A. ∠F≅ ∠B and AC ≅DC
B. BC≅ FC
C. Nothing else is needed to use the HL theorem.

The image by rotation of the triangle ABC with vertices A(x, y) = (8, - 9), B(x, y) = (5, - 4), C(x, y) = (7, - 1) is represented by vertices A'(x, y) = (- 9, - 8), B'(x, y) = (- 4, - 5) and C'(x, y) = (- 1, - 7). The transformation rule is R'(x, y) = (x · cos θ - y · sin θ, x · sin θ + y · cos θ).

In this problem we have the case of triangle set on a Cartesian plane and that must be rotated 90° clockwise, the image can be found by using the following transformation rule:

R'(x, y) = (x · cos θ - y · sin θ, x · sin θ + y · cos θ)

Where:

x, y - Coordinates of the original point.

θ - Angle of rotation, in degrees.

If we know that A(x, y) = (8, - 9), B(x, y) = (5, - 4), C(x, y) = (7, - 1) and θ = - 90°, then the image of the triangle is:

A'(x, y) = (8 · cos (- 90°) - (- 9) · sin (- 90°), 8 · sin (- 90°) + (- 9) · cos (- 90°))

A'(x, y) = (- 9, - 8)

B'(x, y) = (5 · cos (- 90°) - (- 4) · sin (- 90°), 5 · sin (- 90°) + (- 4) · cos (- 90°))

B'(x, y) = (- 4, - 5)

C'(x, y) = (7 · cos (- 90°) - (- 1) · sin (- 90°), 7 · sin (- 90°) + (- 1) · cos (- 90°))

C'(x, y) = (- 1, - 7)

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The equation of the line in slope intercept form that passes through the point (3,4) and is parallel to the line represented by y=3x−2 is y = 3x - 5.  

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the line that passes through the point (3,4) and is parallel to the line represented by y = 3x − 2.

Parallel line have the same slope. Therefore, the slope of the line is 3.

Let's find the y-intercept using (3, 4).

y = 3x + b

4 = 3(3) + b

4 - 9 = b

b = -5

Therefore, the equation is y = 3x - 5

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1. In 60 weeks, both Zac and Jon will earn the same amount, equating to their different earnings.

2. The student's claim that the solution to the equation 200 + 20w = -100 + 25w is w = 50 is false as the solution shows that w = 60.

3. The two correct justifications for the given steps used in solving w are:

The fixed earnings of Zac = $200

Zac's earnings per week = $20

The total earnings of Zac in w weeks = 200 + 20w

Jon's fixed debt so far = $100

Jon's earnings per week = $25

The total earnings of Jon in w weeks = -100 + 25w

To determine the weeks when the total earnings of Zac and Jon will be equal, we can equate the two expressions above as follows and solve for w:

200 + 20w = -100 + 25w

20w - 25w = -300

-5w = - 300

w = -300/-5

w = 60

Thus, we can conclude that in 60 weeks, the earnings of Zac and Jon will become equal.

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Answer:

18 miles

Step-by-step explanation:

To determine how many miles Brent can travel, we need to first determine the cost of the base fare and then subtract that from the total amount of money Brent has. The base fare is $1.23, so we can subtract that from the total amount of money Brent has to find out how much money he has left for the per-mile charge:

14.91 - 1.23 = 13.68

Now that we know how much money Brent has left for the per-mile charge, we can divide that amount by the per-mile charge to find out how many miles Brent can travel:

13.68 / 0.76 = 18 miles

Therefore, Brent can travel a maximum of 18 miles given the amount of money he has available to spend on the ride.

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} \implies \cfrac{-4}{2 +1} \implies \cfrac{ -4 }{ 3 } \implies - \cfrac{ 4 }{ 3 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{- \cfrac{ 4 }{ 3 }}(x-\stackrel{x_1}{(-1)}) \implies y -3 = - \cfrac{ 4 }{ 3 } ( x +1) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y-3)=3\left( - \cfrac{ 4 }{ 3 } ( x +1) \right)}\implies 3y-9=-4(x+1)\implies 3y-9=-4x-4 \\\\\\ 3y=-4x+5\implies \text{\LARGE 4}x+3y=5[/tex]

Answer:

15

Step-by-step explanation:

Answer:

No answer

Step-by-step explanation:

Answer:

x3+y3+z3=k

Let x=a, y=b, and z=c.

