Help-Khan academy geometry-mapping shapes

Help-Khan Academy Geometry-mapping Shapes

Answers

Answer 1

The sequence of transformations that maps triangle DEF into triangle ABC is:

A 90º rotation about point F, then a translation along the directed line segment FC.

What are transformations on the graph of a function?

Transformations in the graph of a function are classified as follows:

Translation: Translation left/right or down/up, changing just the position.Reflections: Over one of the axes or over a line, changing just the orientation.Rotations: Over a degree measure, changing the orientation or the inclination.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor, changing the side lengths of the figure.

For this problem, we have that:

The orientation was changed, hence first it underwent a rotation.Then the position changed, hence after the rotation it underwent a translation.

Thus the correct sequence is given by Sequence B.

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Related Questions

Bob fenced in his backyard. the perimeter of the yard is 22 feet, and the length of his yard is 5 feet. use the perimeter formula to find the width of the rectangular yard in inches: p = 2l 2w. (1 foot = 12 inches)

Answers

The width of yard in inches is 72 inches.

We are given the perimeter and length of yard. We are also given the perimeter of the rectangle, which is as follows -

P = 2l 2w

Rewriting this formula in simplified form, by taking 2 common from both the values  -

P = 2×(l + w), where P refers to perimeter, l refers to length and w refers to width.

Now, keep the values in formula to find the width of rectangle -

22 = 2 × (5 + w)

Shifting 2 to other side of equation and performing division

5 + w = 22÷2

5 + w = 11

Shifting 5 to other side of equation and performing subtraction to find the value of width

w = 11 - 5

w = 6 feet

Now, we need the width in inches. We are given -

1 foot = 12 inches

So, 6 feet = 12 × 6

6 feet = 72 inches

Hence, the width of rectangular yard is 72 inches.

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Answer:

72in

Step-by-step explanation:

Does 44,555 and 45,555 round to 50,000?

Answers

45,555 does, but the other one doesn't.

94.
Scale: 1 in. = 3 ft
The diagram above shows a plan for a community garden. The plan is drawn on a grid made up of 1-inch squares. About how many square yards will be used to grow herbs?

Answers

Answer:

About 9 sq yd

Step-by-step explanation:

First, you know that 3ft. = 1 yd. That means each square is 1 sq yd. The length of the herb garden is 6 squares, while the width is about 1.5 squares. If you multiply those two to find the area, then you get about 9 square yards.

suppose you have an argument that has three premises, all of which are true, and a true conclusion. if so, then the argument must be

Answers

The conclusion might be accurate or inaccurate.

The conclusion could be true or false if an argument has some true premises and some false premises and is valid. You only know that the premises cannot both be true and the conclusion must be false because the argument is sound. But the incorrect premises already rule out the possibility of possessing this set of truth values (that is, you cannot have all true premises). As a result, the argument's validity is unaffected whether the conclusion is true or untrue. As a result, the conclusion of an argument that contains only false premises may or may not be true.

Can an argument have all true premises and a false conclusion?

TRUE. A valid argument cannot, by definition, have a false conclusion and all true premises.

Therefore, a valid argument must have an erroneous premise if it has a false conclusion.

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Please help fast :(

Answers

Answer:

1/2

1/4

1/4

0/16

2 times

Step-by-step explanation:

THERE ARE 16 SQUARES TOTAL

8 triangles: 8/16 = 1/2

4 stars: 4/16 = 1/4

4 empty spaces: 4/16 = 1/4

0 circles = 0/16

8*1/4 is 2, so 2 times.

a line segment has (x1, y1) as one endpoint and (xm, ym) as its midpoint. find the other endpoint (x2, y2) of the line segment in terms of x1, y1, xm, and ym. use the result to find the coordinates of the endpoint (x2, y2) of each line segment with the given endpoint (x1, y1) and endpoint (xm, ym).

Answers

The coordinates are:

For the first line, coordinates are (3, 7).For the second line, the coordinates are (12, 0).

What are coordinates?A coordinate system in geometry is a system that uses one or more numbers, or coordinates, to determine the position of points or other geometric elements on a manifold such as Euclidean space.

