The verticles of a triangle are the points R(3,c),Q(9,2) and R(3c,11) where c is constant. Given that angle PQR is 90​

The quadrilateral is a parallelogram, and since it has a right angle, it is a rectangle.

Thus, we have proved that if a quadrilateral is orthodiagonal, then the midpoints of its sides are the vertices of a rectangle.

To prove that if a quadrilateral is orthodiagonal, then the midpoints of its sides are the vertices of a rectangle, we need to show that the opposite sides of the quadrilateral are parallel and equal in length.

Let ABCD be an orthodiagonal quadrilateral with diagonals AC and BD intersecting at point E. Since the quadrilateral is orthodiagonal, we have ∠BAD + ∠BCD = 90° and ∠ABD + ∠ACD = 90°. Therefore, ∠BAD = ∠ACD and ∠ABD = ∠BCD.

Consider the midpoints of the sides of the quadrilateral. Let M, N, P, and Q be the midpoints of AB, BC, CD, and DA, respectively.

Since M and P are the midpoints of AB and CD, respectively, we have MP || AD and MP = AD/2. Similarly, we have NQ || AB and NQ = AB/2.

Now consider triangles AED and BEC. These triangles are similar, since they have the same angles, and their corresponding sides are proportional. Therefore, we have AE/BE = DE/EC.

Using the midpoint theorem, we have MP = 1/2(AB) and NQ = 1/2(CD). Therefore, we can write BE = BM + MN + NC + CQ = AB/2 + BC/2 + CD/2 + DA/2 = (AB + CD)/2. Similarly, we can write AE = (BC + AD)/2.

Substituting these expressions into our similarity relationship, we get (BC + AD)/(AB + CD) = DE/EC.

Since ∠ABD = ∠BCD, we have BD bisecting ∠ABC and ∠CDA. Therefore, we can apply the angle bisector theorem to triangles ABD and CBD to get AD/AB = CD/BC. Substituting this expression into our similarity relationship, we get (BC + AD)/(AB + CD) = 1.

Therefore, we have DE/EC = 1, which implies that DE = EC. Similarly, we can show that AC = BD.

Finally, since AC and BD are perpendicular bisectors of each other, the opposite sides of the quadrilateral are parallel and equal in length. Therefore, the quadrilateral is a parallelogram, and since it has a right angle, it is a rectangle.

Thus, we have proved that if a quadrilateral is orthodiagonal, then the midpoints of its sides are the vertices of a rectangle.

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Answer:

12.5%

Step-by-step explanation:

[First Value – Second Value] ÷ [(First Value + Second Value) ÷ 2] × 100

[50 - 30] ÷ [ 50 + 30] ÷ 2 × 100

20 ÷ 80 ÷ 2 × 100

0.25 ÷ 2 × 100

0.125 × 100

12.5 %

Answer:

12.5%

!!!!!!!!

Answer:

2 with a remainder of 1

Step-by-step explanation:

9 is not evenly divisible by four so the answer has a remainder of 1.

Hope this helps!

The division of 9 by 4 gives the remainder is 1.

One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical process used for equitable grouping and distribution.

We have to divide 9 by 4.

So, the division is

                               4 | 9 | 2

                                    8

                                ______

                                     1

Here, Quotient = 2 and Remainder = 1.

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Answer:

15

proof on pic......................

hmm im not sure, but I'm going to try to help you!! but I think it is B or D. Maybe but I'm not too sure. though. :((

Answer:

it depends on where the line is

Step-by-step explanation:

if the line is over the .15, then two.

Answer:

It has 2 repeating digits.

Step-by-step explanation:

These digits are 1 and 5.

Hope this helps!

a) The definition of the composite function is: \((f \circ g)(x) = \frac{6}{12 + 2x}\)

b) The domain of the composite function is: (-∞, -6) U (-6, -2) U (-2,0) U (0, ∞).

The composite function of f(x) and g(x) is given by the function rule presented as follows:

(f ∘ g)(x) = f(g(x)).

For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).

The functions for this problem are given as follows:

Hence the composite function is obtained as follows:

\((f \circ g)(x) = f(\left\frac{6}{x}\right)\)

\((f \circ g)(x) = \frac{\frac{6}{x}}{\frac{6}{x} + 2}\)

\((f \circ g)(x) = \frac{\frac{6}{x}}{\frac{12 + 2x}{x}}\)

\((f \circ g)(x) = \frac{6}{12 + 2x}\)

The domain is all real values except x = 0, x = -2 and x = -6, as f(x) is not defined at x = -2 and g(x) is not defined at x = 0 and the composite function is not defined at x = -6, hence the interval notation is:

(-∞, -6) U (-6, -2) U (-2,0) U (0, ∞).

