MATH HELPERS !!! word problems involving average rate of change Please answer correctly, I have this and one more afterwards, but can only post if this is correct

Answer:

y = -2  for  -2 < x ≤ -1

Step-by-step explanation:

Ceiling function

[tex]f(x) = \left\lceil x \right\rceil[/tex]

The least integer that is greater than or equal to x.

Given ceiling function:

[tex]f(x) =\left\lceil x-1 \right\rceil[/tex]

Evaluate values in the given intervals.

[tex]\boxed{-4 \leq x < -3}[/tex]

[tex]\implies f(-4) =\left\lceil -4-1 \right\rceil=\left\lceil -5 \right\rceil=-5[/tex]

[tex]\implies f(-3.1) =\left\lceil -3.1-1 \right\rceil=\left\lceil -4.1 \right\rceil=-4[/tex]

[tex]\boxed{-2 \leq x < -1}[/tex]

[tex]\implies f(-2) =\left\lceil -2-1 \right\rceil=\left\lceil -3 \right\rceil=-3[/tex]

[tex]\implies f(-1.1) =\left\lceil -1.1-1 \right\rceil=\left\lceil -2.1\right\rceil=-2[/tex]

[tex]\boxed{-2 < x \leq -1}[/tex]

[tex]\implies f(-1.9) =\left\lceil -1.9-1 \right\rceil=\left\lceil -2.9 \right\rceil=-2[/tex]

[tex]\implies f(-1) =\left\lceil -1-1 \right\rceil=\left\lceil -2 \right\rceil=-2[/tex]

[tex]\boxed{-4 < x \leq -3}[/tex]

[tex]\implies f(-3.9) =\left\lceil -3.9-1 \right\rceil=\left\lceil -4.9 \right\rceil=-4[/tex]

[tex]\implies f(-3) =\left\lceil -3-1 \right\rceil=\left\lceil -4\right\rceil=-4[/tex]

Therefore, the step that is included in the graph of the given ceiling function is:  y = -2  for  -2 < x ≤ -1.

Graph of the parent ceiling function f(x) = ⌈x⌉

The graph of the parent function has open dots at (x, x+1) and closed dots at (x, x). Each segment is joined with a horizontal line (step).

The open dot means the value is not included, whereas the closed dot means the value is included.

To graph the given ceiling function f(x) = ⌈x - 1⌉

(See attachment).

From inspection of the attached graph of the given ceiling function:

This proves that the only step that is included in the graph of the given ceiling function from the given answer options is:  

Answer:

B. 4:3

Step-by-step explanation:

Divide both by 3:

12/3 = 4

9/3 = 3

4:3

Line segment FG is not tangent to circle E.

What is Tangent:

The tangent is defined as a line touching circles or an ellipse at only one point. Suppose a line touches the curve at P, then the point “P” is called the point of tangency. In other words, it is defined as the line which represents the slope of a curve at that point.

What is Line Segment:

A line segment has two definite endpoints in a line. The length of the line segment is fixed, which is the distance between two fixed points. The length here can be measured by metric units such as centimeters (cm), millimeters (mm) or by conventional units like feet or inches.

Now, According to the problem

The tangent line to a circle makes an angle of 90 degrees with the radius.

If |FG| is tangent to circle E.

then,

30^2 = 26^2 + 17^2

which is not true.

Therefore, line segment FG is not tangent to circle E.

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Associative Property Of Addition illustrated by each equation.

(2√7) . √3 = 2(√7 . √3)

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According to the given statement;

The difference of 9 and the quotient of a number f and 6 is 5.

the value of f is = -24

A variable is an alphabet or term that stands in for an unknowable quantity, value, or number. Particularly in the case of algebraic expressions or algebra, the variables are used. As an illustration, the linear equation x+9=4 has the variables x and 9 as constants.

The variable is a quantity that can change or is not fixed. Typically, in algebra, we use the terms "x" and "y" to express an unknown number. However, this is not unique, and we are free to use any alphabet.

According to the given value;

9 - (f÷ 6) = 5

Subtract 9 from both sides.

