula for perimeter of a rectangle is

P = 2l + 2w, where

Since we're given the perimeter and width this time, we can plug everything into the formula and solve for l:

272 = 2l + 2(59)

272 = 2l + 118

154 = 2l

77 ft = l

We can check our answers for (a) and (b) by plugging in the length and width for (a) into the area formula and seeing whether we get 6319 and plugging in the length and width for (b) into the perimeter formula and seeing whether we get 272

Checking answers for (a):

6319 = 89 * 71

6319 = 272

Checking answers for (b):

272 = 2(77) + 2(59)

272 = 154 + 118

272 = 272

The solution of the equation [tex]\rm 5^{-x/16} = 5[/tex] will be negative 16.

Given that:

Equation, [tex]\rm 5^{-x/16} = 5[/tex]

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

Take log on both sides, then we have

(-x / 16) log 5 = log 5

-x / 16 = 1

x = -16

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The solution to the given problem of equation comes out to be quotient : x² +x+6+2/(x+2)  and remainder is 2.

We have to find the remainder and quotient

Given : synthetic division for

x³ + 3x² + 8x + 14

------------------------

x + 2

Write the problem in synthetic division format

-2  | 1 3 8 14

        -2 -2  

------------------------

    1   1  6

Carry down the leading coefficient, unchanged, to below the division symbol

-2  |    1 3 8 14

          -2 -2

---------------------------

        1  1   6

Multiply the carry - down value by the zero of the denominator, and carry the result up into the next column:

1(-2)=-2

-2 |  1 3 8 14

       -2 - 2

------------------

    1    1   6

=> We get:

As x² +x+6+ 2/(x+2)

and remainder is 2

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The area of the figure is 24.28 cm²

Any figure that we can break and form more than one basic shape from is called a composite figure.

The composite figure can be broken into a right triangle, a rectangle and a semi circle.

area of triangle = 1/2 bh

= 1/2 × 4 × 3

= 2 × 3

= 6 cm²

area of the rectangle = l × w

= 3 × 4

= 12 cm²

area of the semi circle = 1/2 πr²

= 1/2 × 3.14 × 2²

= 3.14 × 2

= 6.28cm²

Therefore the area of the composite figure =

6 + 12 +6.28

= 24.28 cm

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The Surface area of the composite figure is calculated as approximately: 234 sq. cm

Here, we have,

to Find the Surface Area of a Composite Figure:

The surface area of the composite figure is the area surrounding the faces of the solid as a whole. Therefore, we have:

Surface area (SA) = Surface area of the square prism + surface area of the square pyramid - 2(area of base)

Area of base = area of square = 6 * 6 = 36 sq. cm.

Surface area of the square prism = 2a² + 4ah

a = 6 cm

h = 4 cm

Plug in the values:

Surface area of the square prism = 2(6²) + 4*6*4

= 72 + 96

= 168 sq. cm.

Surface area of the square pyramid = 2bs + b²

b = side length = 6 cm

s = slant height = √(8² + 3²) = 8.5 cm

Plug in the values:

Surface area of the square pyramid = 2 * 6 * 8.5 + 6² = 138 sq. cm.

Surface area of the composite figure = 168 + 138 - 2(36) = 234 sq. cm

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complete question:

Find the surface area of each composite figure. Use 3.14 for π. Round to the nearest tenth. 12m. 6cm. 6cm. 4cm.​

The equation of the line is y = -4x - 11.

The equation of the line is y = 3x + 7.

The equation of the line is y = (1/2)x + 12.

We have,

A)

The equation of the line with gradient m = -4 that passes through the point (-2,-3) is:

y - y1 = m(x - x1)

y - (-3) = -4(x - (-2))

y + 3 = -4(x + 2)

y + 3 = -4x - 8

y = -4x - 11

B)

The equation of the line with gradient m=3 that passes through the point (-2,1) is:

y - y1 = m(x - x1)

y - 1 = 3(x - (-2))

y - 1 = 3(x + 2)

y = 3x + 7

C)

The equation of the line with gradient m=1/2 that passes through the point (-4,10) is:

y - y1 = m(x - x1)

y - 10 = (1/2)(x - (-4))

y - 10 = (1/2)(x + 4)

y = (1/2)x + 12

Therefore,

The equation of the line is y = -4x - 11.

The equation of the line is y = 3x + 7.

The equation of the line is y = (1/2)x + 12.

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The determinant of the given 10 x 10 matrix is 1024.

A matrix is described as  a rectangular array or table with rows and columns and numbers, symbols, or expressions that is used to represent a mathematical object or a property of such an object.

