Geometry Question on Foundations, Need Help.

By applying a rotation of 180° counterclockwise to triangle ABC, we have the following:

A rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

In Geometry, rotating a point 180° about the origin in a clockwise or counterclockwise (anticlockwise) direction would produce a point that has the coordinates (-x, -y).

By applying a rotation of 180° counterclockwise (anticlockwise) to triangle ABC, the coordinate of the image of triangle A'B'C' is given by:

(x, y)                         →               (-x, -y)

Points at A = (-4, 0)   →  Points at A' = (-(-4), -(0)) = (4, 0)

Points at B = (-7, -2)   →  Points at B' = (-(-7), -(-2)) = (7, 2).

Points at C = (-7, -2)   →  Points at C' = (-(-9), -(-9)) = (9, 9).

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The statements which are true include the following:

C. Dilations of a triangle are similar to the original triangle.

D. Dilations of perpendicular lines remain perpendicular lines.

F. Dilations of an angle are congruent to the original angle.

In Geometry, there are different types of transformation and these include the following:

Dilation simply refers to a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

In this context, we can reasonably infer and logically deduce that a dilation of perpendicular lines would always remain perpendicular lines because it takes each of the line to another perpendicular line.

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The constant of proportionality is 10 in the given graph which represents the total number of plants and number of seed packets used.

Equivalence between two ratios is referred to as proportionality in algebra. A and B are in the same proportion as C and D in the expression a/b = c/d. When one of a proportion's four quantities is unknown, a proportion is typically used to solve a word problem.

It is resolved by multiplying one numerator by the opposing denominator and equating the result to that of the other numerator and denominator. Any relationship that always has the same ratio is referred to as proportional.

For instance, the ratio of proportionality is the average number of apples per tree, and the quantity of apples in a crop is proportional to the number of trees in the orchard.

Here, when number of seeds packet is 1 plants are 10 and when seeds packet are 5 plants are 50, we can divide each of the variables to find the constant,

10/1 = 10

20/2 = 10

30/3 = 10

Thus, constant is 10 represented as y = kx

where y = no. of plants = 30

k = 10

x = no. of seeds packet = 3

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The source of bias in a survey question is D. a question that is so easy all students give the right answer.

Source bias is the propensity to favor sources of information that corroborate or contradict a certain set of views or values.

When systematic inaccuracy is added to sampling or testing during research, bias emerges. This happens when one outcome or response is preferred over others. Bias can appear at any stage of the research process, including study design, data collection, data analysis, and publication.

It should be noted that when the question is so easy, it ilustrates bias since it was intentional.

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The most appropriate choice for standard deviation will be given by-

Standard deviation is 1.41

What is Variance and standard deviation?

At first, it is important to know about mean of a data.

Mean gives the average value of the data.

Variance is calculated by taking the sum of the square of deviation of each value of the data set and then dividing the sum by the total number of values of the data set.

On taking the square root of the variance, we will obtain the standard deviation of the data set.

Here,

The data set is 2, 2.6, 3.2, 4.35, 4.7, 6.2

Mean = [tex]\frac{2 + 2.6 + 3.2 + 4.35 + 4.7 + 6.2}{6}[/tex]

          = 3.84

Variance = [tex]\frac{(2-3.84)^2+(2.6-3.84)^2+(3.2-3.84)^2+(4.35-3.84)^2+(4.7-3.84)^2+(6.2-3.84)^2}{6}[/tex]

               = [tex]\frac{11.9021}{6}[/tex]

               = [tex]1.983[/tex]

Standard deviation = [tex]\sqrt{1.983}[/tex]

                                = 1.41

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From the information given in the Poisson Distribution, the probability that  that no more than three customers arrive that is P (X≤3) = 0.0817.

What is a Poisson Distribution?

The Poisson distribution is a discrete probability distribution in probability theory and statistics that articulates the likelihood of a specific number of events happening in a fixed interval of time or space if these events occur with a particular frequency mean rate and regardless of the time since the last event.

What Are the Poisson Distribution's Assumptions?

To be correct, all events must be independent of one another, the pace of occurrences must be steady across time, and events cannot occur concurrently. Furthermore, the mean and the variance will be equal.

What is the justification for the above result?

According to a Poisson distribution, seven people come at a checkout counter in a department store every hour on average. i.e λ=7

Probability (P) that no more than three customers arrive is notated as P(X≤3)

= P(X=0) + P(X=1) + P(X=2) + P(X=3)

= Poisson (3,7,1)  

= 0.0817

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Answer:

Length = 9

Step-by-step explanation:

7^2 + 4sqrt2^2 = x^2

49 + 16*2 = x^2

49+32 = x^2

x^2=81

x=9

:] (Tell me if this is wrong)

Answer

The slope of segment AB is equal to the slope of the segment BC.

