EKA MATH²
6 M2 TD Lesson
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A trainer at a gym earns $2,456.75 every month. She earns an extra $4.75 every time she sells
a gym membership. Last month, the trainer sold 32 gym memberships. What is the total amount
of money the trainer earned last month?

On a Cartesian (or "coordinate") plane in which  each point is represented by an ordered pair (x , y) belongs to  x coordinate  , y coordinate .

An ordered pair is a set of numbers in which it gives the location of a point on a coordinate plane.

The ordered pair is always expressed exactly the same way (x , y).

The first number  in an ordered pair represents the x coordinate on the plane while the second number in an ordered pair  represents the y coordinate.

The x-coordinate shoes that  how far away the point is horizontally from the x-axis.

The y-coordinate shows that  how far away the point is vertically from the x-axis.

Quadrant I: the upper-right quadrant of the plane in which all points in this quadrant have  the  positive x coordinates and positive y coordinates as { (+,+)}  ,  {(+,+)}

Quadrant II: the upper-left quadrant of the plane in which all points in this quadrant have negative x coordinates and positive y coordinates

{ (+,-)}{ (+,-)}

Quadrant III: the lower-left quadrant of the plane in which  all points in this quadrant have negative x coordinates and negative y coordinates

{ (-,-)}{(-,-)}

Quadrant IV: the lower-right quadrant of the plane in which  all points in this quadrant have positive x coordinates and negative y coordinates

{(+,-)}{ (+,-)}

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Coordinates (x ,y ) of the given geometrical figure after translation is written as ( x + h , y + k ) where h ∈ R  and k ∈ R.

As given in the question,

Let us consider the coordinates of any geometrical figure is represented by ( x, y ) in the coordinate plane.

Translation is the representation of transformation the change in the location of the given geometrical figure without change in the shape and size.

It can be translated in four ways :

Translation to the right is written as ( x + h , y )

Translation to the left is ( x - h, y)

Translation in the up is ( x, y + k )

Translation in the down is ( x , y - k ).

Therefore, the original coordinate ( x ,y )  after translation written as

( x + h , y + k ) where h ∈ R  and k ∈ R.

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The midpoint of the x-intercepts of f(x) = (x - 2)(x - 4) is (3, 0).

The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.

A compass and straightedge setup can be used to locate the midpoint of the line segment they determine given two points of interest. By initially building a lens out of circular arcs with equal radii centered at the two endpoints and joining the cusps of the lens, one can determine the midpoint of a line segment immersed in a plane. The midpoint of the segment is then the place where the line joining the cusps intersects the segment.

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Please find attached the graph showing the translation transformation of the triangle ΔABC with vertices A(2, 1), B(-1, 2), and C(-2, -1) using the rule (x, y) → (x - 1, y - 3), to produce triangle ΔA'B'C' with vertices A'(1, -2), B'(-2, -1), and C'(-3, -4), created with MS Excel

A translation transformation is one in which the location of the points on the original figure slides by the same amount and in the same direction to form the image.

The vertices of the triangle ΔABC are; A(2, 1), B(-1, 2), and C(-2, -1)

The specified transformation is; (x, y) → (x - 1, y - 3)

Applying the specified transformation, we get;

A(2, 1) ⇒ (x, y) → (x - 1, y - 3) ⇒ A'(2 - 1, 1 - 3) = A'(1, -2)

B(-1, 2) ⇒ (x, y) → (x - 1, y - 3) ⇒ B'(-1 - 1, 2 - 3) = B'(-2, -1)

C(-2, -1) ⇒ (x, y) → (x - 1, y - 3) ⇒ C'(-2 - 1, -1 - 3) = C'(-3, -4)

The vertices of the image ΔA'B'C' of the triangle ΔABC following the transformation, (x, y) → (x - 1, y - 3) are therefore;

A'(1, -2), B'(-2, -1), C'(-3, -4)

