What is -2,3 rotated 90 degrees counterclockwise around the origin?

Answer:  The required factored form of the given expression is [tex](x-6)(2y+5).[/tex]

Step-by-step explanation:  We are given to factorize the following expression :

[tex]E=2xy+5x-12y-30~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We will be using the following property :

[tex]a(b+c)+d(b+c)=(a+d)(b+c).[/tex]

From expression (i), we have

[tex]E\\\\=2xy+5x-12y-30\\\\=x(2y+5)-6(2y+5)\\\\=(x-6)(2y+5).[/tex]

Thus, the required factored form of the given expression is [tex](x-6)(2y+5).[/tex]

estimate  by rounded to the nearest dollars

2 +1 +5 +2 +3 +9 +1 =  $23

-2

23-2 = 21

 yes the amount is reasonable

Answer: 3+1+5+2+3+9+1-1-1=22

The total on the register is reasonable because if you estimate $21.77 to the nearest dollar you would get $22.00.

Step-by-step explanation:

The total number of sides in a polygon with n vertices is = n sides.

We have a Polygon with n vertices.

We have to determine the number of sides of this polygon.

In geometry, a polygon can be defined as a  plane, two-dimensional closed shape bounded with straight sides.

According to the question, we have -

A polygon with n vertices.

The total number of sides in a polygon with n vertices is = n sides.

The sides of the polygon are connected end to end in a cyclic order. The side with endpoints as nth and (n - 1)th vertices is connected to the side with endpoints as (n - 1)th and (n - 2)th vertices and so on.

Hence, the total number of sides in a polygon with n vertices is = n sides.

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Answer:

False

Step-by-step explanation:

If f(x) is a function , then for each value of x  there should be  a single y values

For input 0 there is a output 0

for input 10, the output is 2

for input 15, output is 3

For input 5, we have two output 1 and 3

for single input 5, the function cannot have two outputs 1  and 3

So this f(x) is not a function

Answer:

The measure of length of equal side is 36 cm each.

B is correct.

Step-by-step explanation:

Isosceles triangle ABC has a perimeter of 96 centimeters.

The base of the triangle is BC and measures 24 cm

We need to find the length of equal side of triangle.

AB=AC

The perimeter of triangle is 96 cm

AB + AC + BC = 96

AB + AB + 24 = 96                          ( ∵ AB=AC)

              2AB = 96-24

              2AB = 72

                AB = 36

Hence, The measure of length of equal side is 36 cm each.

The average rate of change of the function over the interval is 2

Finding the average rate of change

From the question, we have the following parameters that can be used in our computation:

The graph

The interval is given as

From x = -3 to x = 3

The function is a quadratic function

This means that it does not have a constant average rate of change

From the graph

y = -8, when x = -3

y = 4, when x = 3

This means that

f(-3) = -8

f(3) = 4

The average rate is calculated using

Rate = (Change in y values)/(Change in corresponding x values)

So, we have

Rate = (4 + 8)/(3 + 3)

Evaluate

Rate = 2

Hence, the average rate of change is 2

Answer:

[tex]r=\frac{25-bh}{h}[/tex]

Step-by-step explanation:

Given : Consider the following equation, [tex]bh+hr=25[/tex]

To find : Solving for r ?

Solution :

The equation is [tex]bh+hr=25[/tex] solve for r,

Subtract 'bh' both side,

[tex]bh+hr-bh=25-bh[/tex]

[tex]hr=25-bh[/tex]

Divide both side by 'h',

[tex]\frac{hr}{h}=\frac{25-bh}{h}[/tex]

[tex]r=\frac{25-bh}{h}[/tex]

Therefore, [tex]r=\frac{25-bh}{h}[/tex]

Answer:  The x-intercept and y-intercept of the given line are (3.6, 0) and (0, -1.2) respectively.  

Step-by-step explanation:  We are given to find the x-intercepts and y-intercepts of the line described by the following equation :

[tex]3x-9y=10.8~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

the x-intercept of a line is the point where the y co-ordinate is 0. Similarly, y-intercept is the point where the x co-ordinate is 0.

Substituting y = 0 in equation (i), we get

[tex]3x-9\times0=10.8\\\\\Rightarrow 3x-0=10.8\\\\\Rightarrow 3x=10.8\\\\\Rightarrow x=\dfrac{10.8}{3}\\\\\Rightarrow x=3.6.[/tex]

So, x-intercept is (3.6, 0).

And substituting x = 0 in equation (i), we get

[tex]3\times 0-9y=10.8\\\\\Rightarrow 0-9y=10.8\\\\\Rightarrow 9y=-10.8\\\\\Rightarrow y=-\dfrac{10.8}{9}\\\\\Rightarrow y=-1.2.[/tex]

So, y-intercept is (0, -1.2).

