Given: ABCD is a parallelogram and AD is perpendicular to BD
Prove: AB congurent to BC​

Answer:

87654321

Step-by-step explanation:

Answer:

99

Step-by-step explanation:

We can set up and solve this equation:

X + X - 50 = X + 49

X = 99

Chords AB and CD intersect at E and AE= EB is Semi circle is drawn with diameter CD. EF perpendicular to CD meet this semi circle at F then AE= EF

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Let M be the midpoint of AB, so EM is perpendicular to AB.

Since OF is a diameter of the circle, angle EOF is a right angle.

Triangles EOF and EMA are similar, since they both have a right angle and angle EFM is congruent to angle EAM, being alternate interior angles of parallel lines.

The corresponding sides are proportional:

EF / EA = EO / EM.

EM is half the length of AB, which is the diameter of the semicircle,

EO must be equal to the radius of the semicircle.

Therefore, we have EF / EA = radius / (diameter / 2) = 2 / 2 = 1,

EF = EA.

Hence, chords AB and CD intersect at E and AE= EB is Semi circle is drawn with diameter CD. EF perpendicular to CD meet this semi circle at F then AE= EF

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There are 6,720 possible ways to arrange the committee in a row, with students grouped by grade.

2 seniors * 5 sophomores * 3 freshman * 2 juniors = 60

60 possible arrangements for the 4 grade levels

60 * 6 (the number of ways to arrange 6 people) = 360

360 * 6 (the number of ways to arrange 6 people) = 2160

2160 * 6 (the number of ways to arrange 6 people) = 12,960

12,960 / 2 (because the order of the two grade levels can be reversed) = 6,720

6,720 possible arrangements for the school dance committee.

The school dance committee is made up of 3 freshman, 5 sophomores, 2 juniors, and 2 seniors. To find out how many ways there are to sit the committee in a row at a meeting if the students must sit together by grade, we first need to calculate the number of possible arrangements for each grade level. Since there are 2 seniors, 5 sophomores, 3 freshman, and 2 juniors, there are 60 possible arrangements for the 4 grade levels. We then multiply this by 6, since there are 6 ways to arrange 6 people. This gives us 360 possible arrangements for the first two grade levels. We then multiply this number by 6 again, since there are 6 ways to arrange 6 people. This gives us 2160 possible arrangements for the first three grade levels. We multiply this number by 6 one more time, since there are 6 ways to arrange 6 people. This gives us 12,960 possible arrangements for all four grade levels. However, since the order of the two grade levels can be reversed, we must divide this number by 2. This gives us a total of 6,720 possible arrangements for the school dance committee.

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Answer:

62 Feet

Step-by-step explanation:

26+36=62

6 + 6 = 12

20 + 30 = 50

12 + 50 = 62

Answer:

The scuba diver is 62 feet deep.

Step-by-step explanation:

We know the scuba diver has dived 36 feet. When he stops to look at the school of fish, he doesn't dive down any further and stays at 36 feet. He then dives down another 26 feet

All we would need to do is add 36 and 26, which would give you your answer of 62.

Answer:

400 calories

Step-by-step explanation:

Let's call the number of calories in the loaded baked potato as P. Then the coleslaw had P-50 calories and the steak had 2P calories.

So the equation for the total number of calories in the meal is:

P + (P-50) + 2P = 1550

4P = 1600

P = 400

Therefore, the loaded baked potato had 400 calories.

Answer:

Below

Step-by-step explanation:

c oleslaw =   p - 50

p = potato

s = 2 p       Summed these = 1550

p-50     + p    + 2p   =  1550      Gather 'like' terms

4p - 50 = 1550                           add 50 to both sides of the equation

4p = 1600                                  divide both sides by 4

p = 400 calories

The slope of the line that models this situation is equal to 2.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Points on x-axis = (0, 8).

Points on y-axis = (4, 20).

Substituting the given data points into the slope formula, we have the following;

Slope, m = (20 - 4)/(8 - 0)

Slope, m = 16/8

Slope, m = 2.

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Answer: 80/3 months

Step-by-step explanation:

Let x be the number of months until Zera reaches her limit.

Then on month x, her charges are 200x, and her payments are 125x.

