If a figure is translated 3 units left and 3 units up, which translation moves the image back to the original position?
A.3 units right and 3 units down
B.3 units left and 3 units up
C. 3 units up
D. 3 units left

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

sin x= 12/ 13

So, B = √13² - 12² = √169 - 144 = √25 = 5

cos x= 5/ 13

So, sin 2x= 2 sin x cos x =2 (12/13)(5/13) = 120/169

and, cos 2x= 1- 2 sin²x

                  = 1- 2( 144 / 169)

                  = -119/ 169

and, tan 2x = sin 2x/ cos 2x = 120/ 169 / (- 119/ 169)= 120/ 119

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Answer: 11

Step-by-step explanation:

we know that : ax² + bx + c = 0

then,

a = −1

b = −22

c = −121

putting the values in the following equation:

x=−b±√b²−4ac ⁄ 2a

=−(−22)±√(−22)²−4⌈(−1)(−121)⌉  ⁄  2(−1)

=22±√484−484  ⁄ −2

=22±√0  ⁄ −2

=22 ⁄ −2

=11 ⁄ −1

=11

Hence the answer for this equation will be 11.

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Answer:

Step-by-step explanation:

Let's call the speed of the boat in the river x miles per hour. The boat travels 2 miles downstream in the same amount of time it takes to travel 2 miles upstream, so the speed of the boat relative to the water is the same in both directions. We can set up the following equation to represent this relationship:

21 - x = x + current speed

Solving for x, we find that the speed of the boat in the river is (21 - x)/2 = 10.5 miles per hour.

We can then use this value to find the current speed of the river. The boat travels 2.6 miles downstream in the same amount of time it takes to travel 2 miles upstream, so the speed of the boat relative to the ground is the same in both directions. We can set up the following equation to represent this relationship:

10.5 + current speed = 10.5 - current speed

Solving for the current speed, we find that it is (10.5 - 10.5)/2 = 0.

Therefore, the current speed of the river is 0 miles per hour.

The elements of the required sets would be

(a) (P∩Q)∪R = {1, 2, 3, 4, 5, 7}

(b) (R∩P)'∪R = {2, 3, 4, 5, 6, 7, 8, 9, 10}

(c) Q'∩(P∪R) = {2, 3, 5, 7}

(d) (P∪Q∪R)'∩(P∩R) = ∅

What are sets?

A set is a mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

Given:

Let the universal set is (S) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

P = {Odd numbers}  = {1, 3, 5, 7, 9}

Q = {Prime Numbers} = {2, 3, 5, 7}

R = {1, 2, 3, 4, 5}

So by using the properties of sets we can find

P' = {2, 4, 6, 8, 10}

Q' = {1, 4, 6, 8, 9, 10}

R' = {6, 7, 8, 9, 10}

P∩Q = {3, 5, 7}

R'∪P' = {2, 4, 6, 7, 8, 9, 10}

P∪R = {1, 2, 3, 4, 5, 7, 9}

P∩R = {1, 3, 5}

P∪Q∪R = {1, 2, 3, 4, 5, 7, 9}

P'∩Q'∩R' = S - P∪Q∪R

                = {6, 8, 10}

Now we can find the elements of the required sets:

(a) (P∩Q)∪R = {1, 2, 3, 4, 5, 7}

(b) (R∩P)'∪R = {2, 3, 4, 5, 6, 7, 8, 9, 10}

(c) Q'∩(P∪R) = {2, 3, 5, 7}

(d) (P∪Q∪R)'∩(P∩R) = ∅

Hence, the elements of the required sets would be

(a) (P∩Q)∪R = {1, 2, 3, 4, 5, 7}

(b) (R∩P)'∪R = {2, 3, 4, 5, 6, 7, 8, 9, 10}

(c) Q'∩(P∪R) = {2, 3, 5, 7}

(d) (P∪Q∪R)'∩(P∩R) = ∅

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The time it takes the trains 2.2 hours to be 396 miles apart.

Time is the duration of an event.

Since two trains leave the station at the same time, one heading west and the other east. The westbound train travels at 85 miles per hour. The eastbound train travels at 95 miles per hour.

