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?

Audrey and Billy are as far as 367 meters apart.

The displacement of an object is its distance covered or moved in a specific direction. Displacement is an example of vector quantity.

A vector quantity is generally any type of quantity which can be expressed in magnitude and direction. Some examples include: weight, displacement, acceleration, force, etc.

Since Audrey walked 285 meters west and Billy walked 213 meters south from the same starting location, then we can determined the distance far apart by applying the Pythagorean theorem.

So that,

/hyp/^2 = /opp/^2 + /adj/^2

Let their distance apart be represented by s,

s^2 = 231^2 + 285^2

      = 53561 + 81225

s  = (134586)^1/2

s = 366.86

Audrey and Billy are as far as 367 meters apart.

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Answer:

15

Step-by-step explanation:

The original number is 25.

We know that,

The sum of the original number is 7 --(i)

When reversed, the value of the number is increased by 45 --(ii)

Therefore, adding (i) and (ii), we get:

7 + 45 = 52

Also, 5 + 2 = 7

Since 52 is the reversed number,

Therefore, the original number is 25.

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Answer:

Expression: 2s + 6

# of Pages Friend Read: 14 pages

Step-by-step explanation:

Let's call the number of pages your sister has read, s, and the number of pages your friend has read, f. We will make our equation first. If your friend has read 6 more than twice as many pages as your sister has, your equation would look like this:

f = 2s + 6

That is your equation for how many pages your friend read, your expression would be just 2s + 6. Now, we will substitute in 4 for s, and we get:

f = 2 * 4 + 6

Multiplying gives:

f = 8 + 6 = 14

So your friend has read 14 pages.

Hope this helped!

Answer:

GCF = 8

LCM = 48

Step-by-step explanation:

Answer:

If you want to find out how many print copies the book is selling, just click the Paperback or Hardcover edition of the book on Amazon, scroll down to Product Details on that page, and find the Amazon Best Sellers Rank for the print edition.

Step-by-step explanation:

The longest tornado ever recorded spanned 219 miles of land as it swept through many states at a pace of 60 miles per hour.

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Answer: chiki

Step-by-step explanation:

A statement which is known as tautology is a type of compound statement in whose result is always the truth value. We don't take in consideration the other individual values in consideration , the result in tautology is always true.

It is one of the most significant part in logical mathematics if we need to find the most accurate answers or findings among a given group of answers.

In mathematics, tautology is used so as to ensure that the results which is obtained are true and exact and not false . A tautology is a compound statement and it will always returns true value. The result in tautology is always true, regardless of what the constituent parts are.

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A book cost $2.00.

In Maths, a variable is an alphabet or term that represents an unknown number or unknown value or unknown quantity. The variables are specially used in the case of algebraic expression or algebra. For example, x+9=4 is a linear equation where x is a variable, where 9 and 4 are constants.

Variables may be classified into two main categories: categorical and numeric. Each category is then classified in two subcategories: nominal or ordinal for categorical variables, discrete or continuous for numeric variables.

Given the no of books purchased by

Alana =4

Petra =2

Angus = 16

So, the total price of 4 books of Alana =$4

Total price for Petra = $2

Total price of Alana and Petra =4x+2x

=6x

Total price for Angus = 16x

But given Angus received a discount  of $15

So price post discount = 16x- 15

According to the question

16x-15 = 6x +5

Adding 15 both sides

16x +15-15 = 6x + 5+15

16x= 6x+20

Subtracting 6x both sides

16x - 6x = 6x - 6x + 20

10x = 20

i.e x=2

Cost of one book = $2

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The exponential function that represents the population is y = a*3^x.

What is exponential function?

The formula for exponential functions is y = ab^x, where b is the constant ratio and a  is the starting point. Observe that as the value of x increases by a constant amount, the value of y increases by a common ratio by looking at a table of ordered pairs. All exponential functions share this trait.

We have to find the exponential function for the given table.

Since,

Exponential function = ab^x

where,

a is the starting point

b is the common ratio.

Here,

Common ratio = 24/8 = 72/24 = 216/72 = 648/216 = 3

So, the function becomes,

Exponential function = y = a*3^x

Hence, the exponential function that represents the population is

y = a*3^x.