Thus, the x-intercept and y-intercept of the given line are (3.6, 0) and (0, -1.2) respectively.  

Answer:

The boundary line should be solid because it have a 'great/less than or equal to' sign

Step-by-step explanation:

Answer: You could use straight angles as a counterexample for the argument all angles are either right obtuse or acute .

The function that best represents the graph of the function which is given is:

               [tex]f(x)=(x-3)^2+1[/tex]

From the graph that is provided to us we observe that the graph passes through the point (3,1).

Hence, we will check which of the following function satisfies this point.

a)

[tex]f(x)=(x-3)^3-1[/tex]

when x=3 we see that:

[tex]f(x)=(3-3)^3-1\\\\i.e.\\\\f(x)=-1\neq 1[/tex]

Hence, option: a is incorrect.

c)

[tex]f(x)=(x+3)^3-1[/tex]

when x=3 we have:

[tex]f(3)=(3+3)^3-1\\\\i.e.\\\\f(3)=9^3-1\\\\i.e.\\\\f(3)=729-1\\\\f(3)=728\neq 1[/tex]

Hence, option: c is incorrect.

d)

[tex]f(x)=(x+3)^3+1[/tex]

when x=3 we have:

[tex]f(3)=(3+3)^3+1\\\\i.e.\\\\f(3)=9^3+1\\\\i.e.\\\\f(3)=729+1\\\\f(3)=730\neq 1[/tex]

Hence, option: d is incorrect.

Now we are left with option: b)

i.e.

b)

[tex]f(x)=(x-3)^2+1[/tex]

Also, when x=3 we have:

[tex]f(3)=(3-3)^2+1\\\\f(3)=0+1\\\\f(3)=1[/tex]

Hence, it passes through the point (3,1)

Also, when we will plot this function we observe that it matches the given graph.

An expression is defined as a set of numbers, variables, and mathematical operations. An equivalent expression for 1.5(3x+4)+0.25(6x+8) is 7x+8.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression can be simplified as,

1.5(3x + 4) + 0.25(6x + 8)

= 4.5x + 6 + 2.5x + 2

= 7x + 8

Hence, an equivalent expression for 1.5(3x+4)+0.25(6x+8) is 7x+8.

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Answer: Option 'C' is correct.

Step-by-step explanation:

Since we have given that

Cost for 5 weeks i.e. 15 classes = $108

Cost of per class is given by

[tex]\frac{108}{15}=7.2[/tex]

Cost for 8 weeks i.e. 24 classes = $125

Cost of per class is given by

[tex]\frac{125}{24}=5.21[/tex]

Amount of saving of per class by taking the 8 week class is given by

[tex]7.2-5.21=\$1.99[/tex]

Hence, Option 'C' is correct.

The correlation coefficient r=0.23 will remain unchanged at 0.23 even after adding a constant to all x-variable values, doubling the y-variable values, and swapping the x and y variables, because the correlation coefficient is unaffected by such transformations.

The correlation between two variables is denoted by the symbol, r, and it measures the strength and direction of a linear relationship between two quantitative variables. When we add a constant to all values of the x-variable or multiply all values of the y-variable by a constant, the correlation coefficient does not change. However, interchanging the x and y variables also does not change the value of r since correlation is symmetrical. Therefore, if r=0.23 initially, after adding 0.14 to all values of x, doubling the y-variable values, and interchanging the two variables, the new correlation will still be 0.23.

Answer:

abc(a + b + c)

That's your answer!!!

Answer:

Step-by-step explanation:dhdjdbfbd

The principle being demonstrated is known as the Symmetric Property, which holds that if an equation or statement is valid, then its switched or flipped version will also be true.

The question refers to a fundamental property in mathematics called the Symmetric Property. The Symmetric Property states that if an equation or statement is true, then its mirror or flipped version will also hold true. In this case, if LM = JK, then under Symmetric Property, it must be true that JK = LM.

For instance: If 5 = 2 + 3, then 2 + 3 = 5.

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The answer is gas because gas particles move so fast they bounce off one another when they collide. Plasma has Negatively AND Positively charged particles within it.

Gases are the state of matter where neutral particles bounce off one another as they collide. This is due to their constant, random motion and the elastic nature of their collisions.

The state of matter that has neutral particles that bounce off one another as they collide is a Gas. This is due to the fact that gases are composed of a large number of particles that are in constant, random motion. These particles collide with each other and with the walls of their container. Importantly, these collisions are perfectly elastic, meaning they conserve both momentum and kinetic energy.

In Liquids and Solids, the particles are held together with stronger intermolecular forces which restrict their motion. In Plasma, the particles are ionized and hence, are not neutral.

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