Let

Also,

Since both trains move in opposite directions and leave at the same time, their distance apart after time t is D' = d + D

= vt + Vt

= 85t + 95t

= 180t

Since D' = 396 miles, we have that

396 = 180t

t = 396 m/180 mph

t = 2.2 hours

So, it takes the trains 2.2 hours to be 396 miles apart.

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The greatest common factor between the given two numbers will be 20.

The greatest common factor is the largest positive number which can be divided into given numbers evenly.

Given that the two numbers are 1240 and 6660. First, factorize each number and find the common multiple of both numbers.

1240 = 2 x 2 x 2 x 5 x 31

6660 = 2 x 2 x 3 x 3 x 5 x 37

The common numbers are,

2 x 2 x 5

4 x 5

20

Therefore, the greatest common factor between the given two numbers will be 20.

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The perimeter of the rectangle can be expressed as 12x+2

The perimeter of a rectangle is the total distance covered by its boundaries or the sides. Since there are four sides of a rectangle, thus, the perimeter of the rectangle will be the sum of all four sides.

The perimeter of a rectangle is given as 2(l+w)

where l is the length and w is the width.

If the length is represented by 4x and width by 2x+1, therefore the perimeter of the rectangle = 2(4x+2x+1)

= 2( 6x+1)

= 12x+2

the perimeter can also be found by adding all the four sides, this means that

perimeter = 4x+4x+2x+1+2x+1=8x+4x+2= 12x+2

therefore the perimeter of the rectangle is 12x+2.

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Answer:

1. The denominator of a fraction represents the number of equal parts the whole is divided into.

2. The numerator of a fraction represents the number of parts being considered.

3. A fraction is in simplest form when the numerator and denominator have no common factors other than 1.

4. The denominator of a fraction must be greater than zero.

5. The numerator of a fraction must be greater than or equal to zero.

6. When two fractions have the same denominator, the fraction with the larger numerator is greater.

7. When two fractions have the same numerator, the fraction with the smaller denominator is greater.

8. To add and subtract fractions, the denominators must be the same.

9. To multiply fractions, multiply the numerators and denominators separately.

10. To divide fractions, invert the second fraction (flip the numerator and denominator) and then multiply.

Step-by-step explanation:

Answer:

For fractions to be added or subtracted, their denominators must match (the bottom value). It just requires adding or subtracting the numerators if the denominators are already equal (the top value). A common denominator must be determined if the denominators are dissimilar.

Step-by-step explanation:

The resulting expression after the expressions are subtracted is 9x - 6y

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

(-x-3y)(−x−3y) is subtracted from (8x-9y)(8x−9y)

Rewrite these expressions properly

So, we have the following representations

(−x−3y) is subtracted from (8x-9y)

When the first equation is subtracted from the second, we have the following representation

8x - 9y - (-x - 3y)

Open the brackets

So, we have

8x - 9y + x + 3y

Evaluate the like terms

9x - 6y

Hence. the solution is 9x - 6y

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It is Syllogism. It is an example of a type of reasoning where a conclusion is reached from two given or assumed propositions, each of which shares a term with the conclusion.

The Greek term "syllogismos," which means "conclusion, inference," is the source of the English word "syllogism." A logical argument employing assertions and deductive reasoning is known as a syllogism. The most important contribution to the topic of syllogisms is attributed to Aristotle. A major premise, a minor premise, and a conclusion make up a syllogism. One phrase from each of the premises and the conclusion are shared.

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Answer:

-3

Step-by-step explanation:

Combining like terms, [tex]x-3x=-2x[/tex]. Since this means the variable terms on both sides combine to have the same coefficient, this means there are no solutions (since the constant terms differ).

Answer:

C.) -3

Step-by-step explanation:

We're looking for an equation with NO SOLUTION.

A.) 5

-2x + 11 = x + 21 + 5x

x = -1.25.

A.)  is INCORRECT

B.) -2

-2x + 11 = x + 21 + (-2)x

x = -10

B.) is INCORRECT

C.) -3

-2x + 11 = x + 21 + (-3)x

No solution

C.) is CORRECT

D.) 2

-2x + 11 = x + 21 + 2x

x = (-2)

D.) is INCORRECT

Relationship to the line y=3/4x and its equation is line B.

What is an equation ?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

y = mx+c

y = 3/4x [which shows that the line B as the points]

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Answer:

3= 26

4= 11 because it is area of triangle

Olivia's quiz average must be 24.4 to achieve a 90 average in algebra.