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Answer:

(- 1, 9 )

Step-by-step explanation:

6x - y = - 15 → (1)

x + 2y = 17 → (2)

multiplying (1) by 2 and adding to (2) will eliminate y

12x - 2y = - 30 → (3)

add (2) and (3) term by term to eliminate y

13x + 0 = - 13

13x = - 13 ( divide both sides by 13 )

x = - 1

substitute x = - 1 into either of the 2 equations and solve for y

substituting into (2)

- 1 + 2y = 17 ( add 1 to both sides )

2y = 18 ( divide both sides by 2 )

y = 9

solution is (- 1, 9 )

The simplified value of x is 44 / 15 or 7 / 5 and value of y is -2

Simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

Given that, simply the following

a) 2(y-1)/3-3(y-2)/4=1

b) 3x=44/5=2x+6

1) 2(y-1) / 3 - 3(y-2) / 4 = 1

Multiplying by 12 to both sides,

8(y-1) - 9(y-2) = 12

8y-8 - 9y+18 = 12

-y + 10 = 12

y = -2

2) 3x = 44 / 5 = 2x+6

3x = 44 / 5

Multiplying by 5 to both sides,

15x = 44

x = 44 / 15

or,

44 / 5 = 2x + 6

Multiplying by 5 to both sides,

44 = 10x + 30

14 = 10x

x = 7 / 5

Hence, the simplified value of x is 44 / 15 or 7 / 5 and value of y is -2

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The second line is 153ft long.

We are making a figure out of the given statment. Where we have the Triangle ABC and other two Triangle ADB and ADC inside Triangle ABC. Here Angle ADC = 80 degress and Angle ACD = 40 egress.

According to given statement and figure,

In triangle ABO, AD= 100 ft

Hence, BD/AD = Cos80

or, BD = (100 * Cos80)

or, BD = 17.36 ft

Now, AB/AD = Sin80

or, AB = (100* Sin 80)

or, AB = 98.48

Now, In case of triangle ABC

AB/AC = Sin40

or, AC = AB/ Sin 40

or, AC = 98.48/ Sin40

or, AC = 153.2 ft (nearly equal to 153 ft)

The second line is 153ft long.

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The problem can be solved using algebra. Let's say the discount rate is x, then the price after discount is:

60000 (1 - x/100)

The price after VAT is:

60000 (1 - x/100) (1 + y/100) = 58986

Where y is the rate of VAT.

Rearranging the equation we get:

(1 - x/100) (1 + y/100) = 58986/60000

Multiply both sides by 100 to get rid of the fractions:

100 (1 - x/100) (1 + y/100) = 981

Expanding and grouping like terms, we get:

100 - x + 100y - xy = 981

We can see that x is in two terms, so we can move one side of the equation and get:

100 - x + 100y = 981 + x

x = (981 + x - 100 + 100y)/100 = (981 + xy - 100y)/100

Now we have x in only one term and we know the value of x is 10%, so we can substitute it:

10 + 10y = 9.81

Solving for y we can find that y = 0.81 or 81%

So the VAT rate is 81%

The inequality that describes these points is y ≤ -1/2(x) -3. The graph is given the attachment.

To graph a linear inequality in two variables (say, x and y), start with y on one side. Consider the related equation obtained by changing the inequality sign to an equality sign. This equation's graph is a straight line.

If the inequality is strict (< or >), draw a dashed line. If the inequality is not strict (≤ or ≥), draw a solid line.

Finally, choose one point that is not on either line ((0,0) is usually the easiest) and determine whether these coordinates satisfy the inequality or not. If they do, shade the half-plane containing that point. If they don't, shade the other half-plane.

Graph each of the system's inequalities in a similar way.

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Answer:

related to their eyes. How would you assign random numbers to conduct a simulation based on this

Multiply each digit by its corresponding place value and add the results: 11 + 0.011

11.011 = 11 + 0.011 = 11.011

Once the bits of the binary number have been multiplied by the corresponding positional weights, the binary number can then be converted into its corresponding decimal number by adding the resulting products.

To convert a number in base 2 (binary), base 8 (octal) or base 16 (hexadecimal) to a base 10 (decimal) number, you can use the following method:

Write the number in base 2, 8, or 16 and the corresponding base 10 place values.

Multiply each digit by its corresponding place value and add the results.

