What are independent and dependent systems?

Answer:

22 ≤ n

Step-by-step explanation:

34≤12+n

22 ≤ n

If you want to divide a polynomial by a linear expression and use synthetic division, the first number or leading coefficient should be a 1. Alternatively known as Ruffini's rule, this division by linear denominator (paper-and-pencil computation).

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The equation of the line is y = √2x - 2. And the coordinate of point A will be (√2, 0).

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

y = 1 - 2 / x²

The x-intercept is given as,

y = 0

1 - 2 / x² = 0

x² = 2

x = √2

The equation of the line that passes through points A (√2, 0) and B (0, -2) will be given as,

(y + 2) = [(0 + 2) / (√2 - 0)](x - 0)

y = √2x - 2

The equation of the line is y = √2x - 2. And the coordinate of point A will be (√2, 0).

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The AC model which Rashmi will prefer to purchase in this case:

Vidyut

The correct option is (b)

Now, According to the question:

The given information is:

Rashmi does not like to spend more than Rs 24,000 for purchasing the AC. So we need to find among the given AC Model that is suitable for Rashmi to purchase.

So the cost of AC Model Vidyut can be considered.

So the amount is Rs 24,425  

Discount provided is 5%

So 5% of 24425

   = 5/100 x 24,425

   = 1221.25

So 24,425 – 1221.25  

Rs 23203.75 will be the cost after discount.

Hence, The AC model which Rashmi will prefer to purchase in this case:

Vidyut.

The correct option is (b).

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The estimated average increase in the car rentals per day for Tuesday through Friday is equal to 51.

As given in the question,

Given table represents the total number of cars every day.

Day           : M    Tu    W    Th       F      Sa     Sun

Total cars : 41   109   158   199  262   313    352

To calculate estimated average for Tuesday through Friday is given by :

Estimated number = xₙ - xₙ₋₁

Day :                  :         Wed -Tue         Thurs - Wed            Friday - Thurs

Estimated cars :      158 - 109 =49         199 - 158 = 41           262 - 199 = 63

Estimated average increase in cars rental is given by

=  ( 49 + 41 + 63 ) / 3

= 153 /3

= 51

Therefore, the estimated average increase in the car rentals per day for Tuesday through Friday is equal to 51.

The above question is incomplete, the complete question is:

The table shows total number of cars rented everyday for a week from Golden State Rentals, What is the estimated average increase in car rentals per day for Tuesday through Friday?

Golden State Car Rentals

Day           : M    Tu    W    Th       F      Sa     Sun

Total cars : 41   109   158   199  262   313    352

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To find the B in Y = MX + B with two points and slope, choose either the point (X₁, Y₁) and slope M, then B is given by an expression Y₁ - MX₁

The slope-intercept form of equation of line is y = mx + b

where m is the slope of the line and b is the y-intercept of the line.

We need to find the value of b i.e., y-intercept when the slope and a point is given.

We know that the equation of line with slope m and passing through point (x₁, y₁) is given by the formula

(y - y₁) = m(x - x₁)

If we have been given two points (lets say (x₁, y₁) and (x₂, y₂)) and a slope, then we use above point-slope form of equation of line by choising one of the point from (x₁, y₁) and (x₂, y₂)

For point (x₁, y₁) and slope m, we simplify equation.

(y - y₁) = m(x - x₁)

y - y₁ = mx - mx₁

y = mx + (y₁ - mx₁)

Comparing above equation with slope-intercept form we get the y-intercept ,

b = y₁ - mx₁

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The two equations are 150 + 5w and 45 + 20w.

In 7 weeks they will have the same amount of $225 and in terms of ordered pairs, it is (7, 225).

If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

Let, the number of weeks be 'w'.

Therefore, From the given information the two equations can be formed as,

150 + 5w and 45 + 20w.

Now, The number of weeks required when they'll have the same amount of money can be obtained if we equate these two equations.

150 + 5w = 45 + 20w.

5w - 20w = 45 - 150.

- 15w = - 105.

w = 105/15.

w = 7 weeks.

They will have 150 + 5×15 = 150 + 75 = 225 each in terms of ordered pairs (7, 225).

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Answer:

94 pence

Step-by-step explanation:

128=20

divide both by 128, so

1 = 0.15625

now times both by 6

6 = 0.9375

£0.94 (rounded)

After 5 seconds, the height will be about 65.5 feet.

One way to predict the height after 5 seconds is to use the equation of the line of best fit. The line of best fit is a line that best represents the relationship between the x and y values in the table.

To find the equation of the line of best fit, we can use the Least Squares Method.