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The solution of the given system of equations is (4, 7).

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given system of equations are y=3x-5 -------(I) and y=1/2 x+5 -------(II)

Substitute equation (I) in (II), we get

3x-5=1/2 x+5

3x-1/2 x=5+5

2.5x=10

x=4

Substitute x=4 in equation (I), we get

y=3(4)-5

y=7

So, solution is (4, 7)

Therefore, the solution of the given system of equations is (4, 7).

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To find the volume of the solid, you need to calculate the area of each cross-section and then multiply that by the thickness of the section (which is the distance along the y-axis).

(a) Squares: The cross-sections are squares with sides of length y. The area of a square is side^2, so the area of each square is y^2. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the square cross-sections is y^2 * y

(b) Semicircles: The cross-sections are semicircles with radii of length y. The area of a semicircle is (pi * r^2) / 2 , so the area of each semicircle is (pi * y^2) / 2. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the semicircular cross-sections is (pi * y^2) / 2 * y

(c) Equilateral triangles: The cross-sections are equilateral triangles with side length of y. The area of an equilateral triangle is (s^2 * √3)/4. so the area of each equilateral triangle is (y^2 * √3) / 4. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the equilateral triangle cross-sections is (y^2 * √3) / 4 * y

(d) Semi-ellipses: The cross-sections are semi-ellipses whose heights are twice the lengths of their bases. The area of a semi-ellipse is πab/2, where a and b are the lengths of the semi-major and semi-minor axes respectively. Therefore the area of each semi-ellipse will be (πy^2)/2. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the semi-ellipse cross-sections is (πy^3)/2

It is important to note that this is a theoretical volume calculation, as the shape of the solid does not have a closed form representation by these functions, but rather, these are an approximation.

Also, for any of these volumes to be meaningful, we have to integrate over the range of the variable y, since it is bounded by the equations y=x, y=0 and x=1, the variable y is limited.

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SOLUTION

Write out the given information

Construct the two- way frequency table

Answer: C

Step-by-step explanation:

Answer: It would be the first one (20 pens for 8$)

Step-by-step explanation: If you divide 20 by 8 then each pencil will be 2.50$. However if you divide 30 by 10 it will be 3 dollars for each pencil so the first deal will be better since you spend less money.

The approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes

Total of 22 is more than 4500 is equivalent to average of 22 is more than \($\frac{4500}{22}\)=204.545

\($$\begin{aligned}P(\bar{x} > 204.545) & =1-P(\bar{x} < 204.545) \\& =1-P\left(\frac{\bar{x}-\mu}{\sigma / \sqrt{u}} < \frac{204.545-195}{35 / \sqrt{22}}\right) \\& =1-P(z < 1.2792) \\\end{aligned}$$\)

                        = 1 - 0.8997

                        = 0.1003

                        = 10.03%

Therefore, the approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.

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Answer:

The answer is A.

Step-by-step explanation:

The statement "Every set can be considered a class" means that every object in set theory, including sets, can be considered a class. This is because classes are simply collections of objects, and sets are a type of collection.

The statement "If S is a set, consider the formula x S and the class {x: x = S}" means that if S is a set, then we can consider the formula x S, which states that x is an element of S, and the class {x: x = S}, which is the class of all objects that are equal to S.

In other words, the statement is saying that every set can be considered a class, and that we can define a class for any set by considering the formula that defines the set and the class of all objects that satisfy that formula.

For example, the set {1, 2, 3} can be considered a class by considering the formula x ∈ {1, 2, 3}, which states that x is an element of the set {1, 2, 3}, and the class {x: x ∈ {1, 2, 3}} is the class of all objects that are elements of the set {1, 2, 3}. This class is equal to the set {1, 2, 3}.

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Answer:

2(x + 6)

Step-by-step explanation:

If we let the number be "x", then the sum of the number and six is x + 6. To find twice the sum, we multiply this expression by 2:

2(x + 6)

Therefore, the expression that represents twice the sum of a number and six is 2(x + 6)

Answer:

bxjfjxucjkkdndjkjhkjjnn

Hello there! :)

The ratio that is equivalent to 15/4 is 45/12 (you multiply the numerator by 3 and the denominator by 3)

Hope it helps!

