Three friends got the prize money worth ​$105,000. The first friend would get twice the amount of the third​ friend's portion. The third friend would get twice the amount of the second​ friend's portion. Determine the amount that each friend would receive.

The common difference will be equal to 3.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression. A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms.

Given that the data for the arithmetic sequence is a₁= -10, an = 26, Sn = 80, and the total number is n = 13.

The common difference will be calculated as,

an = a₁ + d ( n - 1 )

26 = -10 + d ( 13 - 1 )

d = 36 / 12

d = 3

Hence, for the arithmetic progression, the common difference is 3.

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The graph of the trigonometry function g(x) = 4 cos πx is plotted and attached,

The graph is made by picking some x values say 0, 0.5, 1, 1.5, 2 .... and solve for the output y.

For x = 0, y = 4 cos π * 0 = 4

For x = 0.5, y = 4 cos π * 0.5 = 0

For x = 1, y = 4 cos π * 1 = -4

For x = 1.5, y = 4 cos π * 1.5 = 0

For x = 2, y = 4 cos π * 2 = 4

Table of value

x     y

0     4

0.5  0

1      -4

1.5    0

2      4

The graph is plotted by tracing each x and y value and joining the intercepts to form a curve

It can be deduced that the amplitude of the graph is 4 and it completes a revolution in 2 units

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The size of the actual car is 186 inches

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Represent the size of the actual car by x and the size of the model car by y

then y = 1/24 of x

y = x/24

now, y = 7.75

x = 7.75 ×24

x= 186 inches

Therefore if the model size is 7.75 inches, then the size of the actual car is 186 inches

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The actual length of the car is 0.32 inches

A model car is 1/24 the size of the actual car

The length of the model car is 7.75 inches

Therefore the length of the actual car can be calculated as follows

1/24 × 7.75

= 7.75/24

= 0.32

Hence the actual car is 0.32 inches long

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A thermometer's accurate reading of the air's average temperature for a specific time frame, typically a day, a month, or a year.

The temperature for a month as a whole is known as the mean monthly temperature. The thermometer used to record it is well exposed. The average daily temperature for the month is added up and divided by the total number of days in the month to determine the mean monthly temperature.

By adding up the daily mean temperatures for each day of the month, multiplying that total by the number of days in the month, and then subtracting that result, you can find the mean monthly temperature. Add up the 31 mean daily temperatures for January, for instance, and divide the result by 31.

The average air temperature over a specific time period, typically a day, a month, or a year, as measured by an accurately exposed thermometer. In climatological tables, the average temperature is typically determined for each.

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The respective exterior angles are 155°, 55°, 150°

The angle sum property of a triangle states that the sum of interior angles of a triangle is 180°

Given here: The angles of the triangle as 30°, 25°, and 125°

We know that sum of an exterior angle is the sum of the two non-adjacent angles

Thus we have ∠DBC= 30+125=155°

∠ECA=30+25=55°

∠FAD=25+125=150°

Hence, The respective exterior angles are 155°, 55°, 150°

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The measure of angle FAB is 13x6°-3° = 78°-3°=75°.

An angle is a figure formed when two straight lines, or rays, intersect at a single point. There are many different types of angles, including acute angles, obtuse angles, right angles, reflex angles, and straight angles. Angles are measured in degrees, with a full rotation being 360 degrees.

We know outer angle of a triangle is equal to the sum of the two opposite interior angles
So, from triangle ABC,
13x - 3 = 3x + 2 + 55°
So, 13x - 3x = 57° + 3°
So, 10x = 60°
So, x = 60°/10 = 6°
So, Angle FAB = 13 x 6° - 3° = 78° - 3° = 75°

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The difference between two natural numbers is greater than 6 and less than 11. The greater of the two numbers is 14. There are 5 possible values for the unknown number.

