An example of civic virtue is
A) doing chores around the house
B) supporting local sports teams
C) attending and graduating from college
D) volunteering for a community program

The vertices after reflection will be (-6, 1), (-3, 2), (-5, 7) and the vertices after rotation of 180° will be (6, 1), (3, 2), (5, 7).  

A form of Euclidean space isometry in geometry is called a point reflection, also known as a point inversion, center inversion, or asymmetry through a point.

An object is said to have point symmetry if it is unchanged under a point reflection, and central symmetry or being centrally symmetric if it is invariant below a point reflective thinking through its center.

As per the given information in the question,

The given vertices of the triangle are:

D(-6, -1), E(-3, -2), F(-5, -7).

a.

The equation towards reflection in the x-axis: (x, -y)

D = (-6, -1)

Reflected vertex = (-6, 1)

E = (-3, -2)

Reflected vertex = (-3, 2)

F = (-5, -7)

Reflected vertex = (-5, 7)

b.

Now let's find out the rotation of 180° of the given points,

As we can see that the vertices are in the third quadrant because both the points of each vertex are negative, so after rotation of 180° it will move to the 1st quadrant where all the points are positive.  

So,

D = (-6, -1)

After rotation, D = (6, 1)

E = (-3, -2)

After rotation, E = (3, 2)

F = (-5, -7)

After rotation, F= (5, 7)

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For figure 2) the value of the 'x' would be x = 14.

and for figure 3) the value of the 'x' would be x = 17 or x = 1 .

What is the Basic Proportionality Theorem?

The Basic Proportionality Theorem (can be abbreviated as BPT) states that, if a line is parallel to a side of a triangle that intersects the other sides into two distinct points, then the line divides those sides in proportion.

Figure 2)

By using the Basic Proportionality Theorem, we can write

                        [tex]\frac{11}{22}=\frac{x}{42-x}\\\\\frac{1}{2}=\frac{x}{42-x}\\\\42-x=2x\\\\3x=42\\\\x=14[/tex]

Now for figure 3)

            By using Pythagoras' theorem, we can write

                        [tex]24^2+(x+7)^2=(2x-10)^2\\\\576+x^2+14x+49=4x^2-40x+100\\\\3x^2-54x+51=0\\\\x^2-18x+17=0\\\\x^2-17x-x+17=0\\\\(x-17)(x-1)=0\\\\x=17 $ or $ x=1[/tex]

Hence, for figure 2) the value of the 'x' would be x = 14.

and for figure 3) the value of the 'x' would be x = 17 or x = 1 .

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Answer:

<

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is 12

Answer:

x=12

Step-by-step explanation:

[tex]\frac{5}{6}x+3=13\\\frac{5}{6}x+3-3=13-3\\\frac{5}{6}x=10\\6(\frac{5}{6}x)=10(6)\\5x=60\\(\frac{1}{5})5x=60(\frac{1}{5})\\x=12[/tex]

No, there isn’t enough information because only two pairs of corresponding sides can't be used to prove that two triangles are congruent.

What is congruent?

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Here,

We have to prove whether ΔABC and ΔDCB can be proven congruent.

For this, we examine the given diagram and concluded that there isn’t enough information because only two pairs of corresponding sides can't be used to prove that two triangles are congruent.

Hence, No, there isn’t enough information because only two pairs of corresponding sides can't be used to prove that two triangles are congruent.

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Answer:

x = 30 degrees

Step-by-step explanation:

By Parts-Whole Postulate, x + 100 = 130, meaning that x = 30 degrees.

Answer: 30

Step-by-step explanation: 130-100=30

Rate at which 88 copies will get printed is 44 dollars

By using the unitary method to find the value of a single unit, we may use that value to calculate the values of the required number of units.

According to the given information :

Applying the unitary method

we get,

Rate at which 16 copies get printed = 8 dollars

Rate at which one copy gets printed = [tex]\frac{8}{16}[/tex]

Rate at which 88 copies get printed =  [tex]\frac{8}{16}[/tex]×88

                                                            = 44 dollars

Rate at which 88 copies will get printed is 44 dollars.

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Answer:

#1

Step-by-step explanation:

3x4=12 not 7

Answer:

The selected answer should be correct!

Step-by-step explanation:

I did the problem step by step and got 1 5/7 which is the simplified version of 1 15/21.

I hope this helped somewhat!!

The equation for the given linear function is y = 12m + 20.

A linear equation in two variable has the general form as y = ax + by + c, where a, b and c are integers and a, b ≠ 0.

It can be represented as a straight line on a graph.

The given points for the linear function are (2, 44) and (5, 80) respectively.

