Triangle ABC has vertices A(–1, 0), B(4, 0), and C(2, 6). If ΔABC is translated using the function rule (x, y) → (x – 6, y – 5) and then rotated 180° clockwise, what would be the coordinates of the vertices of ΔA’’B’’C’’?

a. A’’(–5, 7), B’’(–5, 2), C’’(1, 4)
b. A’’(7, 5), B’’(2, 5), C’’(4, –1)
c. A’’(7, 5), B’’(2, 5), C’’(4, 1)
d. A’’(–7, –5), B’’(–2, –5), C’’(–4, 1)

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

Work Shown:

A = area of the triangle on top, aka ceiling

A = 0.5*base*height = 0.5*6*8 = 24

B = area of the triangle on the bottom, aka floor

B = A = 24

C = area of the front rectangular face

C = length*width = 10*7 = 70

D = area of the face in back on the left

D = length*width = 6*7 = 42

E = area of the face in back on the right

E = length*width = 8*7 = 56

Total surface area = A+B+C+D+E = 24+24+70+42+56 = 216 square meters

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

Alternative Method:

A = area of the triangle on top, aka ceiling

A = 0.5*base*height = 0.5*6*8 = 24

B = area of the triangle on the bottom, aka floor

B = A = 24

LA = lateral area = wall area

LA = (perimeter of the base)*(height)

LA = (6+8+10)*(7)

LA = 24*7

LA = 168

Total surface area = A+B+LA = 24+24+168 = 216 square meters

According to the question, to calculate the probability of an event which states that flip a coin and not landing on head. That means P = {H,T}

Therefore, the probability can be written as:

Probability of getting tail = [tex]\frac{no of favorable events}{total number of outcomes} = \frac{1}{2}[/tex]

Therefore, the probability of a coin in which head is not landing is [tex]\frac{1}{2}[/tex].

What is Probability?

The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.

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Does the infinite series converge or diverge? The series converges.

If it converges, what is the sum?

a. 1/2 + 3/4 + 9/8 + . . . . .

The sum of the infinite series is -1

What is the sum of the infinite series?

Given:

[tex]a(\text{ the first term})=\frac{1}{2} \\\\r(\text{ thecommon ratio})=\frac{a_2}{a_1} =\frac{3}{2}[/tex]

Since ,[tex]\vert r\vert < 1[/tex], the  infinite series converges.  

The sum of infinite geometric series is:

[tex]S_\infty=\frac{a }{1-r} ; -1 < r < 1\\\\S_\infty=\frac{\frac{1}{2}}{1-\frac{3}{2}}=-1[/tex]

The sum of the infinite series is -1

What is an infinite geometric series?

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Answer:

c ) it either shows diameter or radius

d) I am not sure

C. When elements are represented in a Venn diagram (using circles), the placement of elements inside or outside the circles indicates their relationship to the sets being represented.

D. Yes, the elements written at the intersection of both circles form a subset of the two sets.

C. Place an element inside a circle to indicate that it is a member of the set indicated by the circle.

An element that is positioned at the intersection of two circles denotes an element that is a part of both sets that are symbolized by those circles.

Outside the circles: In a Venn diagram, an element that is positioned outside every circle does not belong to any of the sets being represented.

D. This is so because these components are a part of the intersection of the two sets and as such, they are a part of both sets. In set theory, all of the components that are shared by two sets are contained in their intersection. Due to their simultaneous membership in both sets, the elements at the intersection are a subset of both sets.

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The most commonly used explicit of an arithmetic sequence is given as,

an = a + (n - 1) d

Each term in the sequence can easily be solved/computed without knowing the other terms in the sequence. Now by using the given information, we can say that,

2nd row seat = 12+ 1x2

3rd row seat = 12 + 2 x2

nth seat = 12 + (n-1) x 2

16th row seat = 12 + (16–1) x2 = 42

Since the number of seats is increasing at a constant rate, we can calculate the average number of seats in each row by taking the average of the first and last rows

Average number of seats per row = (12 +42)/2= 27

So total seats = average per row x number of rows

= 27 x 16 = 432.

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Answer:

I might be able to help. :))

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

Work Shown:

M = number of miles

L = cost to rent a luxury car = 1.15M + 16.40

E = cost to rent an economy car = 0.80M+10.95

C = difference in price

C = L - E

C = (1.15M + 16.40) - (0.80M+10.95)

C = 1.15M + 16.40 - 0.80M-10.95

C = 0.35M + 5.45

Don't forget to distribute the negative to each term in the second parenthesis.

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

Optional Section:

Let's say you drove M = 100 miles as an example.

The luxury car would cost L = 1.15M+16.40 = 1.15*100+16.40 = 131.40 dollars to rent.

The economy car would cost E = 0.80M+10.95 = 0.80*100+10.95 = 90.95 dollars to rent.