Please find attached the graph of the triangle ΔABC and its image ΔA'B'C' after the translation (x, y) → (x - 1, y - 3), created with MS Excel

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Answer:

There is one unique solution (-3, 6)

Step-by-step explanation:

Desmos graphing calculator helps a lot with this stuff

Answer: b) there is only one unique solution (-3, 6)

Step-by-step explanation:

Answer:

-23

Step-by-step explanation:

Open up the parenthesis

R - 8 - R - 15

R - R - 8 - 15

-23

Answer:-23    ITS SUPER EASY:0

Step-by-step explanation:

Open up the parenthesis

R - 8 - R - 15

R - R - 8 - 15

-23

The scale factor for the length is 12/8 = 1.5 and the scale factor for the width is 15/10 = 1.5

So the scale factor used to make an enlarged version is 1.5.

A scale factor is a value used to multiply the dimensions of an object in order to increase or decrease its size. It is often represented as a ratio, such as 1:2 or 1/2, which indicates that the new object is half the size of the original object. Scale factors can also be expressed as a decimal or a percentage, such as 0.5 or 50%. Scale factors can be used in various fields such as architecture, cartography, and graphic design.

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Answer:

The answer is 22.4

The graph is forming a function but it is not an one-one function.

If the vertical line test is satisfied, then the graph represents a function and a vertical line will cross it at most once.

If a horizontal line crosses the graph in no more than one spot, the function is one-to-one and passes the horizontal line test.

The graph in this case is made up of several horizontal, non-overlapping lines. It is a function and passes the vertical line test, however a horizontal line can cross the graph at any number of locations (is not one-to-one).

However, the graph is not a one-to-one function.

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Therefore , the solution of the given problem of equation comes out to be 1.45 mph (speed of the current).

A mathematical depiction of two equal things, one on either side of a "equals" sign, is called an expression. Equations can be used to solve common problems. To solve challenges in real life, we frequently turn for pre algebra assistance. Lessons in pre-algebra cover the foundational ideas of mathematics.

Here,

The 15 miles that Bob the Boy Scout must paddle upwards against the current takes him 10 hours.

He discovers that paddling 22.5 miles against the current only took him 5 hours when he turns back.

——

Upstream data: rate = d/t = 15/10 = 1.5 mph, distance = 15 miles, time = 10 hours.

————————

Downstream DATA: rate = d/t = 22/5 = 4.4 mph; duration = 5 hours; distance = 22 miles.

———————-

Equations:

upstream: Downstream, b-c = 1.5 mph; b+c = 4.4 mph

2b = 5.9 mph;

2b = 2.95; add and solve for "b" (speed of the boat in still water)

—-

For "c," use the formula

=> b + c = 4.4

=>2.95 + c = 4.4

=> c = 1.45 mph (speed of the current)

Therefore , the solution of the given problem of equation comes out to be 1.45 mph (speed of the current).

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Answer:

x = 9

Step-by-step explanation:

18 + x = 27

x = 27 - 18

x = 9

Answer:

93.3% i hope this is right

Step-by-step explanation:

percentage increase= final-original/originalx100

58-30/30x100=93.3333%

Subtract the smaller of the two numbers from the larger of the two numbers to discover the difference between them.

Subtract the smaller of the two numbers from the larger of the two numbers to discover the difference between them. The difference between the two numbers is the sum's product.

Subtracting two integers from each other is a type of subtraction.

The process for determining the difference between two decimals and two whole numbers is the same.

We only add a new step.

Finding the difference between 8.967 and 7.2, for instance, could appear more difficult.

To give them all the same amount of decimal places, we must first convert each decimal.

7.2 becomes 7.200 as a result.

The computation may now be done as before:

8.967 - 7.200 = 1.767

Therefore, there is a 1.767 discrepancy between these figures.

In order to find the difference between two fractions, simplify and find the lowest common denominator of each fraction.

