Rectangle A B C D is transformed by a combination of two transformations so that all points on AB are invariant and there are no other invariant points.
The first transformation is
a reflection in the line with equation y = k, where ‘k’
is an integer and k ≠1

Describe fully the second transformation.

(2 marks)

It is a translation by vector
(?)

Step-by-step explanation:

so, the first road is 115 m long, the second is 90 m long.

we should be finished, if we multiply each road length by $100, right ?

well, not quite.

because the 2 roads overlap. for this overlap area we don't need to pay twice.

we have the choice : to which of the 2 roads do we assign the overlap area ?

let's "give" it to the longer road.

so, the cost for the longer road is simply

115 × 100 = $11,500

the cost for the shorter road is then without the overlap area (6 meters : the width of the other road)

(90 - 6)×100 = 84×100 = $8,400

in total the costs are

$11,500 + $8,400 = $19,900

10) Using the equation 98.4 = (12.3)8, it costs $12.30 (cost per unit) per uniform.

11) Using the equation 26.70 = k6, the cost of one bag of apples (unit rate) is $4.45.

The unit rate is the quotient of the total cost divided by the number of items contained.

The unit rate is the same as the average or mean of a data set.

We describe the unit rate as the slope of a linear equation.

The unit rate shows the constant rate of change in an equation.

The total cost of 8 uniforms = 98.4 = (12.3)8

The cost per uniform = 12.30 (98.4/8)

The total cost of 6 bags of apples = 26.70

The cost per unit = 4.45 (26.70/6)

Thus, the unit rate or cost is also described as the variable unit cost.

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Answer:

no, x = -6y+30 is the right answer

Step-by-step explanation:

The value of g(2) = 36 for the given function.

The given function g is defined by,

[tex]g(x) = 4(3)^{x}[/tex]

Now to find the value of g(2), put x = 2 in the given function we get,

g(2) = 4(3)²

g(2) = 4 × 3 × 3

g(2) = 36

Therefore, the value of g(2) = 36 for the given function.

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The solution of the inequalities will be x ≤ 13 and y ≤ 8 / 3.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given that the inequalities are 2x + 2y ≤ 20 and x + 3y ≤ 21.

The inequalities will be solved as:-

2x + 2y ≤ 20

x + 3y ≤ 21

Solve the above equation by eliminating variable y as below,

6x + 6y ≤ 60

-2x - 6y ≤ - 41

______________

3x ≤ 39

x ≤ 13

The value of y will be,

x + 3y ≤ 21

13 + 3y ≤ 21

3y ≤ 8

y ≤ 8 / 3

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The value of x using Pythagoras theorem is x = √30.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Using Pythagoras theorem,

⇒ 5² + base² = 8²

⇒ 25 + base² = 64

⇒ base = √64 - 25
⇒ base = √39

In the other triangle,

x² + 3² = 39

⇒ x² = 39 - 9

⇒ x = √30

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The measure of angle C is 47.86⁰

What is an angle?

Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays. Angles are frequently expressed in degrees and radians, a unit of circularity or rotation. We encounter angles frequently in life. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.

C,U and B are the angles and the  c,u and b are the sides opposite to the angles  C,U and B  respectively.

Law of cosines:

c² = u² + b² - 2ub cos C

58²=78²+48² - 2(78)(48) cos C

3364=6084+2304-7488 cos C

3364 = 8388-7488 cos C

=> 7488 cos C = 8388 - 3364 = 5024

=>  cos C = 5024 /7488 = 0.6709

=> C = arccos(0.6709) = 47.86⁰

So,  the measure of angle C is 47.86⁰

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Yes, the given coordinates X(1,-3), Y(6,1), Z(2,2) are the vertices of a triangle.

1. Calculate the distance between the points X and Y using the distance formula:

d = √[(x2 - x1)2 + (y2 - y1)2]

d = √[(6 - 1)2 + (1 - (-3))2]

d = √[52 + 42]

d = √25 + 16

d = √41

d = 6.4

2. Calculate the distance between the points Y and Z using the distance formula:

d = √[(x2 - x1)2 + (y2 - y1)2]

d = √[(2 - 6)2 + (2 - 1)2]

d = √[(-4)2 + 12]

d = √16 + 12

d = √28

d = 5.3

3. Calculate the distance between the points Z and X using the distance formula:

d = √[(x2 - x1)2 + (y2 - y1)2]

d = √[(1 - 2)2 + (-3 - 2)2]

d = √[(-1)2 + (-5)2]

d = √1 + 25

d = √26

d = 5.1

Since each side of a triangle must have a length greater than 0, and the distances calculated above are all greater than 0, then the given coordinates X(1,-3), Y(6,1), Z(2,2) are the vertices of a triangle.