To find the coordinates:

In Analytical Geometry, the midpoint of a line is calculated as the mean of two points, as follows:

[tex]$$x_m=\frac{x_1+x_2}{2}, y_m=\frac{y_1+y_2}{2}$$[/tex]

Each segment has two endpoints and two midpoints, which are as follows:

(1,-9), as well as its midpoint (2,-1)(-2,18), as well as its midpoint (5,9)

We must be cautious not to add the wrong coordinates.

In the first line A:

[tex]$$\begin{aligned}&2=\frac{1+x_2}{2} \\&4=1+x_2 \\&4-1=-1+1+x_2 \\&x_2=3 \\&-1=\frac{y_2-9}{2} \\&-2=y_2-9 \\&+2-2=y_2-9+2 \\&y_2=-7\end{aligned}$$[/tex]

So (3,7) is the other endpoint where the segment begins (1,-9).

The endpoint of the second line b at (-2,18) and its midpoint (5,9).

[tex]$$\begin{aligned}&5=\frac{-2+x_2}{2} \\&10=-2+x_2 \\&+2+10=+2-2+x_2 \\&x_2=12 \\&9=\frac{18+y_2}{2} \\&18=18+y_2 \\&-18+18=-18+18+y_2 \\&y_2=0\end{aligned}$$[/tex]

So, (12,0) is the opposite endpoint.

Therefore, the coordinates are:

For the first line, coordinates are (3, 7).For the second line, the coordinates are (12, 0).

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The correct question is given below:

A line segment has (x1, y1) as one endpoint and (xm, ym) as its midpoint. Find the other endpoint (x2, y2) of the line segment in terms of x1, y1, xm, and ym. Use the result to find the coordinates of the endpoint of a line segment when the coordinates of the other endpoint and midpoint are, respectively, (1, −9), (2, −1) and (−2, 18), (5, 9).

Consider the arithmetic sequence (87, 83, 79,75...)
A. Find common difference, d
B. Find explicit formula

Answers

Answer:

see explanation

Step-by-step explanation:

A

the common difference d of the arithmetic sequence is

d = a₂ - a₁ = 79 - 83 = - 4

B

the explicit formula of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 83 and d = - 4 , then

[tex]a_{n}[/tex] = 83 - 4(n - 1) = 83 - 4n + 4 = 87 - 4n

4|2x + 5|-7≤9

How would you solve this?

Answers

solate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:

9
2

x


1
2
-
9
2

x

-
1
2
Interval Notation:
[

9
2
,

1
2
]

Answer:

- [tex]\frac{9}{2}[/tex] ≤ x ≤ - [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

inequalities of the type | x | ≤ a , have solutions of the form

- a ≤ x ≤ a , then

4 | 2x + 5 | - 7 ≤ 9 ( add 7 to both sides )

4  | 2x + 5 | ≤ 16 ( divide both sides by 4 )

| 2x + 5 | ≤ 4 , so

- 4 ≤ 2x + 5 ≤ 4 ( subtract 5 from each interval )

- 9 ≤ 2x ≤ - 1 ( divide each interval by 2 )

- [tex]\frac{9}{2}[/tex] ≤ x ≤ - [tex]\frac{1}{2}[/tex]

Solve two thirds times v plus 6 equals one third times v minus 2.

v equals negative eight thirds
v equals eight thirds
v = −24
v = 24

Answers

The value of v using the equation ( 2v/3 ) + 6 = ( v/3 ) - 2 is v = - 24.

Two-thirds of anything is an amount that is two out of three equal parts of it. Similarly, one-third of something is an amount that is one out of three equal parts of it.

Now, we have

Two-thirds times v plus 6 equals one-third times v minus 2.

Hence, when the above statement is expressed as an equation we get:

Two third of v + 6 = one third of v - 2

2/3 × v + 6  = 1/3 × v - 2

( 2v/3 ) + 6 = ( v/3 ) - 2

Adding 2 on both sides of the equation,

( 2v/3 ) + 6 + 2 = ( v/3 ) - 2 + 2

( 2v/3 ) + 8 = ( v/3 )

Subtracting 2v/3 from both sides of the equation,

2v/3 + 8 - 2v/3 = v/3 - 2v/3

8 = ( v - 2v )/3

- v/3 = 8/1

By cross multiplication,

- v × 1 = 8 × 3

- v = 24

Multiplying each side by - 1,

v = - 24

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9x10^4 + 9x10^2 ??

add

Answers

Answer:

90900

Step-by-step explanation:

Answer:

9.09 x 10*4.

