A conjecture and the paragraph proof used to prove the conjecture are shown. Given: R S T U is a parallelogram. Angle 1 and angle 3 are complementary. Prove: angle 2 and angle 3 are complementary. Parallelogram J K L M. A diagonal segment U S is drawn across the parallelogram. Angle R U S is labeled 1. Angle U S T is labeled 2. A ray is extended diagonally up to the left of UT forming an interior angle labeled as 3. Drag an expression or phrase to each box to complete the proof. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. It is given that RSTU is a parallelogram, so RU¯¯¯¯¯∥ST¯¯¯¯¯ by the definition of parallelogram. Therefore, ∠1≅∠2 ​by the alternate interior angles theorem, and m∠1=m∠2 ​by the Response area. It is also given that ∠1 and ∠3 are complementary, so m∠1+m∠3=90° by the Response area. By substitution, m∠2+ Response area = 90°, and so ∠2 and Response area are complementary by the definition of complementary.

Answer:

-1/4

Step-by-step explanation:

A reciprocal is simply defined as the inverse of a value or a number. So if we have a fraction of - 4/1 we can just flip the numerator and the denominator to get -1/4.

The bijection could be defined from the set of numbers and it is proved.

We can define a bijection f from S to T as follows: for any integer x in S, let f(x) = x + 1.

To show that f is a bijection, we need to prove that it is both injective and surjective.

To prove that f is injective, suppose f(x) = f(y) for some x, y in S. Then x + 1 = y + 1, which means x = y. Thus, f is injective.

To prove that f is surjective, let y be an arbitrary element of T. Since y is odd, we can write y = 2n + 1 for some integer n. Now consider the element x = 3n in S. We have f(x) = x + 1 = 3n + 1 = y, so f is surjective.

Therefore, f is a bijection from S to T, so |S| = |T|.

Learn more about Bijection at:

brainly.com/question/13837935

#SPJ4

the jensen measure of performance evaluation for sooner stock fund will be 2.6%.

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

the risk-free return during the sample period was 3%.

performance evaluation for sooner stock fund.

Expected return of Sooner Stock Fund = E(Rp) = 20%

Beta of stock = 1.8

risk free rate Rf = 3%

Market Return Rm = 11%

So, Jensen measure alpha = E(Rp) - Rf - beta*(Rm - Rf) = 20 - 3 - 1.8*(11-8) = 2.6%

Hence the Jensen measure of performance evaluation for the sooner stock fund will be 2.6%.

Learn more about percentages, by the following link.

https://brainly.com/question/24304697

#SPJ4

The y is the variable that used in the different situations like to find the unknown variable, graphing, and function

y in the math is usually used as the variable in function, graphing etc.

y variables can be used in the equation to find the unknown values in the equation

Example = 5y + 10 = 15

Similarly in the graphing the y is used in the slope intercept form

The slope intercept form is

y = mx + b

Y can be used in the function as well

Example: y = 2x + 4

Therefore, the y can be used as the variable in the different situation

Learn more about slope intercept form here

brainly.com/question/9682526

#SPJ4

The value of x from the given isosceles triangle GHJ is 5.

Isosceles triangles are those triangles that have at least two sides of equal measure and two base angles are equal.

In the given isosceles triangle GHJ, GJ=GH, ∠G=38° and ∠J=(14x+1)°.

Since, sides GJ=GH

∠J=∠H

Now, ∠G+∠J+∠H=180° (Angle sum property of a triangle)

⇒ 38°+(14x+1)°+(14x+1)°=180°

⇒ 28x+40°=180°

⇒ 28x=140°

⇒ x=140/28

⇒ x=5

Therefore, the value of x is 5.

To learn more about an isosceles triangle visit:

https://brainly.com/question/10147636.

#SPJ1

"Your question is incomplete, probably the complete question/missing part is:"

If triangle GHJ is isosceles find the value of x.

There were 425 guests at a hotel. 170 guests ordered food. 40 percentage of the guests ordered food.

A percentage is a fraction of a whole in mathematics, which is denoted by the symbol per 100. A single unit out of a hundred, or one hundredth of something, is represented as a single percent, such as 1%. The Latin phrase per centum, which means by the hundred, is where the word percent originates. Percentage does really refer to a hundredth or 1/100 of something.

Given,

Total number of guests = 425

Guest who ordered food = 170

For percentage,

Value/ Total × 100%

170/425 × 100%

0.4 × 100%

40%

There were 425 guests at a hotel. 170 guests ordered food. 40 percentage of the guests ordered food.

To learn more about percentage, visit:

https://brainly.com/question/11902699

#SPJ4

Answer:

Step-by-step explanation:  -73.73 D, If its not and its like A,B, or C and one of them is -73.73 its still going to be correct

The length of one side is 20 ft and the other side of the yard is 33 ft.

