Triangle A has a single transformation performed on it to create Triangle B. Michelle says the single transformation must have been a translation 8 units to the right.
what is the transformation that could have been performed on Triangle A to create Triangle B to prove Michelle's statement is false.

(a)

In the given diagram,

∠α and ∠β can be determined using trigonometric functions,

tan α = Opposite side/Adjacent side

⇒ tan α = 4/6

⇒ tan α = 2/3

⇒ α = tan^-1 (2/3)

⇒ α = 33.7°

Similarly,

tan (α + β) = 4+4/6

⇒ tan (α + β) = 8/6

⇒ tan (α + β) = 4/3

⇒ (α + β) = tan^-1 (4/3) = 53.1°

⇒ 33.7 + β = 53.1°

⇒ β = 19.4°

(b)

For the cables adjacent to the perpendicular height, i.e., adjacent to ∠α, on both the sides

Cable length^2 = 4^2 + 6^2 .............................. (Pythagoras theorem)

⇒ Cable length^2 = 16 + 36

⇒ Cable length^2 = 52

⇒ Cable length = 7.21 m

For the cables far from the perpendicular, on both the sides,

Cable length^2 = 6^2 + 8^2 .............................. (Pythagoras theorem)

⇒ Cable length^2 = 36 + 64

⇒ Cable length^2 = 100

⇒ Cable length = 10 m

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The line shown in the graph have slope of line as 13/27 with rise 13 and run 27.

What is slope of line?
The definition of slope in mathematics is pretty close to how we normally define it. Slope is a mathematical term used to indicate a line's steepness and direction. A line's slope can be inferred from its graph alone, especially in comparison to other lines shown on the same coordinate plane.

The formula to calculate the slope of any line is given by:

[tex]slope = \frac{rise}{run}[/tex]

We know that, '

rise = y₂ - y₁

run = x₂ - x₁

As we can see in the graph

x₂ = 10, y₂ = 3

x₁ = -7,  y₁ = -10

putting the values in above formula

rise = y₂ - y₁ = 3 -(-10) = 13

run = x₂ - x₁ = 10 -(17) = 27

so, slope = 13/27

Hence the slope of the line shown in graph is 13/27.

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

The value of n in the equation 672,342 = 6.72342 x 10n is 10,000

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

Example:

2x = 9 is an equation.

6x+ 2 = 9 is ana equation.

We have,

672,342 = 6.72342 x 10n

Divide both sides by 6.72342

672,342 / 6.72342 = 10n

We get,

100000 = 10n

Divide both sides by 10.

100000 / 10 = n

n = 10,000

Thus,

The value of n in the equation 672,342 = 6.72342 x 10n is 10,000

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Answer:

Add 55.5 and 35, then subtract 36.9.

Step-by-step explanation:

x+36.9=55.5+35

x+36.9=90.5

Subtraction Equality

x + 36.9 + (-36.9)= 90.5 (-36.9)

x = 53.6

Answer:

4

Step-by-step explanation

40 = 5X

X = 10 dollars

Now divide 40/5 = 8

On average, each girl spends $8 dollars

Now write an inequality ,for this situation

5X ≤ 40

(a + b + c + d + e)/5 = 40

The constant rate of change for the tables are:

First table: 10

Second table: 12.

Third table: 1/12.

Last table: 1/10.

To find the constant rate of change (k) of a table of x and y variables, the formula that can be used is:

k = y/x.

Any pair of values, (x, y), from the given table can be used in finding the constant rate of change between the two given variables in each of the tables.

a. The constant rate of change of the first table = 110/11 = 70/7 = 30/3 = 10.

b. The constant rate of change of the second table = 108/9 = 12.

c. The constant rate of change of the third table = 10/120 = 1/12.

d. Constant rate of change for the last table = 10/100 = 1/10.

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Answer as a decimal is -172.

Given :

= (-17.2 x 2.5) x 4

= (-43) x 4

= -172

Therefore the answer as a decimal is -172.

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In geometry, a square is a flat shape with four equal sides and four right angles (90°). A square is an unique sort of parallelogram as well as an equilateral rectangle (an equilateral and equiangular one).

The formula for a2 + b2 + c2 is written as a square plus b square plus c square. A2 + b2 + c2 = (a + b + c)2 - 2(ab + bc + ca) is how it is expanded.

Give an example to explain what square is?

A square has four equal sides, four vertices, and is a closed, two-dimensional object. It has parallel sides on either side. A square is also equivalent to a rectangle with equal length and width. Many objects can be found in your surroundings that have a square shape.