Step-by-step explanation:

9x10^4 + 9x10^2

= 90000 + 900

= 90900

= 9.09 x 10*4.

Brian is throwing a party. He needs 3/4 of a pound of hamburger meat for each person at the party. If 12 people are coming to the party, how many pounds of hamburger meat will Brian need to buy?

Answers

9 pounds of hamburger meat will be needed by Brian.

We are given value for one unit. The calculation is required for more than one units, hence, multiplication will be performed.

As per the given information, amount of hamburger meat required for one person is = 3/4 pound

Amount of hamburger meat required for 12 people = (3/4) × 12

Performing division to find the amount of hamburger meat required for 12 people

Amount of hamburger meat required for 12 people = 3 × 3

Performing multiplication to find the amount of hamburger meat required for 12 people

Amount of hamburger meat required for 12 people = 9 pounds

Therefore, Brain needs to buy 9 pounds of hamburger meat.

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Which liner function represents the line given by the point-slope equation y + 7 = -2/3(x + 6)?

Answers

the linear function that represents the given line is:

y = f(x) = (-2/3)*x - 11

Which linear function represents the given line?

Here we have a line given by a point-slope equation:

y + 7 = (-2/3)*(x + 6)

And we would want to get a function of the form y = f(x). So the first thing we need to do is isolate y in one side of the above equation. If we subtract 7 in both sides we will get:

y = (-2/3)*(x + 6) - 7

Expanding that:

y = (-2/3)*x + (-2/3)*6 - 7

y = -(2/3)*x - 4 - 7

y = (-2/3)*x - 11

Then the linear function that represents the given line is:

y = f(x) = (-2/3)*x - 11

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does the ratio 2/5 to 1/3 has a unit rate of 2/15

Answers

The statement that the ratio 2/5 to 1/3 has a unit rate of 2/15 is; True

How to find the unit rate?

A unit rate is defined as a rate for one of something. This can be written as a ratio with a denominator of one.

For example, if you ran 50 meters in 10 seconds, you ran an average 5 meters in 1 second. Both of the ratios, 50 meters in 10 seconds and 5 meters in 1 second, are rates, but the 5 meters in 1 second is a unit rate.

We are given the ratio 2/5 to 1/3. Now, this can be expressed as;

(2/5)/(1/3) = 2/5 * 1/3 = 2/15

Thus, this corresponds with the given unit rate of 2/15.

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6. A triangle has a perimeter of exactly 24 units. Which of the following could be the vertices of the triangle
(-1,3), (2, -1),(-1,-1)
(6, 0), (6, 7), (0,7)
(-1,-1), (-6, -13), (-9,-9)
(-3,-4), (3,-4), (3,4)

Answers

Answer:

Question:

A triangle has a perimeter of exactly 24 units. Which of the following could be the vertices of the triangle?

A.) (-1,3),(2,-1),(-1,-1)

B.) (6,0),(6,7)(0,7)

C.) (-1,-1),(-6,-13),(-9,-9)

D.) (-3,-4),(3,-4),(3,4)

Triangle and Coordinate Geometry

As the name suggests 'tri-angle' means it has three angles that are formed only when three sides are joined together.

So the triangle is a planner geometry that has three sides and three interior angles. In a triangle, the sum of all three interior angles is always

180

.

If a triangle

A

B

C

has the sides

a

,

b

,

and

c

, then

The perimeter of the triangle:

P

=

a

+

b

+

c

In coordinate geometry, the distance between two points:

D

=

(

x

2

x

1

)

2

+

(

y

2

y

1

)

2

Answer and Explanation:

Given:

The perimeter of the triangle is

24

units.

There are four options with different-different vertices and one of them is correct, so we choose one option randomly and check it for the given perimeter.

