2) AABCD ~ AEFGH
Use the information given to find the missing side of a figure
A)
3
x + 3
F)
x+4
E)
C)
5
B)
>H)

The equation of the parallel line is y = m(x-a) + b.

The equation of the perpendicular line is y = (-1/m)(x-a) + b.

Let the equation of the given line be y = mx + c.

Let the coordinates of the passing point be (a, b).

We need to find the equation of the parallel line.

The slope will remain the same.

y = mx + c'

The line passes through (a, b).

b = ma + c'

y = mx + (b-ma)

y = m(x-a) + b

We need to find the equation of the perpendicular line.

The slope will be the negative reciprocal.

y = (-1/m)x + c"

The line passes through (a, b).

b = (-1/m)a + c"

y = (-1/m)x + (b+a/m)

y = (-1/m)(x-a) + b

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If sequence of transformations that maps △ABC to △A^' B^' C^'.The sequence of transformation is 90 degrees counterclockwise rotation, followed by a vertical translation to the right by 2 unit. The ordered pair-rule for each are  (x,y) tends to (-x,-y)

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

Image is the original shape of the object and final shape ond position of the object is the preimage.

In the given figure,

original image is △ABC and  △A^' B^' C^' is the preimage.

Transformation includes changing the position of a shape.

The steps followed for transformation include rotating the image to 90 degrees counterclockwise rotation, later by a vertical translation to the right by 2 unit.

The ordered pair-rule for each are  (x,y) tends to (-x,-y)

Hence △ABC is the original image and  △A^' B^' C^' is the preimage and The ordered pair-rule for each are  (x,y) tends to (-x,-y)

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The equation of the line can be written  as, y = 9x/4 - 53/4.

Given :

9x -4y = 7 points given : (5, -2)

Writing the equation in the standard form of y=mx+b, we get:

4y = 9x -7

y = (9x/4)  - (7/4)

Thus, the slope of the given line is the coefficient of x which is equal to 9/4.

Let the equation of the line parallel to the given line be y=m1x+b1

Here m1 = 9/4

y = (9x/4) +b1

The line passes through (5,-2), hence the point satisfies the equation. Replacing the x and y coordinates with 5 and -2 respectively,

-2 = 45/4 + b1

-b1 = 45/4 +2

-b1 = 53/4

b1 = -53/4

Hence the equation of the line can be written as,

y = 9x/4 - 53/4.

The slope-intercept form of a  line is one of the most common forms used to represent the equation of a line. The slope-intercept formula can be used to find the equation of a line  given the slope of the  line and the y-intercept (the y-coordinate of the point where the line intersects the y-axis). The equation of a line is an equation that is satisfied by each point  on that line. There are several methods to find this equation of a  line given as

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Answers:

=========================================================

Explanation:

Since none of her sales exceed $2000, this means we can ignore the part that mentions "5% commission on any sales over $2,000".

h = number of hours

s = amount of sales between 0 and 2000

The equation is

m = 9.25h + 0.03s

where m is the amount of money made total for that day

9.25h is the amount of money at $9.25 an hour

The 0.03s represents 3% of the sales

-------------------------

For Monday, we plug in h = 6 hours and s = 325 dollars in sales

m = 9.25h + 0.03s

m = 9.25*6 + 0.03*325

m = 65.25

Lauren earned $65.25 on Monday

-------------------------

Repeat the same idea for Tuesday. This time we plug in h = 9 hours and her sales are s = 595 dollars.

m = 9.25h + 0.03s

m = 9.25*9 + 0.03*595

m = 101.10

She earned $101.10 for Tuesday.

Keep this process going until the entire week is filled out.

The answers are shown above to check your work.

-------------------------

Extra info:

If you added up the amounts earned for Monday through Sunday, then you should get $443.17 as the total amount earned for the entire week.

Divide this over the total number of hours worked (6+9+0+0+8+8+6 = 37 hours) and the effective hourly wage is 443.17/37 = 11.98 dollars an hour.

In a sense, the 3% commission adds an extra $2.73 an hour, since 11.98-9.25 = 2.73

Of course, this won't always be the case since the sales amount will fluctuate week to week. Also, there might be some cases in which Lauren is able to get over the $2000 sales threshold. But it gives a slight sense of what's going on.

Number Series questions

What is Number Series?

A series of numbers is called a number series. We must identify the laws that lead to the production of a number series in order to answer the questions about number series. The questions that might arise from these topics are as varied as these series themselves.

