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The two column proof of the right angles to prove that ∠1 ≅ ∠2 is as shown below

From the given image showing two right angles, we can generate the two column proof to be as follows;

Statement 1: m∠1 = 90° and m∠2 = 90°

Reason 1: Given

Statement 2: ∠1 and ∠2 are right angles

Reason 2: Definition of right angles

Statement 3: m∠1 = ∠2

Reason 3: Transitive Property of Congruence

Statement 4: ∠1 ≅ ∠2

Reason 4: Definition of Congruence

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Answer: The general equation of a parabola with vertex (h,k) is y=a(x−h)2+k y = a ( x - h ) 2 + k . In this case we have (1,3) as the vertex (h,k) and (2,6) is a point (x,y) on the parabola. To find a , substitute the two points in y=a(x−h)2+k y = a ( x - h ) 2 + k .

Profit = Revenue - Cost

Revenue = Q * P

P = 100 - Q/20

C = 0.12Q + 10

Using substitution, we can say that:

Both equations used in the region of profit are linear equations because the exponent or degree used is only 1. Therefore, the region of profit is contained within two linear equations. (Option E)

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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Given the system of equations :

Add the equations to eliminate x :

divide both sides by 13 to find the value of y :

To find x , substitute with the value of y at the first equation :

So, the solution of the system is :

The solution can be written as the order pair (x,y):

Answer:

4044

Step-by-step explanation:

2000+2000= 4000

22+22= 44

4000+44= 4044

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

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.

If 98 out of 350 dog owners bought Pedigree Chum dog food so 28 percentage of the makers that prefer Pedigree Chum.

As per the question statement, In a survey of 350 dog owners and it was found that 98 bought Pedigree Chum dog food. We are supposed to find the percentage of the makers that prefer Pedigree Chum.

Given that, 98 out of 350 dog owners bought Pedigree Chum dog food

So the percentage can be calculated by the formula,

(98/350)*100 = 0.28*100 = 28%

Hence, 28% of the makers that prefer Pedigree Chum.

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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:  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:

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

Derivative of   [tex]f(x)= (\frac{cosx}{\sqrt{x} })=\frac{-2xsin(x)- cos(x)}{2x\sqrt{x} }[/tex]

How to calculate the derivative?

[tex]f(x) = \frac{cosx}{\sqrt{x} }[/tex]

The derivative is given by,

[tex]= > \frac{d}{dx} (\frac{cosx}{\sqrt{x} })[/tex]

Applying Quotient rule :

[tex](\frac{f}{g} )^{'} = \frac{f^{'}.g - g^{'}.f}{g^{2} } \\[/tex]

[tex]\frac{d}{dx} (\frac{cosx}{\sqrt{x} })=\frac{\frac{d}{dx}(cosx)\sqrt{x} - \frac{d}{dx} \sqrt{x}(cosx)}{(\sqrt{x} )^{2} } \\[/tex]

Considering derivatives in the numerator,

[tex]\frac{d}{dx} (cosx)= - sinx\\\\\frac{d}{dx} (\sqrt{x} )=\frac{1}{2\sqrt{x} }[/tex]

Now,

[tex]\frac{d}{dx} (\frac{cosx}{\sqrt{x} })=\frac{(-sinx)\sqrt{x} - \frac{1}{2\sqrt{x} } (cosx)}{(\sqrt{x} )^{2} } \\\\\text{ Taking LCM }\\\\=\frac{-2xsin(x)- cos(x)}{2x\sqrt{x} }[/tex]

What is a derivative?

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Apply square root to both sides of the equation:

Add 4 to both sides of the question:

The possible measures  for the other two angles will be that the sum of that angle must be 90 degree.

A triangle is considered to be 3-sided polygon in some cases  Each triangle has three sides and three angles, a few of which may be the same. The portion of the plane enclosed by the triangle is said the triangle interior, whereas the leftover portion is the exterior. Since we are  given that  one of the angles of the  given is a right angle, according to one of the rules of the triangle the sum of all the interior angles of a triangle should be 180, for the triangle ABC,

=>A+B+C = 180

=>A+90+C= 180

=>A+C= 180-90

=>A+C=90

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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:

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

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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Answer:

3/4

-2

Step-by-step explanation:

y = mx + b

Start at the y-intercept. It is (0, -2), so b = -2.

You have

y = mx - 2

Now start at (0, -2). We need to go up and right to the next easy-to-read point on the line. Go up 3 (rise). Go right 4 (run).

slope = rise/run = 3/4 = m.

Now you have

y = 3/4 x - 2

Answer:

See below

Step-by-step explanation:

Use two convenient integer coordinates to calcuate m= slope

I'll use   8,4  and  -4, -5      slope m =   (-5-4)/(-4-8)  = -9/-12 = 3/4

from the graph, the y-axis intercept (b )   is -2

slope - intercept form of a line is given by

y= mx + b

y = 3/4 x -2

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

Amanda and Diana given right solution set.

The solution set of given graph of inequality is,

x < 4.

Now, The solution of given created inequality,

Amanda:-  -3x + 5 > -7

       => -3x> -7 -5

       => - 3x > -12

        => 3x < 12

         => x < 4

So, it is correct

Briana:- 1/2 (2x - 4)> 2

       => 2x - 4  > 4

       => 2x > 8

       => x > 4

It is wrong

Courtney:-   -7x+8 > -3x + 24

      =>   -7x + 3x > 24 - 8

      => -4x > 16

      => 4x < -16

     => x < -4

It is wrong

Diana:- 9x -6 < 3x + 18

         => 9x - 3x < 18 + 6

         => 6x < 24

       => x < 4

So, it is right

Hence, Amanda and Diana given right solution set.

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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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the child would take 11.5 days (working 24 hours per day) to fill the swimming pool

an empty swimming pool is in the shape of a rectangle 10 meters long, 5 meters wide and 2 meters deep.

filling rate =2*10*π*(0.1)^2

or 0.002 π cubic meters per minute

or 0.12 cubic meters per hour

or 2.88 cubic meters per day

volume to fill = 100 cubic meters

how many days to fill ? × days= 2.88π × x=100

this implies x= 100/2.88π

   x= 11.05

the complete question is

an empty swimming pool is in the shape of a rectangle 10 meters long, 5 meters wide and 2 meters deep. a child starts to fill the pool using a saucepan with a circular base having a diameter of 20cm and a depth of 10 cm. the child can fill the saucepan and empty it into the pool twice per minute. how many days would it take the child (working 24 hours per day) to fill the pool? don’t round to the nearest day.

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Answer:

The equation is:

y = -3x + 3

The values needed to complete the relative frequency table in the context of this problem are as follows:

The relative frequency of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

To find the relative frequency for boys, we look at the frequency two-way table, and consider that out of 110 boys, 76 went to 4-year colleges and 34 went to two year colleges, hence the relative frequencies are found as follows:

For girls, we also look at the frequency two-way table, and consider that out of 121 girls, 83 went to 4-year colleges and 38 went to two year colleges, hence the relative frequencies are found as follows:

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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