For example, to convert the base 10 number 11.011 to a base 10 number:

Write the number and the corresponding base 10 place values: 11.011

Multiply each digit by its corresponding place value and add the results: 11 + 0.011

11.011 = 11 + 0.011 = 11.011

As the number is already in base 10, it does not need to be converted. The value is 11.011

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Answer:

21x

Step-by-step explanation:

5x+14=19x

3x-5=-2x

-2x-19x=21x

The domain of x=4 is (−∞,∞) and range is {y|y=4} .

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

(−∞,∞)

{x|x ∈ R}

y=4

is a straight line perpendicular to the y-axis, which means that the range is a set of one value  {y|y =4}

Set-Builder Notation:{y|y =4}.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

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Step-by-step explanation:

it means that the graph of the function above y=x must be the mirrored image of the graph under y=x.

it means that the function applied to itself gives x.

f(f(x)) = x

e.g.

f(x) = 5 - x

f(f(x)) = 5 - (5 - x) = 5 - 5 + x = x

so, this f(x) is its own inverse.

Answer:

Step-by-step explanation:

from the graph we konw the ∠ABD=∠DBC, because ∠DBC=20, so ∠ABD=20

Since you're feeding it three times a day, you should feed your goat 0.74 ounces per feeding.

The act of feeding involves giving a baby a mother's breast milk, either directly from the breast or by expressing (pump-out) the milk from the breast and giving it to the baby in a bottle.

In the traditional method of measurement, a pound is used to measure weight. In the conventional system, ounces are smaller weight units that are defined in terms of pounds. 1 pound Equals 16 ounces.

Goats typically need around 2% to 4% of their body weight in feed per day. If your goat weighs 7 pounds, and you want to feed it 2% of its body weight per day, you would need to feed it 0.14 pounds of food per day, or 2.24 ounces per day. Since you're feeding it three times a day, you should feed it 0.74 ounces per feeding.

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The value of a₂₆ in the  arithmetic sequence aₙ=  14 + 9n is 248.

The correct option is D.

A series of integers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

Given:

An arithmetic sequence,

aₙ=  14 + 9n

We have to find the value of a₂₆.

That means, n = 26.

Substitute the value of n = 26 to the sequence,

a₂₆ =  14 + 9(26)

a₂₆ =  14 + 234

a₂₆ =  248

Therefore, the value of a₂₆ is 248.

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In the given equation, Mario can make 2.25 batches of cookies using all of his chocolate chips.

First, you can find out how many total cups of chocolate chips Mario has by multiplying the number of cups per unit (3/4) by the number of units (1).

[tex]3/4 cups * 1 = 3/4 cups\\[/tex]

Then you can divide the total amount of chocolate chips Mario has by the amount of chocolate chips needed per batch:

[tex]3/4 cups / 1/3 cup/batch = 3/4 cups * 3/1 cup/batch = 9/4 cups/batch[/tex]

Finally, you can convert this to a whole number by dividing both the numerator and denominator by their greatest common factor, which is 1:

[tex]9/4 cups/batch = (9/1) / (4/1) = 9/4 = 2.25 batches[/tex]

Mario can make 2.25 batches of cookies using all of his chocolate chips.

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Ms. Wickham folded 200 report cards and Ms. Cho folded 300 report cards, giving Ms. Cho an average of 100 report cards.

Ms. Wickham and Ms. Cho together folded 500 report cards.

Ms. Wickham folded 200 report cards

(200/500 = 2/5)

Ms. Cho folded 300 report cards

(300/500 = 3/5)

Mr. Leiva and Mr. Gamory folded 300 report cards.

Ms. Cho folded more report cards than Ms. Wickham, by

100 (300 - 200 = 100).

Ms. Wickham and Ms. Cho together folded 500 report cards, with the ratio of Ms. Wickham's report cards to Ms. Cho's being 2:3. Ms. Wickham folded 200 report cards, while Ms. Cho folded 300. At the end of the day, Mr. Leiva and Mr. Gamory folded an average 300 report cards. This meant that Ms. Cho folded more report cards than Ms. Wickham, by 100. Therefore, Ms. Cho folded 400 report cards in total, while Ms. Wickham only folded 300.

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Answer:

Step-by-step explanation:

Solve for x: -24 = 6x

-24 = 6x

x = -24 : 6

x = -4

---------------------

check

-24 = 6(-4)

-24 = -24