Q1. In the given figure, ABCD is a parallelogram. Complete each statement along with the definition or property used.
(i) AD = ……….. (ii) DC = ……….. (iii) ∠DCB = ………..
(iv) ∠ADC = ……….. (v) ∠DAB = ……….. (vi) OC = ………..
(vii) OB = ……….. (viii) m∠DAB + m∠CDA = ………..

The area of the given shape is 46 cm²

Formulas used:

Area of the triangle = (1/2) × Base × Height

Area of rectangle = Base × Width

Here we have  

The composite figure with a right-angled triangle and a rectangle

In a right-angled triangle,

The base of the triangle = 3 cm

Height of the triangle = 4 cm

Area of the triangle

= (1/2) × base × height

= (1/2) × 3 × 4

=  (1) × 3 cm × 2 cm

=  6 cm²  

In rectangle,

Length of the rectangle = 10 cm

Width of the rectangle = 4 cm

Area of the rectangle

= Length × Width

= 10 cm × 4 cm

= 40 cm²

By the above calculations,

Area of the given figure = Area of triangle + Area of rectangle

= 6 cm² + 40 cm² = 46 cm²

Therefore,

The area of the given shape is 46 cm²

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The factors of 5x as calculated from the data given is found to be as 5, x and  1 .

On factorizing 5x we can write it as ,

5 x 1 x x .

Therefore the factors are 5 , 1 and x.

There are some integers which are positive and can divide a number completely leaving no remainders. Such integers are known as factors for a number. If we want to get a product by multiplying two numbers , we will have to multiply two factors. Each number is a multiplier of itself.

The prime factor is the factor of a given number that is also a prime number. Factors are numbers that are multiplied together to produce another number.

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Julie read 79 pages after 26 minutes and Cassie read 79 pages after 26 minutes.

What are linear equations?

A linear equation is a mathematical equation that can be written in the form of Ax + By = C, where A, B and C are constants and x and y are variables.

Let's call the number of pages that both friends read x. We know that Julie's reading speed is 3 pages per minute and Cassie's reading speed is 2 pages per minute.

We can set up the equation:

x = 3t + 9 (where t is the time in minutes that Julie takes to read x pages)

x = 2t + 35 (where t is the time in minutes that Cassie takes to read x pages)

We know that they read the same number of pages, so we can set the two equations equal to each other:

3t + 9 = 2t + 35

We can then solve for t:

t = 26 minutes

So it took them 26 minutes to read the same number of pages. We can use that value to find the number of pages that they read:

x = 3t + 9 = 3(26) + 9 = 79 pages

Hence, Julie read 79 pages after 26 minutes and Cassie read 79 pages after 26 minutes.

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Julie read 79 pages after 26 minutes and Cassie read 79 pages after 26 minutes.

What are linear equations?

A linear equation is a mathematical equation that can be written in the form of Ax + By = C, where A, B and C are constants and x and y are variables.

Let's call the number of pages that both friends read x. We know that Julie's reading speed is 3 pages per minute and Cassie's reading speed is 2 pages per minute.

We can set up the equation:

x = 3t + 9 (where t is the time in minutes that Julie takes to read x pages)

x = 2t + 35 (where t is the time in minutes that Cassie takes to read x pages)

We know that they read the same number of pages, so we can set the two equations equal to each other:

3t + 9 = 2t + 35

We can then solve for t:

t = 26 minutes

So it took them 26 minutes to read the same number of pages. We can use that value to find the number of pages that they read:

x = 3t + 9 = 3(26) + 9 = 79 pages

Hence, Julie read 79 pages after 26 minutes and Cassie read 79 pages after 26 minutes.

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Answer:

16/11

Step-by-step explanation:

Let x = 1.45454...

Multiply both sides by 100:

100x = 145.454...

Subtract both sides by x:

100x - x = 145.454... - x

100x - x = 145.454... - 1.45454...

99x = 144

x = 144/99

The term can be simplified in lowest as 16/11. Hence, 1.45454... can be written as the ratio of two integers of 16/11

Autumn and Terry can talk because the distance between them is 2 miles

Polly and terry can not talk because the distance between them is 2.27 miles.

Polly and Autumn's distance can talk because the distance between them is 1.56 miles.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Autumn and Terry distance = 2 mile

Polly and Autumn's distance = x miles

Polly and terry's distance = y miles

Now,

Applying the Sin rule of a triangle.

2 / sin 59° = x / sin 42° = y / sin 79°

2 / 0.86 = x / 0.67 = y / 0.98

Find x.

2 / 0.86 = x / 0.67

x = 1.56

Find y.

2/0.86 = y / 0.98

y = 2.27

Now,

Polly and Autumn's distance is 1.56 miles.

This means they can talk.

Polly and terry's distance is 2.27 miles.