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The inverse function of the power of two functions is the binary logarithm, sometimes known as log base 2.

Given,

For each real number n, according to the general logarithm, can be expressed as an exponential function.

n = aˣ

The logarithm form is written as follows: Log base 2 is the power to which 2 must be raised to obtain the value of n.

logₐ n = x

Here, "a" is a base that is a positive real integer, and "x" is an exponent. For each real number x, the formulas for log base 2 functions are provided as;

x = log₂ n

That is equivalent to,

2ˣ = n

The base 0 logarithm and negative logarithms are not defined by the real number system.

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The numerical value of both the mole and Avagadro’s number is 6.022 x 10²³. That is why the mole is equal to Avogadro's number.

The Avogadro constant, A, is the number of particles (such as atoms, molecules, or ions) in one mole of something. Its value is modernly defined as exactly 6.022 140 76 × 10²³. (As it is a pure number, it has no units.)

So, in 1 mol of helium, which has a mass of (very close to) 4 g, there is A

atoms; in 1 mol of sucrose, with a mass of 342 g, there are A molecules.

We can have moles of other kinds of things, including subatomic particles. The amount of charge known as the faraday is the charge of one mole of electrons (A of them; about 96 500 C).

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Gross income means all income you receive in the form of money, goods, property, and services that isn't exempt from tax.

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Correct answer:

(-1, 8)

(-2, 6)

(1, 4)

Answer:

Correct choices are:

(-1, 8)

(1, 4)

which would correspond to the second and fourth entries of your options

Step-by-step explanation:

Best way to solve this problem is to plug in x and y values for each ordered pair and see if these values result in a consistent equation. It is impossible to solve the equation since there are two unknowns and only one equation

Here is each ordered pair and resulting y value when x value is plugged in

(-1, 2) ==> y = 2, x = -1
6 - 2(-1) = 6 + 2 = 8
This is not equal to the given value of y =2. So incorrect

(-1, 8)
We figured out from above that when x = -1, y = 8 so this is a correct choice

(-2, 6) ==> x = -2, y = 6

6 - 2(-2) = 6 + 4 = 10
Does not match y-value; incorrect

(1, 4) ==> x = 1, y = 4

6 - 2(1) = 6 - 2 = 4

This matches the given value of y so correct choice

The polynomial x° 9x* 3x 5 has a degree of 3.

The highest power of a polynomial's variable is the polynomial's degree. The maximum power of the variable in the polynomial x* 9x* 3x 5 is 3, indicating that the polynomial has a degree of 3.

The highest power of a polynomial's variable is the polynomial's degree. The polynomial x*9x* 3x 5 has a degree of 3 since the largest power of the variable is 3, which is 3. A polynomial's degree is equal to the largest power of the variable it contains. The maximum power of the variable.

The polynomial x* 9x*3x 5 is 3, indicating that the polynomial has a degree of 3. The easiest way to do this is to look at the polynomial's variable's highest exponent. The polynomial's degree reveals its level of complexity and the quantity of its solutions. In order to ascertain a polynomial's type, number of terms, and root values, it is crucial to understand the degree of the polynomial.Understanding a polynomial's degree also aids in predicting the kind of graph it will generate.

Complete question:

What type of polynomial is the expression 9x² 30x25 What degree does the polynomial x3 9x2 3x5 have?What distinguishes the two polynomials?

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The expression 9x² + 30x + 25 is a third degree (or cubic) polynomial.

To determine the degree of a polynomial, we look at the term with the highest degree of x. In this case, the highest degree is x², which has an exponent of 2. Therefore, this polynomial is a third degree polynomial.

Another way to determine the degree is to look at the number of terms in the polynomial, which is three in this case. A polynomial with three terms is typically referred to as a cubic polynomial. In general, the degree of a polynomial with n terms is equal to n - 1.

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The solution for the given system of equations is (5.5, 4.333).The correct option is B

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line in point slope form can be also written as-

y - y1 =m (x - x1)

We have the following set of equations -

4x − 15y = −43

2x − 3y = −2

These are the equations of a straight line. Plotting the graphs and finding the point of intersection would give us the solution. It can be seen from the graph that the solution is given by coordinate - (5.5, 4.333).

Therefore, the solution for the system of equations is (5.5, 4.333).