We apply the knowledge that the determinant of a diagonal matrix is the product of its diagonal entries in order to find the determinant of a 10 x 10 matrix with 2s on the main diagonal and zeros elsewhere,

Determinant = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2

We then calculate for the product and have:

Determinant = [tex]2 ^ 1^0[/tex] = 1024

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Answer:

11.49

Step-by-step explanation:

a^2+b^2=c^2

think of this as a triangle, we are going to use Pythagorean theorem.

the hypotenus is 14 ft and one of the legs is 8 ft. so the other leg is x

8^2 + x^2 = 14^2

64 + x^2 = 196

subtract the 64 on both sides

x^2 = 132

to counter the square we square root it

so x = the square root of 132 which comes out to a decimal

11.489....

rounded it would be 11.49

hope this helped

The numerical value of x in the inscribed angle and intercepted arc is 4.

An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.

The relationhip between an an inscribed angle and intercepted arc is expressed as:

Inscribed angle = 1/2 × intercepted arc.

From the image:

Inscribed angle XZY = 14x + 4

Intercepted arc XY = 30x

Value of x = ?

Plug these values into the above formula and solve for x.

Inscribed angle = 1/2 × intercepted arc.

14x + 4 = 1/2 × 30x

14x + 4 = 15x

15x = 14x + 4

15x - 14x = 4

x = 4

Therefore, x has a value of 4.

Option D) 4 is the correct answer.

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The area of a right triangle with a height of 8 yards and a base of 17 yards is 136 square yards.

The area of a right triangle with a height of 8 yards and a base of 17 yards can use the formula for the area of a triangle:

Area = (base x height) / 2

Substituting the given values into the formula get:

Area = (17 x 8) / 2

Area = 136 square yards

The area of the right triangle is 136 yd².

To understand why this formula works can visualize the right triangle as half of a rectangle.

The height of the triangle is one side of the rectangle and the base of the triangle is the adjacent side of the other half of the rectangle.

The area of the rectangle is the product of its height and base is twice the area of the right triangle.

The product of the height and base by 2 to get the area of the right triangle.

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The area of triangle A is 98 sq cm. Option B is correct.

Since triangle A is a scaled version of triangle B, the ratio of their areas is equal to the square of the ratio of their corresponding side lengths.

If the dimensions of triangle A are twice the dimensions of triangle B, then the ratio of their side lengths is 2:1.

The ratio of their areas, therefore, is (2:1)² = 4:1.

Given that the area of triangle B is 24.5 sq cm, we can find the area of triangle A by multiplying 24.5 by the ratio of their areas:

Area of triangle A = 24.5 × 4 = 98 sq cm

Therefore, the area of triangle A is 98 sq cm.

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The range of the set {0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 5} is 5.

The range of a set of numbers is the difference between the largest and smallest numbers in the set.

The set is {0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 5}.

The range first need to identify the smallest and largest numbers in the set.

The smallest number is 0 appears three times.

The largest number is 5.

The range is:

5 - 0 = 5

The range of the set {0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 5} is 5.

The range is a measure of the spread or variability of a set of numbers.

It tells us how much the values in the set differ from each other.

The range of 5 indicates that the values in the set are spread out over a range of 5 units.

The set includes consecutive integers from 0 to 5 with multiple occurrences of some of these integers.

While the range provides a measure of the spread it is only one of many measures that can be used to describe the characteristics of a set of data.

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Answer:

Step-by-step explanation:

4x/3 + x/6 =6

get a common denominator first

8x/6 + x/6 =6

then add

9x/6 = 6

multiply by six

9x = 36

divide by 9

x= 4

When Y is increased by 44%, X increases by 20%.

If X is proportional to the square root of Y, then we can express this relationship as X = k√Y, where k is the constant of proportionality. Now, let's consider the scenario where Y is increased by 44%.

Let's denote the initial value of Y as Y₀. When Y is increased by 44%, the new value of Y becomes Y₁ = Y₀ + 0.44Y₀ = 1.44Y₀.

Since X is proportional to the square root of Y, we can write the initial value of X as X₀ = k√Y₀, and the new value of X as X₁ = k√(1.44Y₀).

