what is the value of the expressionwhat is the value of the expression (3.2+0.2)2+12

Therefore, the value of x that will make the triangles similar by the SSS similarity theorem is approximately 73.51.

To determine the value of x that will make the triangles similar by the SSS (Side-Side-Side) similarity theorem, we need to identify the corresponding sides of the triangles and set up a proportion.

Let's denote the corresponding sides of the two triangles as follows:

Triangle 1: Side A = 15, Side B = 59, Side C = 77

Triangle 2: Side A' = 9, Side B' = x, Side C' = 96

According to the SSS similarity theorem, for two triangles to be similar, the ratios of the corresponding sides must be equal.

Therefore, we can set up the following proportion:

A / A' = B / B' = C / C'

Substituting the given values, we have:

15 / 9 = 59 / x = 77 / 96

To find the value of x, we can solve the second equation in the proportion:

59 / x = 77 / 96

Cross-multiplying, we get:

59 * 96 = 77 * x

Simplifying further:

5664 = 77x

Dividing both sides by 77:

x = 5664 / 77

Calculating this value:

x ≈ 73.51

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The values of  unknown variable on equating the matrices are w =±9 ,

k =-6 , f= -7

A matrix is arrangement of numbers in the form of rows and columns  such that a rectangular array is formed . if number of rows is m and number if columns is n then we say that the matrix is of order m*n .

Let [ a  b ] and [ c   d ] be two 1*2 matrices

Equating these two matrix [ a  b ]  =  [ c   d ] means that entries of both the matrix are identical a=c  and b =d , entries at same places (row and column wise ) in both matrix have to be identical.

Given that  two matrices [ -12  -w²  2f  3 ] and [ 2k  -81  -14  3 ] are equal and we need to find the unknown variables w, f, k

If   [ -12  -w²  2f  3 ]  =   [ 2k  -81  14  3 ] then their terms are identical

 AS  -12 = 2k

Dividing both sides by 2

⇒ k = -12/2 = -6

As - w² = -81

⇒ w² = 81

Taking square root  both sides

⇒ w = ± 9

As  2f = -14

Dividing both sides by 2

⇒ f = -14/2 = -7

The values of the variable w, f, k after equating both the matrices are

k = -6 , w = ±9 , f = -7

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Answer:

  (a)  The two triangles are similar by AA

Step-by-step explanation:

Similar triangles have congruent corresponding angles and proportional corresponding side lengths.

The third angle in triangle ABC is found using the fact that the sum of angles is 180°.

  ∠C = 180° -∠A -∠B

  ∠C = 180° -97° -46° = 37°

Two of the angles, A and C, match the measures of two of the angles in triangle DEF. The matches are ...

  ∠A = ∠D = 97°

  ∠C = ∠F = 37°

The two triangles are similar by AA.

__

Additional comment

The similarity statement can be ΔABC ~ ΔDEF.

Answer:

x= 0 and Y= 6

Step-by-step explanation:

The odds of the randomly selected student being a guy or having spectacles are 18/25.

We can use the inclusion-exclusion principle and a Venn diagram to solve this problem.

Let B be the event that the student is a boy, and G be the event that the student wears glasses. Then, we have:

P(B or G) = P(B) + P(G) - P(B and G)

From the given information, we know that:

P(B) = 10/25 = 2/5

P(G) = 12/25

P(B and G) = 4/25

Therefore,

P(B or G) = 2/5 + 12/25 - 4/25

= 18/25

So the probability that the student chosen at random is a boy or wears glasses is 18/25.

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Answer:Bobby can run 2 miles in 15 minutes.

Step-by-step explanation:

We can use proportion to find how far Bobby can run in 15 minutes, given that he runs 10 miles in 75 minutes.

Let d be the distance Bobby can run in 15 minutes.

We can set up the proportion:

distance/ time = distance/ time

Using the values we know:

10 miles / 75 minutes = d / 15 minutes

Simplifying:

d = (10 miles / 75 minutes) x 15 minutes

d = 2 miles

1 at each vertex

An exterior angle of a polygon is an angle formed by a side of the polygon and the extension of an adjacent side. In the case of a triangle, each exterior angle is formed by one of the triangle's sides and the extension of an adjacent side.

