Write a rule of reflection
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The series of rotations are : (x, y) -----> (y, -x) → (y, -x) ----> (x, y).

The total rotation is 360 degrees. So the figure is the original figure itself.

First a figure is rotated 270 degrees counterclockwise about the origin.

A 270 degree counterclockwise rotation is given by the co-ordinate transformation, (x, y) -----> (y, -x)

Then the figure is again rotated 90 degrees counterclockwise about the origin. A 90 degree counterclockwise rotation is given by, (x, y) -----> (-y, x)

So combining with the above transformation, the 90 degree counterclockwise rotation gives, (y, -x) ----> (x, y).

Thus the total rotation transformation is in turn, (x, y) ----> (x, y).

Thus the total rotation in counterclockwise direction about the origin is 360 degrees. So the final figure is the original figure itself.

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The equation which is useful to find the amount in gallons of water to the number of minutes since filling started is 25 + 11x therefore, it takes 5 minutes to have 80 gallons of water.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

The amount of water initially in the trough = 25 gallons.

The rate of adding water = 11 gallons per minute

Therefore, the total amount (A) of water in x minutes will be,

A = 25 + 11x

The number of minutes to have 80 gallons of water is,

80 = 25 + 11x

11x = 55

x = 5 minutes.

Hence "The equation which is useful to find the amount in gallons of water to the number of minutes since filling started is 25 + 11x therefore, it takes 5 minutes to have 80 gallons of water".

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Answer:

8.33

Step-by-step explanation:

He has to be at work by 10:30, but it takes 20 mins to walk

So, 10:30-20 minutes=10:10

We then look at the arrival time closest to this, which would mean he would arrive at 10.06.

trace this back the bus would gett him at 8:38, but its a 5min walk.

8:38-5 minutes+8.33

hope this helps :)

The horizontal asymptote is y = -2

The horizontal asymptote is an equation of the form y = k, for some constant k, is a straight line parallel to x-axis.

Horizontal asymptotes are found for rational functions of polynomials when x becomes extremely large, or, as x → ∞.

The function given is, f(x) = (-2x²+3x+5)/(x²+1)

Horizontal asymptote is given by,

y = [tex]\lim_{x \to \infty} \frac{-2x^2+3x+5}{x^2+1}[/tex]

   =  [tex]\lim_{x \to \infty} \frac{x^2(-2+\frac{3}{x} +\frac{5}{x^2}) }{x^2(1+\frac{1}{x^2}) }[/tex]

   =  [tex]\lim_{x \to \infty} \frac{(-2+\frac{3}{x} +\frac{5}{x^2}) }{(1+\frac{1}{x^2}) }[/tex]

   = -2

So the horizontal asymptote of f(x) is, y = -2

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Answer:

A) y = -2

Step-by-step explanation:

The rules to find the horizontal asymptote (HA) is shown below

Y = A if the numerator and denominator have same highest exponent for example

A^3

B^3

Y = 0 if the numerator have lower exponent and denominator have higher exponent for example

A^1

B^2

None HA if the numerator have higher exponent and denominator have lower exponent for example

A^2

B^1

And the equation shown in the question have same exponent so the answer is -2

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Answer:

x = 17

Step-by-step explanation:

Given angles are vertical angles and they have equal measurements.

We can write the following equation to find the value of x based on this information:

8x - 27 = 6x + 7 transfer like terms to the same side of the equation

8x - 6x = 27 + 7 add/subtract

2x = 34 divide both by 2

x = 17

Answer:

The equation is:

y = -3x + 3

Answer: 4:30

Step-by-step explanation:

Answer:

oh palak cl NC do off is sold em Ms do off do off dlc so off do off sum is sold arrowroot

Answer:

A number closer to 0 is generally less than a number more away from 0. When it comes to negative numbers the closer the number to 0, the greater it is.

Step-by-step explanation:

If you need further help please let me know.

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Step 1

Given;

Required; To write the equation in factored form

Step 2

Find the two factors that when added gives you x and when multiplied gives -20x²

Step 3

State the x-intercept

Hence, the x-intercepts are;

x=4

x=-5

A pair of shoes cost 102.23

Arithmetic: Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. The basic operations of math are addition, subtraction, multiplication and division. Also called higher arithmetic, theoretical arithmetic.