To find the percentage increase in X, we can calculate the difference between the new and initial values of X and express it as a percentage of the initial value:

Percentage increase in X = ((X₁ - X₀) / X₀) * 100

Substituting the values, we get:

Percentage increase in X = ((k√(1.44Y₀) - k√Y₀) / k√Y₀) * 100

Simplifying the expression, we find:

Percentage increase in X = ((√1.44 - √1) / √1) * 100

Percentage increase in X = (1.2 - 1) x 100

Percentage increase in X = 0.2 x 100

Percentage increase in X = 20%

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Note that the  the probability that both spins result in the same color is 0.28

Probability of getting ...


red on both spins = (1/5) x   (1/5) = 1/25

yellow on both spins = (1/5) x  (1/ 5) =  1/25

blue on both spins = (1/5) x  (1/5 =  1/25

pink on both spins = (2/5)x (2/5) =  4/25

So the total   probability of getting the same color in both spins is computed as        

= 1/25 + 1/25 +  1/25 +  4/25

= 7/25 or 0.28

So the correct asnwer is 0.28 or 7/25

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Compare the linear relationships shows that

Equation B has the greater slope. It has a slope of 106, and Equation A has a slope of 58, which is smaller.

Equation A is given as y = 58x

The slope is 58

For Equation B  

Slope of Equation B = (change in y) / (change in x)

= (729 - 623) / (13 - 12)

= 106 / 1

= 106

Comparing the slopes, we can see that the slope of Equation B (106) is greater than the slope of Equation A (58)

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The answer would be C - "Cheetah B has a higher ratio of miles per minute than Cheetah A because 17 over 8 is less than 56 over 20."

also "get it right please" ?! how rude

The value of x in the circle using the intersecting secants and tangents equation is 4

From the question, we have the following parameters that can be used in our computation:

The circle

The value of x in the circle can be calculated using the intersecting secants and tangents equation

So, we have

6² = x * (x + 5)

When expanded, we have

x² + 5x - 36 = 0

When factored, we have

(x + 9)(x - 4) = 0

Using the zero product property , we have

x = -9 or x = 4

The valiue of x cannot be negative

So, we have

x = 4

Hence, the value of x in the circle is 4

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The profit function is given as follows:

P(x) = -0.5x² + 53x - 300.

The profit if 53 mowers are sold is given as follows:

P(53) = -$1,598.5. (loss).

The profit function is obtained as the subtraction of the revenue function by the cost function, as follows:

P(x) = R(x) - C(x).

The functions for this problem are given as follows:

Hence the profit function is given as follows:

P(x) = -0.5x² + 91x - (38x + 300)

P(x) = -0.5x² + 53x - 300.

The profit if 53 mowers are sold is given as follows:

P(53) = -0.5(53)² + 53(2) - 300

P(53) = -$1,598.5.

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The average weight of a sample of objects is 94.83 pounds and the spread of the weights around the mean is measured by the sample standard deviation, which is 31.16 pounds.

The given data shows the weights (in pounds) of adult wild mountain lions captured and released for the first time in the San Andres Mountains.

(a) Using a calculator with mean and sample standard deviation keys, we can find the sample mean weight x and sample standard deviation s.

[tex]x = (70 + 107 + 130 + 128 + 60 + 64) / 6 = 94.83 \pounds\\\\s = \sqrt{\frac{(70 - 94.83)^2 + (107 - 94.83)^2 + ... + (64 - 94.83)^2} {5}}[/tex]

= 31.16 pounds

Therefore, the sample mean weight x is 94.83 pounds and the sample standard deviation s is 31.16 pounds.

(b) To find a 75% confidence interval for the population average weight u of all adult mountain lions in the specified region, we can use the formula:

CI = x ± t*(s/√n)

where CI is the confidence interval, x is the sample mean weight, t is the t-score for the desired confidence level (75% in this case), s is the sample standard deviation, and n is the sample size (6 in this case).

From the t-table, the t-score for a 75% confidence level with 5 degrees of freedom is 2.015.

Plugging in the values, we get:

CI = 94.83 ± 2.015*(31.16/√6) = (63.6 pounds, 126.1 pounds)

Therefore, we can be 75% confident that the true population average weight of all adult mountain lions in the specified region is between 63.6 pounds and 126.1 pounds.

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18 will be the result of the given problem.

Applying the order of operations (PEMDAS), we first calculate the value inside the parentheses, which is 3 + 6 = 9.

Then we multiply 4 by 9, which gives 36.

Finally, we divide 36 by 2, which gives the final answer of 18. Therefore:

4 x (3 + 6) ÷ 2 = 18

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It is a right triangle is the ratio of the length of one leg to the

length of the other leg = x/x =1/1. C.

In a 45-45-90 right triangle, the two acute angles are each 45 degrees, and the right angle is 90 degrees.

The special property of a 45-45-90 triangle is that its two legs are congruent, meaning they have the same length.

