An architect designs two similar triangular patios. The first patio has angle measures of (x − 10)°, (y + 25)°, and 60°. The second patio has angle measures of (x – 5)°, 55°, and 65°. Find the values of x and y.

Answer:

1.42

Step-by-step explanation:

Answer:

if you want ans area of cylider is 2πrh+2πr2

Step-by-step explanation:

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Cash was paid for salaries during 2014 was $55,100. These are the formulas for calculating the cash salary received in 2014:

Salary paid in cash = Salary expense in 2014 - Reduction in salary payable

The difference between the balance due for salaries at the end of each year—that is, at December 31, 2013 and December 31, 2014—can be used to determine the decline in salaries payable:

Salaries payable at December 31, 2013, compared to salaries payable at December 31, 2014, are $3,700, $1,800, and $1,900, respectively.

The drop in the balance of salaries payable from 2013 to 2014 indicates that the business paid more compensation than it incurred for the year. As a result, the 2014 salary payments in cash are:

Cash paid for salaries equals salaries paid in 2014 less salaries payable, or $57,000 minus $1,900, or $55,100.

Hence, (A) $55,100 is the correct response.

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Answer:

V = πr²(h/3)

Step-by-step explanation:

83.74 = πr²(5/3)

R = 4.00 in

Diamater = 2r = 2 x 4.00 = 8 inches

The equation x² + 4x + 9 = 0 are complex numbers: x = -2 + i√5 and x = -2 - i√5.

To find the solutions for the equation x² + 4x + 9 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Comparing this equation with the given equation x² + 4x + 9 = 0, we can see that a = 1, b = 4, and c = 9.

Plugging in these values into the quadratic formula, we have:

x = (-4 ± √(4² - 4(1)(9))) / (2(1))

x = (-4 ± √(16 - 36)) / 2

x = (-4 ± √(-20)) / 2

Since the value inside the square root is negative, we know that the solutions will involve complex numbers. Simplifying further, we have:

x = (-4 ± i√20) / 2

x = (-4 ± 2i√5) / 2

Simplifying the expression by dividing both the numerator and denominator by 2, we get:

x = -2 ± i√5

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x = -1 and y = -13, (-1,-13) is the solution to the system of equation y = 3x - 10 and y = -2x - 15.

Given the system of equation in the question;

To find the solution to the system of equation, replace the occurrence of y in the second equation with y = 3x - 10  and solve for x.

y = -2x - 15

3x - 10 = -2x - 15

Add 10 to both sides

3x - 10 + 10 = -2x - 15 + 10

3x = -2x - 15 + 10

Add 2x to both sides

3x + 2x = -2x + 2x - 15 + 10

3x + 2x = - 15 + 10

Add like terms

5x = -5

x = -5/5

x = -1

Now, to solve for y, replace all occurrence of x with -1 in the first equation and solve for y.

y = 3x - 10

y = 3( -1 ) - 10

y = -3 - 10

y = -13

Therefore, the solution to the system of equation is (-1,-13).

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9514 1404 393

Answer:

  11.9 cm

Step-by-step explanation:

Arc length is given by ...

  s = rθ . . . . . . θ is the central angle in radians

Your central angle is 85°, so is (85/180)π radians = 17/36π radians.

Then the arc length is ...

  s = (8 cm)(17/36π) ≈ 11.9 cm

The length of the 85° arc is about 11.9 cm.

A- The average rate of change of g(x) over the interval [-2, 2] is 4, B- the instantaneous rates of change at the endpoints are different from the average rate of change over the interval.

A) To find the average rate of change of the function g(x) over the interval [-2, 2], we need to compute the difference quotient:

average rate of change = [g(2) - g(-2)] / [2 - (-2)]

First, we find the values of the function at the endpoints of the interval:

g(-2) = \(-2^{3}\) - 6 = -14

g(2) = \(2^{3}\) - 6 = 2

Substituting these values into the

average rate of change = (2 - (-14)) / (2 - (-2)) = 16 / 4 = 4

Therefore, the average rate of change of g(x) over the interval [-2, 2] is 4.

B) To compare this rate with the instantaneous rates of change at the endpoints of the interval, we need to find the derivatives of the function at x=-2 and x=2 using the power rule of differentiation:

g'(x) = 3\(x^{2}\)

g'(-2) = 3\(-2^{2}\) = 12

g'(2)  = 12

The instantaneous rate of change at x=-2 is 12, and the instantaneous rate of change at x=2 is also 12. These values are equal to the average rate of change over the interval [-2, 2], which is 4.