This means they can not talk.

Thus,

Polly and Autumn can talk.

Polly and terry can not talk.

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The percentage sugar of 19. 00 g milk chocolate bar is 60.53%. The value of 60.53 is rounded to two decimal points.

What does mean of two decimal points?

To make decimal values simpler to grasp and utilise in calculations, they are frequently rounded off. The second place to the right of the decimal point, or the hundredths place, is used to round a decimal value to two decimal places. For instance, you can round 2.83620364 to two decimal places as 2.84 and 0.7035 to two decimal places as 0.70. If you look closely, you'll see that we changed 2.83 to 2.84 by adding a single digit to the first number's hundredths position. However, we did not add 1 to the digit at the hundredths place of the second integer (i.e 0).

Given that a chocolate bar with a weight 19.00 gram milk, contains 11. 50 g of sugar.

To find the percentage, we will calculate the amount of suger in 100 gram of chocolate bar in the same ratio..

19.00 gram milk chocolate bar contains 11. 50 g of sugar.

Apply unitary method:

1 gram milk chocolate bar contains 11. 50/19 g of sugar.

100 gram milk chocolate bar contains (11. 50/19) × 100 g of sugar.

                                                                = 60.526

The digit at the thousandth place of the number 60.526 is 6 which is more than 5. thus add 1 with the hundredth place digit to round to two decimal places.

60.526  ≈ 60.53

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Answer: To obtain the standard form of a linear equation, we want to rearrange the equation in the form Ax + By = C. Here are the standard forms of the given equations:

5x - 6y = 12

3y - 2x - 6 = 0

7x + y - 63 = 0

14x - y + 16 = 0

To obtain the slope-intercept form of a linear equation, we want to rearrange the equation in the form y = mx + b, where m is the slope and b is the y-intercept. Here are the slope-intercept forms of the given equations:

There is no y-intercept, so this equation does not have a slope-intercept form.

y = (2/3)x + 2

y = (1/7)x + 9

y = (-7/2)x + 8

Step-by-step explanation:

The triangle ABC, along with it's image after the reflection x = -3, is given on the graph presented at the end of the answer.

The coordinates for the original vertices of the triangle are given as follows:

A(-5, -6), B(-4, -3) and C(-3,-7).

The reflection line is given as follows:

x = -3.

The reflection lines is a vertical line, meaning that for the reflected triangle, the y-coordinate remains constant, while the x-coordinate means that the triangles will be on the same distance relative to the reflected line, however on the opposite direction.

Vertex A has a x-coordinate two units left of x = -3, hence the coordinates of the image will be two units right, hence:

A'(-3 + 2, -6) = (-1, -6).

Vertex B has a x-coordinate one unit left of x = -3, hence the coordinates of the image will be one unit right, hence:

B'(-3 + 1, -3) = B'(-2,-3).

Vertex C remains at the same position, as it has a x-coordinate of -3.

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Answer:

18.84

Step-by-step explanation:

x is the hypotenuse of the triangle.

For the 48° angle, 14 is the opposite leg.

The trigonometric ratio that relates the opposite leg to the hypotenuse is the sine.

sin 48° = opp/hyp

sin 48° = 14/x

x × sin 48° = 14

x = 14/sin 48°

x = 18.84

Answer:

x^4

Step-by-step explanation:

[tex]x {}^{5} \times \frac{x {}^{3} }{x {}^{4 \\ } } \\ \\ \frac{ {x}^{8} }{x {}^{4} } \\ \\ x {}^{8 \: - \: 4} \\ {x}^{4} [/tex]

a) After 8 hours, a person earned $148 in wages.

The function is, $x = 18.5 y

b) The linear function to represent the table is, y = 10x -4

A function with one or two variables and no exponents is referred to as a linear function. It is a function with a straight line as its graph.

Given:

a) After 8 hours, a person earned $148 in wages.

So, the unit rate change = 148/ 8

                                         = 18.5

So, if y represents the number of hour and $x the wages, then the function is

$x = 18.5 y

b) The unit rate change for the function is

= (56-36)/(6-4)

= 20/ 2

= 10

So, the linear function to represent the table is

y - 36 = 10(x - 4)

y- 36 = 10x - 40

y = 10x -4

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In the year 1582, January 1st was adopted for the new year celebration

An equation is used to show the relationship between numbers and variables.

Polynomials consist of exponents of variables and numbers forming an equation using operations of addition and subtraction. The degree of a polynomial determines it type such as linear, quadratic, cubic and so on.

