80 yd 39 yd c=yards what is the length of the hypotenuse nearest tenth

qrs = p2 + s2q is the correct answer of the following equation. The equation z2 + (p + iq)z + r + is = 0, where p, q, r and s are real and non-zero roots, has the following relationships: qrs = p2 + s2q

Explanation: Given,z2 + (p + iq) z + r + is = 0 Comparing it with the standard quadratic equation,az2 + bz + c = 0we get, a = 1, b = p + iq, c = r + is Using the quadratic formula, the roots of the quadratic equation are given by, z = (-b ± √(b2 - 4ac))/2a= (-b ± √(b2 - 4ac))/2where √(b2 - 4ac) is the discriminant of the quadratic equation. Therefore,√(b2 - 4ac) = √((p + iq)2 - 4(r + is))= √(p2 + 2ipq - q2 - 4r - 4is)= √((p2 - q2 - 4r) + i(2pq - 4s))Therefore, the roots of the quadratic equation are,z1 = (-b + √(b2 - 4ac))/2a= (-p - iq - √(p2 - q2 - 4r) - i(2s - pq))/(2z2 = (-b - √(b2 - 4ac))/2a= (-p - iq + √(p2 - q2 - 4r) - i(2s - pq))/(2Therefore,pq = -c/pr = s(1 + q2/p2)qrs = (r + is)(1 + q2/p2) = p2 + s2q(since r = pqs - s2 from the third expression)Therefore, qrs = p2 + s2q Ans: qrs = p2 + s2q

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To minimize the cost, we can take the derivative of the total cost equation with respect to x and set it equal to zero:

d(Total cost)/dx = 0

Solving this equation, we get x ≈ 20 feet. So, the length of the side perpendicular to the river is approximately 20 feet.

To solve this problem, we will use the area of the rectangle and the cost of the fencing.

Given, the enclosed area is 2,000 square feet. Since it is a rectangle, the area is length × width. Let x be the length of the sides perpendicular to the river, and y be the length of the side parallel to the river. So, the area is given by x × y = 2,000.

Next, we consider the cost of the fencing. The side parallel to the river (y) has a cost of $7 per foot, and the other two sides perpendicular to the river (x) have a cost of $4 per foot. Additionally, the four corner posts cost $30 each.

Total cost of fencing = 2 * (cost of x sides) + cost of y side + cost of corner posts
Total cost = 2(4x) + 7y + 4(30)

Now we need to find x in terms of y or y in terms of x to minimize the total cost. From the area equation, we can write y in terms of x:

y = 2,000 / x

Now, we plug this into the total cost equation:

Total cost = 2(4x) + 7(2,000 / x) + 4(30)

To minimize the cost, we can take the derivative of the total cost equation with respect to x and set it equal to zero:

d(Total cost)/dx = 0

Solving this equation, we get x ≈ 20 feet. So, the length of the side perpendicular to the river is approximately 20 feet.

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The correct answer is event correlation.

Event correlation is a technique for making sense of a large number of events and pinpointing the few events that are really important in that mass of information. This is accomplished by looking for and analyzing relationships between events.

Event can be defined as a set of outcomes of an experiment. In other words, an event in probability is the subset of the respective sample space. So, what is sample space? The entire possible set of outcomes of a random experiment is the sample space or the individual space of that experiment

One example of event correlation can occur with intrusion detection. Perhaps there is an employee account that hasn't been accessed for years, and suddenly a large number of login attempts are noticed. That account may start executing suspicious commands.

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To calculate the total profit you have to multiply whats earned by the time:

The company earned a profit of 25 millions.

Answer:

Mean of data set 28,44,20,20 = (28+44+20+20)/4 = 112/4=28.

Step-by-step explanation:

The average rate of change of g(x) from x = 3 to x = 7 is -5.

To find the average rate of change of the function g(x) = -x² + 4x + 2 over the interval [3, 7], we need to calculate the change in the function values over this interval and divide by the length of the interval.