These integers that start at 1 and go all the way up to infinity are known as natural numbers or counting numbers. You can use numbers to count things, represent or exchange money, determine the temperature, tell the time, and many other things. Since they are used to count things, these numbers are known as "natural numbers." It may be 5 glasses, 6 books, 1 bottle, and so on while counting the objects. Thus, counting numbers is a different term for natural numbers. Natural numbers are a group of all whole integers other than 0. These numbers are crucial to daily interactions and communication.

Let's call the unknown number x. We know that:

x - 14 > 6 and x - 14 < 11

x > 20 and x < 25

Now we can see that there are 5 possible values for x: 21, 22, 23, 24 and 25.

Therefore, there are 5 possible values for the unknown number.

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Upon solving the given polynomial equation, Correct option is C, [tex]\frac{- 2(x + 6)}{(x + 4)(x-4)}[/tex]

An equation with many terms made up of integers and variables is referred to as a polynomial equation. Exponents for polynomials can range in value. A polynomial's degree is represented by its highest exponent. How many roots can be found in a polynomial problem is indicated by the degree. For instance, the equation has three roots if the largest exponent is 3.

The values of x where y = 0 are the roots of the polynomial equation. The polynomial equation can be written using its roots if we are aware of them.

Given ,

[tex]\frac{x}{x^{2} - 16 } - \frac{3}{x - 4}[/tex]

Taking [tex]\frac{1}{(x - 4)}[/tex] as common factor,

[tex]\frac{1}{(x - 4)} (\frac{x}{x + 4} - 3 )[/tex]

Taking LCM,

[tex]\frac{1}{(x - 4)} (\frac{x - (3 \times (x+4)}{x + 4} )[/tex]

[tex]\frac{x - 3x - 12}{(x + 4)(x-4)}[/tex]

[tex]\frac{- 2x - 12}{(x + 4)(x-4)}[/tex]

[tex]\frac{- 2(x + 6)}{(x + 4)(x-4)}[/tex]

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The height of the roof is 21 inches.

Any triangle with any two sides that have the same length is known as an isosceles triangle. An isosceles triangle has two equal-sized angles that are opposite from one other and have equal sides. In other terms, an isosceles triangle is a triangle with two congurrent sides.  

Here we have,

Tony is building a doghouse, and the front view of the roof is an isosceles triangle.  

As we consider, the front view as an isosceles triangle

Side of the triangle = 29 inches

Base of the triangle = 40 inches

When we draw a line along the height of the triangle, it will divide the base equally and forms two right-angle triangles.

Let 'x' be the height of the triangle  

If we apply the Pythagorean theorem,

=> 29² = 20² + x²  

=> 841 = 400 + x²

=> x² = 441

=> x² = (21)²    

Hight of the triangle = 21

Therefore,

The height of the roof is 21 inches.

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Answer:

8.60cm

Step-by-step explanation:

a/sinA=b/sinB

15/sin90⁰=x/sin35⁰

cross multiply

15sin35⁰=xsin90⁰

8.6036=x

x=8.60cm

The quadratic equation represented by the table is

y = x² + 6x - 9.

A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that function takes.

Given is a quadratic function in tabular form as -

(x)   :   1     2   3   4

f(x)  :   -2  -5  -6  -5

The general form of a quadratic function is -

y = ax² + bx + c

For the point (1, - 2), we can write -

- 2 = a + b + c

For the point (2, - 5), we can write -

- 5 = 4a + 2b + c

For the point (3, - 6), we can write -

- 6 = 9a + 3b + c

Now, let's assume that -

a = x

b = y

c = z

Now, we can write the equations as -

- 2 = x + y + z             ... (1)

- 5 = 4x + 2y + z          ... (2)

- 6 = 9x + 3y + z           ... (3)

Subtracting Eq(1) from Eq(2) -

4x + 2y + z - (x + y + z) = - 5 + 2

4x + 2y + z - x - y - z = - 3

3x - y = - 3                       ... (4)

Subtracting Eq(2) from Eq(3) -

9x + 3y + z - (4x + 2y + z) = - 6 + 5

5x - y = - 1                          ... (5)

From the graph, we get -

x = 1

y = 6

Then, we can write {z} as -

- 2 = x + y + z

z = - 2 - x - y

z = - 2 - 1 - 6

z = - 9

So, we get -

x = 1

y = 6

z = - 9

Now, we can write -

a = x = 1

b = y = 6

c = z = - 9

So, we will get the quadratic equation as -

y = x² + 6x - 9

Therefore, the quadratic equation represented by the table is

y = x² + 6x - 9.