The polynomial having a degree of 3 is cubic while that with a degree of 2 is quadratic and that with degree of 1 is linear

The year that January 1st was adopted as new year can be gotten using the function:

f(x) = 3x³ - 7x² - 5x + 7

f(9) gives the year that it was adopted. Substituting x = 9 gives:

f(9) = 3(9)³ - 7(9)² - 5(9) + 7

f(9) = 1582

In the year 1582, the new year was celebrated at January 1st

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Shortest distance between start and end point is 55.9 miles

According to given statement,

Terry had to travel south 50 miles and then west 25 miles.

We are taking X as a start point and Z is end point.

In triangle XYZ, we are taking angle Y to be of 90 degrees, which qualifies the Triangle XYZ to qualify Pythagorean theorem [The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right angle triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.]

XY = 50 miles

YZ= 25 miles

XZ^2 = XY^2 + YZ ^2

XZ^2 = (50) ^2 + (25) ^2 = 3125

XZ = 55.9

Shortest distance between start and end point is 55.9 miles

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The minimum number of entries needed in order to cover the total cost of the T-shirts is 94.

What is linear inequality?

A linear inequality is an inequality that can be written in the form of

ax + b > c or ax + b < c or ax + b = c

Where x and y are variables and a,b,c are constants.

The cost of the T-shirts plus VAT is £400 + (17.5/100) * £400 = £400 + £70 = £470

In order to cover the total cost of the T-shirts, you need to find out how much money you will make from the entry fees.

Let's call the number of entries N. The total revenue from the entry fees is N * £5 = £5N

So, in order to cover the cost of the T-shirts, the revenue from the entry fees must be greater than or equal to the cost of the T-shirts plus VAT:

£5N ≥ £470

To find the minimum number of entries needed, you can divide both sides of the inequality by 5:

N ≥ £470 / £5

N ≥ 94

Hence, the minimum number of entries needed in order to cover the total cost of the T-shirts is 94.

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The minimum number of entries needed in order to cover the total cost of the T-shirts is 94.

What is linear inequality?

A linear inequality is an inequality that can be written in the form of

ax + b > c or ax + b < c or ax + b = c

Where x and y are variables and a,b, and c are constants.

The cost of the T-shirts plus VAT is £400 + (17.5/100) * £400 = £400 + £70 = £470

In order to cover the total cost of the T-shirts, you need to find out how much money you will make from the entry fees.

Let's call the number of entries N. The total revenue from the entry fees is N * £5 = £5N

So, in order to cover the cost of the T-shirts, the revenue from the entry fees must be greater than or equal to the cost of the T-shirts plus VAT:

£5N ≥ £470

To find the minimum number of entries needed, you can divide both sides of the inequality by 5:

N ≥ £470 / £5

N ≥ 94

Hence, the minimum number of entries needed in order to cover the total cost of the T-shirts is 94.

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The explanation can be used to informally derive the formula for the volume of a cylinder, which is the correct answer would be option (D).

Usually, a cylinder was a three-dimensional solid, one of the most fundamental curvilinear geometric forms. It is a prism with a circle as its basis in elementary geometry. In some recent fields of geometry and topology, a cylinder can alternatively be defined as an infinite curved surface.

Given that, Which explanation can be used to informally derive the formula for the volume of a cylinder

We know that the volume of a cylinder = πr²h

So, consider option (D).

A cylinder is similar to a circular stack. The volume of the cylinder would be equal to the area of the circle multiplied by the cylinder's height. The height of the cylinder reflects the number of circles in the stack.

Therefore, we get the formula πr²h, where πr² represents the area of the circle and h the height of the circle.

Hence, With this reasoning, we may get the formula for cylinder volume informally.

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Answer:

-0.05

Step-by-step explanation:

10x+0.5

10x=-0.5

x=-0.5/10

x=-0.05

Answer:

So I would say when the number of classes is lower fishing is less expensive and when the number of canoeing classes is lower it's less expensive

Step-by-step explanation:

You have to make sure to pay attention to the label and the points in the graph and the table

Answer:

35/4=8.75

Step-by-step explanation:

You and your 3 friends add up to 4 people so you do 35 divided by 4 and get 8.75

Answer:

Step-by-step explanation:

35/3 = p

p = 11.67 per person

The dimensions of the original sandbox was 2 ft X 2 ft..

Let, The original has a length of Xft and a width of Xft

The area of original sandbox is X^2 ft^2

As per given statement,

The new sandbox would have a length of (X+4)ft and a width of (X+5)ft

So, the area of new sand box would be: (X+4)(X+5) ft^2

Given, the area of new sandbox will be 38 square feet greater than the area of the original sandbox.

so,

X^2+38 = (X+4)(X+5)

or, X^2+38 = X^2 + 9X + 20

Eliminating X^2 from both side

0r, 9X+ 20 = 38

0r, 9X = 18

0r, X = 18/9 = 2

So, we assumes that the original has a length of Xft and a width of Xft

then the dimensions of the original sandbox was 2 ft by 2 ft.