Let's denote the length of each leg as "x."

To determine the ratio of the length of one leg to the length of the other leg, we can compare the lengths.

Let's call the length of one leg "a" and the length of the other leg "b."

Since the two legs are congruent, we have a = b = x.

The ratio of the length of one leg to the length of the other leg is a:b = x:x.

Simplifying the ratio, we have a:b = 1:1.

This means that the length of one leg is equal to the length of the other leg in a 45-45-90 right triangle.

To recap:

Both legs have the same length, which is a property unique to this type of triangle.

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This is the equation of a hyperbola, since it has a constant difference between the distances from any point on the curve to two fixed points (known as the foci). In this case, the foci are located at (-2, 0) and (2, 0).

To convert the given polar equation, r(1+3sinθ) = 4, to a rectangular equation, we can use the following equations:

x = rcos(θ)

y = rsin(θ)

Substituting r(1+3sinθ) = 4, we get:

x = r*cos(θ) = (4/(1+3sinθ))cos(θ)

y = rsin(θ) = (4/(1+3sinθ))*sin(θ)

Simplifying further, we can use the identity sin^2(θ) + cos^2(θ) = 1 to get:

x = 4cos(θ)/(1+3sinθ)

y = 4sin(θ)/(1+3sinθ)

Therefore, the rectangular equation of the conic section in terms of x and y is:

x = 4cos(θ)/(1+3sinθ)

y = 4sin(θ)/(1+3sinθ).

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Part A: The total value of the loan with simple interest is $59,660.50.

Part B: The total value of the loan with quarterly compounded interest is $60,357.91.

Part C: The total value of the loan with continuously compounded interest is $60,441.82.

Part D: The best choice for the small business owner is the loan with simple interest, as it has the lowest total value and thus the lowest cost to repay.

Part A:

To calculate the total value of the loan with simple interest, we can use the formula:

[tex]Total value = Principal \times (1 + interest rate \times time)[/tex]

Where,

Principal = $50,000

Interest rate = 5.25% = 0.0525

Time = 3 years and 8 months = 3.67 years.

[tex]Total $ value = $50,000 \times (1 + 0.0525 \times 3.67) = $59,660.50[/tex]

Therefore, the total value of the loan with simple interest is $59,660.50.

Part B:

To calculate the total value of the loan with quarterly compounded interest, we can use the formula:

[tex]Total value = Principal \times (1 + (interest rate / n))^{(n \times time) }[/tex]

Where,

Principal = $50,000

Interest rate = 5.25% = 0.0525

Time = 3 years and 8 months = 3.67 years

n = 4 (since interest compounds quarterly)

[tex]Total value = $50,000 \times (1 + (0.0525 / 4))^{(4 \times3.67) } = $60,357.91[/tex]

Therefore, the total value of the loan with quarterly compounded interest is $60,357.91.

Part C:

To calculate the total value of the loan with continuously compounded interest, we can use the formula:

[tex]Total value = Principal \times e^{(interest rate \times time)}[/tex]

Where,

Principal = $50,000

Interest rate = 5.25% = 0.0525

Time = 3 years and 8 months = 3.67 years

[tex]Total value = $50,000 \times e^{(0.0525 \times 3.67) } = $60,441.82[/tex]

Therefore, the total value of the loan with continuously compounded interest is $60,441.82.

Part D:

From the calculations in Parts A, B, and C, we can see that the loan with continuously compounded interest has the highest total value of $60,441.82.

This is followed by the loan with quarterly compounded interest with a total value of $60,357.91, and finally the loan with simple interest with a total value of $59,660.50.

Therefore, the best choice for the small business owner would be to take the loan with simple interest, as it has the lowest total value and thus the lowest cost to repay.

However, if the small business owner is willing to pay a higher cost for the loan, they could consider the loan with quarterly or continuously compounded interest, which have higher total values.

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Answer:

Hi!, if you need help right away, chat with a tutor!

Step-by-step explanation:

The standard deviation of the data set is 11.75.

To calculate the standard deviation of the data set, we first need to find the variance, which is the average of the sum of squares of the differences between each data value and the mean. We already calculated the sum of squares of the differences in Part (c), which is 828.

The formula for variance is:

variance = sum of squares of differences / number of data values

Since we have six data values, the variance is:

variance = 828 / 6

variance = 138

Now we can calculate the standard deviation, which is the square root of the variance:

standard deviation = sqrt(variance)

standard deviation = sqrt(138)

standard deviation = 11.75 (rounded to two decimal places)

Therefore, the standard deviation of the data set is 11.75.

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