To get the average for the quiz, we first evaluate for the sum of the test average and the homework average, and the subtract the result from 90 average in algebra.

the test average = (92/100) × 55

test average = 50.6

100% homework average implies Olivia got a homework average of 15

Let x be the quiz average, so that

x = 90 - (50.6 + 15)

x = 90 - 65.6

x = 24.4

Therefore, the quiz average of 24.4 is what Olivia needs to achieve a 99 average in algebra.

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The mean amount won based on the expectation formula of probability will be - 2/13.

The probability of an event occurring is defined by probability.

Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.

Probability of winning = 4/52 = 1/13

Probability of lossing = 1 - 1/13 = 12/13

The mean amount or expectation is given as,

E(X) = 10 × (1/13) + - 1(12/13)

E(X) = 10/13 - 12/13

E(X) = - 2/13

Hence "The mean amount won based on the expectation formula of probability will be - 2/13".

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The number of ways the 6 books can be arranged on the 4 shelves by Amanda is 360 ways

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

Total number of books, n = 6

Total number of shelves, r = 4

The number of ways the books could be arranged on the shelves is calculated using the following permutation formula

Total = ⁿPᵣ

Where

n = 6 and r = 4

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

Total = ⁶P₄

Apply the permutation formula

ⁿPᵣ = n!/(n - r)!

So, we have the following representation

Total = 6!/2!

Evaluate the quotient

Total = 360

Hence, the number of ways is 360

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The area of the rectangle training field is 4264 m².

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

We know the area of a rectangle is (length×width).

So, The area of the rectangle 82m long and 52m wide is,

= (82×52) m².

= 4264 m².

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Using the formula of combination and the provided condition that any child can get any number of books, The answer is 637.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. We use permutation to determine how many possible ways we have to arrange items from a collection system.

The required formula is:

[tex]C(n,r) = \frac{n!}{r!(n-r)!}[/tex]

where, n= total number of objects in the set.

r= number of choosing objects from the set.

from the given data, total number of books = n= 5

number of children we need to distribute, r= 10

total possible ways of distribution= C(10,1)+C(10,2)+C(10,3)+C(10,4)+C(10,5)

=10+45+120+210+252

=637

hence, we have total 637 possible ways to distribute.

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After solving, the value of f^(-1)(g(7)) is 6.

In the given question, we have to find the f^(-1)(g(7)).

The given table of functions f and g is:

x          f(x)                   y          g(x)  

-3          1                     -2          -5

0          4                     1            -4

1           5                     5            2

6         -6                     7           -6

To find the value of f^(-1)(g(7)) we put the value of g(7) from the table. As we can see in the table that at the value of g(x) at point 7 is -6.

Then we find the value of from the table of f(x).

f^(-1)(g(7)) = f^(-1)(-6)

The value of f^(-1)(-6) from the table f(x) is

f^(-1)(g(7)) = 6

Hence, the value of f^(-1)(g(7)) is 6.

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To find out how far the seagull flew while the sailor was watching, you can use the following steps:

Calculate the total distance the seagull flew in 28 seconds. You can do this by multiplying the seagull's speed (11 meters per second) by the time it flew (28 seconds):

Distance = Speed * Time

= 11 meters/second * 28 seconds

= 308 meters

Calculate the time the sailor watched the seagull fly. You can do this by dividing the total time the seagull flew (28 seconds) by 4:

Time = 28 seconds / 4

= 7 seconds

Calculate the distance the seagull flew while the sailor was watching. You can do this by multiplying the seagull's speed (11 meters per second) by the time the sailor watched the seagull fly (7 seconds):

Distance = Speed * Time

= 11 meters/second * 7 seconds

= 77 meters

Therefore, the seagull flew 77 meters while the sailor was watching.

What are conditional problems?

Conditional problems are problems that involve determining the likelihood or probability of an event occurring under certain conditions. They often involve the use of probability and statistics to evaluate the likelihood of different outcomes or to make predictions about future events.

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The total years taken to double the money according to Compounding will be 13.75 years.

What is compound interest?

Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.