This leaves her with 200x - 125x = 75x dollars owed.

we need to see when this equals 2000, so she hits her limit:

2000 = 75x

.: x = 2000/75 = 80/3

She can continue her pattern for 80/3 months, (≈26.666667)

The length of earthworm will be 4 cm after 4 hours. And the length is 14 cm after 49 hours.

Proportions are defined when two or more ratios are made to be equal to each other.

Two quantities are said to be directly proportional if a positive change in one quantity also lead to a positive change in the other quantity.

If a is proportional to b, we denote it as a ∝ b.

Given,

Length of an earthworm, l ∝ square root of the number of hours, n, which have elapsed since it's birth.

l ∝ √n

l = k √n, for some constant k.

If a worm is 2 cm long after 1 hour, we can write it as,

2 = k × √1

⇒ k = 2

So the proportionality constant is 2.

After 4 hours,

l = k √4

l = 2 × 2 = 4 cm

If the length is 14 cm,

14 = 2 √n

√n = 14 / 2

√n = 7

n = 7² = 49 hours

Hence the length of worm is 4 cm after 4 hours. It will take 49 hours to grow to a length of 14 cm.

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The equations x° + 65° = 180°, x° = z° and y° = 65° are true for the values of x, y and z. The solution has been obtained by using angles and line.

What are angles and line?

Straight lines with little depth or width are present. There are many different types of lines, including perpendicular, intersecting, transversal, etc. A figure called an angle is one in which two rays originate from the same point.

We are given that 2 lines intersect to form 4 angles which are 65°, x°, y°, z°.

1. x° + 65° = 180°

We know that angles on a straight line form a linear pair i.e. their sum is 180°. So, this statement is true.

2. x° = z°

We know that vertically opposite angles are equal. So, x° will be equal to z°. Thus, this statement is true.

3. y° = 65°

We know that vertically opposite angles are equal. So, y will be equal to 65°. Thus, this statement is true.

4. x° = 65°

This statement is false because these are the angles on a straight line which must add up to 180°.

5. x° + y° + z° = 115°

We know that angles in a circle add upto 360°. We know one angle as 65°. So, the remaining angles should add upto 295°. Thus, the statement is false.

Hence, the equations x° + 65° = 180°, x° = z° and y° = 65° are true for the values of x, y and z.

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Question: Which equations are true for the values of x, y, and z? Select three options.

2 lines intersect to form 4 angles as shown in the figure. Clockwise, from top, the angles are: 65 degrees, x, y, z.

x degrees + 65 degrees = 180 degrees

x degrees = z degrees

y degrees = 65 degrees

x degrees = 65 degrees

x degrees + y degrees + z degrees = 115 degrees

Answer:

1. not a function

Since x=5 produces y=9 and y=0, it can't be a function

2. it is a function because there is one value of y for every value of x

3. A circle is not a function. because it doesn't pass the vertical line test

4. I think is d but not sure has been a while since I have done these questions so sorry if I am wrong :)

Step-by-step explanation:

have a nice day and good luck

True. The rule of thirds is a photography and visual arts guideline that involves dividing an image into thirds using two horizontal lines and two vertical lines, and then placing the image's most important elements at the intersection points or along the lines.

This aids in the creation of a balanced and visually appealing composition. This results in nine rectangular areas of equal size, with four intersection points where the lines cross.

The rule of thirds principle suggests that the points of intersection or the lines themselves are ideal places to position the composition's most important elements. The resulting image is more visually balanced and pleasing to the eye as important elements are placed in these areas.

It is important that, however, that the rule of thirds is not a hard and fast rule, and that there were times when breaking it can result in more dynamic and interesting compositions. The rule of thirds is merely a tool for artists and photographers to use in order to create more effective and engaging images.

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Cases are on display OA 619,200 cubic inches.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.
To calculate the number of cubic inches needed for 360 cases of 12-ounce cans of soft drink, we need to multiply the number of cases (360) by the volume of each case. The volume of each case can be calculated by multiplying its length (16 inches), width (10.75 inches) and height (5 inches):

Volume = 16.00 inches x 10.75 inches x 5.00 inches = 828 cubic inches

Therefore, 360 cases of 12-ounce cans of soft drink require (360 x 828) = 619,200 cubic inches.