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The required slope of the curve at the designated point P is 1/4.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,

The slope of the curve at point p is given as
= rise/run

From the graph,
rise = 2 and run = 8
slope of the curve at point P = 2 / 8 = 1/4

Thus, the required slope of the curve at the designated point P is 1/4.

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Answer:

n = - 8

Step-by-step explanation:

0.4n = 4 + 0.9n ( subtract 0.9 from both sides )

- 0.5n = 4 ( divide both sides by - 0.5 )

n = - 8

The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions.

Given data :

1. We split it into the following:

[tex]\sqrt{4*6}[/tex]

Now, we use the radical rule which states that,

[tex]\sqrt{ab} = \sqrt{a} *\sqrt{b}[/tex] a,b > 0

So, we get,

[tex]\sqrt{4}[/tex] [tex]\sqrt{6}[/tex]

= 2[tex]\sqrt{6}[/tex]

2. We split it into the following:

[tex]\sqrt{12*9}[/tex]

Now, we use the radical rule which states that,

[tex]\sqrt{ab} = \sqrt{a} *\sqrt{b}[/tex] a,b > 0

So, we get,

[tex]\sqrt{12}[/tex] [tex]\sqrt{9}[/tex]

= 6 [tex]\sqrt{3}[/tex]

3.  √7 . √14 =

  = √7 . √7 .√2

     = 7.√2

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Four rules of multiplication are :

1. 0 × a = 0 , a ∈ R.

2. 1 × a = a  , a ∈ R.

3. -a × -a = + a² , +a × +a = + a²,  , a ∈ R.

4. a × b = b × a, a and b ∈ R.

As given in the question,

Four rules of the multiplication are given by :

1. Zero × any number = 0

0 × a = 0 , a ∈ R.

Example : 0 × 5 = 0

2. One  × any number = Number itself.

1 × a = a  , a ∈ R.

Example : 1 × 5 = 5

3. Multiply two numbers with same sign gives positive negative.

-a × -a = + a , +a × +a = + a,  , a ∈ R.

Example : -2× -2 = 4

3 × 3 = 9

4. Multiplication of two numbers in any order does not affect the result.

a × b = b × a, a and b ∈ R.

Example : 2 × 3 = 3 × 2

Therefore, the four rules of the multiplication are :

1. 0 × a = 0 , a ∈ R.

2. 1 × a = a  , a ∈ R.

3. -a × -a = + a² , +a × +a = + a²,  , a ∈ R.

4. a × b = b × a, a and b ∈ R.

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Step-by-step explanation:

x1, y1 = (-5,-2)

slope,m = -6/5

general equation, y= MX + C

(y-y1)/(x-x1)=m

(y+2)/(x+5)=-6/5

5y+10=-6x-30

5y=-6x-40

y=-(6x/5) - 8

The Chang family has been traveling for 18 hours, thus, t-value is 18.

A significant t-score, also known as a t-value, implies that the groups are distinct, whereas a small t-score suggests that the groups are similar. Degrees of freedom are the values in a study that are open to change and are crucial for determining the significance and reliability of the null hypothesis.

D(t) = 2,280 - 60t

D(t) = 1,200; find t.

D(t) = 2,280 - 60t

1200 = 2280 - 60t

From both sides of the equation, deduct 2280.

1200 - 2,280 = 2280 - 60t - 2,280

- 1080 = - 60t

multiplied by -60 on both sides

- 1080 / -60 = - 60t / -60

18 = t

t = 18

The Chang family had travelled for 18 hours, according to this.

The Chang family has been traveling for 18 hours, t = 18.

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The complete question is,

Having just returned from a cross-country road vacation, the Chang family is traveling back home. They can visualize their distance from home in miles after t hours of travel by using the function D(t) = 2,280 - 60t during the journey. If D(t) = 1,200, what does t represent? That value stands for what?

A.t = 20; the Chang family has been traveling for 20 hours.

B. t = 20, meaning the Chang family will need to travel 20 more hours to reach home.

The Chang family has been traveling for 18 hours, thus c. t = 18.

The Chang family must go home for an additional 18 hours using the formula D. t = 18.

The volume of cylinder = 15,869.56 mm.

The formula for determining a cylinder's volume is the base area times the height. Volume of a cylinder is r2h cubic units.

To calculate a box's volume, you need to know its height, width, and depth. The volume can be calculated by multiplying these three dimensions.

Assume for the moment that the spherical discs are stacked h levels high. The volume of the cylinder will now be calculated by multiplying the discs' base areas by their heights, "h". Therefore, r2h is used to represent the volume of a cylinder with base radius r and height h. The amount of material required to fill an object can be calculated using the volume of the object.

