what is the equation after you rotate y=x^2 over the origin?

The number of distinguishable permutations in the given letters are:

a.) Bigger= 720

b.) Hollywood = 362,880

C.) possess = 5040

Permutation is defined as the arrangement of data set in a definite form which involves multiplication from the given number to 1.

The word 'bigger' contains 6 letters. Therefore the permutation of 6 = 6×5×4×3×2×1 = 720

For the word 'hollywood' contains 9 letters. Therefore the permutation of 9 =9×8×7× 6×5×4×3×2×1= 362,880

For the word 'possess' contains 7 letters. Therefore the permutation of 7 = 7× 6×5×4×3×2×1 = 5040.

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The permutation and combination expressions have their values to be ⁸C₇ = 8 and ¹¹P₅ = 55440

From the question, we have

⁸C₇ and ¹¹P₅

The combination expression: ⁸C₇

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 8 and r = 7

Substitute the known values in the above equation

Total = ⁸C₇

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

⁸C₇ = 8!/7!1!

Evaluate

⁸C₇ = 8

(b) The permutation expression: ¹¹P₅

The number of ways of selection could be drawn is calculated using the following permutation formula

Total = ⁿPᵣ

Where

n = 11 and r = 5

Substitute the known values in the above equation

Total = ¹¹P₅

Apply the permutation formula

ⁿPᵣ = n!/(n - r)

So, we have

¹¹P₅ = 11!/6!

Evaluate

¹¹P₅ = 55440

Hence, the values are 8 and 55440

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For a system of Linear equations in two variables there can be infinite number of solutions.

The linear equation in two variable is the representation of a straight line.

To give an example;

Let f(x) be a linear equation of two variables.

Then,

f(x) = Ax + By

Then the solution for f(x) would be any value of x coordinate corresponding to y coordinate that satisfies the equation, i.e The sum of the product of the x coordinate with A and the product of the y coordinate with B should be equal to f(x).

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The real zeroes of the given polynomial are located at (1, 2).

The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero.

Given that, x⁴-2x³+x-2

Checking the real zeroes,

Considering point (1, 2)

y = 2 and x = 1

Putting the values,

x⁴-2x³+x-2 = 1-2+1-2 = 2

And, y = 2

Therefore, LHS = RHS

Hence, The real zeroes of the given polynomial are located at (1, 2).

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a. Angle g is corresponding to angle c.

b. Angle f is alternate to angle d.

c. Angle d is corresponding to angle h.

d. Angle c is vertically opposite to angle a.

e. Angle c is alternate to angle e.

f. Angle f is vertically opposite to angle h.

g. Angle e is corresponding to angle a.

h. Angle e is vertically opposite to angle g.

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During the time period of 20 years the percent decreases in the country's population is 3.28%.

Percentage is a number or ratio which is a fraction of hundred.

Given,

Population of the country in 1990 = 152 million

Population of the country in 2010 = 147 million

Percent decrease in the population will be ,

= [ (1990's population - 2010's population)/1990's population ]*100

= [ (152 - 147 )/152]*100

= [5/152]*100

= 3.28%

Hence , the decrease in the population will be 3.28%.

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Answer:

x = 44°

Step-by-step explanation:

We can take angles as,

→ x = ?

→ y = 52° (opposite angles are equal)

→ z = ?

The value of z will be,

→ z + 96° = 180°

→ z = 180° - 96°

→ [ z = 84° ]

Now the value of x will be,

→ x + y + z = 180°

→ x + 52° + 84° = 180°

→ x + 136° = 180°

→ x = 180° - 136°

→ [ x = 44° ]

Hence, the value of x is 44°.

Answer:

x = 2y - 65

Step-by-step explanation:

Answer:

2. 13

3. 3

4. 5

7. 4

8. 37

9. 5

Step-by-step explanation:

Denominator: same as the denominator of the fraction in the mixed number.

Numerator:

1. Multiplying the denominator of the fraction by the whole number, and

2. Adding that number to the numerator of the fraction

The numerator signifies the total parts taken, and the denominator indicates the entire parts as a whole.