Then, a3+b3+c3=k

This is a Diophantine equation, which has no general solution. To find particular solutions, we must use trial and error.

Step-by-step explanation:

Using quicksort with median-of-three partitioning and a cutoff of 3. we will get  1, 1, 3, 2, 3, 4, 5, 5, 5, 6, 9.

The Original input is 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5.

We get on the basis of the median after sorting the first, middle, and final elements 3, 1, 4, 1, 5, 5, 2, 6, 5, 3, 9.

As a result, we select pivot = 5. It also provides after the pivot is removed or hidden 3, 1, 4, 1, 5, 3, 2, 6, 5, 5, 9.

It is necessary to swap the two fives. However, in the subsequent swap, p and q cross. turn is traded back with the p:

3, 1, 4, 1, 5, 3, 2, 5, 5, 6, 9

It is now time to quickly sort the first eight elements of the array in a recursive fashion:3, 1, 4, 1, 5, 3, 2, 5,

and after sorting the three relevant elements, we get 1, 1, 4, 3, 5, 3, 2, 5.

As a result, we select the pivot value of 3, and after hiding this pivot once more, we get:

1, 1, 4, 2, 5, 3, 3, 5

A switch takes place between 4 and 3: 1, 1, 3, 2, 5, 4, 3, 5

Now, because the next swap crosses the pointer, the pivot needed to be swapped: 1, 1, 3, 2, 3, 4, 5,

and the following is the result: 1, 1, 3, 2, 3, 4, 5, 5, 5, 6, 9

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The horizontal and vertical asymptotes of the hyperbola equation (x + 1)² / 25 - (y - 3)² / 16 = 1 are y = 4x / 5 + 19 / 5 and  y = -4x / 5 + 11/5 respectively

An asymptote of the curve y = f(x) or in the implicit form: f(x,y) = 0 is a straight line such that the distance between the curve and the straight line lends to zero when the points on the curve approach infinity. This can be said to be a line that a curve approaches but never touches.

Basically, we have three types of asymptotes which are horizontal asymptotes, vertical asymptotes and oblique asymptotes.

In the hyperbola equation given

(x + 1)² / 25 - (y - 3)² / 16 = 1

The equation of asymptotes are;

Horizontal asymptotes : y = 4x / 5 + 19 / 5

Vertical asymptotes : y = -4x / 5 + 11/5

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The other five function values are sin(Ф)= -4/5, tan(Ф)= 4/3, cot(Ф)= 3/4, sec(Ф)= -5/3 and csc(Ф)= -5/4.

Since x is in IIIrd quadrant sin and cos will be negative but tan will be positive

given cos x= -3/5

We know that

sin²x + cos²x=1

sin²x+(-3/5)²=1

sin²x+9/25=1

sin²x=1-9/25

sin²x=16/25

sinx= ±√16/25

sinx= ±4/5

since, x is in IIIrd quadrant.

As sinx is negative IIIrd quadrant,

∴sinx= -4/5

tanx=sinx/cosx

      =-4/5÷-3/5

      =4/3

cotx=1/tanx

      =1/4/3

      =3/4

cosecx=1/sinx

           =1/-4/5

           =-5/4

secx=1/cosx

       =1/-3/5

       =-5/3

Hence, The other five function values are sin(Ф)= -4/5, tan(Ф)= 4/3, cot(Ф)= 3/4, sec(Ф)= -5/3 and csc(Ф)= -5/4.

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Answer:y=2.50x+5

Step-by-step explanation:

y=2.50x+5

that's all i can do with the information provided

Answer:

Step-by-step explanation:

On solving the provided question, we got that 18 no. of glasses of punch was Lucas able to fill

a mathematical procedure. The most frequent operations are add, subtract, multiply, and divide . However, there are numerous others, including squaring, taking the square root, logarithms, etc. If it's not a number, it's probably an operation.