Main body:

Given :

rate = 2%

amount = $1700

Total amount = $2200

Compounded monthly,

so formula becomes,

Total amount = amount (1+r/400)^4t

T = A([tex](1+r/400)^{4t[/tex]

2200 = 1700(1 +2/400)^4t

22/17 = (1 +1/200)^4t

22/17 = (1.005)^4t

1.29 = (1.005)^4t

taking log on both sides

0.11/0.002 = 4t

t = 13.75 years.

Hence the time taken to double the money is 13.75 years.

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y-intercept of given function is y = 1

How to graph the function?

The collection of ordered pairings with the (x,y). (x,y) sign is known as the graph of a function in mathematics, where  f(x)=y. x and  f(x) are Cartesian coordinates of points in two-dimensional space, and in the typical scenario where they are real numbers, they constitute a subset of this plane.

Given function , f(x) = 2· [tex]3^{x}[/tex]

Graph of the function is given below:

As the given graph is intersecting the y-axis at y=1 So, y-intercept of given function is y = 1

Therefore, y-intercept is y = 1

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Answer:

1.3 is the common difference.

Step-by-step explanation:

Answer:

10-x

Step-by-step explanation:

Answer:

To solve this problem, we can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side of a right triangle. Since the angle formed by the ladder and the ground is 72 degrees, we can consider the horizontal distance between the base of the ladder and the wall to be the adjacent side of the right triangle, and the height of the ladder to be the opposite side.

We can set up the following equation to represent this relationship:

tan(72^{\circ}) = opposite/adjacent

Substituting the values given in the problem, we get:

tan(72^{\circ}) = 26 feet / adjacent

To find the value of the adjacent side, we can solve for "adjacent" in the equation above. We can do this by dividing both sides of the equation by 26 feet and then taking the inverse tangent (tan^(-1)) of both sides:

adjacent = 26 feet / tan(72^{\circ})

Using a calculator or a table of tangent values, we can find that the value of tan(72^{\circ}) is approximately 3.73. Substituting this value into the equation above, we get:

adjacent = 26 feet / 3.73

Solving this equation, we find that the horizontal distance between the base of the ladder and the wall is approximately 6.99 feet. Rounding this value to the nearest hundredth of a foot, we get an answer of approximately 6.99 feet.

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Answer: 8.03

Step-by-step explanation:

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=3\\ y=-3 \end{cases}\implies y=a(x-3)^2 - 3\hspace{5em}\textit{we also know that} \begin{cases} x=2\\ y=-1 \end{cases} \\\\\\ -1=a(2-3)^2 -3\implies 2=a(-1)^2\implies 2=a~\hfill \boxed{y=2(x-3)^2 -3}[/tex]

A table of values that models this situation is as follows;

Distance (miles)               Time (hour)

120                                          0

150                                          1

180                                          2

210                                          3

240                                          4

An equation for D in terms of t representing Elizabeth's distance from city A, t hours after leaving her house is d = 30t + 120.

Mathematically, a constant of proportionality (time) for Elizabeth's journey (distance) with respect to time can be represented with the following mathematical expression:

d = kt

Where:

Therefore, the required function that relates the distance (d) and speed (s) at t hours is given by;

d = 30t + 120

Next, we would develop a table of value;

At time (t) = 1 hour, we have;

Distance, d = 30(1) + 120

Distance, d = 150 miles.

At time (t) = 2 hours, we have;

Distance, d = 30(2) + 120

Distance, d = 180 miles.

At time (t) = 3 hours, we have;

Distance, d = 30(3) + 120

Distance, d = 210 miles.

At time (t) = 4 hours, we have;

Distance, d = 30(4) + 120

Distance, d = 240 miles.

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Answer:

Step-by-step explanation:

The line parallel to line y= -x + 7  is y= -x + 9.

What is slope intercept form?

The intercept formula y = mx + b is used when you know the slope of the line you are examining, and the specified point is also the y-intercept (0, b). In this formula, b represents the y-value of the y-intercept.

Solution: We will use slope intercept formula y= mx + b

Given that the parallel line passes through (4,5), which means x=4 and y=5

Also, m = -1

Putting value of x and y in slope intercept form to find b, we get

y=mx + b

⇒ 5= (-1x4) + b

⇒ 5= -4 +b

⇒5 + 4= b

⇒b=9

Now putting value of b and m in slope intercept form, we get the parallel line

y= -x + 9

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