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Answer:

Your answer is: C) 400

Step-by-step explanation:

The data is symmetric because some students have phones and some do not. The correct option is B.

A histogram is a simplified representation of the distribution of numerical data. The phrase was first used by Karl Pearson at the outset.

Rectangles are used in a histogram, a type of visual representation of statistical data, to show how frequently data points occur throughout a range of subsequent numerical intervals of equal width.

In the most common sort of histogram, the independent variable and dependent variable are shown along the horizontal axis and the vertical axis, respectively.

The histogram is a frequently used graphing tool. It is used to summarize data that is measured on an interval scale, whether it be continuous or discontinuous.

It is widely applied to give the primary properties of the data distribution a practical way to be illustrated.

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Answer: B. The data is symmetric because some students have phones and some do not.

Step-by-step explanation:

The explicit formula for the geometric series is [tex]a_n = 3(5)^{n-1}[/tex].

A geometric series is one in which there is a constant separating the two succeeding numbers. In other words, to create a geometric progression, each succeeding term is multiplied by the constant term.

Given that the geometric sequence is,

3, 15, 75......

The common ratio of the series is calculated as the ratio of the second term to the first term,

r = 15 / 3

r = 5

The explicit formula can be written as:-

[tex]a_n = a_1(r)^{n-1}[/tex]

[tex]a_n = 3(5)^{n-1}[/tex]

Therefore, the formula is [tex]a_n = 3(5)^{n-1}[/tex].

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Answer:

27 children.

Step-by-step explanation:

Let's call the number of children who chose apples x. Then, the number of children who chose bananas is 0.25x. The number of children who chose watermelon is 60 - x - 0.25x = 60 - 1.25x.

Since 30% of the children chose apples, we know that:

0.30 * 60 = x

So, x = 18, which means 18 children chose apples.

And since 25% of the children chose bananas, we know that:

0.25 * 60 = 0.25x = 15

So, 15 children chose bananas.

Finally, the number of children who chose watermelon is:

60 - 18 - 15 = 27 children.

As per unitary method, Reeta's salary is 21,000 rupees.

The unitary method is a technique of solving problems by assuming a unit value and then finding out the required value in terms of that unit.

In this problem, we can assume Reeta's salary to be the unit value and then find out how much she spent on car repair work and how much money she has left using this unit value.

Let's assume Reeta's salary to be x rupees. Now, according to the problem, she has spent 2/7 of her salary on car repair work. So, the amount of money she spent on car repair work can be calculated as:

2/7 * x

Using the unitary method, we can now find out how much money she has left with her. We know that she has 15,000 rupees left. So, we can set up the following proportion:

2/7 * x = x - 15,000

Simplifying this equation, we get:

2x = 7(x - 15,000)

2x = 7x - 105,000

5x = 105,000

x = 21,000

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The slope on the line containing the points (14,-42) is 1.06, as stated in the preceding sentence (-48,24).

The % slope is calculated by multiplying the distance between two locations by the differences in elevation above them. The difference in height between two places is referred to as "rise." The distance between it sites is known as the run. Therefore, the formula for percent slope is (rise / run) x 100.

The slope's formula is as follows:

m = (y₂-y₁)/x₂-x₁)

In the formula, replace the point values as follows:

m = (24-(-42))/(-48-14)

Make the fraction simpler:

m = (24-(-42))/(-48-14)

m = 66/-62

m = 1.06

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Bob gave the cashier $15.26 for the bag of beans.

To find the value of x, we need to subtract the cost of the beans from the total amount given to the cashier. The cost of the beans is $2.37, and the change received is $17.63.

Therefore, the value of x can be calculated as:

x = Total amount given to the cashier - Cost of the beans

x = $17.63 - $2.37

x = $15.26

A cashier is an employee who works in a retail or service industry, responsible for handling cash, credit card payments, and providing customer service. They are often the first and last point of contact for customers in a business. Cashiers use a cash register or computer system to record transactions, and must be able to accurately count money, make change, and reconcile the cash drawer at the end of their shift.