~Just a felicitous girlie

\(SilentNature ;)\) is here to help

Answer:

-72x + 10y

Step-by-step explanation:

First apply the Distributive Property of Multiplication:

-8(6x - 7y) becomes -48x + 7y and -(24x - 3y) becomes -24x + 3y.

Combining like terms, we get -72x + 10y

Answer:

-21x+53y

Step-by-step explanation:

learned it

The dimensions listed above are thus neither exact nor precise.

In the given question the chocolate chip cookies weigh 17.27 g, 13.05 g, 19.46 g, and 16.92 g, respectively and we have to classify the following set of measurements as accurate, precise, both, or neither.

It is the "value" that a buyer is prepared to pay for an object, particularly a used or second-hand car; typically, the "real worth" of any used car is a predetermined price tag after determining its value based on its condition and usage.

The chocolate chip cookies weigh 17.27 g, 13.05 g, 19.46 g, and 16.92 g, respectively. This demonstrates that the weight of chocolate chips is not comparable to their actual worth.

The dimensions listed above are thus neither exact nor precise.

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Answer:

y = csc(x - 3/4\(\pi\))

Step-by-step explanation:

I forgot how to answer questions like these. I went ahead and tried re-learning this to answer this.

So, the first step is to recognize that this graph can only be the reciprocal function of sin or cosine. I will think of sine.

y = sin(x)

Look at where the x-coordinate of the sin is. (-3/4PI). This is going to be the c value. { y = asin(x-c) }

y = sin(x - 3/4\(\pi\))

Now, what is the a value? or amplitude? Well, it's just 1.. and the simplest explanation is just to look at my picture.

Now, if we were to graph this, we would end up with the correct x and y values, but the shape is wrong, and the easiest way to fix this is to just take the recpriocal of the sine function.

y = csc(x - 3/4\(\pi\))

Thank you for this question, I re-learned something I forgot back in pre-calc haha.

Answer:

The answer is B

Step-by-step explanation:

Answer:

To find the total balance after three years, we can use the formula for continuous compounding:

A = Pe^(rt)

Where A is the total balance, P is the principal (initial amount), e is Euler's number (approximately 2.71828), r is the annual interest rate as a decimal, and t is the time in years.

In this case, P = $12,000, r = 0.0125 (1.25% expressed as a decimal), and t = 3. Plugging these values into the formula, we get:

A = $12,000 x e^(0.0125 x 3)

A = $12,000 x e^(0.0375)

A = $12,000 x 1.038163

A = $12,458.54

Therefore, the total balance after three years is $12,458.54.

Answer:

It will take 2 hours, 13 minutes and 20 seconds for both pipes to fill the pool.

Step-by-step explanation:

Given that an inlet pipe can fill an empty swimming pool in 5hours, and another inlet pipe can fill the pool in 4hours, to determine how long it will take both pipes to fill the pool, the following calculation must be performed:

1/5 + 1/4 = X

0.20 + 0.25 = X

0.45 = X

9/20 = X

9 = 60

2 = X

120/9 = X

13,333 = X

Therefore, it will take 2 hours, 13 minutes and 20 seconds for both pipes to fill the pool.

Answer:

it's the 'D' ..............,..

The Intel pays $7,760 to Bally Manufacturing on August 14.

The first step in calculating what Intel Corporation pays Bally on August 14 is to determine the net price of the machinery after the trade discount and the return of $100 due to defects.

The trade discount of 40% is calculated as follows:

Discount = List price × Discount rate

Discount = $13,100 × 0.40 = $5,240

So the net price of the machinery after the trade discount is:

Net price = List price - Discount

Net price = $13,100 - $5,240 = $7,860

After Intel returns $100 of machinery, the cost of the machinery is further reduced to:

Net price after return = Net price - Return

Net price after return = $7,860 - $100 = $7,760

Since the payment terms are 3/10 EOM (end of month), Intel receives a discount of 3% if payment is made within 10 days. The 10-day period begins on August 1 and ends on August 10 (the payment due date). Since Intel pays the bill on August 14, payment is late and the 3% discount does not apply.

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Answer:

8 hours and 29 minutes

Step-by-step explanation:

As he left at 9:20 am and the question said he arrived at 5:49, we must assume he came at pm. So next we just work out the difference between those times, which will leave you with that answer.

Answer:

8 units

Step-by-step explanation:

Area of square:

length * width

2 * 3

= 6  units

Area of triangle:

1/2 * base * height

1/2 * 2 * 2

= 2 units

Area of entire shape:

6 + 2

= 8 units

So, the area of the shape is 8 units.

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