This means that the function g(x) is not a linear function over the interval [-2, 2], and the instantaneous rates of change at the endpoints are different from the average rate of change over the interval.

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According to the information, it can be inferred that the answer is No, because informing the students that there will be a $10 increase... (option B).

This question is not valid because it specifies information that would surely change the answer of the respondent.

The information that the question reveals is that there is going to be a raise, this will cause a refusal in people to accept that raise just to see a live band.

According to the above, the question is invalid because it reveals information that will modify the answer of those who respond.

Note: This question is incomplete because the options are missing. Here are the options:

A. No, because questions about musical preferences are always invalid because you cannot measure people's opinions on subjective manners like music and other creative arts.

B. No, because informing the students that there will be a $10 increase in the cost of a prom ticket may make them more likely to say that they would not like a live band to perform.

C. No, because students should be given a sample of the band's music to allow them to offer a more informed opinion.

D. No, because a random sample of all seniors in the country should have been taken to determine if a live band should perform at this high school's senior prom.

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The ratio of AB:BC:CD is 33 : 7 : 48.

A ratio indicates the number of times one number contains another.

Given that, AB : BD = 3:5 and AC : CD = 5:6, and the points A, B, C, and D lie in order on a straight line.

Since AB : BD = 3:5, let AB = 3x and BD = 5x.

Since AC : CD = 5:6, let AC = 5y and CD = 6y

Now, the points A, B, C, and D lie in order on a line, therefore,

BC = AC - AB

BC = 5y - 3x   (1)

Similarly,

BC = BD - CD

BC = 5x - 6y   (2)

Using equation (1) and (2) it follows:

5y - 3x = 5x - 6y

5y + 6y = 5x + 3x

11y = 8x

y = (8/11)x

Now, the ratio to be found is:

AB : BC : CD

Substitute the values:

3x : 5y - 3x : 6y

Substitute y = (8/11)x:

3x : 5(8/11)x -3x : 6(8/11)x

3x : (40 - 33)/11 x : (48/11)x

3 : (7/11) : (48/11)

33 : 7 : 48

Hence, the ratio of AB:BC:CD is 33 : 7 : 48.

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In a paired design, each pair of observations does not necessarily consist of measuring the same individual twice. Instead, a paired design involves matching pairs of individuals or units based on certain criteria or characteristics and then measuring each individual in the pair under different conditions or at different time points.

This design is often used to compare the effects of different treatments or interventions within the same individuals or to control for individual-specific factors. In a paired design, the pairing could be based on various factors such as age, gender, pre-existing conditions, or other relevant characteristics. For example, in a study evaluating the effectiveness of a new medication, researchers may pair individuals with similar characteristics (e.g., age, gender, severity of the condition) and then administer the new medication to one individual in each pair while providing a placebo to the other individual. By measuring the outcomes within each pair, the researchers can directly compare the effects of the medication and the placebo within the same individuals.

The key aspect of a paired design is that the pairs are matched based on certain criteria, and each pair represents a unique combination of individuals. This allows for a more controlled comparison within the pairs and helps minimize the influence of individual-specific factors on the outcomes of interest.

In summary, a paired design involves matching pairs of individuals based on certain characteristics and comparing the outcomes within each pair. It does not require measuring the same individual twice but rather focuses on comparing different conditions or treatments within matched pairs of individuals.

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The properties justify the steps are taken to solve the system 2a+7b=0 3a-5b=31 as Multiplication, Substraction, Division,  Simplify, etc.,

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

'The properties that justify the steps taken to solve the system 2a + 7b = 0, 3a - 5b = 31 are:

2a + 7b = 0, 3a - 5b = 31

10a + 35b = 0, 21a - 35b = 217   <-------> Multiplication property of equality.

31a = 217                                      <-------> Substraction property of equality.

a = 7                                            <-------> Division property of equality.

2(7) + 7b = 0,                             <-------> Substitution property of equality.