The change in the function values between x = 3 and x = 7 is:

g(7) - g(3) = (-7² + 47 + 2) - (-3² + 43 + 2) = (-49 + 28 + 2) - (9 + 12 + 2) = -20

Therefore, the average rate of change of g(x) over the interval [3, 7] is:

average rate of change = change in function values / length of interval

= -20 / (7 - 3)

= -5

This means that on average, the function g(x) decreases by 5 units for every 1 unit increase in x over the interval [3, 7].

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Answer:

y=x+1.75

4x-2y = 4

The answer is (3. 75, 5.5)

Step-by-step explanation:

If you plot the two equations on Desmos' Graphing Calculator, you will see that the solution is intersected at (3.75, 5.5).

using exponents, On simplifying the equation, we get =4m+8.

The PEMDAS order of operations must be followed when you want to simplify a mathematical equation without using parenthesis (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). There are no parenthesis in the expression, so you may start looking for exponents. If it does, first make that simpler.

Work simplification is to develop better work processes that boost output while cutting waste and costs.

Simplifying an expression is the same as solving a mathematical issue. When you simplify an equation, you essentially try to write it as simply as you can. There shouldn't be any more multiplication, dividing, adding, or deleting to be done when the process is finished.

Given equation,

m-(8-3m)

=m-8+3m

=4m+8

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The solution to the system of inequalities y ≤ 2x + 2 and y < -2x - 3 can be represented by a graph. The inequality y ≤ 2x + 2 represents a line with a slope of 2 and y-intercept of 2. The inequality y < -2x - 3 represents a line with a slope of -2 and y-intercept of -3. ( The graph attached)

The inequality y ≤ 2x + 2 represents a line in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 2 and the y-intercept is 2. To graph this inequality, we can first plot the line by using the y-intercept, which is the point (0,2) on the graph. Then, we can use the slope to find additional points that fall on the line, such as (1,4) or (-1,0). Once we have plotted several points, we can connect them to form the line.

The inequality y < -2x - 3 represents a similar line, but with a different slope and y-intercept. In this case, the slope is -2 and the y-intercept is -3. To graph this inequality, we can use the same process as before by first plotting the y-intercept (0,-3), and then using the slope to find additional points that fall on the line.

The solution to the system of inequalities is the area that lies on one side of the first line and the opposite side of the second line, which is the area between the two lines. This area can be represented by shading the region below the first line and above the second line on the graph. It is important to note that the solution region is not including the lines themselves, because the inequalities are strict inequalities.

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Answer:

y = 10

Step-by-step explanation:

Since we are given that x=5, we can substitute x for 5 in the given equation:

5 + 2y - 25 = 0

Then, we can solve for y:

2y = 25 - 5

2y = 20

y = 10

Answer:10

Step-by-step explanation: 5+2x10-25=0

5+20 equal 25

The best answer to submit for (515 x 0.0025) + 24.57 is 25.8575.

A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts. Decimal notation is the name for the method used to represent numbers in the decimal system. The Hindu-Arabic numeral system has been expanded to include non-integer values.

To find the answer to the expression (515 x 0.0025) +24.57, we can simplify it by performing the multiplication and addition in the correct order:

(515 x 0.0025) + 24.57 = 1.2875 + 24.57 = 25.8575

Therefore, the best answer to report is C. 25.8575.

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Assuming the track is straight, the distance at which they are apart one hour before they meet is; 30 km

We are told that a Nonstop trains leave Toronto and Montreal at the same time each day going to the other city along the main line.

Speed of Train 1 = 120 km/h

Speed of Train 2 = 90 km/h

Time spent by train 1 = 1 hour

Time spent train 2 = 1 hour

Formula for distance is;

Distance = Speed * time

If they leave the same time each day, it means that;

Distance of train 1 = 120 * 1 = 120 km

Distance of train 2 = 90 * 1 = 90 km

Thus, distance at which they will be apart before meeting each other is;

Distance apart = 120 - 90

Distance apart = 30 km

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The horizontal distance between the base of the ladder and the wall is approximately 16.06 feet.

To find the flat distance between the foundation of the  stool and the wall, we utilize geometry. For this situation, we can utilize the sine capability, which relates the contrary side of a right triangle to the hypotenuse and the point inverse the contrary side.