The slope can be obtained as,

m = (80 - 44)/(5 - 2)

   = 36/3

   = 12

Substitute the value of m in the general form y = mx + c to obtain,

y = 12x + c

Now, substitute x = 2 and y= 44 in the above expression as,

44 = 12 × 2 + c

=> c = 44 -24

=> c = 20

Thus the linear function can be written in the form of equation as,

y = 12m +  20

Hence, the equation of the function for the given case is y = 12m + 20.

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The fourth degree polynomial function with zeros 5, -5, 5i, and -5i. written  in factored form is

The zeros of a polynomial function is the the value of x when the function is equal to zero

The zero is also called the root of the polynomial

To find the polynomial we equate to the zeros

the first

x = 5

x - 5 = 0

the second

x = -5

x + 5 = 0

the third

x = 5i

x - 5i = 0

the fourth

x = -5i

x + 5i = 0

Bringing the terms together

(x - 5) (x + 5) (x - 5i) (x + 5i)

Therefore the polynomial of zeros 5, -5, 5i, and -5i is gotten in factored form in the form (x - 5) (x + 5) (x - 5i) (x + 5i)

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Answer:

1. y = 5

2. y = 2x - 1

3. x = -1

9 is the mean of clusters

What are equivalent equations?

Equivalent equations are algebraic equations that are having identical roots or solutions. By adding or subtracting the same number or expression to both side of an equation we get an equivalent equation. Also by multiplying or dividing both sides of an equation by the same non zero number we get equivalent equation.

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Answer:

7 cm ; 10 cm ; 14 cm

Step-by-step explanation:

x = y + 3

z = 2y

x + y + z = 31

y + 3 + y + 2y = 31

4y = 31 -3

4y = 28

4/4 y = 28/4

y = 7

z = 7(2) = 14

x = 7 + 3 = 10

32 more blue marbles need to be added to the bag so that the probability of randomly drawing a blue marble is 3/4

A bag contains 10 red marbles, 7 blue marbles, and 3 green marbles.

we need to find the numbar of blue marbles need to be added to the bag so that the probability of randomly drawing a blue marble is 3/4

Let the number of blue marbles added be n,

required probability P = 3/4

Total marbles = 10 + 7 + 3

                      = 20

Number of blue marbles=7

Using definition of probability,

(7 + n)/(20+n) = 3/4

4(7+n)=3(20+n)

28+4n=60+3n

n = 32

Therefore, we need to add 32 more blue marbles to make the probability of randomly drawing a blue marble be 3/4.

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The midpoint of the line segment is (1, 2). Then the correct option is B.

Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).

Then the coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

The endpoints of the line segment are (-1, 7) and (3, -3). Then the mid-point of the line segment will be given as,

(x, y) = [(-1 + 3) / 2, (7 - 3) / 2]

(x, y) = (2/2, 4/2)

(x, y) = (1, 2)

The midpoint of the line portion is (1, 2). Then the right choice is B.

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The swimming pool was on sale for $1206.2, which is 18.5% less than its initial $1429.35 cost.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

Here,

Sale price after discount=$1206.2

Discount percent=18.5%

Original price=1206.2+18.5%*1206.2

=$1429.35

The original price of the swimming pool was $1429.35 as It was at sale price of $1206.2 with the discount of 18.5%.

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Answer: 6

Step-by-step explanation:

Remember:

Anything in | | is considered positive.

Simplified:

1+2+x=9

3+x=9

Solve for x:

x=9-3

x=6

Answer:

[tex]\frac{85}{17}[/tex]

Step-by-step explanation:

[tex]\frac{8.5}{1.7}[/tex] multiply the top and bottom by 10

[tex]\frac{85}{17}[/tex]

The length of side q to the nearest 10th of an inch is 4.1 inches.

The sine rule for a triangle ABC is a/sinA = b/sinB = c/sinC.

Given, In ΔPQR, p = 4.7 inches, ∠P=76°, and ∠Q=57°.

∴  the length of q can be obtained by,

p/sinP = 1/sinQ.

4.7/sin76° = q/sin57°.

4.7/0.97 = q/0.84.

q = (4.7×0.84)/0.97.

q = 4.1 inch.

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Th value of the equation f ( x ) is given as

when x = 0 , f ( 0 ) = 5

when x = 1 , f ( 1 ) = 7

when x = 5 , f ( 5 ) = 15

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given as

f ( x ) = 2x + 5

Now , the values of the function f ( x ) can be determined when we substitute for the values for x in the equation

So , in order to find f ( 0 ) , substituting the value for x as x = 0, we will get the value for the function

a)

when x = 0

The equation is f ( x ) = 2x + 5

f ( 0 ) = 2 x 0 + 5

f ( 0 ) = 5

So , the value of f ( 0 ) = 5

b)

when x = 1

The equation is f ( x ) = 2x + 5

f ( 0 ) = 2 x 1 + 5

f ( 0 ) = 7

So , the value of f ( 0 ) = 7

c)

when x = 5

The equation is f ( x ) = 2x + 5

f ( 0 ) = 2 x 5 + 5

f ( 0 ) = 15

So , the value of f ( 0 ) = 15

Therefore , the values of the equations are f ( 0 ) = 5 , f ( 1 ) = 7 , f ( 5 ) = 15