14 + 7b = 0,                              <-------> Simplify  

7b = -14,                                   <-------> Simplify  

b = -14/7,                                  <-------> Division property of equality.

b = -2

Therefore, the properties justify the steps are taken to solve the system 2a+7b=0 3a-5b=31 as Multiplication, Substraction, Division,  Simplify, etc.,

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a) The solution of the power series is p = -1, 1.

b) Yes,  p is there a polynomial solution

Power series methods are a powerful tool for solving differential equations. In this case, we will be using power series methods to solve the differential equation (1-x)y - xy' + py = 0 and to find out for what values of p, there is a polynomial solution.

Substituting the power series expansions of y and y' into the differential equation (1-x)y - xy' + py = 0,

Now, we equate the coefficients of each power of x to zero:

For x⁰, we get: (1-x)a0 + pa0 = 0, which gives a0(1+p) = 0. Since we want a non-zero polynomial solution, we must have a0 ≠ 0. Therefore, we must have 1 + p = 0, i.e., p = -1, for a polynomial solution.

For x¹, we get: -a1 - xa1 + pa1 = 0, which gives a1(1-p) = 0. Again, since we want a non-zero polynomial solution, we must have a1 ≠ 0. Therefore, we must have 1 - p = 0, i.e., p = 1, for a polynomial solution.

Thus, the only values of p for which there is a polynomial solution are p = -1 and p = 1.

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Answer:

\(\frac{1}{40}\)

Step-by-step explanation:

Answer:

1/40

Step-by-step explanation:

\(\frac{1}{8}\) ÷ \(\frac{5}{1}\)

\(\frac{1 x 1 }{8 x 5}\) = 1/40

The correct answer to the question is option c) An effect modifier.

A case-control study is a type of observational study that compares two groups of individuals: those who have the disease or outcome under investigation (cases) and those who do not (controls).

It aims to determine if an exposure or risk factor is associated with the development of the disease or outcome.

In this case, the results of the study indicate that there is a difference in the odds ratio (OR) between the two strata, which suggests that the characteristic being studied is an effect modifier.

An effect modifier is a factor that modifies the effect of the exposure on the outcome and leads to different measures of association across different levels of the factor.

Therefore, the characteristic is an effect modifier as it leads to different ORs in the two strata.

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Answer:

Options B, D and E

Step-by-step explanation:

Given equation is,

-4x + 5y - 12 = 8

-4x + 5y = 20

If a point given in the options lie on the line, point will satisfy the equation.

Option A.

For a point (5, 0),

-4(5) + 5(0) = 20

-20 = 20

False

Therefore, (5, 0) will not lie on the given line.

Option B

For (-2, 2.4)

-4(-2) + 5(2.4) = 20

8 + 12 = 20

20 = 20

True.

Therefore, (-2, 2.4) will lie on the given line

Option C

For (8, 5),

-4(8) + 5(5) = 20

-32 + 25 = 20

-7 = 20

False

Therefore, (8, 5) will not lie on the line.

Option D

For (10, 12)

-4(10) + 5(12) = 20

-40 + 60 = 20

20 = 20

True.

Therefore, (10, 12) will lie on the line.

Option E

For (0, 4)

-4(0) + 5(4) = 20

20 = 20

True.

Therefore, (0, 4) will lie on the line.

Options B, D and E are correct.

The Niagara Falls incline railway rises vertically by approximately 98 feet.

The angle of elevation of 30° indicates the angle between the incline railway and the horizontal ground. The total length of the incline railway is given as 196 feet.

To find the vertical rise, we can use trigonometry. The vertical rise can be determined by calculating the sine of the angle of elevation and multiplying it by the total length of the incline railway:

Vertical rise = Total length × sine(angle of elevation)

Vertical rise = 196 ft × sin(30°)

Vertical rise ≈ 196 ft × 0.5

Vertical rise ≈ 98 ft

Therefore, the Niagara Falls incline railway rises vertically by approximately 98 feet.

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Answer:

423

Step-by-step explanation:

Answer:

-423

Step-by-step explanation:

Hope This Helps!

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It should be noted that the value of angle x if m∠3=4x+10 and m∠4=5x is 10.

It should be noted that from the information, m∠3=4x+10 and m∠4=5x are equal angles.

Therefore, it should be noted that we will equate them

4x + 10 = 5x

Collect like terms

5x - 4x = 10

x = 10

Therefore, the value of x is 10.

In conclusion, it should be noted that the value of angle x if m∠3=4x+10 and m∠4=5x is 10.

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If m∠3=4x+10 and m∠4=5x are equal. Find x.

Answer:

The break even point is 380.