1) 2*3/5 = 13/5

2) 4*2/3 = 14/3

3) 6*4/5 = 34/5

4) 5*3/4 = 23/4

5) 7*2/5 = 37/5

6) 9*1/5 = 46/5

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Answer:

Glitzy Generalizations , Card Arranging , Plain people , Testimonial , Bandwagon , Using names are the six techniques used by propaganda.

Step-by-step explanation:

Information—especially that which is slanted or deceptive—used to advance or publicize a specific political cause or point of view.

Glitzy Generalizations

Use expressions or words that sound appealing and are widely accepted.

Card Arranging

Using only those ideas and facts that support your argument.

Plain people

Tell voters that you are a normal person with same needs and beliefs as theirs.

Testimonial

Persuades people to do something by leveraging their popularity as a celebrity or athlete.

Bandwagon

Encourages a tendency to follow the crowd

Using names

Put a bad name on your opponent.

Glitzy Generalizations , Card Arranging , Plain people , Testimonial , Bandwagon , Using names are the six techniques used by propaganda.

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Answer:

Step-by-step explanation:

3< 0 + 2

3 < 2

the inequality is false because 3 is greater than 2, so the ordered pair (0,3) can’t be a solution of the inequality

Answer:

(0, 3) is not a solution to y < x + 2.

Step-by-step explanation:

Plug the given coordinates in to the inequality:

(0, 3)  →  x = 0,  y = 3

y < x + 2

3 < 0 + 2

3 ≮ 2

(0, 3) is not a solution to y < x + 2.

Answer:

75%

Step-by-step explanation:

First, you subtract 200 from 350 to get the difference, which is 150.

Then, you do 150 divided by 200 since 200 is the starting number and it is increasing by 150.

150/200 = 0.75

To convert the decimal into a fraction multiply by 100.

0.75*100 = 75

Using the perimeter and and slant height, the surface area of the square pyramid is 96cm²

The surface area of a square pyramid is the sum of the areas of all its 4 triangular side faces with the base area of the square pyramid.

The surface area of a square pyramid is the product of half the perimeter of the square and it's slant height

data;

Perimeter of a square = 4a

a = side length

The perimeter of this square = 4 * 8 = 32cm

The surface area of the square pyramid = 1/2 * 32 * 6 = 96cm²

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The equations are matched as below and the graph is plotted and attached

A log-log graph, also known as a log-log plot, is a two-dimensional graph of numerical data used in science and engineering that use logarithmic scales on both the horizontal and vertical axes.

The exponential graph is the opposite of logarithmic graph

In the given functions

log (x) is logarithmic function

10× is exponential function

Similarly, the natural exponent graph is the opposite of natural logarithm graph

in the given functions

e× is the natural exponential

ln (x) is the natural logarithm

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In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range.

The group of all outputs of a function is called its range. for example: Let's have a look at the function f: A→ B, where f(x) = 2x and A and B each represent a "collection of natural numbers. The domain in this case is A, and the co-domain is B. The range then appears as the function's output. so Set of all even natural numbers is the range.

A relation between a number of set of inputs with only one output corresponding to each of the input is called function.

Example:

Y = 2x

1. First, we have to write the function y=f(x) and then solve the equation for x and taking out equation of form x=g(y).

Suppose we have a function y=x2+1 and we have to find it range so,

we have to solve it for x to get

x=√y-1.

2. Now we have to find the domain of g(y), and this is simply the range of function f(x).

For our example,

y−1≥0, so [1,∞) is the range of f(x)=x2+1.

3. If we can't solve equation for x, then we can try it by drawing the graph of the function and find its range.

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The speed of the wind is 100 miles per hour.

Speed is the ratio of distance traveled and the time taken to travel the distance.

Given that, the twin-engine aircraft can fly 960 miles from city A to city B in 3 hours with the wind.

Let the speed of the wind and the aircraft be w and p respectively.

The net speed with the wind is:

w + p

Since the distance between the cities is 960 miles and the aircraft covers it in 3 hours with the wind, the net speed with the wind is:

w + p = 960/3

w + p = 320

p = 320 - w

Similarly, the net speed against the wind is:

p - w = 960/8

p - w = 120

Substitute p = 320 - w into the above equation:

320 - w -w = 120

2w = 320-120

w = 100

hence, the speed of the wind is 100 miles per hour.