Explanation

Similar triangles have the same set of interior angles.

And it is one these angles, that determines the slope of the line segment AB or BC.

For the two triangles, that angle is the same because they are similar triangles.

So,

The slope of segment AB is equal to the slope of the segment BC.

Hope this Helps!!!

Answer:

4.8x10^11

480000000000

Step-by-step explanation:

The most appropriate choice for quadratic equation will be given by

Width of safety zone is 7.84 m

What is equation and Quadratic equation?

A statement that shows the equality between two mathematical expressions by connecting the two mathematical expression with an equal to (=)  sign is called equation.

A two degree equation is known as quadratic equation.

Let [tex]ax^2+bx +c[/tex] be a quadratic equation (a ≠ 0)

Then

[tex]x = \frac{-b \pm \sqrt{b^2 -4 \times a \times c}}{2\times a}[/tex]

Here,

Let the width of the safety zone be x metre

Length of rectangular park = 50m

Breadth of rectangular park = 30m

Area of rectangular park = [tex]50 \times 30[/tex]

                                         = [tex]1500[/tex] [tex]m^2[/tex]

Length of rectangular park with safety zone = (x + x + 50) m

                                                                         = (2x + 50) m

Breadth of rectangular park with safety zone = (x + x + 50) m

                                                                         = (2x + 30) m

Area of rectangular park with safety zone = (2x + 50)(2x + 30) [tex]m^2[/tex]

                                                                      = [tex]4x^2 +60x + 100x + 1500[/tex]

                                                                      = [tex](4x^2 + 160x +1500) m^2[/tex]

Area of safety zone = [tex]4x^2 +160x+1500-1500[/tex]

                                 = [tex]4x^2 +160x[/tex]

By the problem,

[tex]4x^2 +160x=1500[/tex]

[tex]4x^2 +160x-1500=0[/tex]

[tex]4(x^2 +40x-375)=0[/tex]

[tex](x^2 +40x-375)=0[/tex]

[tex]x = \frac{-40 \pm \sqrt{40^2 -4 \times 1 \times (-375)}}{2\times 1}[/tex]

[tex]x = \frac{-40 \pm \sqrt{1600 +1500}}{2\times 1}[/tex]

[tex]x = \frac{-40 \pm \sqrt{3100}}{2}[/tex]

[tex]x = \frac{-40 \pm 55.68}{2}[/tex]

[tex]x = \frac{-40 + 55.68}{2}[/tex] or [tex]x = \frac{-40 - 55.68}{2}[/tex]

[tex]x =7.84[/tex] or [tex]x = -47.84[/tex]

[tex]x = -47.84[/tex] is not possible as width cannot be negative

so [tex]x = 7.84[/tex] m

Width of safety zone is 7.84 m

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Answer:

76%,4/5,0.9,9/8

Step-by-step explanation:

Answer:

u=11

Step-by-step explanation:

7u-12u+17=-38-combine like terms

-5u=-38-17

-5u=-55

-u=-11

which means u=11

Answer:

u = 11

Step-by-step explanation:

7u + 17 - 12u = - 38 , that is

- 5u + 17 = - 38 ( subtract 17 from both sides )

- 5u = - 55 ( divide both sides by - 5 )

u = 11

The result is -

Rational are numbers which can be written with in form p/q, in which q and p are integers and q≠0. is a negative number.

For the given number-

π, 5/4, -8, 2.35 bar, 19/7, 8, 0

All numbers except π are rational as they are either ending number or have the bar which means they will repeat after some point.

π is the only number which have the value 3.14........and so o such that, it is nether terminating nor repeating.

Thus, π is the irrational number.

Therefore, rational numbers are- [5/4, -8, 2.35 bar, 19/7, 8, 0]

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One box of oaties will be enough for two groups of children.

We can state the box of oaties is enough for everyone, if the amount required by number of children in each group is less than or equal to 12.

So, amount of cereal required by younger/older children = amount required by one child × number of children

Amount of cereal required by younger children = 1/3 × 11

Amount of cereal required by younger children = 11/3 cups of cereal

Amount of cereal required by older children = 3/4 × 10

Amount of cereal required by younger children = 15/2 cups of cereal

Amount of cereal = 12 - (11/3 + 15/2)

Taking LCM in the bracket, we get 6

Amount of cereal = 12 - (11×2 + 15×3/6)

Solving the bracket

Amount of cereal = 12 - (22 + 45/6)

Performing addition = 12 - (67/6)

Amount of cereal = (12×6 - 67)/6

Amount of cereal = 72 - 67/6

Performing subtraction in numerator

Amount of cereal = 5/6

As 5/6 cups of cereal is remaining, thus, a box of oaties will be enough for 11 younger children and 10 older children.