Cost of 3 pairs of shoes and a dress = 352.50

Cost of dress = 45.50

Cost of 3 pairs of shoes = Cost of 3 pairs of shoes and a dress - the cost of dress = 352.20 - 45.50

= 306.7

So, the cost of each pair of shoes will be = Cost of 3 pairs of shoes/Number of pairs bought

= 306.7/3

= 102.23

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The total number of questions that Fred answered incorrectly is 8.

From the information given, a perfect score on a test with 25 questions is 100 and each question is worth 4 points while Fred got a score of 68 on the test.

Therefore, let the number of questions that are got be x.

Based on the information given, this will be:

4 × x = 68

4x = 68

Divide

x = 68 / 4 = 17

The number of questions that he missed will be:

= Total questions - Correct answers.

= 25 - 17.

= 8

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[tex]\lim_{x \to \\pi } \frac{cosx + sin(2x)+1} {x^2 -\pi^2}[/tex] of the Correct option is (B) i.e.,  1/[tex]\pi[/tex]

Given:

[tex]\lim_{x \to \\pi } \frac{cosx + sin(2x)+1} {x^2 -\pi^2}[/tex]

To solve the above function:

Now, According to the question:

[tex]\lim_{x \to \\pi } \frac{cosx + sin(2x)+1} {x^2 -\pi^2}[/tex]

Differentiate with respect to x above function:

[tex]\lim_{x \to \\pi } \frac{-sinx + 2cosx} {2x}[/tex]

Substitute the value of limit in x tends [tex]\pi[/tex], it means x = [tex]\pi[/tex]

= [tex]\frac{2cos\pi - sin\pi }{2\pi }[/tex]

= 2/ [tex]2\pi[/tex]

= 1/[tex]\pi[/tex]

Hence, The Correct option is (B) i.e.,  1/[tex]\pi[/tex]

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Given

Principal = $2419

rate = 2.54%

time = 7 years

compounds quarterly

After 7 years, the amount deposit is now $2888.08, subtract by the principal amount to get the interest.

Therefore, the interest that he will earn after 7 years us $469.08.

Answer:

6x^2 - 11x + 3

Step-by-step explanation:

(fg)(x) is just multiplying f(x) and g(x)

This gives: (2x-3)(3x-1) = 6x^2 - 2x -9x - (3*(-1)) = 6x^2 -11x + 3

Answer: r=-26

Step-by-step explanation:

[tex]\displaystyle\\(5,r)\ \ \ \ (10,1)\ \ \ \ slope \ m=5\\\\\boxed {m=\frac{y_2-y_1}{x_2-x_1} }\\\\x_1=5\ \ \ \ \ x_2=10\ \ \ \ \ y_1=r\ \ \ \ y_2=-1\ \ \ \ \ m=5\\\\Hence,\\\\5=\frac{-1-r}{10-5} \\\\5=\frac{-1-r}{5}[/tex]

Multiply both parts of the equation by 5:

[tex]5(5)=-1-r\\\\25=-1-r\\\\25+r=-1-r+r\\\\25+r=-1\\\\25+r-25=-1-25\\\\r=-26[/tex]

Answer:

u= 18.37

Step-by-step explanation:

-7/8 u= -21

We have to isolate the variable. Since the -7 is being divided, you would take it to the other side and multiply.

8u= -21 * -7

8u= 147

u= 147/8

u= 18.37

Step 1: Write out the formula for Probability

Step 2: Writing out the data

The number of times R occur in the word LIBRARY is 2.

The total number of alphabets in the word LIBRARY is 7.

Therefore, number of events= 2

Total number of events= 7

Answer:

[tex]\textsf{C.} \quad r=\dfrac{27-P}{3P}[/tex]

Step-by-step explanation:

Given formula:

[tex]A=P(1+rt)[/tex]

Given values:

Substitute the given values into the given formula and solve for r:

[tex]\begin{aligned}A&=P(1+rt)\\\\\implies 27&=P(1+3r)\\\\\dfrac{27}{P}&=\dfrac{P(1+3r)}{P}\\\\\dfrac{27}{P}&=1+3r\\\\\dfrac{27}{P}-1&=1+3r-1\\\\\dfrac{27}{P}-1&=3r\\\\3r&=\dfrac{27}{P}-\dfrac{P}{P}\\\\3r&=\dfrac{27-P}{P}\\\\\dfrac{3r}{3}&=\dfrac{\dfrac{27-P}{P}}{3}\\\\r&=\dfrac{27-P}{3P}\end{aligned}[/tex]