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Given the expression:

The GCF of p^4 and p^3 = p^3

And the greatest common factor of 16 and 4 = 4

so,

So, the factors of the given expression will be:

Answer:

- 26

Step-by-step explanation:

(3−√7)(3−√7)

9 - 3√7 -3√7 + √7√7

9 - 6√49 + √49

9 - 6*7 + 7

9 - 42 + 7

= -26

Answer:

40, 80, 120

Step-by-step explanation:

-they’re common multiples of 2, 4, 8, and 10

Perimeter that remains after the semicircle is removed = 377.77

How to find area of the paperboard ?

Length of paper board = 28

Width of paper board = 18

Now, the area of the board =  28 * 18 = 505

Radius of the semi circle = Half of the width of the paperboard = 9

so the area of paperboard is 505 and semicircle is 127.23 .

TO find area of paper board after the cutting semi circle = 505 - 127.23

                                                                                              = 377.77

 The remaining area of rectangle is 377.77

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Answer:

P = 63 inches

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

here b = 2x - 6 , h = 4 and A = 60 , then

[tex]\frac{1}{2}[/tex] × 4 ×(2x - 6) = 60

2(2x - 6) = 60 ( divide both sides by 2 )

2x - 6 = 30 ( add 6 to both sides )

2x = 36 ( divide both sides by 2 )

x = 18

2x - 6 = 2(18) - 6 = 36 - 6 = 30

perimeter (P) is the sum of the 3 sides , so

P = 18 + 30 + 15 = 63 inches

Answer:

g(x) = 4x - 23

Step-by-step explanation:

We will assume a linear function for g(x)

This will be of the form g(x) = ax + b where a and b are constants

Given the info,

g(3) = a(3) + b = -11

g(7) = a(7) + b = 5

Thus we have two equations in a and b
3a + b = -11  [1]
7a + b = 5    [2]

Subtract [1] from [2]:
7a + b - (3a + b) = 5 - (-11)
7a + b - 3a - b = 5 + 11

4a = 16

a = 4

Substitute for a in equation [2]:

4(7) + b = 5
28 + b = 5

b = 5-28 = -23

So equation of g(x) is
g(x) = 4x - 23

Using an average credit card amount of $500 and an annual percentage rate of 18%, the monthly interest payment is $7.5.

It is possible to calculate the monthly interest payment as follows:

I = [tex]\frac{PNR}{100}[/tex]

Given P = 500, N = 1, R = 18%

[tex]I = \frac{500*1*18}{100}[/tex]

[tex]I = \frac{9000}{100}[/tex]

[tex]I = 90[/tex]

Yearly Interest is $[tex]90[/tex]

Monthly interest :

[tex]M.I = \frac{18}{12}[/tex]

[tex]M.I = 1.5%[/tex]

Monthly interest payment = $[tex]500*1.5[/tex]= $[tex]7.5[/tex]

Monthly interest payment:

The percentage of the monthly payment earmarked for paying off the loan charge is referred to as the monthly interest payment.

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Answer: 150.72 in^3

Step-by-step explanation:

the radius (r) is 2 because the diameter of the cylinder is 4.

the height (h) is 12 (obviously because that's provided in the picture.)

the formula to find the volume of the cylinder is:

[tex]3.14(2^2)\times 12[/tex]

therefore, it is 150.72 in^3

i hope this helps :)

Answer:

[tex]2x + 6y = 36[/tex]

[tex]x + 3y = 18[/tex]

Answer:

C

Step-by-step explanation:

find the gradient of the 2 points (2,6) &(-3,2)

y2-y1/x2-x1...use the gradient formula

-2-6/-3-2

=-8/-5

=8/5

therefore the line parallel to this line will have the same answer

Therefore C is correct

Answer:

1.1l +0.4+0.3+0.5

answer = 2litres 3milimetres

Answer:

that is the lowest term I think

To answer this question we first draw the triangle to help us:

As a note on the problem: This is not necessarily the triangle we have, we drew just to helps us solve it.

Now, to find the angle J we can use the law of cosines:

Plugging the values we have and solving for J we have:

Therefore the angle J is 60°.

The first step to solving the equation is to; C. add x to both sides

The second step  to solving the equation is to; C. cube both sides

Solving the equation for x initially yields; C. two possible values

Checking the solutions shows that; D. none are valid solutions

We are given the linear equation;

4x[tex]^{1/3}[/tex] - x = 0

From the linear equation above, seeing that we have an x that is raised to the power of one-third, and we have a single x variable, the first step would be to add x to both sides to get;

4x[tex]^{1/3}[/tex] - x + x = 0 + x

4x[tex]^{1/3}[/tex] = x

Now, to remove the fraction root, what we will now do as the second step is to cube both sides to get;

(4x[tex]^{1/3}[/tex])³ = x³

4³x = x³

64x = x³

Divide both sides by x to get;

x² = 64

Take square root of both sides to get;

x = ±√64

x = ±8

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The most appropriate choice for acceleration will be given by

Acceleration of the body = 7.59 [tex]m/s^2[/tex]

What is acceleration of a body?