Let the length of the side opposite to the house be x ft.

We know that the yard to be fenced is rectangular. Hence the opposite sides of the yard are going to be equal.

It is given that the side opposite to the wall is 13 ft less than the length f the other two sides.

Hence the length of the side adjacent to the house will be

(x + 13) ft

The fencing needs to be done on these three sides. We already know that the length that has been fenced is 86 ft.

Hence, we get

x  +  x + 13  +  x + 13  =  86

or, 3x + 26 = 86

or, 3x = 86 - 26

or, 3x = 60

or, x = 60/3

or, x = 20.

Hence the length of one side is 20 ft and the length of the other side is

20 + 13

= 33 ft.

To know more about linear equations visit

https://brainly.com/question/24346515

#SPJ4

The perimeter of the triangle passing through the points A, B, C is 27.5 cm.

A triangle's perimeter and side lengths are measured in the same unit. If the sides' lengths are measured in a different unit, first convert them to that unit. Example 1: Calculate the triangle's perimeter from the information provided. A perimeter is a closed path that encloses, surrounds, or delimits a one-dimensional length or a two-dimensional shape. The circumference of a circle or an ellipse is its outermost boundary.

There are many uses in real life for perimeter calculations. The length of fence needed to enclose a yard or garden is known as the calculated perimeter.

From the figure,

The triangle is passing through the points A(4, 0), B(-6, 5), C(3, 3)

By using distance formula, we have to calculate the lengths of AB, BC, CA

Length of AB=√(-6-4)²+(5-10)²

=√125

Length of BC=√(3+6)²+(3-5)

=√85

Length of CA=√(3-4)²+(3-10)²

=√50

The perimeter of a triangle=AB+BC+CA

=√125+√85+√50

=11.18+9.22+7.07

=27.47≈27.5

Therefore, the perimeter of the triangle is 27.5 cm.

To know more about perimeter of a triangle, visit:

https://brainly.com/question/29507476

#SPJ1

In order to get 0.100 g of [tex]^{133 }_\ {54} \ Xe[/tex] , the hospital needs to order for a  minimum amount of 0.4 g of.

Given that:

A hospital needs 0.100 g of [tex]^{133 }_\ {54} \ Xe[/tex]

and it takes 10 days for the shipment to arrive:

the half life [tex]t_{\frac{1}{2}[/tex]  = 5 days.

So, since the half life = 5 days ;

decay constant [tex]\lambda = \frac{In_{2} }{t_{\frac{1}{2} } } }[/tex]

where:

        [tex]No=?[/tex]

       [tex]N=0.100\\\\t=10days\\\\N(t)=N_{o} e^{-\lambda\ t} \\\\0.1=N_{o}e^{-In\ 4} \\\\0.1=N_{o}e^{In\ \frac{1}{4} }\\\\0.1=\frac{N_{o}}{4} \\\\N_{o}=01*4\\\\N_{o}=0.4\ g[/tex]

Therefore, In order to get 0.100 g of [tex]^{133 }_\ {54} \ Xe[/tex] , the hospital needs to order for a  minimum amount of 0.4 g of.

To know more about this visit,

https://brainly.com/question/16049325

#SPJ4

The equation of the line that passes through the point (−11,−14) is y = x - 3.

What is the slope of the line?

A line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run" (change in y divided by change in x).

We have,

The line that passes through the point (−11,−14)

With Slope (m) = 1,

The general equation of a straight line is

y = mx + c,

where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

so here,

y = mx + c,

(-14) = 1(-11) + c

c = -14 + 11

c = -3

The equation becomes:

y = x - 3.

Hence, the equation of the line that passes through the point (−11,−14) is

y = x - 3.

To learn more about the slope of a line visit,

brainly.com/question/16949303

#SPJ1

As per the concept of function, the arguments supplied to the IF function, in order, are the condition for execution, the result if condition is true, and the result if condition is false.

What is meant by function?

In math, function refers an expression, rule, or law that defines a relationship between one variable also known as the independent variable and another variable also known as the dependent variable.

Here we need to find the missing term of the given statement the arguments supplied to the if function, in order, are the condition for execution.

Here we have given that, the if function refers decision-making statement that guides a program to make decisions based on specified criteria.

When the IF statement executes one set of code if a specified condition is met (TRUE) or another set of code evaluates to FALSE.

To know more about function here.

https://brainly.com/question/28193995

#SPJ4

Answer:6.47 ft^2

Step-by-step explanation:

Answer:

t=24+41=65

Step-by-step explanation:

The value of t>24 and is 41 more than 24. So 24+41=t.

24+41=65, so t=65.

-Hope this helped & Happy Holidays!

Answer:

480 minutes

Step-by-step explanation:

One hour is 60 minutes, so 8*60 will give you your answer.