Using the least squares method, we can calculate the slope of the line which is m=12.5, and the y-intercept which is b=3.

Therefore, the equation of the line of best fit is: y = mx + b

y = 12.5x + 3

We can use this equation to predict the height after 5 seconds by substituting x = 5 into the equation:

y = 12.5(5) + 3

y = 62.5 + 3

y = 65.5

So, after 5 seconds, the height will be about 65.5 feet.

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Answer: 6.9 miles

Step-by-step explanation:

Just divide 12,144 by 1,760 it's pretty simple

Cheers

-RsmBro

Answer: 6.9 miles

Step-by-step explanation:

12144yd / 1760

= 6.9mi

The number of more games that Lucy sells than Finley will be 28 games.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Mathew, Lucy, and Finley sold a total of 56 games at a car boot sale. The ratio of games that they each sold is 2:5:1.

Let 'x' be the common factor. Then the equation is given as,

2x + 5x + 1x = 56

8x = 56

x = 7

Then the number of more games that Lucy sells than Finley will be given as,

⇒ 5 × 7 - 1 × 7

⇒ 35 - 7

⇒ 28

The number of more games that Lucy sells than Finley will be 28 games.

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30 such passwords are possible.

6 choices for the 1st, then 5 choices for the 2nd,

The first two are alphanumeric, and the latter three are numbers.

There are 26 letters.

Ten digits are present.

There are no repetitions among the two available letters. However, it is irrelevant which sequence they are in. He can choose from 2x4x3, or 24 distinct passwords. so: 6*5=30

or  nPk=n!/(n-k)!  with n=6 and k=2

Consequently, the total number of passwords that can be created while still adhering to the limitations set

so: 6*5=30

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y = mx + b is the slope-intercept form of the equation of a straight line. In the equation y = mx + b, m is the slope of the line and b is the intercept.

Now, According to the question:

y = mx + b is the slope-intercept form of the equation of a straight line. In the equation y = mx + b, m is the slope of the line and b is the intercept. x and y represent the distance of the line from the x-axis and y-axis, respectively. The value of b is equal to y when x = 0, and m shows how steep the line is.

The equation of a straight line with slope m passing through the origin (0,0) is given by:

y = mx

Hence, the y-intercept at the origin is zero

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When the triangle ABC is rotated 180 degrees around the origin, the length of A'C' is 3 units.

The angle of rotation is a unit of measurement in mathematics that expresses the angle at which a figure is rotated around a fixed point, frequently the center of a circle. A rotation of 310 degrees can also be referred to as a rotation of -50 degrees because a clockwise rotation is regarded as a negative rotation. A rotation is a transformation in which every point of a figure is turned through a predetermined angle and in a predetermined direction around a fixed point. The fixed point is referred to as the rotational center. The term "angle of rotation" refers to the rotation's amount and is expressed in degrees.

Here,

Rotating the triangle doesn't change the length of its sides.

So, length of AC=length of A'C'

length of AC=3 units

length of A'C'=3 units

The length of A'C' is 3 units when the triangle ABC is rotated 180° about the origin.

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Answer: The triangle inequality states that each side of a triangle must be shorter than the sum of 2 other sides.

Step-by-step explanation: Please make me Brainliest.

Answer:

x=-64/5 and y=24/5

Step-by-step explanation:

1/2 x+3y=8 --------(i)

x+y=-8------------(ii)

from equation (ii), y=-8-x -------(iii)

substitute (iii) into (i)

1/2 x +3(-8-x)=8

1/2 x-24-3x=8

-5/2 x -24=8

-5/2 x= 8+24

-5/2 x= 32

-5x= 64

x=64/-5= -64/5

substitute x into (iii)

y=-8-(-64/5)

y= -8+64/5

y=(-40+64)/5

y=24/5

The total paid amount to the finance company if the loan is repaid in 40 years is $198,076.910617.

A loan is a source of funding in the form of debt that is taken out by the lender who charges interest as the price of the loan. The borrower is expected to make payments to the lender on a regular basis, usually monthly. This payment settles the interest charged on the outstanding balance and partially reduces the principal balance of the loan.

We have, A couple gets financing for 80% of the $150,000 purchase price of a house.