Step-by-step explanation:

36x + 200 = 76x

200 = 76x - 36x

200 = 40x

200/40 = x

5 = x

C = 36(5) + 200            R = 76(5)

C = 180 + 200              R = 380

C = 380

Answer:

The breakeven point is 5 units

Step-by-step explanation:

C is the cost ($) and R is the revenue ($).

We are told that :

R=76x

C=36x+200

Profit would be the Revenue minus the Cost:

Profit = R - C

The "breakeven point" is the situation in which there is neither a profit nor a loss.  That means that the total profit equals the total cost for x units. We want to find the value of x that would result in no profit or loss: Profit = 0.

0 = R-C

====

Profit = 76x - (36x+200)

Profit = 40x - 200

0 = 40x - 200         [The Breakeven Point]

-40x = -200

x = 5 units

5 units results in 76*5 or $380 in revenue.

5 units results in a cost of 36*(5)+200 or $380 in costs.

The result is breakeven (Profit = $390 - $380) of $0.00

Answer: ab + 16 fsxewcvrvfe

Answer:

16+ab

Step-by-step explanation:

5(6-ab)+2(-7+3ab)

30-5ab-14+6ab (distribute)

16-5ab+6ab (subtract)

16+ab (collect like terms)

The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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Answer:

y = 2x + 11

Explanation:

N/A

Answer: 4x+40 dollars

Step-by-step explanation:

1. Define: since a ticket costs x dollars and 10$ for a drink and candy, your expression would be x+10 dollars.

2. Distrubute: Since there are 4 people, it would be:

4*(x+10)

3. Simplify: 4*(x+10) => 4x+40

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Henry swims at 1.6 laps per minute and Larry swims at 7 laps per minute. Henry swims at a 5.4 slower rate than Larry.

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

The equation and the graph

From the equation, we have

Henry: y = 1.6x

Larry: y = 7x

The coefficients of x in the above equations represent their rates

This means that

Henry: = 1.6 laps per minute  

Larry:= 7 laps per minute

When the rates are compared, we have

Difference = 7 -1.6

Evaluate

Difference = 5.4

Hence, the values that complete the blanks are 1.6, 7 and 5.4

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To find the volume of a cone, we use the formula V = 1/3πr²h, where r is the radius of the base and h is the height of the cone.

In this case, we know that r = 4 units and h = 11 units. Therefore, the volume of the cone can be calculated as follows:

V = 1/3 × π × 4² × 11

≈ 183.27 cubic units

Since we are asked to choose the approximate answer, the closest option is (A) 161.337 cubic units. However, this is not an exact answer but an approximation, so we can say that the volume of the cone is approximately 161.337 cubic units.

Therefore, the answer is (A) 161.337 cubic units.

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Given: 68 x 20

The product of the question will be = 1,360

68

x 20

=====

1360

The Comparison Test tells us that the original series\(Σ(5^k / (3^k + 4^k))\)from k=1 to infinity also diverges.

Based on your question, you want to determine if the series \(Σ(5^k / (3^k + 4^k))\) from k=1 to infinity converges or diverges. To analyze this series, we can apply the Comparison Test.

Consider the series \(Σ(5^k / 4^k)\)from k=1 to infinity. This simplifies to \(Σ((5/4)^k)\), which is a geometric series with a common ratio of 5/4. Since the common ratio is greater than 1, this series diverges.

Now, notice that\(5^k / (3^k + 4^k) ≤ 5^k / 4^k\) for all k≥1. Since the series \(Σ(5^k / 4^k)\)diverges, and the given series is term-wise smaller, the Comparison Test tells us that the original series \(Σ(5^k / (3^k + 4^k))\) from k=1 to infinity also diverges.

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\(6(1+3) < 3(21+6)\)

\(6(1+3)\\6(4)\\=24\)

_______

\(3(21+6)\\3(27)\\=81\)

\(24 < 81\)

\(\fbox{True}\)

Hope this helps!

Answer:

B. 8x² + 18x - 5

Step-by-step explanation:

(2x + 5)(4x - 1)

Use the distributive property to multiply 2x + 5 by 4x - 1.

8x² - 2x + 5(4x) + 5(-1)

8x² - 2x + 20x - 5

Combine 20x and -2x to get 18x.

8x² + 18x - 5

The expression for the area of the rectangle is 8x² + 18x - 5, which is B.