Answer:

Step-by-step explanation:

Theres 60 minutes in 1 hour, and you are trying to find how many in 8 hours, so you would multiply 60 by 8. The answer would be 480 minutes

The inequality that models Cassie situation is t ≥ 49.25  

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.

Cassie is swimming backstroke for her team at the Tri-County Swim Meet. The fastest time so far is 49.25 seconds. Cassie wants to either beat or tie for the fastest time.

The inequalities that models the story is as follows:

let

Cassie has to equal the record or beat the record.

Therefore, the inequalities that represent the story is t ≥ 49.25

learn more on inequality here:https://brainly.com/question/29948253

#SPJ1

Answer: 26

Explanation: Well, by using the formula to find volume of frustum. (this can be shown in a easier way or harder i choose my own way)

Step 1: The hight is: h=15h=15

Step 2: The top radius of the frustum is: r=19r=19

Step 3: The lower base radius of the frustum is: R=26R=26

Message: If you found this helpful let me know by giving a small thanks! :)

Answer:

Step-by-step explanation:

eazy 102

If Point M lies on AB, AB = 24 , and BM = 13, then the length of AM is; 11 units

We are given the following parameters;

Length of line segment AB = 24

Length of line segment BM = 13

Now, we are told that M lies on the line segment AB and as such;

If BM = 13, then it means that;

AM + BM = AB

AM + 13 = 24

AM = 24 - 13

AM = 11 Units

We conclude that the length of AM is 11 units.

Read more about length of line segment at; https://brainly.com/question/24778489

#SPJ1

Answer:

x=4

Step-by-step explanation:

If we were to perform a reduction, the scale factor would be ½. This means we have to divide by 2. 14÷2=7 and 12÷2=6.

Line segment AB is equal to 7.

Line segment BC is equal to 6.

AB: If you want to double check, 4+3=7

BC: 2×4=8 and 8-2=6

Answer:

11.4x-11.4y

Step-by-step explanation:

Distribute the 11.4

11.4x-11.4y

The minimum cost for the area can be fenced is $1920

It is given that the area of the rectangular field is 900 m²

Let the length of one side of the field be x m

Therefore, the length of the other side will be

900/x

The perimeter of the rectangular field

= 2(length + breadth)

= 2(x + 900/x)

= 2x + 1800/x  m

Therefore, the cost of fencing will be

$(32x + 28800/x )

Let f(x) = 32x + 28800/x

We need to minimize f(x)

Differentiating with respect to x and equating it to 0 gives us

32 - 28800/x² = 0

or, x² = 28800/32

or, x² = 900

or, x = 30

This is because the length cannot be negative hence -30 cannot be a value

Now

f''(x) = 57600/x³

f''(30) = 2/1333

Since f"(x) is positive, x = 30 is the minimum value of x for which the cost is minimum.

Hence, the minimum cost will be

f(30)

= 960 + 960

= $1920

To know more about minimization visit

https://brainly.com/question/21286880

#SPJ4

Complete Question

A rectangular field is to have an area of 900 m² and is to be surrounded by a fence. The cost of the fence is 16 dollars per meter of length. What is the minimum cost this can be done for?

Considering the graph of this equation, with time represented on the horizontal axis and elevation on the vertical axis, the signs for the slope are as follows;

In Mathematics, a slope is also referred to as gradient and it is typically used to describe both the ratio, direction, and steepness of the function of a straight line.

Mathematically, the rate of change is also referred to as slope or gradient and it can be calculated by using this formula;

Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change, m = (y₂ - y₁)/(x₂ - x₁)

In this scenario, the sign of the slope of the graph of this plane's equation, with time being represented on the horizontal axis and elevation on the vertical axis are as follows;

In conclusion, the slope of a graph would be positive because there is an increase in the variables on the cartesian coordinate.

Read more on slope here: https://brainly.com/question/19392759

#SPJ1

Complete Question:

Suppose that during its flight, the elevation e (in feet) of a certain airplane and its time t in minutes since takeoff, are related by a linear equation. Consider the graph of this equation, with time represented on the horizontal axis and elevation on the vertical axis. For each situation, decide if the slope is positive, zero, or negative.

a. The plane is cruising at an altitude of 37,000 feet above sea level.

b. The plane is descending at rate of 1000 feet per minute.

c. The plane is ascending at a rate of 2000 feet per minute.

Answer:

To determine which region represents the solution to a system of linear inequalities, you need to graph each inequality on the same coordinate plane and then find the intersection of the regions that satisfy each inequality. This intersection is the solution to the system of linear inequalities, as every point in this region satisfies all of the inequalities in the system.