Hence ,

Th value of the equation f ( x ) is given as

when x = 0 , f ( 0 ) = 5

when x = 1 , f ( 1 ) = 7

when x = 5 , f ( 5 ) = 15

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Jeff bicycles 144 miles at the rate of r mph. The same trip would have taken 3 hours longer if he had decreased his speed by 4 mph. The value of r is 16.

What is speed ?

The speed at which an object's position changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Given that it only has a direction and no magnitude, speed is a scalar quantity.

144/r= t

144/(r-4)-144/r = 3

LCM r(r-4)

144r-144(r-4)/r(r-4)=3

Simplify [tex]$\frac{144 r-144(r-4)}{r(r-4)}: \frac{576}{r(r-4)}$[/tex]

[tex]\frac{576}{r(r-4)}=3[/tex]

Multiply both sides by r(r-4)

[tex]\frac{576}{r(r-4)} r(r-4)=3 r(r-4)[/tex]

Simplify

576=3 r(r-4)

Solve [tex]$576=3 r(r-4): \quad r=16, r=-12$[/tex]

r=16, r=-12

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a) The probability of rolling a total of 5 is 1/9.

b) If a pair of fair dice 360 times, then 40 times you will get a total of 5.

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

The number of 5 in the table is 4.

The total number of outcomes is 6 × 6 = 36

The number of outcomes of favorable event is 4.

Total number of outcomes is 36.

The probability getting total of 5 after rolling the pair of dice is

=4/36

Divide the denominator and numerator by 4:

= 1/9

If 360 time the pair of dice rolled, the number of times to get total 5 is

360 × (1/9)

= 40.

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The height of the soil in the new planter is 4/3 feet

Consider the old planter

The height of the prism = [tex]1\frac{1}{2}[/tex] feet = 3/2 feet

The length of the prism = [tex]3\frac{2}{3}[/tex] feet = 11/3 feet

The width of the prism = 2 feet

The volume of the rectangular prism = Length × width × height

= 11/3 × 2 × 3/2

= 11 cubic feet

The area of the base of the new planter = [tex]8\frac{1}{4}[/tex] square feet = 33/4 square feet

The volume of both planter will be equal

The base area × height = volume

33/4 × h = 11

h = 11 / (33/4)

h = 11 × 4/11

h = 4/3 feet

Therefore, the height of the new planter is 4/3 feet

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The function f(x) is 4x5 – 3x has exactly 5 roots according to the Fundamental Theorem of Algebra.

The correct answer is therefore d) 5 roots.

Complete question :

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?

f(x) = 4x5 – 3x

1 root

2 roots

4 roots

5 roots

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In linear equation, The domain defines the values of numbers of flower arrangements that

can be expected from the florist.

The practical domain of the function is; All integers from 0 to 25, inclusive.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

The domain of the function = The possible number of flower arrangements

that can be sold

The possible number of flower arrangements that can be sold = Whole

numbers from 0 to 25

Therefore;

The possible number of flower arrangements that can be sold = 0 ≤ x ≤ 25

Where;

x = An integer

Which gives;

The domain of the function, D = {0 ≤ x ≤ 25 | x ∈ Z}

Therefore;

The practical domain of the function if the florist sells 25 flower

arrangements is D = All integers from 0 to 25, inclusive.

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Answer:

Step-by-step explanation:

-6y = -5x + 36

y = 5/6x - 6

The diagram 2 represents the model that depicts the ratio given in the story.

Ratio is the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

Given is that Peace Park sets up an outdoor ice-skating rink each winter. Yesterday afternoon, there were 5 skaters who brought their own skates for every 3 skaters who rented skates.

The given ration of 5 skaters for every 3 skaters is shown in the

diagram 2. In the first column, five blocks are colored and in the second

column, three boxes are colored.

Therefore, the diagram 2 correctly represents the model in the story.

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Answer:

C. 45,257

Step-by-step explanation:

5280 * 60 = 316,800

316,800 ÷ 7 = 45,257

The distance between two consecutive rest stops is 45257 feet.

Division is the process of dividing a number by a given number.

Given that, the 60-mile road is divided into 7 equal parts.

The length of each part is:

60/7 mile

Given that;

1 mile = 5280 feet

Therefore;

60/7 mile = (60/7)5280 feet

60/7 mile ≈ 45257 feet

Hence, the distance between two consecutive rest stops is 45257 feet.

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