Firstly we chose the option

D

:

The vertices of the triangle are:

P

(

3

,

4

)

,

Q

(

3

,

4

)

,

and

R

(

3

,

4

)

Using the distance formula:

D

=

(

x

2

x

1

)

2

+

(

y

2

y

1

)

2

So

P

Q

=

(

3

+

3

)

2

+

(

4

+

4

)

2

=

6

2

+

0

=

6

u

n

i

t

And

Q

R

=

(

3

3

)

2

+

(

4

+

4

)

2

=

0

+

8

2

=

8

u

n

i

t

And

P

R

=

(

3

+

3

)

2

+

(

4

+

4

)

2

=

6

2

+

8

2

=

36

+

64

=

100

=

10

u

n

i

t

So

The perimeter of the triangle

P

Q

R

is:

Perimeter

=

P

Q

+

Q

R

+

P

R

=

6

+

8

+

10

=

24

u

n

i

t

s

Step-by-step explanation:

how many time does 13 go into 26

Answers

Answer:

2

Step-by-step explanation:

13+13=26

Answer:

Twice

Step-by-step explanation:

13+13=26

This list gives information about a video collection.
Study the list carefully. Then, use the drop-down menu to complete the statement
below about the list.
It
make sense to add the items on the inventory because these quantities
have meaning for the inventory.
The number 299
Romance:
74
Comedy: 123
Action: 102
Total: 299
CLEAR
be expressed using the same unit.
CHECK

Answers

Answer:

oh no I lost the Answer is was 18369

Answer:

Step-by-step explanation:

a major disadvantage of correlations is that they cannot make a(n) blank statement. multiple choice question.

Answers

A major disadvantage of correlations is that they cannot make a cause-and-effect statement.

What are correlations?

Correlations are statistical measures that describe the size and direction of a relationship between variables.

Correlations are expressed as numbers. Correlations establish that relationships exist but do not explain if the change in one variable is caused by the change in another variable's value.

The disadvantages of correlations include:

There are no causes and effects.Results can find no inference.The strength of the relationship is not explained.There is the possibility of a confounding factor.

Thus, a major disadvantage of correlations is that they cannot make a cause-and-effect statement.

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If a first integer is represented by the variable x, then which of the following would be the next four consecutive odd integers?
Choose the correct answer below.
A. x+1, x+2, x+3, x+4
B. x+2, x+4, x+6, x+8
Points: 0 of 1
C. x, x+2, x+4, x+6
OD. x+1, x+3, x+ 5, x+7

Answers

the next four consecutive odd integers will be given by the option (B) x + 2, x + 4, x + 6 and x + 8.

We are given that:

The first integer is represented by the variable x.

We need to find the next four consecutive odd integers.

We know that the difference between the two consecutive odd integers will always be 2.

So, this means, we can always get the next odd integers by adding 2 to the previous one.

So, we get that:

x + 2

x + 2 + 2 = x + 4

x + 4 + 2 = x + 6

x + 6 + 2 = x + 8

Therefore, we get that, the next four consecutive odd integers will be given by the option (B) x + 2, x + 4, x + 6 and x + 8.

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The slope for a wheelchair ramp for a home has to be 1/2.

If the vertical distance from the ground to the door bottom is 3 ft, find the distance the ramp has to extend from the home in order to comply with the needed slope.

Answers

In order to comply with the required slope, the ramp must extend 36 ft from the house.

What do we mean by Distance?Distance is a mathematical or qualitative measure of the distance between two objects or points. Distance can refer to a physical length or an estimate based on other criteria in physics or everyday usage (e.g. "two counties over").

So, to find the distance:

The formula of slope:

m = change in vertical height/change in horizontal height

Vertical distance is now given as 3 ft.

To conform to the given slope, this means that:

1/12 = 3/x

Cross multiply:

x = 3 × 12x = 36 ft

Therefore, in order to comply with the required slope, the ramp must extend 36 ft from the house.

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A city park measures 7/8 mile wide by 3/4 mile long. What is the area of the park?

Answers

Area = length x width

Length = 3/4 mile = 0.75
Width = 7/8 mile = 0.875

0.75 x 0.875 = 0.66 miles²

.
Nickels: Someone offers to double the amount of money you have every
day for 1 month (30 days). You have 1 nickel. On the first day, you will
have 2 nickels worth $.10. On the second day, you will have 4 nickels
worth $.20. How much money will you have on the 30th day?

Answers

Answer: you will have $53,687,091.2 dollars once you reach the thirty-day milestone.

Step-by-step explanation:

Multiply 0.05 by 2 thirty times to get your answer.