The difference in rental costs is L-E = 131.40-90.95 = 40.45 dollars.

Or you could say C = 0.35M+5.45 = 0.35*100+5.45 = 40.45

This means you pay $40.45 more if you go for a luxury car instead of an economy car.

Answer:

c

Step-by-step explanation:

its one full square and 1/4

Answer:

(-15, -15)

Hope this helps!

Answer:

-24 < -2 < -7/4 < 1/2 < √5

Step-by-step explanation:

Answer: 30,000 rounded to 1 significant figure

I hope this helped!

The unknown variable's result of the equation 24² + x² = 26² is 10

To solve this problem we must establish the equation, isolate the variable following the rules of clearance and solve the operations:

24² + x² = 26²

576 + x² = 676

x² = 676 - 576

x² = 100

x = [tex]\sqrt{}[/tex]100

x = 10

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

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The number of books published by a small publishing company is 3240.

Given that, a small publishing company is planning to publish a new book. The production costs will include one-time fixed costs and variable costs.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of books be x.

With one method, the one-time fixed costs will total $44,714, and the variable costs will be $11.50 per book.

That is, 44,714+11.50x

With the other method, the one-time fixed costs will total $17,174, and the variable costs will be $20 per book.

That is, 17,174+20x

Now, the number of books produced will the costs from the two methods be the same.

So, 44,714+11.50x=17,174+20x

⇒ 44,714-17,174=20x-11.50x

⇒ 8.5x = 27540

⇒ x=3,240

Therefore, the number of books published by a small publishing company is 3240.

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Answer:

Step-by-step explanation:

How many solutions does each of the following equations have?

6(x-3)+12=6x-6

6x - 18 + 12 = 6x - 6

-18 + 12 = -6

-6 = -6

0 = 0

Answer:

Step-by-step explanation:

It is given that we need to find the correct measurement indicated by the arrows on the lines to the left​.

Now, let us have a look at the figure;

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The term "intercepted arc" refers to an arc that is "cut off" or "lies between" the specified angle's sides.

The measure of < LRQ is 112.5.

The term "intercepted arc" refers to an arc that is "cut off" or "lies between" the specified angle's sides.

An arc is a segment of a circle's circumference. An intercepted arc is thus one formed when one or two different chords or line segments cut across a circle and meet at a common point known as a vertex.

If an angle is inscribed in a circle, then the measure of the angle equals one half the measure of its intercepted arc.

So, [tex]$m \angle L R Q=\frac{1}{2}(m \overparen{L N Q})$[/tex]

The sum of the measures of the central angles of a circle with no interior points in common is 360 .

Here, 360 is divided into 8 equal arcs and each arc measures

360/ 8 = 45.

Then, m LNQ = m LM + m MN + m NO + m OP + m PQ = 5(45) = 225.

[tex]$m \angle L R Q=\frac{1}{2}(225)=112.5$[/tex].

Therefore, the measure of < LRQ is 112.5.

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The combined cost of 2 yards of yellow and 1 yard of purple fabric is  $17.69.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now it is given that,

Length of yellow fabric = 5 yards

Length of purple fabric = 8 yards

Let x be the cost of per yard purple fabric.

Then, cost of per yard yellow fabric = 2 + x

Now since, Total amount paid is $62.80

Therefore,

5(2 + x) + 8x = 62.8

expanding the brackets we get,

10 + 5x + 8x = 62.8

Solving we get,

10 + 12x  = 62.8

or, 12x = 52.8

⇒ x = 62.8/12

⇒ x = $5.23

Thus the cost of per yard purple fabric = $5.23

Similarly, cost of per yard yellow fabric = 2 + 5.23 = $7.23

Thus, combined cost of 2 yards of yellow and 1 yard of purple

fabric = 2*$5.23 + $7.23

= $10.46 + $7.23

= $17.69

Thus, the combined cost of 2 yards of yellow and 1 yard of purple fabric is  $17.69

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Answer:

B. Squaring, 2

Step-by-step explanation:

When you Square a number, doing the opposite is finding the square root. When squaring a number, you multiply the number by itself, the number it raises the the power of 2.

hope it will help you...good luck

The simplification by combining like terms of -(3z -5) + z is -2z + 5.

According to the given question.

We have an expression -(3z -5) + z.

As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same.  when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.

Since, we have to combine the like terms of the given expression -(3z - 5)  +z.

Here -3z and z both are the like terms.

So, we subtract coeffcients of z to simplify the given expression.

Therefore, the simplification of the expression -(3z - 5)  +z is given by

-(3z - 5) + z

= -3z + 5 + z

= -3z + z + 5

= -2z + 5

Hence, the simplification by combining like terms of -(3z - 5) + z is -2z + 5.