When an exterior angle is formed at a vertex of a polygon, the measure of the exterior angle is equal to the sum of the measures of the two interior angles adjacent to it. In the case of a triangle, the sum of the measures of the two interior angles adjacent to the exterior angle is always 180 degrees (which is the sum of the measures of all three interior angles of a triangle).

Since each exterior angle of a triangle is formed by two interior angles, and the sum of the measures of those interior angles is always 180 degrees, there can only be one exterior angle at each vertex of a triangle. Therefore, a triangle has one exterior angle at each vertex.

The closest answer to the p-value for this result is 0.0124.The p-value for this result, we need to first calculate the test statistic. Since we are testing a proportion, we will use the z-test.

The formula for the z-test is:
z = (p - P) / sqrt(P * (1 - P) / n)
where p is the sample proportion, P is the hypothesized population proportion, n is the sample size, and sqrt is the square root function. In this case, our sample size is n = 120, and our hypothesized population proportion is P = 0.85. Our sample proportion is p = 94/120 = 0.783.

Plugging in these values, we get:
z = (0.783 - 0.85) / sqrt(0.85 * 0.15 / 120) = -2.24
The p-value, we need to look up the area to the left of this value on the standard normal distribution. Using a table or calculator, we can find that this area is approximately 0.0124.

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8 inches :) (im pretty sure)

Answer:

B

Step-by-step explanation:

A door isn't about the size of my foot

Not the size height of my house

Not the size of my street

Sooooooo...

Answer:

Step-by-step explanation:

We know that:

Solution:

Hence, the cost of 1 yard of fabric is $9.

Answer:

1708

Step-by-step explanation:

16 x 7 x 15 + 11 + 17 (start left to right since you need to multiply first)

112 x 15 + 11 + 17

1680 + 11 + 17

1691 + 17

1708

The inverse Laplace transform of L⁻¹{s²−14s+58/s} is \(e^{2t} + e^{12t}\). This is obtained by factoring the expression and using the table of Laplace transforms to find the corresponding function in the time domain.

To find the inverse Laplace transform of L⁻¹{s² −14s+58/s}, we need to identify the corresponding function in the time domain.

The expression s²−14s+58/s can be factored as (s-2)(s-12)/s.

Using the table of Laplace transforms, we can determine the inverse Laplace transform as follows:

L⁻¹{s²−14s+58/s} =  L⁻¹{(s-2)(s-12)/s}

From the table, we know that  L⁻¹{s-a/s} = \(e^{at}\), where "a" is a constant.

Therefore, applying this property, we have

L⁻¹{s²−14s+58/s} =  L⁻¹{(s-2)(s-12)/s} = \(e^{2t} + e^{12t}\)

Hence, the inverse Laplace transform of  L⁻¹{s²−14s+58/s} is \(e^{2t} + e^{12t}\).

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9514 1404 393

Answer:

  (1, 7)

Step-by-step explanation:

Fill in x=1 and do the arithmetic.

  h(1) = 4(1) +3 = 7

The coordinate pair is ...

  (x, h(x)) = (1, h(1)) = (1, 7)

Answer:

x/2x+3 + 2x +3/x = 184 /65

x(2x + 3)–1 + (2x+3)x-1 = 184/65

(2x + 3)x / (2x +3)x = 184/65

2x² + 3x / 2x² + 3x = 184/65

1x= 184/64

x = 184/64

Step-by-step explanation:

Given that: {x/(2x+3)} + {(2x+3)/x} = 184/65

⇛[{(x*x) + (2x+3)(2x+3)}/{(x)(2x+3)}] = 184/65

⇛[{x² + 2x(2x+3) + 3(2x+3)}/(2x²+3x)] = 184/65

⇛[{x² + 4x² + 6x + 6x + 9}/(2x²+3x)] = 184/65

⇛[{x² + 4x² + 12x + 9}/(2x² + 3x)] = 184/65

⇛{(5x² + 12x + 9)/(2x² + 3x)} = 184/65

On applying cross multiplication then

⇛184(2x² + 3x) = 65(5x² + 12x + 9)

Multiply the number outside of the brackets with numbers and variables in the brackets on LHS and RHS.