Price of house = 150,000

Loan = 80% × 150,000 =120,000

rate of interest = 6%

For monthly compounding, rate

= 0.06/12=0.005

time period , n = 40 years

For adjusted for monthly payment = 40 × 12 = 480 months

Now, calculate the monthly payment,

[tex]Payment = \frac{loan \times r}{1 - {(1 - r)}^{ - n} } [/tex]

[tex] = \frac{120,000 \times 0.005}{1 - {(1 + 0.005)}^{ - 480} } [/tex]

[tex] = \frac{600}{0.908737} = 660.25[/tex]

Total payment = Monthly payment × number of months

Total payment= 660.25× 300 = 198,076.910617

Hence, total amount paid to finance company is $198,076.910617.

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The derivative of inverse tangent of 4x is

[tex](tan^{-1}x)' = \frac{1}{(1 + x^2)}[/tex] is the formula for tan inverse x's derivative. Finding tan inverse x's derivative with regard to x is the process of differentiation of tan inverse x. The derivative of tan inverse x can alternatively be thought of as the rate of change of tan inverse x, which is represented by the expression [tex]\frac{1}{(1 + x^2)}[/tex].

The derivative of inverse tangent of 4x is [tex]\frac{4}{(16x^2+1)}[/tex]

The derivative of [tex]tan^{-1}(4x)[/tex] can be represented using the derivative of formula.

[tex]tan^{-1}(x)=\frca{1}{(1+x^2)}[/tex]

[tex]\frac{d}{dx} tan^{-1}(4x)=\frac{1}{16x^2+1}\times\frac{d}{dx}(4x)[/tex]

[tex]\frac{d}{dx} tan^{-1}(4x)=\frac{1}{(16x^2+1)}\times4\times\frac{d}{dx}(x)[/tex]

as we know that [tex]\frac{d}{dx}x=1[/tex]

[tex]\frac{d}{dx} tan^{-1}(4x)=\frac{4}{(16x^2+1)}[/tex]

The derivative of inverse tangent of 4x is [tex]\frac{4}{(16x^2+1)}[/tex].

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The answer of seven times the quantity of three plus one is 24.

What is expression?

A finite combination of symbols that are well-formed in accordance with context-dependent rules is referred to as an expression or mathematical expression in mathematics.

A mathematical expression is a phrase that contains a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math.

Consider, the given expression

"Seven times the quantity of three plus one."

"Three" means ' 3 '

"one" means ' 1 '

"the quantity three plus one" means  ' (3 + 1) '

"Seven times the quantity ..." means  ' 7(3  + 1)'

That's the expression.

One of the rules for handling these things is that you should always

take care of anything inside parentheses first.  So do that.

(3 + 1)  =  4

Now you can can write the expression like this:    ' 7(4) ' .

That's just  24.

Hence, the answer of seven times the quantity of three plus one is 24.

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1. A goal scored represents as 73 to 99.

2. All the 5 shots does the goalie need to save.

In the given question,

The goalie on the Ice blades hockey team saves the opponent's shots = 73%

The other team takes 5 shots in the final 10 minutes.

1. We have to find which digits represent a goal scored.

As given the paired digits 00 to 99 represent 100 shots.

Let 00 to 72 = a shot that is saved. So a goal scored represents as 73 to 99.

2. For a group to be a success, we have to find how many of the 5 shots does the goalie need to save.

A saved shot is represented by the numbers 00 to 72, and a goal is represented by the numbers 73 to 99. Thus, in the groups, it is necessary to save all five shots.

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The complete question is:

The goalie on the Ice blades hockey team saves (blocks) 73% of the opponent's shots. With 10 minutes to go, the Ice blades are ahead by one goal, and they will win if the other team does not score.

The other team takes 5 shots in the final 10 minutes. The Ice blades do not score any more goals. The table shows pairs of random digits. The pairs in each group simulate the 5 shots taken by the opponent.

1. The paired digits 00 to 99 represent 100 shots.

Let 00 to 72 = a shot that is saved. Which digits represent a goal scored? Explain.

2. Each group represents the 5 shots taken by the other team. To win the game, the Ice blades cannot let the other team score any goals.

For a group to be a success, how many of the 5 shots does the goalie need to save?

Answer:

height of the cone is 25 cm.

Step-by-step explanation:

by using the formulas for the surface area of a cylinder and a cone to find the total surface area of the solid object.

The formula for the surface area of a cylinder is 2πr(r+h) where r is the radius and h is the height.

The formula for the surface area of a cone is πr(r+l) where r is the radius and l is the slant height.

Let's assume that the radius of the cylinder and cone is 'r'.

Now we know that :

2πr(r+30) + πr(r+l) = Total surface area

We are given that the cost of painting the total surface area is Rs. 3036 at the rate of Rs. 150 per 100 sq cm. So we can use this information to find the total surface area.