At first it is important to know about velocity of a body.

The rate of change of displacement of a body is called velocity of a body. Velocity is a vector quantity.

The rate of change of velocity of a body is called acceleration.

Acceleration is also a vector quantity as the direction is taken into account

Here,

Initial velocity of an object = 23m /s

Final velocity of an object = 85 m/s

Time  = 8.3 s

Acceleration of the object =

                                              [tex]\frac{85 - 23}{8.3}\\\\\frac{63}{8.3}\\\\[/tex]

                                              7.59 [tex]m/s^2[/tex]

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Step-by-step explanation:

hope this helps!! the explanation is in my working. bring the "4" from the "40" (8 x 5) to the top of "1"

Answer:

59

Step-by-step explanation:

To mutlipy a decimal by a whole number, just multiply it like normal

118 x 5 = 590

11.8 has one decimal place so your answer will have one too

59.0 which is the same as 59

Step-by-step explanation:

-3(1+6r) = -3-18r =14-r

17r = -17 Therefore, r = -1

Answer:

Step-by-step explanation:

Systems of equations may be solved in one of two manners:  substitution and graphing.  This requaests they be solved by substitution, but I'll add the graphing solution, also.

Substitution:

We want to eliminate one of the two variables to result in an expression that only has one of the two remaining.  We can do that by manipluating one of the equations such that, when it is combined with the other, results in the elimination of one of the variables.

Given:

-2x-y=-9

5x-2y=18

we can multiply or divide one of the equations so that one of the terms has equal, but opposite, values.  We could multiply the first equation by 2.5 so that it becomes -5x -2.5y = 9*(2.5).  Then it could be added to the second to eliminate the x term.

My preference is to find a way to avoid fracticious fractions, so I will multiply the first equation by -2 so that we can eliminate y:

-2*(-2x-y =-9)

4x+2y = 18

No add this to the second equation:

  4x+2y = 18

  5x-2y = 18

   9x = 36

     x = 4

Since x = 4:

-2x-y=-9

-2*(4)-y=-9

-8 - y = -9

y = 1

The solution is (4,1).  It is the point the satisfies both equations.

-2x-y=-9

-2(4)-(1)=-9  

-8-1=-9   YES

----

5x-2y=18

5(4)-2(1)=18

20 - 2 = 18  YES

Graphing:

The solution to these equations is the point at which the lines intersect.  See the attached graph.  The lines intersect at (4,1).

Since 1978, the graph shows the dollar cost of a medical procedure as a function of time, d. In 1993 year does it represent.

The cost of treatment when d = 1 is $273

Given that,

Since 1978, the graph shows the dollar cost of a medical procedure as a function of time, d.

We have to find in which year does it represent.

Let the equation be

y=150×[tex]e^{at}[/tex]

Where t is the time for year

According to the figure,

y pass (0.5,202.50)

We get,

202.5=150×[tex]e^{0.5a}[/tex]

[tex]e^{0.5a}[/tex]=1.35

Now,

150×(1.35)³=150×[tex](e^{0.5a})^{3}[/tex]

150×(1.35)³=150×[tex]e^{1.5a}[/tex]

1.5 is for 15 years.

1978+15=1993.

Therefore, in 1993 year does it represent.

The graph represents an exponential function:

[tex]$$y=a b^x$$[/tex]

When (x, y)=(0,150), the equation becomes

[tex]$$\begin{aligned}&150=a b^0 \\&a=150\end{aligned}$$[/tex]

When (x, y)=(0.5,202.5), the equation becomes [tex]$202.5=a b^{0.5}$[/tex]

Substitute 150 for a

[tex]$$202.5=150 b^{0.5}$$[/tex]

Divide both sides by 150

[tex]$$1.35=b^{0.5}$$[/tex]

Square both sides

b=1.82

So, the equation of the graph is:

y=150 * 1.82^x

When x=1, we have:

[tex]$$\begin{aligned}&y=150 * 1.82^1 \\&y=273\end{aligned}$$[/tex]

Hence, the cost of treatment when d=1 is [tex]$\$ 273$[/tex].

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Table A represents a function.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Functions are crucial instruments in the creation of mathematical models because we continually develop beliefs about connections between variables in nature and society. Typically, functions in school mathematics contain numerical inputs and outputs and are frequently specified by algebraic expressions.

Given,

Table A represents a function,

A visual table with columns and rows that shows the function in relation to the input and output is called a function table. Function tables are frequently referred to as function machines by younger students. Each function has a rule that governs how the input and output are related to one another.

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Answer:

-6

Step-by-step explanation:

Replace the variable x with 1 in the expression.

f(1)=−4−2

Then simplify -4 and -2 (subtract 2 from -4)

= -6