⇛388x² + 582x = 325x² + 780x + 584

⇛388x² + 582x -325x² - 780x - 584 = 0

⇛388x²-325x² + 582x-780x - 584 = 0

⇛63x² - 198x - 584 = 0

⇛8(7x² - 22x - 65) = 0

⇛7x² - 22x - 65 = 0

Now,

This is of the form ax² + bx + c = 0, Where, a = 7, b = -22 and c = -65

Using the quadratic formula x = [{-b±√(b²-4ac)}/2a] , we get

x = [{-(-22)±√(-22)² - 4(7)(-65)}/{2(7)]

x = [{-(-22)±√(-22*-22) - 4(7)(-65)}/{2(7)]

x = [{22 ± √(484 + 1820)}/14]

x = [{22 ± √(2304)}/14]

x = {(22 ± 48)/14}

x = {(22 + 48)/14} or {(22 - 48)/14}

x = (70/14) or (-26/14)

x = 5 or x = -13/7

Therefore, x = 5 or -13/7

Answer: Hence, the value of x for the given equation is 5 or -13/7.

Please let me know if you have any other questions.

From standard normal distribution table, The minimum score among those who received scholarships was approximately 710.

To find the minimum score among those who received scholarships, we need to find the corresponding z-score using the standard normal distribution table.

Given that 2.28 percent of the students who had the highest scores received scholarships, we can find the z-score corresponding to this percentile. The z-score represents the number of standard deviations the score is above or below the mean.

Using a standard normal distribution table or a calculator, we find that the z-score corresponding to the 2.28th percentile is approximately -2.04.

Now, we can calculate the minimum score by using the z-score formula:

z = (x - mean) / standard deviation

Rearranging the formula, we can solve for x (the minimum score):

x = z * standard deviation + mean

Substituting the values:

x = -2.04 * 75 + 500

x ≈ 710

Therefore, the minimum score among those who received scholarships was approximately 710.

The minimum score among those who received scholarships was approximately 710 on the mathematics part of the SAT at UTC.

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There is sufficient evidence that the valve performs above the specifications.

Null Hypothesis (H0): The mean pressure of the valve is equal to 5.3 lbs/square inch

Alternative Hypothesis (H1): The mean pressure of the valve is greater than 5.3 lbs/square inch

To test whether the valve performs above the specifications, a hypothesis test can be used. The test statistic used will be a t-test since the sample size is below 30. The critical value at the 0.05 level is 1.645. The formula for the t-test is: t = (X-μ)/(s/√n) , where X is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the known values, the t-test is calculated as: t = (5.5-5.3)/(0.7/√100) = 2.571. Since this value is greater than the critical value at the 0.05 level (1.645), we can reject the null hypothesis and conclude that there is sufficient evidence that the valve performs above the specifications.

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Given the arithmetic sequence in the question, we can deduce that the common difference, d, is 4 and the first term, a1, is 4. The below formula will be used to solve for the 60th term of the sequence;

Where a1 = first term = 4

d = common difference = 4

n = number of term = 60

Let's go ahead and substitute the given values into our equation;

Therefore, the 60th term of the sequence is 240.

The solution is, at 500 miles, will the rental fee be the same under both plans A and B.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

from the given information, we get,

Plan A:   y = .2x + 75

Plan B:   y = .35x

Find an xy pair that satisfies both (intersection)

Substitute Plan B's y for Plan A

.35x = .2x + 75

.35x - .2x = 75

.15x = 75

x = 500

Hence, The solution is, at 500 miles, will the rental fee be the same under both plans A and B.

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Student's mean score of the class is 80.6.

Mean:

Mean or the average of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

Given,

A student receives test scores of 62, 83, and 91. the student's term project score is 88 and her homework score is 76. each test is worth 20% of the final grade, the term project is 25% of the final grade, and the homework grade is 15% of the final grade.

Here we need to find the student's mean score in the class.

First, we have to convert the percentage into decimal,

Then

=> 20% = 0.20

=> 25% = 0.25

=> 15% = 0.15

Then we have to find the scores from it,

Test A is 0.20 of the total and scores 62.

Test B is 0.20 of the total and scores 83.

Test C is 0.20 of the total and scores 91.

Project F is 0.25 of the total and scores 88.

Work H is 0.15 of the total and scores 76.