3036*100/150 = 2022 sq cm

Now we can substitute this value of total surface area in the above equation.

2πr(r+30) + πr(r+l) = 2022

Now we can solve for 'l' (slant height of the cone)

we know that the slant height of the cone is 25 cm so we can substitute this value in the above equation.

2πr(r+30) + πr(r+25) = 2022

Solving this equation, we get the height of the cone = 25 cm.

So the height of the cone is 25 cm.

To translate a horizontal graph, you need to adjust the x-axis. This can be done by shifting the graph to the left or right. Additionally, you can stretch or shrink the graph by adjusting the scale of the x-axis.

A horizontal graph is a type of graph that is used to represent data in a two-dimensional space. To translate a horizontal graph, you must adjust the x-axis. This can be done by shifting the graph to the left or right. Additionally, you can stretch or shrink the graph by adjusting the scale of the x-axis. This can be done by changing the number of points on the x-axis, or by making the intervals between points larger or smaller. When translating a graph, it is important to make sure that the y-axis remains unchanged as this will ensure that the data is accurately represented. Translating a horizontal graph is a useful way to compare and analyze data. It allows you to see how changes in one variable affect the other variables in the data set. It is also an essential skill for data analysis and is used in many different fields, such as finance and economics.

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Each absolute value graph will take the form of a "V." A negative slope and a positive slope make up its two sections.

Each absolute value graph will take the form of a "V." A negative slope and a positive slope make up its two sections. They meet at the vertex, which is where they do. An absolute value graph can be folded in half along its symmetry axis.The parent function, or most fundamental function, of absolute value functions is y = |x|.

Let's now plot the answers to the equations y = |x-1| and its parent function.

You'll see that the function is nothing more than the parent function moved over. One unit has been added to the right of the vertex. This is due to the fact that |x - 1| Equals 0 when x = 1, since |1 -1| = 0. Wherever the absolute value inside the value is zero, that is the vertex.

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The sum of angles in the images result in -

First image - Neither (neither complementary nor supplementary angle)

Second image - Neither (neither complementary nor supplementary angle)

Third image - Complementary (sum of angles resulting in 90°)

What are complementary and supplementary angles?

When two angles are added together, complementary and supplementary angles are defined. Two angles are said to be supplementary angles because they combine to generate a linear angle when their sum is 180 degrees. When two angles add up to 90 degrees, however, they are said to be complementary angles and together they make a right angle.

In the first image it can be seen that the two angles measure 90° and 89° respectively.

On adding the two angles the sum is obtained as -

90° + 89° = 179°

Therefore, this is neither a complementary angle nor a supplementary angle.

In the second image it can be seen that the two angles measure 63° and 47° respectively.

On adding the two angles the sum is obtained as -

63° + 47° = 110°

Therefore, this is neither a complementary angle nor a supplementary angle.

In the third image it can be seen that the two angles measure 61° and 29° respectively.

On adding the two angles the sum is obtained as -

61° + 29° = 90°

Therefore, this is a complementary angle as the sum of the two angles equals 90°.

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-6a² + 4a² + 3 is the quotient of the given expression: (36a⁴- 24a⁴ - 18a²) ÷ (-6a²).

It is known as the quotient to divide two integers. The dividend is the quantity being divided, and the divisor is the quantity being divided. The quotient is the outcome of the division.

The sum is the result of multiplying two or more numbers together. The difference is determined by the result of subtracting the two values. The result of multiplying two or more integers is what is known as the product. The quotient is what remains after dividing two numbers.

Given that,

= (36a⁴- 24a⁴ - 18a²) ÷ (-6a²)

= - 6a² + 4a² + 3

thus, -6a² + 4a² + 3 is the quotient of the above expression.

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Answer:

-357

Step-by-step explanation:

Multiply 17 and -21 on your calculator

Answer:

-357

Step-by-step explanation:

• means multiplication

17 • —21?

17 × (-21)

= -357

Find the Lowest Common Multiple (LCM) between the denominators as the first step. Step 2: Multiply each fraction's numerator and denominator by a certain amount to give them the LCM as their new denominator. Step 3: Change the denominator but add or subtract the numerators.

Fractions with Differing Numerators: Adding and Subtracting Fractions:

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Contradictions, also referred to as No Solution Equations, are the final category of equations.

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Answer: [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

    We can use this formula to solve.

    We will substitute the known points and simplify. I will use the points (0, -5) and (-3, -4)

                [tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }=\frac{-5--4}{0-3} =\frac{-5+4}{-3} =\frac{-1}{-3}= \frac{1}{3}[/tex]