Solution

[tex]\boxed{r=\dfrac{27-P}{3P}}[/tex]

Answer:

4044

Step-by-step explanation:

2000+2000= 4000

22+22= 44

4000+44= 4044

The complementary angle of the angle is 11.7 degrees

Angles are formed when two or more lines intersect. This in other words means that angles is the measure of space between the intersection of rays or lines

The measure of the angle is given as

Angle = 78.3 degrees

Complementary angles add up to 90 degrees

So, we have the other angle to be

Other angle = 90 - 78.3

Evaluate the difference

Other angle = 11.7

Hence, the other angle is 11.7

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The average pay-per-hour of the year for Elise will be 13.73 pounds.

From the information, in 2016 she earned £2100 and in 2017 she was awarded a 3% increase on her monthly salary.

Therefore, the new salary will be:

= 2100 + 3%(2100)

= 2100 + 63

= 2163

Now she worked for 42 hours per week for 45 weeks. This will be:

= 42 × 45

= 1890 hours

Therefore, the total earnings for the year will be:

= 2163 × 12 months

= 25956

The average pay-per-hour of the year will be:

= Total amount / Number of hours

= £25956 / 1890

= £13.73

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The solutions to the system of equations are x=5, z=1,y=-3

What is system of equations?

Given equations:

x+y+z=3

3x+(y/3)-2z=12

-5x-6y+3z=-4

Solving by using the substitution method:

[tex]\begin{bmatrix}x+y+z=3\\ 3x+\left(\frac{y}{3}\right)-2z=12\\ -5x-6y+3z=-4\end{bmatrix}[/tex]

Substitute x=3-y-z

[tex]\begin{bmatrix}3\left(3-y-z\right)+\frac{y}{3}-2z=12\\ -5\left(3-y-z\right)-6y+3z=-4\end{bmatrix}[/tex]

Substitute z={8y+9}/{15}

[tex]\begin{bmatrix}-y+8\left(-\frac{8y+9}{15}\right)-15=-4\end{bmatrix}[/tex]

simplify

[tex]\begin{bmatrix}\frac{-79y-72}{15}-15=-4\end{bmatrix}[/tex]

Substitute y=-3

[tex]z=-\frac{8\left(-3\right)+9}{15}[/tex]

z=1

For x=3-y-z

Substitute z=1,y=-3

x=3-(-3)-1

x=5

The solutions to the system of equations are:

x=5, z=1,y=-3

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Answer:  The slope of (-8, 18) and (-14, -3) would be 3.5.

Step-by-step explanation:  By using a simple calculator, specifically the TI-84 Plus CE, you can put the points you mentioned in stat and it’ll give you an equation based on those points.  The equation I got was y = 3.5x + 46.  The number attached to the X is your slope.

Answer: 48

Step-by-step explanation:
Convert 40% to a decimal = 0.4
Multiply 0.4 x 120 = 48

Answer:

48

Step-by-step explanation:

40\100×120

=48

( fourth divided by one hundred multiplied by one hundred and twenty is equal to 48)

The percentage of the people surveyed that arrive at their office after 7am is 6.7%.

The percentage of the people surveyed that arrive at their office after 7:59 am is 64%

From the information, Miranda did a survey of what time people get to their office on Monday morning and the table shows her results.

The number of people that arrived before 7.59am is 15.

The total number of people surveyed will be:

= 15 + 39 + 75 + 21

= 150

The percentage of the people surveyed arrive at their office before 7 am will be:

= 10 / 150

= 6.7%

The percentage of the people surveyed that arrive at their office after 7:59 am will be:

= (75 + 21) / 150.

= 96/150

= 0.64

= 64%

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Answer:

the number of people is 15 so you would do 15/150=10percent

b) 66 percent

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 1) and (x₂, y₂ ) = (1, 7) ← 2 points on the line

m = [tex]\frac{7-1}{1-(-2)}[/tex] = [tex]\frac{6}{1+2}[/tex] = [tex]\frac{6}{3}[/tex] = 2

use either of the 2 points on the line

using (- 2, 1 ) , then

y - 1 = 2(x - (- 2) ) , that is

y - 1 = 2(x + 2) ← equation in point- slope form