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The function for the amount after {t} years can be written as -

[tex]$710(1 + 0.45/12nt)^{nt}[/tex]

Compound interest is the addition of interest to the principal sum of a loan or deposit. Mathematically -

[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]

where -

[A] = final amount

[P] = initial principal balance

[r] = interest rate

[n] = number of times interest applied per time period

[t] = number of time periods elapse

Given is that $710 is invested in an account earning 3.7% interest (APR), compounded monthly.

We can write -

A = 710(1 + 0.37/12)¹²⁽¹⁾

A = 710(1 + 0.037/12)¹²

A = 710(1 + 0.031)¹²

A = 710(1.031)¹²

A = 710 x 1.45

A = 1029.5

Let the annual growth rate be R. Then, we can write the function for annual growth rate after {t} years as -

1029.5 = [tex]$ 710(1 + R/1)^{t}[/tex]

1029.5 = [tex]$710(1+R)^{t}[/tex]

1.45 = [tex]$(1 + R)^{t}[/tex]

1.45 = 1 + tR + .....                        {Binomial expansion}

Neglecting the binomial series from the third term as the value of the terms become negligible -

1.45 = 1 + tR

R = 0.45/t

Function for the amount after t years can be written as -

[tex]$710(1 + 0.45/12nt)^{nt}[/tex]= A

Therefore, the function for the amount after {t} years can be written as -

[tex]$710(1 + 0.45/12nt)^{nt}[/tex]

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[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- 6}(x-\stackrel{x_1}{3}) \implies y +4= -6 (x -3) \\\\\\ y+4=-6x+18\implies {\Large \begin{array}{llll} y=-6x+14 \end{array}}[/tex]

The equation to model the given situation is 120 - 4.5t= 75 and the solution to the equation is 10 minutes.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation.

The balloon will reach an altitude of 75 meters above the ground.

Now, 120-75 =45 meters

Let t be the time to descends 45 meters

So, 120 - 4.5t= 75

= -4.5 t = 75-120

= -4.5t = -45

= t = -45/(-4.5)

= t = 10 minutes

Hence, the equation to model the given situation is 120 - 4.5t= 75 and the solution to the equation is 10 minutes.

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The student is partially correct as -5 is less than -4 but ln |-5| is not less than ln |-4|.

What is reasoning?

We can ascertain the veracity of the supplied propositions using mathematical reasoning, often known as the mathematical reasoning principle.

A student said that -5 is less than -4.

This statement is correct and the reasoning is -

According to the number line, 0 is the midpoint.

From 0 to the right side of infinity the digits increases.

So, 1 is bigger than 0, 2 is bigger than 1, 3 is bigger than 2, and so on.

Similarly, from 0 to the left side of negative infinity the digits decreases.

So, -1 is smaller than 0, -2 is smaller than -1, -3 is smaller than -2, and so on.

The student also said that ln |-5| is less than ln |-4|.

This statement is false and the reasoning is -

First simplify ln |-5| and ln |-4| -

ln |-5| = ln (5)

ln (5) = 1.6094

ln |-4| = ln (4)

ln (4) = ln (2^2)

ln (2^2) = 2 ln (2)

2 ln (2) = 1.3862

Therefore, the student is partially correct.

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There is no sufficient evidence at the 0.05 level to substantiate the publisher's claim

Note that the significance level, also known as alpha or α, is a measure of the strength of the evidence that must be present in your sample before you will reject the null hypothesis and conclude that the effect is statistically significant

In conclusion, the advertiser failed to reject the null hypotenuse so this would mean there is not sufficient evidence at the 0.02 level of significance to say that the percentage of people who own a Rolls Royce is higher than 47%

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On solving the question resultant answer from the given data we have  algebraic  expression 5/48 could be  0.10

Algebraic expression can be defined as the combination of  constants , variables and operators. Algebraic expressions are the concept of expressing numbers using letters or alphabets without specifying their real values. The basics of algebra taught us a way to specific an unknown value the usage of letters which includes x, y, z, and many others. those letters are called here as variables. An algebraic expression may be a combination of each variables and constants. Any value this is positioned before and increased through a variable is a coefficient.