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The complete question is -

Diane serves breakfast to two groups of children at a daycare center. One box of oaties contains 12 cups of cereal. She needs 1/3 cup for each younger child and 3/4 cup for each older child. Todays group includes 11 younger children and 10 older children. Is one box of oaties enough for everyone?

Answer:

a = −b + p + 8

Step-by-step explanation:

a + b - 8 = p solve for a

a + b - 8 = p

subtract b from both sides:

a + b - 8  - b = p - b

a - 8 = p - b

add 8 to both sides:

a - 8 + 8 = p - b + 8

a = p - b + 8

rearrange for alphabetical order:

a = −b + p + 8

Answer:

a = p + 8 - b

Step-by-step explanation:

Step 1: Add 8 both sides

[tex]\displaystyle{a+b-8+8=p+8}\\\\\displaystyle{a+b=p+8}[/tex]

Step 2: Subtract b both sides

[tex]\displaystyle{a+b-b=p+8-b}\\\\\displaystyle{a=p+8-b}[/tex]

Note: You can also subtract b both sides first then add 8 both sides.

Therefore, the new equation when a-term is the subject is [tex]a=8+p-b[/tex].

Please let me know if you have any questions!

Evaluation of fog(-1) = 1/3

Given,

f(X)=2x+3/x-1

g(X)=3x+1

a) Evaluate:

(f o g)(x) = f(g(x))

             = 2(g(x)) + 3/(g(x)) - 1

             = 2(3x + 1) + 3/(3x + 1) - 1

             = 6x+2+3/3x+1-1

(f o g)(x) = 6x+5/3x

i) fog(-1) = 6(-1)+5/3(-1)

            = -6+5/-3

            = -1/-3

fog(-1)   = 1/3

Hence, a.)evaluate: (f o g)(x) = 6x+5/3x

i.)fg(-1)​: fog(-1)   = 1/3

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Answer:

gvs-qvzp-hst please join once I beg you

Answer:

Plan A is cheaper by 2 dollars when watching 6 movies

Step-by-step explanation:

plan a: y=x+18

plan b: y=3x+8

6+18=24

18+8=26

Answer:9x-4

Step-by-step explanation:

Answer:

It simplifies to 9x-4

x= 4/9 or 0.4

Step-by-step explanation:

Answer:

it -8 2÷-14=-7 x=-7

-7+-1=-8

Answer:

[tex]125x^{18}y^{6}[/tex]

Step-by-step explanation:

Given expression:

[tex]\left(5x^6y^2\right)^3[/tex]

Apply the exponent rule that states that raising a number to a power of 1 yields the original number:  5 = 5¹.

[tex]\implies \left(5^1x^6y^2\right)^3[/tex]

[tex]\textsf{Apply exponent rule} \quad (abc)^n=a^n \cdot b^n \cdot c^n:[/tex]

[tex]\implies \implies \left(5^1\right)^3 \cdot \left(x^6\right)^3 \cdot \left(y^2\right)^3[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 5^{(1 \cdot 3)} \cdot x^{(6 \cdot 3)} \cdot y^{(2 \cdot 3)}[/tex]

[tex]\implies 5^3x^{18}y^{6}[/tex]

Carry out 5³:

[tex]\implies 5 \cdot 5 \cdot 5 \cdot x^{18}y^{6}[/tex]

[tex]\implies 25 \cdot 5 \cdot x^{18}y^{6}[/tex]

[tex]\implies 125x^{18}y^{6}[/tex]

I have attached the image.

Answer:

He can buy 9 bagels

Step-by-step explanation:

6 divided by $0.65 gets you 9.230769230769231. We have to round this down so he can get 9 bagels.

Answer:

5x-8=42

Step-by-step explanation:

5x-8=42

   +8  +8

5x=50

50÷5

10

Answer:

900⁰

Step-by-step explanation:

Use the formula:

(n-2)×180 =sum of interior angles.

n= number of sides

(7-2) × 180= 5×180= 900⁰

Answer:

Choice A I think, i'm not really sure!

Answer:

There are 3 tennis balls in every can

Step-by-step explanation:

18/6 = 3

Answer:

Equation of a line given two points:

Line equation: y = 3x

Slope = 3

Intercept = 0

Answer:

2 quinoa because it will comit 4 plus6