We know that the volume of cylinder = πr²h

Given,

height = 14 mm

radius = 19 mm

V = π × 19 × 19 × 14

⇒  V = 15,869.56 mm

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The system of equations x + 2y = 3, 2x + 4y = 15 is an example of no solution.

If (a₁/a₂) = (b₁/b₂) ≠ (c₁/c₂), then there will be no solution. This sort of system of equations is called an inconsistent pair of linear equations. If we plot the graph, the lines will be parallel, and the system of equations has no solution.

Given equations are x + 2y = 3

2x + 4y = 15

a₁ = 1, b₁ = 2, c₁ = -3

a₂ = 2, b₂ = 4, c₂ = -15

a₁/a₂ = 1/2

b₁/b₂ = 1/2

c₁/c₂  = 1/5

a₁/a₂ = b₁/b₂ ≠ c₁/c₂

So, the system of equations has no solution.

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Answer: A partition of a line segment is a point that divides the segment into a certain ratio of segments. In this case, point P partitions the segment AB in the ratio 3 to 1.

To find the coordinates of point P, we can use the following method:

Let the point P be (x,y)

The ratio of the segments AP:BP is 3:1, so we can use the proportion: (AP)/(BP) = 3/(1+3) = 3/4

We can use the coordinates of points A and B to find the coordinates of point P. The x-coordinate of P is (3/4) times the difference in x-coordinates of A and B, plus the x-coordinate of A. And the y-coordinate of P is (3/4) times the difference in y-coordinates of A and B, plus the y-coordinate of A.

So, using the coordinates of A and B:

x = (3/4)(-5 - 7) + 7 = -4

y = (3/4)(4 - (-4)) -4 = 3

Therefore, the coordinates of point P are (-4,3)

Step-by-step explanation:

The equation you provided is a linear equation that can be solved by isolating the variable y on one side of the equation. To find the solution for y, we need to follow these steps

First, we will simplify the equation by combining like terms: 2.8y + 0.2y = 5y – 14 + 6 3y = 5y – 8

Next, we need to get y alone on one side of the equation by subtracting 3y from both sides: 0 = 2y - 8

We will add 8 to both sides of the equation: 8 = 2y

Finally, we will divide both sides of the equation by 2 to find the solution for y: y = 4

So the solution for the linear equation 2.8y + 6 + 0.2y = 5y – 14 is y=4.

It's worth mentioning that this is the only solution that this equation has since it's a linear equation which has only one answer.

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Answer:

b = 11

Step-by-step explanation:

2(3b + 6) = 78 (divide both sides by 2 )

3b + 6 = 39 ( subtract 6 from both sides )

3b = 33 ( divide both sides by 3 )

b = 11

Answer:

2(3b+6) = 78

6b+ 12 = 78

Subtract 12 from both sides

6b+ 12 = 78

6b+12-12=78-12

6b = 66

b = 11

The solution for the system of equations as given in the task content is; x = 1 and y = 7.

It follows from the task content that the solution for the given system of equations is to be determined.

On this note, since the given equations can be written as;

-5x + 2y = 9

y = 7x

Therefore, by substitution of y for 7x in the first equation; we have;

-5x + 2 (7x) = 9

-5x + 14x = 9

9x = 9

x = 9/9 = 1

Hence, since y = 7x; y = 7 (1) = 7.

Ultimately, the solution for the system of equations is such that; x = 1 and y = 7.

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The pair of expressions 4p + 3c and (c +2p)(2) are not equivalent because they aren't equal.

This is referred to as the expressions that work the same even though they look different.

we were given: 4p + 3c and (c +2p)(2)

: 4p + 3c = (c +2p)(2)

: 4p + 3c = 2c + 4p

They are not equal thereby making them not to be equivalent.

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The full question:

determine whether each pair of expressions are equivalent 4p + 3c and (c +2p)(2)

The factors for the expression (3x+7)(3x-7)

squared the given 9x² = 3x 49 = 7 if the operation in the first unfactor form is negative the factored form's operation will be positive and negative,  = (3x+7)(3x-7)

The factored form occurs when a quadratic expression is a product of two factors, each of which is a linear expression. By expanding, or multiplying out the factors, an equation in factored form may be restated in standard form.

Several strategies may be used to derive the factored form of a quadratic equation Ax2+Bx+C=0 , A x 2 + B x + C = 0.

Factored form assists us in determining the function's x-intercepts or zeros.

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