0.05 * 2^30

0.05 * 1,073,741,824 = $53,687,091.2 or 10,737,418.24 nickels.

A restaurant had 9 days to sell 56 gallons of ice cream before it expired. How much should they sell each day?

5 gallons
5 gallons

6 6/4 gallons
6 6/4 gallons

6 1/2 gallons
6 1/2 gallons

6 2/9 gallons

Answers

Answer:

6 2/9

Step-by-step explanation:

56 divided by 9 is 6.22 and 2/9 is .22

The restaurant should sell 6 2/9 gallons of ice cream each day. Because,
56/9 = 6.22222222222222222…..
And,6.2222….. is equal to 6 2/9

If f(x)=-2x+3then f(3)-f(4)

Answers

I am smart math tutor

if asked to evaluate the following expression (5x+25) for x=3,5,-5,0 how many different substitutions will you make?

Answers

we did 4 different substitutions to evaluate the expression in 4 different values of x.

when x = 3 we get 40when x = 5 we get 50when x = -5 we get 0when x = 0 we get 25.

How to evaluate an expression?

Here we have a linear expression that depends on the variable x, and can be written as:

(5x + 25)

And we want to evaluate this in some different values of x. This just means that we need to replace the value of x by different numbers.

First, let's use x = 3

This will give:

(5*3 + 25) = 15 + 25 = 40

Then we use x = 5

(5*5 + 25) = 25 + 25  = 50

Then we use x = -5

(5*-5 + 25) = -25 + 25  =0

Finally, we evaluate in x = 0.

(5*0 + 25) = 0 + 25 = 25

So we did 4 different substitutions to evaluate the expression in 4 different values of x.

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#11 i Solve -14>w+3 or 3w > -27 Solution: or​

Answers

The values of the inequalities will be:

1. -14>w+3 = w < -17

2. 3w > -27 = w > -9

How to explain the inequality?

It should be noted that an inequality simply means the expression that illustrates that the variables aren't equal. This can be used by uinng less than, greater than, etc.

The inequalities will be:

-14>w+3

Collect like terms

-14 - 3 > w

-17 > w

w < -17

3w > -27

Divide both side by 3

3w/ 3 > -27/3

w > -9

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What is the percentage efficiency of a motor that does 60J of work from 240J of electrical energy?

Answers

Answer:

25% is the correct answer

How can you adjust both numbers and use compensation to find $7.99 + $19.99 mentally?

Answers

The adjustment of both numbers and using compensation to find $7.99 + $19.99 mentally is $27.98

How to calculate the value?

It should be noted that compensation is the mental strategy in Mathematics used for addition by adjusting one of rte addends.

It should be noted that $7.99 is almost the same as $8. It should be noted that $19.99 is the same as $20. This is the compensation or the numbers.

Therefore, the addition of the numbers $7.99 + $19.99 will be:

= $7.99 + $19.99

= $27.98

In conclusion, the answer is $27.98.

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find the percentage if the denominators are not the factors of 100

Answers

Answer:

external factors that impact negatively on lifestyle choices namely.unsafe road use

Sue's science class is competing to see who can build the tallest tower. Each group of students gets 10 newspapers and 2 meters of tape. Sue's group decides to roll up each of their newspapers. Then, they tape each roll with 125 millimeters of tape. How many meters of tape do they have left?

Answers

The amount of tape left in metres is 0.75 metres.

How to find the length of the tape left in metres?

Each group of students gets 10 newspapers and 2 meters of tape.  

This means the total length of tape for each group of student is as follows:

length of tape for each group = 2 metres

Sue's group decides to roll up each of their newspapers. Then, they tape each roll with 125 millimetres of tape.

Each roll of the 10 newspaper was taped with 125 mm tape.

Hence,

total taping = 125 × 10

total taping = 1250 mm

Let's convert from millimetres to metres.

Therefore,

1 mm = 0.001 m

1250 mm = ?

cross multiply

amount of taping done by Sue's group = 1.25 m

Therefore,

amount of meters of tape left = 2 - 1.25 = 0.75 metres

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Solve for x in the diagram below

Answers

The value of x will be 34°

Given that

(x+12)°+100°+x° are forming linear pair

Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°. Such angles are also known as supplementary angles.