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The solution of the simultaneous equation is given by (-7 , 4) .

A pair of simultaneous equations is the most common representation of a pair of straight lines in the cartesian plane.

For solving a pair of simultaneous equation we can use various procedures such as the matrix method, substitution or the method of elimination.

The given pair of simultaneous equation is given as:

x=−2y+1

3x+8y=11

Let us solve the equations by the method of substitution:

From the first equation we take the value of x and put it in the second equation:

3x + 8y = 11

or, 3 ( -2y + 1 ) + 8y = 11

or, -6y +3 +8y = 11

or, 2y + 3 = 11

or, 2y = 8

or, y = 4

Substituting the value of y as 4 in the first equation we get:

x = − 2y + 1

or, x = - 2 × 4 +1

or, x = -8 +1

or, x = -7

Therefore the solution set of the pair of equations is given by (-7 , 4) .

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The system of equations that can be used to determine the cost for each pound of jellybeans and almonds is

5x + 3y = 16

2x + 6y = 22

The cost of one pound of jellybeans is $1.25.

The cost of one pound of almonds is $3.25.

Given this two equations:

5x + 3y = 16 equation 1

2x + 6y = 22  equation 2

Take the following steps to determine the required values:

Multiply equation 1 by 2

10x + 6y = 32 equation 3

Subtract equation 2 from equation 3

8x = 10

Divide both sides of the equation by 8: x = 10 / 8

x = 1.25

Substitute for x in equation 1:

5(1.25) + 3y = 16

6.25 + 3y = 16

3y = 16 - 6.25

3y = 9.75

y = 9.75 / 3

y = 3.25

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The steps 5 and 6 in the construction of a new line segment  ensures the lengths are equal.

A line segment in geometry has two different points on it that define its boundaries. Alternatively, we may define a line segment as a section of a line that joins two points.

Below are the steps for copying a line segment:

Hence steps 5 and 6 are the steps in the construction of a new line segment which ensures the lengths are equal.

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Answer:

Step-by-step explanation:

2500+150x=3000+125x

150x-125x=3000-2500

25x=500

x=500/25

x=20 mo

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

2500+150*20=3000+125*20

5500=5500 total paid after twenty months

Hope this helps! ;0

The minimum area is 14.25 cm^2while the maximum area is 15.75 cm^2

In mathematics, area of rectangle refers to the product of length of the rectangle and width of the rectangle. The unit is in square units. Area shows the extent a surface or a plane covers

Given data

size of rectangular plate = 5 cm by 3cm.

the length should be within   = 0.25 of 5 cm  

This means the length, L of the rectangular plate can be mathematically represented as

5 - 0.25 ≤ L ≤ 5 + 0.25

4.75 ≤ L ≤ 5.25

Area of rectangle =  Length × Width.

Width = 3

minimum length = 4.75

maximum length = 5.25

minimum length

= 4.75 * 3

= 14.25 cm^2

maximum length

= 5.25 * 3

= 15.75 cm^2

Therefore, the minimum area is 14.25 cm^2while the maximum area is 15.75 cm^2

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Answer: a=√3    b=√6

Step-by-step explanation:

We have a right-angled isosceles triangle

Hence, a=√3

According to the sine theorem :

[tex]\displaystyle\\\frac{b}{sin90^0} =\frac{a}{sin45^0} \\\\\frac{b}{1} =\frac{\sqrt{3} }{\frac{\sqrt{2} }{2} } \\\\b=\frac{2\sqrt{3} }{\sqrt{2} } \\\\b=\frac{2\sqrt{3}(\sqrt{2)} }{\sqrt{2} (\sqrt{2}) } \\\\b=\frac{2\sqrt{6} }{2} \\\\b=\sqrt{6}[/tex]

The length of A'B' is 2 unit when Line segment AB has a length of 2 units. It is translated 6 units to the right on a coordinate plane.

What is Translation ?

Translation is a rigid transformation in which a figure or a line segment is shifted or moved without changing its shape and size.

That is, if the measurement of segment AB is 2 unit then after translation by any factor its measurement will not change,

So, the measurement of segment A'B' would be 2 unit.

Verification :

Let the coordinates of A and B are (x₁, y₁) and (x₂, y₂) respectively,

Also, the rule of translation 6 unit right is,

(x,y) → (x + 6, y)

By the distance formula,

The measure of segment AB = √(x₂- x₁)² + (y₂ - y₁)²

Thus, if A'B' is the transformed segment of segment AB,

Then, coordinates of A' and B' are (x₁ + 6, y₁) and (x₂ + 6, y₂)

So, the measure of segment A'B' =

√(x₂ + 6 - x₁ - 6)² + (y₂ - y₁)² = √(x₂- x₁)² + (y₂ - y₁)²

Hence, the measure of AB = measure of A'B'.

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