So, the given expression , 5/48

5/48 = 0.10

The resultant answer from the given expression 5/48 could be 0.10

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The correct question is -

Solve the equation.

p= −6p=48

Please help I suck at math

Answer: uhm...

Step-by-step explanation:

2...?

Answer:

Step-by-step explanation:

Name the property of the real numbers illustrated by the equation

The equation of the function shown in the graph is f(x) = (-2x)^2.

In mathematics a function is a relation between two states that assigned to each element of the first set exactly one element of the second set in order words it is the rule that is describe how unstead of values is related to another set a values function are used to model real voice scenario and to solve mathematical problems example of function include linear equation polynomials and trigonometric function.

This is based on the equation of the parent function, which is f(x) = (-/-)^2. The graph shows that the function has been shifted two units to the left, which is why the coefficient of x is -2 instead of -1.

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Step-by-step explanation:

(7 - 6)/(4 - p)= 1/9

4 - p = 9

-p= 5

p = -5

Answer:

x = 32

Step-by-step explanation:

the sum of the exterior angles of a polygon is 360°

All the indicated angles in the diagram are exterior angles of the polygon.

sum the 5 exterior angles and equate to 360

2x + 71 + 85 + 44 + 3x = 360

5x + 200 = 360 ( subtract 200 from both sides )

5x = 160 ( divide both sides by 5 )

x = 32

Answer:

[B] 6²

Step-by-step explanation:

Given:

[tex]\frac{6^4\cdot \:6^3}{6^5}[/tex]

Solve:

Add the exponents - [tex]6^4 \times 6^3=6^7[/tex]

Now we have - [tex]\frac{6^7}{6^5}[/tex]

Exponent Rule: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]

Which means - [tex]\frac{6^7}{6^5}=6^{7-5}[/tex]

Subtract the exponent - [tex]6^2[/tex]

Hence, the answer is [B] 6²

RevyBreeze

Answer:

Degree measure of each angle is 90⁰, 47⁰ and 43⁰

Step-by-step explanation:

since the triangle is right angled, we assume that Q and S are the other angles of this triangle R

Thus using the concept that angles inside a triangle add up to 180⁰ and we already have one angle as 90⁰( since the triangle is right angled). we therefore know that Q + S = 90⁰

5x - 13 + 4x - 5 = 90⁰

9x = 108

x = 12

We now replace x in Q and S to get the angles

Q = 5(12) -13

= 47⁰

S = 4(12) - 5

= 43⁰

The number of pecans in each bucket will be 20 and 35.

From the information, there are 55 pecans are put in 2 buckets where one has 15 more than the other. An expression show the relationship between the variables.

In this case, 55 pecans put them in 2 buckets where one has 15 more than the other.

This will be:

x + x + 15 = 55

2x + 15 = 55.

Collect the like terms

2x = 55 - 15

2x = 40

Divide

x = 20

The other number will be:

x + 15.

= 20 + 15

= 35

The numbers are 20 and 35.

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55 pecans are put in 2 buckets where one has 15 more than the other. What is the amount in each bucket.

Answer:

GCF = 8

LCM = 48

Step-by-step explanation:

Because 5 is represented by the polynomial 5x0, the answer is yes.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

An example of a polynomial of a single indeterminate x is x² − 4x + 7.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials.

For instance, the polynomial 3x+2x-5.

By noticing which formulas only contain the operations of addition, subtraction, multiplication, and non-negative integer exponents, the polynomials may be located. Expressions with additional operations are considered non-polynomial expressions.

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Answer:

no

Step-by-step explanation:

3x2=6 ;-;

Is it possible for [tex]3\times2[/tex] to equal 1?

[tex]3\times2=6[/tex]

[tex]6\neq 1[/tex]

Therefore, [tex]3\times2[/tex] DOES NOT equal to 1.