As mentioned, adjacent angles are angles that are next to each other. If you are sitting next to someone in class or on the bus, you could say that you are adjacent to them. More specifically, adjacent angles share a vertex and have a common side.

(x+12)°+100°+x°= 180°

⇒ x+ 12+ 100+x = 180°

⇒ 2x+112 = 180°

⇒ 2x = 180- 112

⇒ 2x = 68

⇒ x= 68/2

⇒ x= 34

For verification we will put value of x

(34+12)°+100°+34°

⇒ 46°+100°+34°

⇒146°+34°

⇒ 180°

So here we can see that by putting value of x we are getting the sum of 180°

Therefore value of x is 34

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helpppp plssssssssss According to the segment, what is the foundation of police authority? Which founding father contributed the least to American independence? What is the difference between -21 and -8? smith, a. (2009). emotional empathy in autism spectrum conditions: weak, intact or heightened? journal of autism developmental disorder, 39, 1747-1748 Animals play many different parts in myths and legends. True or False Multiply. 6/7 4/15A. 8/35B. 14/45C. 5/11D. I don't know CRAFT FAIR Kylie is going to try to sell two of her oil paintings at the local craft fair. She is hoping to earn at least $400.a. Write the inequality that represents the constraint of the situation, where x is the price of the first oil painting, and y is the price of the second.b. Graph the inequality that represents the constraint on the sale. mayas penny bank is 1/2 full. after she adds 120 pennies,it is 2/3 full. How,many pennis can mayas bank hold? When it comes to getting a job or position and you don't let anything stand in your way that's called what? NEED HELP ASAPPPPWhich of the following statements is TRUE? A. Proper exercise equipment is always the most expensive B. Running shoes are the best shoe to buy no matter what type of exercising you are doing C. Clothes made from lightweight, breathable fabrics are appropriate for exercising D. All of the above WHAT THINGS MIGHT CAUSE DISPUTES IN A PARTNERSHIP? Scott is experiencing gallstones. The gall stones have caused cholecystities (inflammation of his gallbladder). Scotts condition affects which body system? 5- b = 2t Solve for t or f I give extra points Dara and Lexi were working on a project for class. They had to create aposter that persuaded other students to take action about climate.change. Lexi was taking a long time to come up with the headings foreach section of the poster. Dara was growing irritated.Finally, Dara lost her patience. "Can you really not think of what to say?"she yelled. I've been waiting 10 minutes!""Actually, Dara, no, Lexi explained quietly. "I was just wondering.whether each section should start with a letter to spell out the word"action" when they are all put together.""Oh," said Dara. "That is a good idea. Sorry,""And I should remind you that I was patient a moment ago while youspent 10 minutes trying to make up your mind over what color markerto use.""O.K., that's a fair point," said Lexi. "Sorry"What are two themes of this text?OA. Often the flaws that annoy us are the ones we also have, and weshould strive to give others the benefit of the doubt.OB. The best decisions are those made quickly, and your style is asimportant as your message.C. When you waste time, you lose track of what's important, andfriendship involves being tolerant of others' faults.D. Being kind is more important than being correct, and patience is agood quality to have+ Not sure if its right can someone make sure Women think people are important. Men, are more interested in getting the machine rights?are you agree and why? Students have a small steel ball and a large steel ball, and they have a short ramp and a tall ramp.The students want to find out if a ball's size affects how far it can roll. They also want to find out if the height of the ramp affects how far the ball can roll.They do the following experiment: (second image)The students finish conducting their tests and conclude that using a taller ramp and a larger ball will make the ball roll further. Is their conclusion based on a reliable experiment?A.Yes, because they used the same color balls.B.No. They did not do an additional test to compare the results using the short ramp.C.No. The small ball should have been pushed with more force.D.Yes, because they changed the height of the ramp. The inventor of a new game believes that the variable cost for producing the game is $0.50 per unit and the fixed costs are $4,300. the inventor sells each game for $1.89. let x be the number of games produced. (a) the total cost for a business is the sum of the variable cost and the fixed costs. write the total cost c (in dollars) as a function of the number of games produced. c = (b) write the average cost (in dollars) per unit c = c x as a function of x. c = If x varies directly as y and when x = 5, y = 20. Find the relationship between x and y.