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Answer:

Step-by-step explanation: Inverse property of addition

The correct statement is -4<x<-3

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here: The graph of a polynomial function.

let the function be f(x) then from the graph we can clearly observe that

f(x)>0 for x∈[-4,-3)

Thus x lies between -4<x<-3

Hence, The answer is -4<x<-3

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Therefore , the solution of the given problem of trapezium comes out to be they are similar , therefore each side of trapezium will be equal

so x = 3

A trapezoid is a quadrilateral in American and Canadian English that has at least one pair of parallel sides. It is known as Trapezium in the United Kingdom and other English-speaking countries. In Euclidean geometry, a trapezoid is invariably a convex quadrilateral. The trapezoid's base is defined as its parallel sides. An identical one set of opposite sides that are parallel to one another define a trapezoid.

Here,

Given :

we have similar trapezium as a figure 1 and figure 2

So ,

We can see :

they are in ratio

as,

=> 10/6 = 5/x

=> x = 5*6/10

=> x =30/10

=> x =3

since they are similar , therefore each side of trapezium will be equal so x = 3

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Answer:None

Step-by-step explanation:

It is given that m∠AOB = 42° and m∠EOF = 66°. By the congruent rule m∠EOF ≅ m∠BOC. Therefore, m∠BOC = 66°. By the sum of m∠AOB and m∠BOC, m∠AOC = 108°, and by the supplementary rule m∠AOC + m∠COD = 180°. After application of the supplementary rule, m∠COD = 72°

Congruent angles are angles that have the same measure, in degrees and are often represented by the symbol "≅"

m∠EOF and m∠BOC are vertical angles and so they are equal and satisfy the congruent rule.

The angles m∠AOB and m∠BOC form the larger angle m∠AOC so;

m∠AOC = 42° + 66° = 108°

The supplementary rule states that if two angles add up to 180°, they are considered supplementary angles, thus m∠AOC + m∠COD = 180° is correct as m∠AOC and m∠COD both lie on a straight line AD.

Therefore, application of the supplementary rule will give the size of the angle m∠COD = 72° as follows:

108° + m∠COD = 180°

m∠COD = 180 - 108°

m∠COD = 72°.

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The number of terms in the sequence is 10.

It is a sequence where the difference between each consecutive term is the same.

Example:

2, 4, 6, 8, 10 is an arithmetic sequence.

We have,

First term = -10

Last term = 26

Sum of all the terms = 80

We need to find how many terms are in the sequence.

Now,

Sum of n terms of an arithmetic sequence = n/2 x (First term + Last term)

So,

80 = (1/2)n (-10 + 26)

2 x 80 = n x 16

n = 10

Thus,

The value of n is 10.

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Answer:

We can use algebra to solve this problem. Let's call the unknown number x.

We are given that 10% of x is 40, so we can write that as:

x * 10% = 40

x * 0.1 = 40

We are also given that 55% of x is 220, so we can write that as:

x * 55% = 220

x * 0.55 = 220

We can now use these two equations to solve for x.

From the first equation, x = 40 / 0.1 = 400

We can substitute that value of x into the second equation to check if it's true.

400 * 0.55 = 220

Now, we have the value of x, we can use it to find 65% of that number.

x * 65% = x * 0.65 = 400 * 0.65 = 260

So, 65% of that number is 260

Answer:

260

Explanation:

Formulate: 220+40

----------------------/\  You should know the answer by now

Answer:

8z

.......................