To graph the solution, you can use a number line for each variable and plot the inequalities as points or lines on the coordinate plane. For example, if the system of linear inequalities is given by the equations y > 2x + 3 and y < -x + 5, you can plot the lines y = 2x + 3 and y = -x + 5 on the coordinate plane and find the intersection of the two lines. This intersection represents the solution to the system of linear inequalities, as every point in this region satisfies both inequalities.

Another way to find the solution to a system of linear inequalities is by using algebra to solve the system. This involves writing the equations in standard form, eliminating variables, and solving for the remaining variable. The solution can then be written as a set of ordered pairs that represent the points on the coordinate plane that satisfy the system of linear inequalities.

In either case, the solution to a system of linear inequalities is the region of the coordinate plane that satisfies all of the inequalities in the system.

Step-by-step explanation:

This study inferential statistics help psychologists obtain the goal of Prediction.

What is prediction in statistics?

To know more about predictions check the below link:

https://brainly.com/question/25955478

#SPJ4

The half-life of the substance is of 10.31 years.

What is exponential?

The exponential is an example of a mathematical function that is useful in determining if something is increasing or decreasing exponentially is the exponential function. As implied by its name, an exponential function uses exponents. But take note that an exponential function does not have a variable as its exponent and a constant as its base (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

a sample of a radioactive substance decayed to 93% of its original amount after a year.

The half-life is t for which:

exp(-0.067 t) = (0.5)

ln(0.5) = -0.067 t

t = 10.31 years.

Hence the half-life of the substance is of 10.31 years.

Learn more about exponential, by the following link.

https://brainly.com/question/2456547

#SPJ4

The longest professional tennis match ever played lasted a total of 11 hours and 5 minutes 665 in minutes or 665 minutes.

Given that:

The longest professional tennis match ever played lasted a total of 11 hours and 5 minutes.

Time = 11 hours and 5 minutes

We know that,

1 hour = 60 minutes.

Also, need to know that 1 minute = 60 seconds.

So, multiply hours by 60 to convert hours into minutes and add it with minutes to find the value of time in minutes.

i.e. Time = 11 x 60 minutes + 5 minutes

∴Time = 660 minutes + 5 minutes

          = 665 minutes

Hence, 665 minutes was the time the longest professional tennis match ever played lasting a total of 11 hours and 5 minutes.

To learn more about minutes visit: https://brainly.com/question/15600126

#SPJ4

Answer:

Below

Step-by-step explanation:

Question 1:

The quadratic equation is of the form ax^2 + bx + c = 0, where a, b, and c are constants. If one solution of the equation is 7-13i, the other solution must be the complex conjugate of 7-13i, which is 7+13i. To find the complex conjugate of a complex number, you simply need to change the sign of the imaginary part of the number. In this case, the complex conjugate of 7-13i is 7+13i.

Question 2:

1. (4-3i) (-7+21)

To add two complex numbers, we need to add their real parts and imaginary parts separately. In this case, we have:

(4-3i) (-7+21)

= (4 - 7) + (-3i + 21)

= -3 + 18i

2. (-7+6i)+(2-3i)+(4+5i)

To add multiple complex numbers, we can add them one at a time using the same procedure as before. In this case, we have:

(-7+6i)+(2-3i)+(4+5i)

= (-7+2) + (6i - 3i) + (4 + 5i)

= -5 + 3i + 4 + 5i

= -1 + 8i

3. (-6-i)/4-2i

To divide two complex numbers, we need to multiply the numerator and denominator by the complex conjugate of the denominator. In this case, we have:

4. (-6-i)/4-2i

= (-6-i)(4+2i)/(4-2i)(4+2i)

= (-24 - 2i + 6i - i^2)/20

= (-24 + 4 -1)/20

= (-21)/20

= -1.05 - 0.05i

5. (-2-7i)(-2+7i)

To multiply two complex numbers, we use the FOIL method, which involves multiplying the First, Outer, Inner, and Last terms separately and then adding the results. In this case, we have:

(-2-7i)(-2+7i)

= (-2 * -2) + (-2 * 7i) + (-7i * -2) + (-7i * 7i)

= 4 + (-14i) + 14i + 49

= 4 + 49

= 53

6. (5-3i)-(-2-6i)

To subtract two complex numbers, we need to add the first number to the opposite of the second number. In this case, we have:

(5-3i)-(-2-6i)

= (5-3i) + (2 + 6i)

= 7 + 3i

This is the final answer for each of the problems.

The number is 4.

If you take a number, times by 3 then add 5, you get (3x + 5).

If you take the same number and times by 7 then subtract 8, you get (7x - 8).

Set the equations equal to each other:

3x + 5 = 7x - 8

Subtract 3x from both sides:

5 = 4x - 8

Add 8 to both sides:

13 = 4x

Divide both sides by 4:

4 = x

Therefore, the number is 4.