9/2= quarts of iced tea

9/4= quarts of lemonade

After mixing,

punch for a party = 9/2 + 9/4 = 27/4

He fills 3/8 =  quart of punch

No. of glasses of punch was Lucas able to fill = 27/4 X  8/3  = 18

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Answer + Step-by-step explanation:

In the attach pdf

The other five trigonometric function values are cos(∅) = 11/61, tan(∅) = 60/11, sec(∅) = 61/11, csc(∅) = 61/60 and cot(∅) = 11/60

From the question, we have the following parameters that can be used in our computation:

sin(∅) = 60/61

The cosine of the angle can be calculated using

sin²(∅) + cos²(∅) = 1

Substitute the known values in the above equation, so, we have the following representation

(60/61)² + cos²(∅) = 1

This gives

cos²(∅) = 1 - (60/61)²

Evaluate the like terms

cos²(∅) = 121/3721

Take the square root of both sides

cos(∅) = 11/61

The tangent of the angle can be calculated using

tan(∅) = sin(∅)/cos(∅)

Substitute the known values in the above equation, so, we have the following representation

tan(∅) = (60/61)/(11/61)

Evaluate

tan(∅) = 60/11

The other ratios of the angle are calculated as follows

sec(∅) = 1/cos(∅) = 61/11

csc(∅) = 1/sin(∅) = 61/60

cot(∅) = 1/tan(∅) = 11/60

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The reason (B) Corresponding Angles Theorem can be used to fill in the blanks in the given question.

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry.

A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

So, extend segments JM and JK beyond points M and J, respectively, and draw points P and Q.

It is assumed that a parallelogram with segments JM parallel to segments KL and JK parallel to segments ML is presented.

Draw point P and extend segment JM past point M through construction.

Through construction also Continue segment JK draws point Q after point J. 

Consequently, the Alternate Interior Angles Theorem ∠MLK≅∠PML and ∠JML≅∠QJM (1)

Then, the corresponding angles theorem ∠PML≅∠KJM and ∠QJM≅∠LKJ is applied (2)

Equations (1) and (2) and the transitive property of equality are used to create:

∠MLK≅∠KJM and ∠JML≅∠LKJ

As a result, the supplied parallelogram JKLM's opposite angles are congruent. So it was proved.

Therefore, the reason (B) Corresponding Angles Theorem can be used to fill in the blanks in the given question.

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Correct question:
The following is an incomplete flowchart proving that the opposite angles of parallelogram JKLM are congruent:

Parallelogram JKLM is shown where segment JM is parallel to segment KL and segment JK is parallel to segment ML. Extend segment JM beyond point M and draw point P, by Construction. An arrow is drawn from this statement to angle MLK is congruent to angle PML, Alternate Interior Angles Theorem. An arrow is drawn from this statement to angle PML is congruent to angle KJM, numbered blank 1. An arrow is drawn from this statement to angle MLK is congruent to angle KJM, Transitive Property of Equality. Extend segment JK beyond point J and draw point Q. An arrow is drawn from this statement to angle JML is congruent to angle QJM, Alternate Interior Angles Theorem. An arrow is drawn from this statement to angle QJM is congruent to angle LKJ, numbered blank 2. An arrow is drawn from this statement to angle JML is congruent to angle LKJ, Transitive Property of Equality. Two arrows are drawn from this previous statement and the statement angle MLK is congruent to angle KJM, Transitive Property of Equality to opposite angles of parallelogram JKLM are congruent.

Which reasons can be used to fill in the numbered blank spaces?

a. Alternate Interior Angles Theorem

b. Corresponding Angles Theorem

c. Same-Side Interior Angles Theorem

d. Same-Side Interior Angles Theorem

There are 407.83 square feet living room.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

The carpet cost $4.15 per square foot and $97 to have it stalled.

And, Their total bill is $1, 789.50.

Now,

Let number of square feet living room = x

So, We can formulate;

⇒ 4.15x + 97 = 1,789.50

Solve for x as;

⇒ 4.15x = 1,789.50 - 97

⇒ 4.15x = 1,692.5

⇒ x = 1,692.5 / 4.15

⇒ x = 407.83 square feet

Thus, There are 407.83 square feet living room.