41) 44, 41, 38, 35, 32, 29, 26

In this we are subtracting 3 from each numbers

44 - 3 = 41

41 - 4 = 38

Similarly,

26 - 3 = 23

23 - 3 = 20

42) 6, 10, 14, 18, 22, 26, 30

In this we are adding 4 on each numbers

6 + 4= 10

10 + 4 = 14

Similarly,

30+4 = 34

34 + 4 = 38

43)34, 30, 26, 22, 18, 14, 10

In this we are subtracting 4 from each numbers

34 - 4 = 30

30 - 4 = 26

Similarly,

10 - 4 = 6

6 - 4 = 2

44) 2, 44, 4, 41, 6, 38, 8

In this we subtract the alternative number from three and add other alternative with 2 from each numbers

2 + 2 = 4

44 - 3 = 41

4 + 2 = 6

41 - 3 = 38

Similarly,

38 - 3 = 35

8 + 2 = 10

45) 32, 29, 26, 23, 20, 17, 14

In this we are subtracting 3 from each numbers

32 - 3 = 29

29 - 3 = 26

Similarly,

14 - 3 = 11

11 - 3 = 8

46) 14, 14, 26, 26, 38, 38, 50

In this the numbers are repeated and added by 12

14, 14 + 12 = 26

26, 26 + 12 = 38

Similarly,

50, 50 + 12 = 62

47) 8, 12, 9, 13, 10, 14, 11

In this the numbers are added by 1 alternatively

8 + 1= 9

12 + 1= 13

Similarly,

14 + 1 = 15

11 + 1= 12

48) 4, 7, 26, 10, 13, 20, 16

4 + 3 = 7

7 + 3 = 10

26 - 6 = 20

Similarly,

20 - 6 = 14

16 + 3 = 19

49) 3, 8, 10, 15, 17, 22, 24

In this the number are added alternatively with 5 and 2

3 + 5 = 8

8 + 2 = 10

Similarly,

24 + 5 = 29

29 + 2 = 31

50) 17, 14, 14, 11, 11, 8, 8

In this first subtraction of three and then repeat and again subtract three

17 - 3 = 14

14, 14 - 3 = 11

Similarly,

8 - 3 = 5

5, 5

51) 13, 29, 15, 26, 17, 23, 19

In this the alternative number are adding by 2 and subtracting by 3

13 + 2= 15

29 - 3= 26

Similarly,

23 - 3= 20

19 + 2= 21

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The range of the distance from A to C is greater than 3.3 feet and less than 29.1 feet. That is, 3.3 feet < AC < 29.1 feet

From the question, we are to determine the range of the distance between A and C

From one of the properties of a triangle, we have that the length of a side of a triangle is greater than the positive difference between the two other sides and is lesser than the sum of the two other sides of the triangle.

That is,

If AB, BC, and AC are the sides of a triangle,

Then,

AB > |BC - AC|

and

AB < BC + AC

From the given information,

AB = 16.2 feet

BC = 12.9 feet

∴ AC > 16.2 feet - 12.9 feet

AC > 3.3 feet; OR 3.3 feet < AC

and

AC < 16.2 feet + 12.9 feet

AC < 29.1 feet

Thus,

3.3 feet < AC < 29.1 feet

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Answer:

8.18

Step-by-step explanation:

Answer:

8.18

Step-by-step explanation:

8.50

-0.32=8.18

you subtract 0.32 from 8.5 meaning you are going to add a zero on 8.5 because the number that you are subtracting has two numbers after the decimal point

Answer:

the slope is 1/2

when you rewrite the equation in slope intercept form it will be

y= 1/2x +2

Answer:

if there are 12 cubes, there must be 3 rows of 4 since its a prism. 1288 square root is 35. something

Step-by-step explanation:

Answer:

Slope: 1/4

Step-by-step explanation:

The slope formula is rise/run.

Find the two points at which the line crosses.

Hope this helps :)

Tips: To find the slope, you can find the change in y over the change in x. Pick any two points on the line, for example: (0,3) and (4,4). To find the change in y, take the y value of one ordered pair and subtract it from the other. Then take this value and divide it by the difference of the corresponding x values.

ex:

4-3/4-0

slope: 1/4

You can also count the “rise” over “run” from (0,3). You can see that you move up 1 unit and right 4 units to get to (4,4), meaning the slope is 1/4 (rise 1, run 4)

Answer:

6x

Step-by-step explanation:

4 * 3x = 12x

12x / 2 = 6x

Answer:

ignoring the decimal. The order from greatest to least is 2, 4, 5, 6, and 8

If 12 out of 18 students prefer summer sports, then the fraction of students prefer winter sports is 33.33%

Total number of students = 18

The number of student prefer summer sports = 12

Then the number of student who prefer winter sports = Total number of students - The number of student prefer summer sports

= 18 - 12

= 6 students

The percentage is number that can be represented as the fraction of 100.