Let x be the flat distance between the foundation of the stepping stool and the wall. Then, utilizing the given point of 64 degrees, we can compose:

sin(64) = inverse/hypotenuse

where the hypotenuse is the length of the stepping stool, which is 18 feet.

Addressing for the contrary side, which is the even distance we need to find, we get:

inverse = sin(64) x hypotenuse

inverse = sin(64) x 18

inverse = 16.06 feet

Accordingly, the even distance between the foundation of the stepping stool and the wall is roughly 16.06 feet.

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Answer:

Height Length: ( About ) 3.3 yards; Option B

Step-by-step explanation:

~ We are given the Area of this triangle, so let us apply the area of a triangle formula 1/2 * base * height ~

The base is known the be 4.1 yards, the Area 6.8 yards^2, so let us substitute these values into the formula for a triangle as to solve for height. At the same time let us declare x ⇒ height of the triangle:

6.8 = 1/2 * 4.1 * x,

6.8 = 2.05 * x,

x = 6.8/2.05,

Height Length: ( About ) 3.3 yards

Answer:

25\(\sqrt{3}\) +60

Step-by-step explanation: The first thing you need to do is realize that, this figure is a isosceles trapezoid due to the markings on each side.

So now we know both sides are 10.

We also know the the top two angles are congruent to each other and so are the bottom two angles due to the trapezoid being isosceles.

So the top two angles are 120 degrees and bottom two angles are 60 degrees.

It seems like we can't find the sides, let's try drawing two lines from each top angle all the way down to form two right triangles.

Wow, these two triangles are special right triangles in the form of

30 - 60 - 90 degrees.

shorter side = n

longer side = n\(\sqrt{3}\)

hypotenuse = 2n

So, 2n = 10

n = 5 for the short side

The bottom base is 4\(\sqrt{3}\) + 5 + 5 = 10 + 4\(\sqrt{3}\)

The longer side is  5\(\sqrt{3}\).

The area of trapezoid = (base1 + base2)/2 * height

= (4\(\sqrt{3}\) + 10 + 4\(\sqrt{3}\))/2 * 5\(\sqrt{3}\) = (10 + 8\(\sqrt{3}\))/2 * 5\(\sqrt{3}\) = (5+4\(\sqrt{3}\))*5\(\sqrt{3}\) = 25\(\sqrt{3}\) +60

So, 25\(\sqrt{3}\) + 60 is our answer.

Answer:

  60 +25√3

Step-by-step explanation:

In the figure of the isosceles trapezoid below, the angles at C and D are supplementary to the given angle, so are 60°. That makes triangle BDE a 30°-60°-90° right triangle, which has side length ratios ...

  DE : BE : BD = 1 : √3 : 2 = 5 : 5√3 : 10

Triangle BDE can be relocated to the other end of the figure to become triangle CAD'. Then the area of concern is that of the rectangle with height 5√3 and length 5+4√3. The area is then ...

  Area = lh = (5√3)(5 +4√3) = 5·5√3 +5·4·3

  Area = 60 +25√3 . . . square units

_____

In the figure, 6.93 = 4√3, and 8.66 = 5√3, 16.93 = 10+4√3.

Answer:

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

Each triangle face has height of 7 ft and base of 0.6 ft and the base of the pyramid is the square with side of 0.6 ft.

Total surface area includes a square base and four triangular faces and the measure of it is:

The matching choice is B.

Answer:

The answer is 0.01. We assume you are converting between dollar bill and penny. You can view more details on each measurement unit: Dollar or penny The main non-SI unit for U.S. currency is the dollar. 1 dollar is equal to 100 penny. Note that rounding errors may occur, so always check the results.

Step-by-step explanation:

Answer:

Huh? ---

Yea, there are 100 pennies in a dollar....

Increasing control risk will not have an impact on substantive testing sample size if all other factors remain constant.

If all other factors remain constant, then the substantive testing sample size will remain the same. The increase in control risk will affect the auditor’s overall assessment of risk and may result in the auditor deciding to perform more tests of controls, but it will not necessarily affect the substantive testing sample size.

Increasing control risk will not have an impact on substantive testing sample size if all other factors remain constant.