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Answer:

Center = (-2, -3)

Radius = 5

Step-by-step explanation:

The golden ratio can be found using the following formula if we take x as the width, and y as the length of the rectangle:

[tex]\frac{y}{x} =\frac{x+y}{y} =1.618[/tex]

What is the golden ratio?

The golden ratio is a unique proportion between two values where the ratio of the two values equals the ratio of their sum to the bigger of the two values.

If we take a square of sides A,B,C,D.

Locate the midpoint of any one side of the square by bisecting it.

Connecting the midpoint (say) P to a corner of the opposite side.

Placing the compass on point P, and the width set to match the distance of P to one of the opposite sides, we draw an arc.

By extending the line where P sits, we see that the arc intersects at a point. say Q.

Extending the opposite line to P, we see that the point Q drawing parallel to the side, we see that it intersects at another point R.

Now, the rectangle AQRD is a golden ratio rectangle.

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The speed of the canoe in still water is 3 miles per hour and the speed of the water current is 2 miles per hour. The correct options are B and D.

One or many equation having same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given that the system of equations;

x + y = 5

x - y = 1

Solving the above equations by elimination we get

x = 3 and y = 2

Where, x represents the canoe's speed with no water current (in still water) and y represents the speed of the water current, in miles per hour.

Therefore, the speed of the canoe in still water is 3 miles per hour and

the speed of the water current is 2 miles per hour.

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All of the assertions are false. A statistically significant finding does not necessarily imply that the null hypothesis has been proven incorrect, nor does it indicate how likely it is to be true.

Generally speaking, the word "norm" describes something that is customary, typical, anticipated, or standard. Norms are established definitions of beneficial attitudes and actions that ought to be commonplace, or "the norm," whenever a group is working together. They apply to cooperation and collaboration.

When the variances are known and the sample size is large, a z-test is a statistical test that is used to assess whether two population means differ from one another.

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(a) 794g of the initial sample will be left in the sample after 25 years. (b) Time taken to decay to half of its original amount is 3.39 years.

Isotopes(200g) are atoms that have the same number of protons in their nucleus, but a different number of neutrons. This means that they have the same atomic number, but a different atomic mass. Because of this, isotopes have different physical and chemical properties. Isotopes can be stable, meaning that they do not undergo radioactive decay, or they can be unstable, meaning that they will undergo radioactive decay over time.

(a) Substituting 25 for t in the expression, we get:

[tex]A(25) = 200e^{0.0541 \times 25}[/tex]

         [tex]= 200e^{1.3525}[/tex]

Thus, after 25 years, there will be

[tex]200e^{1.3525} = 2003.97[/tex]

794 g of the initial sample left in the sample.

(b) We want to find t such that

[tex]A(t) = 200e^{0.0541}[/tex]                                          

       = 100.

Solving for t, we get:

[tex]= 200e^{0.0541} \times t=100[/tex]

Dividing both sides by 200 and applying the natural logarithm to both sides, we get:

0.0541 × t = ln(0.5)

Therefore,

[tex]t = \frac{ln(0.5)}{0.0541}[/tex]

  = 3.39 years.

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A)the interval on which f is increasing is x ∈ (π/2, 3π/2), The interval on which f is decreasing x∈ ( 0, π/2), (3π/2,2π)

B) local minimum = -6

local  maximum = 6

C) Inflection points are (π/6,-3/4), (5π/6,-3/4).

Local maxima are points in an interval where the values of the function at those points are never greater than the values of the function nearby. Local minima, on the other hand, are locations where the values of the function nearby are higher than the values of the function itself.