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Answer:

no

Step-by-step explanation:

The inequalities that have the same graph as x<4 are:

Hence, option(B) , (C) and (D) are correct.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

x +6 < 10 ⇒ x < 10-6 ⇒ x < 4

5x < 20 ⇒ x< 20/5 ⇒ x < 4.

x-2 > 2 ⇒ x < 2 + 2 ⇒ x < 4.

Hence, option(B) , (C) and (D) are correct.

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Your question is incomplete but most probably the question was:

Select all the inequalities that have the same graph as x <4.

A. x < 2.

B. x+6 < 10

C. 5x < 20

D.  x-2 > 2

E. x <8

Answer: Sara's mean quiz score is 12

Step-by-step explanation:

Mean is the Sum of the Terms divided by the number of terms.

If we add up every score we get 60, we then will divide this by how many scores there were (5).

60/5 = 12

Answer:

1. 6
2. 15

Step-by-step explanation:

4 pumpkins: $32
=> 1 pumpkin = 32 : 4 = $8
- He will have to sell 48 : 8 = 6 pumpkins to make $48

- He sold: 120 : 8 = 15 pumpkins that day

The option 1 "Simple random sampling, because the people in the sample are accessible and available" is correct for the most appropriate in studying the opinions of stay-at-home mothers in all towns across the country.

In the given question, we have to find which sampling method is the most appropriate in studying the opinions of stay-at-home mothers in all towns across the country.

As we know that, you must carefully consider how you will choose a sample that is representative of the group as a whole if you want to make accurate conclusions from your data. It is known as a sampling method.

Every individual in the population has an equal chance of being chosen in a simple random sample. The entire population should be included in your sampling frame.

You might utilize instruments like random number generators or other methods that just rely on chance to carry out this kind of sampling.

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The complete question is:

Which sampling method is the most appropriate in studying the opinions of stay-at-home mothers in all towns across the country?

(1) Simple random sampling, because the people in the sample are accessible and available

(2) Stratified sampling, because there are specific subgroups to investigate

(3) Systematic sampling, because of the ease in selecting every nth person

(4) Cluster sampling, because the studied population is spread across a wide area such that simple random sampling would be difficult to implement

(5) All the above sampling methods

To know whether Elena is correct or not, you need to find out the height of each stack of file folder.

Assume that all 200 files have the same height.

Let the height of each file folder be m inches.

So, by unitary method the height of each file folder would be,

m = Total height of stack / Number of file folders

here, the total height of stack = 5.125 inches

And the number of file folders = 200

So, m = 5.125 / 200

m = 0.0256 inches

But Elena guesses that each file folder is 0. 035 inches thick.

This means, Elena is wrong as the answer Elena gave is too large than the actual answer.

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Answer: a. Plotting a graph of the data on a graph paper, you can represent the time on the x-axis and the temperature on the y-axis. And plot the given points (15,20), (30,30), (45,40), (60,50), (75,60), (90,70) as ordered pairs on the graph. This will give you a line graph, showing the temperature increasing over time.

b. To find the linear model, T(x), for the temperature of the liquid with respect to time, you can use the slope-intercept form, y = mx + b, where y is the temperature, x is the time, m is the slope and b is the y-intercept. Using two of the given points, you can find the slope of the line by calculating the change in y over the change in x,

m = (y2 - y1) / (x2 - x1).

where x1,y1 and x2,y2 are two distinct points on the graph.

Once you have the slope, you can use one of the points to find the y-intercept, by substituting the point's coordinates into the slope-intercept form equation and solving for b.

Once you have the slope and y-intercept, you can write the linear model as T(x) = mx + b

c. To find the temperature of the water after 85 minutes, you can substitute the value of x = 85 into the linear model equation that you found in the previous step to get the corresponding value of y (temperature).

Please keep in mind that the temperature and time value here are random and are not based on any real-life scenario, and they were provided to show you the concept of linear model.

Step-by-step explanation:

Answer:

150 of 400 can be written as:

150400To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100

150400 × 100100= (150 × 100400) × 1100 = 37.5100Therefore, the answer is 37.5%

If you are using a calculator, simply enter 150÷400×100 which will give you 37.5 as the answer.

Step-by-step explanation:

The probability that exactly 4 cars will enter the car wash in an hour is 0.195

Generally, This is a Poisson process, where the mean number of cars entering the car wash is 4 cars per hour. The probability of exactly 4 cars entering in an hour is given by the Poisson probability mass function:

P(X = 4) = (e^(-4) * 4^4) / 4!

where e is approximately 2.71828, and 4! is

4 * 3 * 2 * 1 = 24.

Plugging in the values, we get:

P(X = 4) = (2.71828^(-4) * 4^4) / 24

P(X = 4) =0.195

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