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Answer:

It is B and D

Answer:

18. A' (0, 0)

     B' (0, -4)

     C' (5 ,-5)

     D' (5, -1)

19. lines of symmetry:

Letter G- no lines

Letter E- horizontal through the middle line

Letter O- vertical and horizontal

Letter M- vertical through the middle

Letter T- vertical through the middle

Letter R- no lines

Letter Y- vertical through middle

20.

Figure 1- 4

Figure 2- 8

Figure 3- 5

Answer:

Step-by-step explanation:

a.) The population is years measured after 2000 so 2000 is 0. Any number to the 0 power is 1 so the population is 23.1 (million).

b.) 28.3 = \(23.1e^{0.0152t}\)

1.22510823 ≈ \(e^{0.0152t}\)

ln 1.22510823 ≈ 0.0152t

t≈13.4 MILLION

Answer:

x = 2

y = -3

Step-by-step explanation:

The given equation is,

22(x + yi) + (28 + 4i) = 72 - 62i

By solving this equation further,

22x + 22yi + 28 + 4i = 72 - 62i

(22x + 28) + (22y + 4)i = 72 - 62i

Now both the sides of the equation is in the form of complex number,

By comparing real and imaginary parts given on both the sides,

22x + 28 = 72

22x = 72 - 28

22x = 44

x = 2

22y + 4 = -62

22y = -62 - 4

22y = -66

y = -3

Therefore, x = 2 and y = -3 are the values for which the given equation is true.

Answer:

equation of the line is y =  -  \(\frac{11}{2}\) x- 52

The position of the particle at time t is given by s = f(t) = t^3 - 15t^2 + 72t, So, at t = 3 seconds, the particle's position is 108 feet.

Let's proceed with the calculation.

The law of motion for the particle is given by the function f(t) = t^3 - 15t^2 + 72t, where t represents time in seconds and s represents the displacement of the particle in feet.

To calculate the position of the particle at a specific time t, we substitute the value of t into the function f(t).

For example, let's calculate the position of the particle at t = 3 seconds:

f(3) = (3)^3 - 15(3)^2 + 72(3)
     = 27 - 135 + 216
     = 108 feet

So, at t = 3 seconds, the particle's position is 108 feet.

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Answer:

y=20

Step-by-step explanation:

2y+21 = 3y+1

Subtract 2y from both sides,

21 = 3y-2y +1

Subtract 1 from both sides,

y = 20

Answer:

y = 20

Step-by-step explanation:

2y + 21 = 3y + 1,

21 = y + 1,

20 = y

Use the regression equation for predictions only if the graph of the regression line on the scatterplot confirms that the regression line fits the points reasonably well. Therefore, the correct answers are options A, B and D.

For each participant in many research, we measure more than one variable. For instance, we track rainfall and plant growth, the quantity of eggs and nesting environment, the number of young, and soil erosion and water volume. Instead of analysing each variable independently (univariate data), we collect pairs of data and try to come up with ways to characterize bivariate data, which involves measuring two variables on each individual in our sample. We start by looking for a correlation between these two variables using the data at hand.

Numerous different kinds of associations between two variables can be found using a scatterplot.

Therefore, the correct answers are options A, B and D.

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To find T((5, -4)), we can use the linearity property of linear transformations. First, we can express (5, -4) as a linear combination of the given basis vectors:(5, -4) = 5*(1, 2) + (-6)*(0, 1)

Since T is a linear transformation, we can apply it to each term separately:

T((5, -4)) = T(5*(1, 2) + (-6)*(0, 1))

Using the linearity property of T, we have:

T((5, -4)) = 5*T((1, 2)) + (-6)*T((0, 1))

From the given information, we know that T((1, 2)) = (2, 3) and T((0, 1)) = (1, 4). Substituting these values, we get:

T((5, -4)) = 5*(2, 3) + (-6)*(1, 4)

= (10, 15) + (-6, -24)

= (10 + (-6), 15 + (-24))

= (4, -9)

Therefore, T((5, -4)) is (4, -9). None of the options provided match this result, so the correct answer is not among the given choices.

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