A point of inflection is the location where a curve changes from sloping up or down to sloping down or up; also known as concave upward or concave downward. Points of inflection are studied in calculus and geometry. In business, the point of inflection is the turning point of a business due to a significant change.

f(x) = 3cos^2 -6sin(x)

f'(x) = 6cosx d(cosx)/dx -6cosx

f'(x) = 6cosx( -sinx) - 6cosx

f'(x) = -6cosx ( sin x +1)

f"(x) = -6d (cosx)/dx (sinx +1) + -6cosx d ( sin x +1)/dx

f"(x) = -6 ([tex]cos^{2}x - sin^{2}x[/tex]) + 6sinx

a).the interval on which f is increasing is

f'(x)>0

-6cosx ( sin x +1) >0

6cosx ( sin x +1) <0

x ∈ (π/2, 3π/2)

The interval on which f is decreasing

f'(x)<0

-6cosx ( sin x +1) <0

6cosx ( sin x +1) >0

x∈ ( 0, π/2), (3π/2,2π)

since the function is decreasing till x = π/2

so x = π/2 is local minimum (x,y) = ( π/2, -6)

it increasing till 3π/2 and then decreasing

x = 3π/2 is local  maximum values (x,y) = ( 3π/2, 6)

local minimum = -6

local  maximum = 6

c). inflection points. f"(x) = 0

f"(x) = -6 ([tex]cos^{2}x - sin^{2}x[/tex]) + 6sinx = 0

-6 (1-2sin^{2}x) + 6sinx = 0

2[tex]sin^{2}x[/tex] + 2sinx -sinx -1 = 0

sinx = 1/2,-1

x = (π/6,5π/6)

concave up f"(x) >0

-6 (1-2sin^{2}x) + 6sinx > 0

x ∈ (π/6,5π/6)

concave down f"(x) <0

(2sinx -1)(sinx+1) <0

x ∈ (0,π/6) (5π/6,3π/2),(3π/2, 2π)

Inflection points are (π/6,-3/4), (5π/6,-3/4).

A)the interval on which f is increasing is x ∈ (π/2, 3π/2), The interval on which f is decreasing x∈ ( 0, π/2), (3π/2,2π)

B) local minimum = -6

local  maximum = 6

C) Inflection points are (π/6,-3/4), (5π/6,-3/4).

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The expressions are given to solve and reduce the answer to their simplest form.The x is 1/8.

We move all terms to the left:

7/8x-8-(1/8x-2)=0

Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R

Domain of the equation: 8x-2)!=0

x∈R

We get rid of parentheses

7/8x-1/8x+2-8=0

We multiply all the terms by the denominator

2*8x-8*8x+7-1=0

We add all the numbers together, and all the variables

2*8x-8*8x+6=0

By multiply elements

16x-64x+6=0

We add all the numbers together, and all the variables

-48x+6=0

We move all terms containing x to the left, all other terms to the right

-48x=-6

x=-6/-48

x    =   1/8

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Answer:

9.

[tex] \frac{1}{6} [/tex]

10.

[tex] \frac{1}{3} [/tex]

Answer:

x=7

isosceles triangle

Step-by-step explanation:

To find the perimeter we just add all the sides so we do that for this too

(X+4)+(2x+2)+(16)

And we set it equal to 43 since that is perimeter

(X+4)+(2x+2)+(16)=43

Combine like terms

3x+22=43

   -22.  -22

3x=21

/3.  /3

x=7

And if we fill in the x we find BG and AG are equal so this is an Isosceles triangle

Hopes this helps

Answer:

x = 7

Isosceles triangle

Step-by-step explanation:

The perimeter of a two-dimensional shape is the distance all the way around the outside.

Given values of triangle BAG:

Therefore:

⇒ AG + AB + BG = perimeter

⇒ 16 + x + 4 + 2x + 2 = 43

⇒ x + 2x + 16 + 4 + 2 = 43

⇒ 3x + 22 = 43

⇒ 3x + 22 - 22 = 43 - 22

⇒ 3x = 21

⇒ 3x ÷ 3 = 21 ÷ 3

⇒ x = 7

Substitute the found value of x into the expressions for AB and BG to find their lengths:

⇒ AB = x + 4

⇒ AB = 7 + 4

⇒ AB = 11

⇒ BG = 2x + 2

⇒ BG = 2(7) + 2

⇒ BG = 14 + 2

⇒ BG = 16

As sides BG and AG are both 16 units in length, the triangle is an isosceles triangle (as it has two sides of equal length).

The possible amounts Susan will spend on candy is $25 and above.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this situation, since Susan will buy more than 6 pounds of candy, the same expression will be illustrated by x.

x > ($4 × 6)

x > $24

In this case, she'll have to spend $25 or more.

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