Answer: D, 128 boxes

Step-by-step explanation:

There are 8 cutting machines that each cut 12 boxes every 3/4 minutes. 8x12=96. Divide that by 3 which is 32 boxes a 1/4 minute. Then multiply that by 4 to get a whole minute which is 128 boxes.

Considering the definition of an inequality, the required inequality is for x ≤  4.6 and the number of people who can go to the amusement park must be less than 4.

An inequality is an inequality between two algebraic expressions of one or more unknowns, connected through the signs:

The inequality between the two algebraic expressions only holds, or rather, is only true for certain values of the unknown.

Being "x" the number of people who can go to the amusement park, and considering that:

the inequality that expresses the previous relationship is

10.50 + 32.50x ≤ 160

Solving:

32.50x ≤ 160 - 10.50

32.50x ≤ 149.5

x ≤ 149.5÷ 32.5

x ≤ 4.6

Finally, the required inequality is for x ≤  4.6 and the number of people must be less than 4.

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monthly payments for the student loan will be $212.66.

What is simple interest?

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

The formula for simple interest is:

S = p*t*r/100

where P is the principal amount of money, R is the interest rate as a decimal, T is the time.

student loan totaling $63,800 when you graduate from college.

The interest rate is APR = 4%, and the loan term is 25 years.

S = 63,800*4*25/100 =63800

Monthly it will take 63800/12*25 =  $212.66

Hence, monthly payments for the student loan will be $212.66.

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Answer: One solution

Step-by-step explanation:

21x - 33 = 6x + 12

15x = 45

x = 3

One solution

On solving the provided question, we can say that the equation is, y = -48.3 ÷ (-7)=​48.3/7 = 6.9

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

here,

the equation is, y = -48.3 ÷ (-7)=​48.3/7 = 6.9

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The number of years after which the population of North Dakota equals the population of South Dakota is 150.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

North Dakota:

Population in 2012 = 0.3 million

Growth rate per year = 0.017 million

The population after x years.

= 0.3 + 0.017x

South Dakota:

Population in 2012 = 0.9 million

Growth rate per year = 0.013 million

The population after x years.

= 0.9 + 0.013x

Now,

The number of years after which the population is equal.

0.3 + 0.017x = 0.9 + 0.013x

Solve for x.

0.017x - 0.013x = 0.9 - 0.3

0.004x = 0.6

x = 0.6/0.004

x = 150

Thus,

After 150 years, the population will be the same.

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Answer:

In real world context, h(10) would represent the height of the balloon above the ground. To find the value of h(10), substitute t with 10 in the equation

height = 210-15t

height = 210-15(10)

height = 210-150

height = 60

Answer:

y = -5x +77

Step-by-step explanation:

Slope intercept form is

y = mx+b  where m is the slope and b is the y intercept

77 - y = 5x

Subtract 77 from each side

77-y-77 = 5x-77

-y = 5x-77

Multiply each side by -1

y = -5x +77

Answer:

y = - 5x + 77

Step-by-step explanation:

Slope intercept form means,

Here,

m - slope of the line

c - y intercept

And now to write the given expression in slope intercept form you can simply make y the subject in the equation.

Let us write it now.

77 - y = 5x

Subtract 77 from both sides.

-y = 5x - 77

To make y value positive multiply the whole equation by -1.

y = - 5x + 77

Find 10% of 50 by dividing 50 by 10. Then multiply the result by 4 is how to determine 40% of 50 which is denoted as option A.

This is referred to as the process of splitting a number or an amount into equal parts.

40% of 50 = 40/100 × 50 = 2000/100 = 20

Another method is finding the 10% of 50 by dividing 50 by 10 which will be 50/10 = 5. Then multiplying the result by 4 to get 20 which is why option A was chosen as the correct choice.

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Answer:

$7.50

Step-by-step explanation:

The price of a hot dog today is $0.75 * (1 + 220%) = $2.38.

In another 45 years, the price will be $2.38 * (1 + 220%) = $7.50.