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For any two members of the set, addition will result in a value that is also a member of the set, if the set is closed.

It is speaking of a set, (the mathematical concept) and the operation, here, addition. For any two members of the set, addition will result in a value that is also a member of the set, if the set is closed.

Yes, whole numbers are closed under addition

It is speaking of a set, (the mathematical concept) and the operation, here, addition. For any two members of the set, addition will result in a value that is also a member of the set, if the set is closed.

So the set of whole numbers are closed under addition

Addition of the set of positive integers is closed because the sum of any two integers is also an integer.

Consider subtraction. Positive numbers are not closed under subtraction because picking a larger number to subtract from a smaller one results in a negative number result.

Therefore,  For any two members of the set, addition will result in a value that is also a member of the set, if the set is closed.

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Answer:

Step-by-step explanation:Is there more to the question

The formula for slope-intercept form is: y = mx + b

    m = the slope of the line

    b = the y-coordinate of the y-intercept, (0,b)

In this case, the slope is 3, since you go up 3 and to the right 1 to get from the point at (1,1) to the point at (2,4).  3/1 = 3

The line crosses the y-axis at (0,-2), so your b-value is -2.

The equation is y = 3x - 2.

In general, lines that increase (go uphill) from left-to-right have a positive slope.  Lines that decrease (go downhill) from left-to-right have a negative slope.  

Answer:

[tex]\begin{aligned}\textsf{(a)} \quad y&=-6x^2\\y&=4x^2-2\end{aligned}[/tex]

[tex]\textsf{(b)} \quad x=\dfrac{1}{4}y^2[/tex]

Step-by-step explanation:

A graph is symmetric with respect to the y-axis if for every point (a, b) on the graph, there is also a point (-a, b) on the graph.

Linear functions are not symmetric with respect to the y-axis.

Quadratic functions are symmetric with respect to the y-axis if the y-axis is their axis of symmetry, so when the variable x is squared.

Cubic functions are not symmetric about the y-axis.

Square root functions are not symmetric about the y-axis.

There are two quadratic functions with x² in the given answer options.

Test to see if they are symmetric with respect to the y-axis.

Test for symmetry

To determine if a graph is symmetric with respect to the y-axis, replace all the x's with (−x).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the y-axis.

Given function:

[tex]y=-6x^2[/tex]

Replace x with (-x):

[tex]\implies y=-6(-x)^2[/tex]

[tex]\implies y=-6x^2[/tex]

Therefore, as the function is equal to the original function, this function is symmetric with respect to the y-axis.

Given function:

[tex]y=4x^2-2[/tex]

Replace y with (-y) and x with (-x):

[tex]\implies y=4(-x)^2-2[/tex]

[tex]\implies y=4x^2-2[/tex]

Therefore, as the function is equal to the original function, this function is symmetric with respect to the y-axis.

A graph is symmetric with respect to the x-axis if for every point (a, b) on the graph, there is also a point (a, -b) on the graph.

Linear functions are not symmetric with respect to the x-axis.

Quadratic functions are symmetric with respect to the x-axis if the x-axis is their axis of symmetry, so when the variable y is squared.

Cubic functions are not symmetric about the x-axis.

Square root functions are not symmetric about the x-axis.

There is one quadratic functions with y² in the given answer options.

Test to see if it is symmetric with respect to the x-axis.

Test for symmetry

To determine if a graph is symmetric with respect to the x-axis, replace all the y's with (−y).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the x-axis.

Given function:

[tex]x=\dfrac{1}{4}y^2[/tex]

Replace y with (-y):

[tex]\implies x=\dfrac{1}{4}(-y)^2[/tex]

[tex]\implies x=\dfrac{1}{4}y^2[/tex]

Therefore, as the function is equal to the original function, this function is symmetric with respect to the x-axis.

The school will purchase 10 tables and 80 chairs.

With the aid of mathematical expressions, algebra is the area of mathematics that helps to depict situations or problems. We employ definite or fixed-value numbers in algebra, such as -1, 5, 0, 06, etc. In addition to using numbers, algebra also makes use of variables like x, y, and z.