It is denoted by the percentage sign "%"

Then the fraction of students who prefer winter sports = (Number of student who prefer winter sports /Total number of students )×100

= (6/18) × 100

= 33.33%

Hence, if 12 out of 18 students prefer summer sports, then the fraction of students prefer winter sports is 33.33%

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Composition Functions

Composition functions are functions that combine to make a new function. We use the notation ◦ to denote a composition.

f ◦ g is the composition function that has f composed with g. Be aware though, f ◦ g is not

the same as g ◦ f. (This means that composition is not commutative).

f ◦ g ◦ h is the composition that composes f with g with h.

Since when we combine functions in composition to make a new function, sometimes we

define a function to be the composition of two smaller function. For instance,

h = f ◦ g (1)

h is the function that is made from f composed with g.

For regular functions such as, say:

f(x) = 3x

2 + 2x + 1 (2)

What do we end up doing with this function? All we do is plug in various values of x into

the function because that’s what the function accepts as inputs. So we would have different

outputs for each input:

f(−2) = 3(−2)2 + 2(−2) + 1 = 12 − 4 + 1 = 9 (3)

f(0) = 3(0)2 + 2(0) + 1 = 1 (4)

f(2) = 3(2)2 + 2(2) + 1 = 12 + 4 + 1 = 17 (5)

When composing functions we do the same thing but instead of plugging in numbers we are

plugging in whole functions. For example let’s look at the following problems below:

Examples

• Find (f ◦ g)(x) for f and g below.

f(x) = 3x + 4 (6)

g(x) = x

2 +

1

x

(7)

When composing functions we always read from right to left. So, first, we will plug x

into g (which is already done) and then g into f. What this means, is that wherever we

see an x in f we will plug in g. That is, g acts as our new variable and we have f(g(x)).

Answer:

The answer is -71.124

Step-by-step explanation:

Since there is a subtraction sign next to a negative it becomes addition.

so the equation becomes -95.004 + 23.88 which were going to flip around to 23.88 - 95.004

So,

     23.880

  -  95.004

-------------------

       -71 .124

The Solution.

Your company partially funds 85% of the total coverage. That gives

The percent of the insurance coverage that will be paid by you is

Thus, the correct answer is 15%.

Solution

Given the probability of event A happening is P(A) = 7/10

the probability of event A not happening P(A') = 1 - 7/10 = 3/10

The answer is 3/10

let us find the slope using 2 points

Therefore let us find y

The range of the given function f(x) = x² + 2 is found as 33/16.

For the given question.

The function is given as;

f(x) = x² + 2

The range of the function for the domain of 1/4.

From the definition of domain put x = 1/4 in the function, the range will be obtained.

f(1/4) = (1/4)² + 2

f(1/4) = 1/16 + 2

f(1/4) = 33/16

Thus, the range of the given function f(x) = x² + 2 is found as 33/16.

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Step-by-step explanation:

Answer

Explanation

AB is parallel to CD and then, there's a transversal that cuts across the two lines. We are given that Angle 3 = 120°

But we ca see from the figure that Angle 3 and Angle 2 lie on the same straight line.

And we know that the sum of angle on a straight line is 180°.

Hence,

(Angle 3) + (Angle 2) = 180°

120° + Angle 2 = 180°

Angle 2 = 180° - 120°

Angle 2 = 60°

Then again, we can see that AAA

Answer:

2x+8=15

2x=15-8

2x=7

divide both sides by the coefficient of x

x=7/2

x=3.5

Answer:

Express each number in scientific notation.

1) 0.0056 = 5.6 × 10^-3

3) 4,085 = 4.085 × 10³

5) 0.000796 = 7.96 × 10^-4

Standard and Scientific Notations

50,413 = 5.0413 × 10^4

11 = 1.1 × 10^1

11 = 1.1 × 10^1

2) 24,010 = 2.401 × 10^4

4) 0.017 = 1.7 × 10^-2

6) 952 = 9.52 × 10^2

8) 0.004 = 4 × 10^-3

Answer:

$370

Step-by-step explanation:

20m times 18.5per m

20x18.5=$370

Answer:

Rs370

Step-by-step explanation:

Here,

1m= Rs18.50

Therefore, 20m = 20*18.50

= 370

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Upper fence of the statistics below provide a summary of the distribution of heights of 200 randomly selected elementary students from across Pennsylvania (in inches) is 115.5.

The Upper Fence serves as the "upper limit" of the data, and any data that lies outside these restrictions is likely to be an anomaly. Q3 + 1.5 IQR, where Q3 is your third quartile and IQR is your interquartile range, can be used to compute the upper fence. An outlier is any value in your dataset that is higher than the upper fence.

Given Data

Min = 39

Q1 = 43

Median(IQR) = 45

Q3 = 48

Max = 56

Upper fence = Q₃ + (1.5(1QR)

Upper fence = 48 + 1.5(45)

Upper fence = 48 + 67.5

Upper fence = 115.5

Upper fence of the statistics below provide a summary of the distribution of heights of 200 randomly selected elementary students from across Pennsylvania (in inches) is 115.5.

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