Multiply across:

=> A = (0.2 * 62) = 12.4

=> B = (0.2 * 83) = 16.6

=> C = (0.2 * 91) = 18.2

=> F = (0.25 * 88) = 22

=> H = (0.15 * 76) = 11.4

Now we have to add all these values to find the mean,

=> A + B + C + F + H

=> 12.4 + 16.6 + 18.2 + 22 + 11.4

=> 80.6

Therefore, the mean of that student is 80.6

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Answer:

16/1071

Step-by-step explanation:

The average is the given by summing all the numbers and deciding by how many numbers you have

So, the answer is given by:

(-1/12 + 4/17 - 3/28) / 3 which yields to 16/1071

Answer:

Step-by-step explanation:

its B

Solution:

Given;

The simple interest, I, is;

Thus, the amount to be repaid is;

The amount that must be repaid is $24,992

Answer:

33

Step-by-step explanation:

33 appears most.

Answer:

200

Step-by-step explanation:

6.6 divided by 3.3 is 2

10^-2 divided by 10^-4 is 10^2 or 100

2 times 100 is 200

The trapezoidal rule is a numerical integration method that frequently overestimates the real value of a function's definite integral.

The trapezoidal rule is a strategy for approximating the definite integral in calculus. The trapezoidal rule works by computing the area of the region under the graph of the function f(x) that is approximated as a trapezoid. The trapezoidal rule is commonly used to calculate the area under curves. This is achievable if the overall area is divided into smaller trapezoids rather than rectangles. The Trapezoidal Rule integration determines the area by approximating the area under a function's graph as a trapezoid. The midway rule uses rectangular areas to approximate the definite integral, whereas the trapezoidal rule uses trapezoidal approximations to approximate the definite integral. Simpson's approach works by first approximating the original function with piecewise quadratic functions.

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Using geometric sequence concepts, it is found that the sum of the first 10 terms is of 4068.6.

The nth term of a geometric sequence is given by:

\(a_n = a_1q^{n-1}\)

The sum of the first n terms is given by:

\(S_n = \frac{a_1(q^n-1)}{q - 1}\)

In this problem, the sequence is:

\(\frac{16}{25}, \frac{8}{5}, 4, 10,...\)

Hence:

\(a_1 = \frac{16}{25}, q = \frac{10}{4} = 2.5\)

Then, the sum of the first 10 terms is:

\(S_{10} = \frac{\frac{16}{25}(2.5^{10}-1)}{2.5 - 1} = 4068.6\)

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Options A , C , E ,  F , H are true for the statement population that is finding the probability.

Given that,

We have to choose the correct answer for the given statement that is finding the probability.

We know that,

Calculating a situation's probability allows us to determine its probability. Many things are difficult to determine with 100% accuracy. We can only anticipate the probability of an event occurring, or how likely it is, using it. A probability can be range 0 and 1, where 0 indicates an impossibility and 1 indicates a certainty. The probability of each event in a sample space is one.

Therefore, Options A , C , E ,  F , H are true for the statement population that is finding the probability.

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The exchange rate of the euro/pound expressed to four decimal places is 1.0100 euro/pound.

To find the exchange rate of the euro/pound, we can use the given exchange rates of dollar/pound and dollar/euro.

Let's denote the exchange rate of euro/pound as E.

Given:

Exchange rate of dollar/pound = 1.21 dollar/pound

Exchange rate of dollar/euro = 1.22 dollar/euro

To find the exchange rate of euro/pound, we can divide the exchange rate of dollar/euro by the exchange rate of dollar/pound:

E = (Exchange rate of dollar/euro) / (Exchange rate of dollar/pound)

E = 1.22 dollar/euro / 1.21 dollar/pound

Simplifying this expression, we get:

E = 1.01 euro/pound

Therefore, the exchange rate of the euro/pound, is 1.0100 euro/pound.

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Simplified form of the expression is,

⇒ 14 + 7√3

And, The distance of the sea level is,

⇒ d = 3/√2

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 7 ./ (2 - √3)

Now, We can simplify as;

⇒ 7 ./ (2 - √3)

⇒ 7 (2 + √3) / (2 - √3)(2 + √3)

⇒ 14 + 7√3 / (4 - 3)

⇒ 14 + 7√3

Here, The formula is,

d = √(3h/2)

Where, d is distance and h is eye level height.

Hence, The distance of the sea level at 5 feet is,

d = √(3h/2)

d = √(3×3/2)

d = 3/√2

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