They also need to be proficient in using technology, such as scanners and card readers, to process transactions. In addition, cashiers must have good communication skills to interact with customers, answer questions, and resolve any issues. Other responsibilities may include stocking shelves, maintaining a clean and organized workspace, and ensuring that customers receive accurate pricing and promotional discounts.

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Answer:

Step-by-step explanation:

Mariana's quote: 135

Vicent's quote: 34x+67

Say x=1, 34(1)+67=101

For 1 hour of Vincent's work it would be $101.

Say x=2. 34(2)+67=135

Vincent would have to work for two hours to charge the exact same as Mariana.

We can rewrite ln(27000) in terms of ln(5) and ln(6) as ln(27000) = 3ln(5) + 3ln(6) by using logarithmic property.

Due of their connection to exponential functions, logarithmic functions are crucial. Logarithms can be used to examine exponential equations and the properties of exponential functions.

We can use the logarithmic property that says:

log_a(xⁿ) = n×log_a(x)

to break down 27000 into factors that involve 5 and 6.

First, we can write:

27000 = 5³× 6³

When we take the natural logarithm of both sides, we obtain:

ln(27000) = ln(5³ × 6³)

Using the property above, we can simplify this expression as:

ln(27000) = ln(5³) + ln(6³)

Using another logarithmic property that says:

log_a(bⁿ) = c×log_a(b)

we can further simplify the expression:

ln(27000) = 3ln(5) + 3ln(6)

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Answer:

To substitute x = 2 and y = 1 into the expression 4x^-3 y^-2, we simply replace x with 2 and y with 1:

4 * (2)^-3 * (1)^-2 = 4 * (1/8) * (1) = 4/8 = 0.5

So the expression 4x^-3 y^-2 evaluated at x = 2 and y = 1 is equal to 0.5.

Step-by-step explanation:

The value of the missing side of the given triangle would be = 12

To calculate the value of the missing length the Pythagorean formula can be used such as;

c² = a² + b²

where;

C =?

a = 11

b = 5

C² = 11²+5²

= 121 + 25

= 146

C =√ 146

C = 12

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The probability that the orange has a mass of more than 80g is (y/x).

Given is that one of the oranges is chosen at random from the crate of oranges.

Assume that the total number of oranges are {x} and the oranges with a mass of greater than 80 are {y}. So, we can write -

P{E} = y/x

Therefore, the probability that the orange has a mass of more than 80g is (y/x).

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Matrix A is: A = [1 2 3] and Matrix B is: B = [1]

                         [2 4 6]                                 [2]

                         [1 1 1]                                    [3]

An example of a 3x3 matrix A and a 3x1 matrix B such that the solution set of Ax = b is a line in R³ that does not contain the origin:

A = [1 2 3]

   [2 4 6]

   [1 1 1]

B = [1]

   [2]

   [3]

To check that the solution set of Ax = b is a line in R³, we can solve for x in terms of a parameter t:

Ax = b

[1 2 3] [x1] = [1]

[2 4 6] [x2]   [2]

[1 1 1] [x3]   [3]

Ax = b

x1 + 2x2 + 3x3 = 1

2x1 + 4x2 + 6x3 = 2

x1 + x2 + x3 = 3

Dividing the second equation by 2 and subtracting it from the first equation, we get:

-x1 - x2 = -1

Solving for x2 in terms of x1 and x3, we get:

x2 = -x1 + 1 - (3/2)x3

Solving for x3 in terms of a parameter t, we get:

x3 = t

Then, x1 can be expressed in terms of t as:

x1 = -t + 1

Therefore, the solution set of Ax = b is:

x = [-t + 1]

   [-t + 1 - (3/2)t]

   [t]

which is a line passing through the point (1, 1/2, 0) with a direction vector [-1, -3/2, 1].

A × [0; 0; 0] = [0; 0; 0]

Therefore, the origin is not on the line of solutions.

So, Matrix A is:

A = [1 2 3]

     [2 4 6]

      [1 1 1]

and Matrix B is:

B = [1]

     [2]

     [3]

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Answer:

x = y/(m + 3)

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ xm = -3x + y

Then the value of x will be,

→ xm = -3x + y

→ xm + 3x = y

→ x(m) + x(3) = y

→ x(m + 3) = y

→ x = y/(m + 3)

Hence, value of x is y/(m + 3).