Given that a school can spend $5200 on tables and chairs. The tables cost 200$ and the chairs cost 40$. There will be 8 chairs around each table.

We have to determine the number of tables and chairs will the school purchase.

Let us consider x represents the tables and y represents the chairs.

Tables cost = 200x    chairs cost= 40y

200x + 40y = 5200   ----(1)

There will be 8 chairs around each table.

1 table = 8 chairs

t = 1/8c

x =  (1/8)y                  (t means x and c means y)

substitute x value in equation(1)

200(1/8)y + 40y = 5200

(200/8)y + 40y = 5200

25y + 40y = 5200

65y = 5200

y = 5200/65

y = 80              

Substitute y value in equation (1)

200x + 40(80) = 5200

200x + 3200 = 5200

200x = 5200 – 3200

200x = 2000

X = 2000/200

X = 10

Therefore the school will purchase 10 tables and 80 chairs.

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The values of a and b are;

⇒ a = 3

⇒ b = 3

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

An exponential function is,

⇒ f (x) = a bˣ

And, It passes through the points (0, 3) and (3, 81).

Now,

Since, It passes through the points (0, 3) and (3, 81).

Hence, Substitute x = 0 ,  f(x) = 3 in the function,

⇒ f (x) = a bˣ

⇒ 3 = a b⁰

⇒ a = 3

And, Substitute x = 3 ,  f(x) = 81 and a = 3 in the function,

⇒ f (x) = a bˣ

⇒ 81 = 3 b³

⇒ b³ = 27

⇒ b = 3

Thus, The values of a and b are;

⇒ a = 3

⇒ b = 3

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By using a linear combination, we can write our number using only hundreds and ones as:

2,857 = 28*100 + 57*1

To write the number using only hundreds and ones we need to write our number as a linear combination of ones and hundreds, so we can write:

2,857 = a*100 + b*1

There are multiple solutions for this, we can use b to cover the ones and the tens, so:

57 = b*1

57 = b

And we can use a to cover the hundreds and thousands, so:

2,800 = a*100

2,800/100 = a

28 = a

Then we can write our number using only hundreds and ones as:

2,857 = 28*100 + 57*1

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Proved

Used identities

If the length of two segments is equal then the two segments are congruent.

If l(AB) = l(CD) then seg AB ≅ seg CD.

Two line segments to be congruent if and only if they have the same length.

Two shapes are congruent if they are exactly the same shape and exactly the same size. In congruent shapes, all corresponding sides will be the same length and all corresponding angle will be the same measure.

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The value of x in the Algebraic expressions is x = w / (56+r).

What is Algebra?

Algebra is a branch of mathematics focused on the study of mathematical symbols and the rules for manipulating those symbols. In algebra, letters and other symbols represent numbers, which can be manipulated and combined to solve equations and other mathematical problems. Algebra is used in a variety of different fields, from engineering to economics, and is essential for anyone studying mathematics. Algebra can be used to solve problems involving linear equations, quadratic equations, polynomials, and more. Algebra also provides an important foundation for more advanced fields of mathematics, such as calculus. By learning the basics of algebra, students can gain an understanding of key mathematical concepts and gain the skills necessary to solve complex problems.

The solution is,

given:        19x + rx  = -37x + w

            ( 19x + 37x) = w - rx

                56x + rx  = w

                 x(56+r )  = w

                             x = w / (56+r)

Therefore the value of x in the algebraic expression is  x = w / (56+r).

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Answer:

27

Step-by-step explanation:

first you multiply 6x4 which is 24 the you divive 15 by 5 you'll get 3 then you add 24 + 3 and your answer is 27

The number that Goran can choose, which will be multiples of 2, 6, and 8, between 67 and 113 are 72, 96

To find out the numbers that Goran can choose, find the multiples of 2, 6, and 8 that are between 67 and 113. Then the common multiples of these numbers within that range, are the numbers to be chosen.

Multiples of 2 between 67 and 113 :

68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112

Multiples of 6 between 67 and 113 :

72, 78, 84, 90, 96, 102, 108,

Multiples of 8 between 67 and 113 :

72, 80, 88, 96, 104, 112

The numbers that are multiples of 2, 6, and 8 are:

72, 96

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