9 - 9 - (f ÷ 6) = 5 - 9

Simplify.

- (f ÷ 6) = -4

Distribute -1 throughout the parenthesis.

-f ÷ -6 = -4

Multiply both sides by -6.

-f ÷ -6 × -6 = -4 × -6

Simplify.

-f = 24

Divide both sides by -1.

-f ÷ -1 = 24 ÷ -1

Simplify.

f = -24

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Answer:

3b - 5 = 6

Step-by-step explanation:

3b - 5 = 6

The First Amendment to the Constitution affect American society as D. The right to a free press allows Americans to have access to many independent sources of news and information.

It should be noted that Constitution simply refers to the rules and laws that guide a group of people especially a country.

In this case, the First Amendment to the Constitution affect American society as The right to a free press allows Americans to have access to many independent sources of news and information.

In conclusion, the correct option is D.

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The correct answer is "The right to a free press allows Americans" to have access to many independent sources of news and info

Explanation:

The First Amendment to the constitution was ratified in 1791, in this it was established government could not interfere in the right to exercise religion or assemble as well as the rights of freedom of speech and freedom of the press. This last aspect implies the government cannot interfere in the circulation of information, according to this, citizens have the right to create sources of news and information to report news or express opinions. Thus, the First Amendment affects American society because "the right to a free press allows Americans to have access to many independent sources of news and info".

The average rate of change of the equation is 35

The equation is given as

y  = 35x^1

Evaluate the quotient x^1

So, we have

y  = 35x

The above equation is a proportional linear equation

A proportional linear equation is represented as

y = mx

Where

m represents the average rate of change

By comparison, we have

m = 35

Hence, the average rate of change of the equation is 35

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Complete question

Given the equation y = 35x^1 where x is distance and y is height, calculate the average rate of change

Answer:

0.7/2=0.35

Step-by-step explanation:

Answer:22.05

hope it help

and have a good day

Answer:

45

Explanation

35% is 63

so 5% is 9

so 100% is 180 cuz 5 multiplied by 20 is 100

so 25 % is 25 divided by 100 is 0.25×180 which is 45

hope that helps

By elimination, the solution of the system of equations, 3x + 2y = 6 and 3x + 3 = y, is (0 , 3).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.

Rearranging equation 2 to standard form,

3x + 3 = y     (equation 2)

3x - y = -3

Subtracting the two equations will eliminate the variable x.

3x + 2y = 6     (equation 1)

3x  -   y = -3     (equation 2)

0x + 3y = 9

y = 3

Substitute the value of y to any of the two equations and solve for x.

3x + 2y = 6     (equation 1)

3x + 2(3) = 6

3x = 6 - 6

3x = 0

x = 0

Hence, the solution of the system of equations is (0 , 3).

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Answer:

19

I first do plus 2and 7 and 10=z

The center and radius of the circle given by the equation x^2 + 2x + 1 + y^2 = 4 is (-1 , 0) and 2, respectively.

The standard form of the equation of circle is given by

(x - h)^2 + (y - k)^2 = r^2

where (h , k) is the location of the center and r is the radius of the circle.

On the other hand, the general form of the equation of  circle is given by

x^2 + y^2 + Dx + Ey + F = 0

where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.

If the equation of the circle in general form is x^2 + 2x + 1 + y^2 = 4, then the coefficients are:

D = 2

E = 0

F = 1 - 4 = -3

If D = -2h and D = 2, then

2 = -2h

h = -1

If E = -2k and E = 0, then

0 = -2k

k = 0

If F = h^2 + k^2 -r^2 and F = -3, then

-3 = (-1)^2 + 0^2 - r^2

r^2 = 1 + 0 + 3

r^2 = 4

r = 2

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How much would the commission be on a 650,000 house? $39,000

Given:

Rate of the house 1= $8,00,000

Commission for the house 1=$48,000

Rate of the house 2= $6,50,000

Commission for the house 2=x

What is the commission for the house 2?

8,00,000 ⇒48,000

6,50,000 ⇒ x (directly proportional)

On cross multiplication,

[tex]8,00,000 *x= 48,000*6,50,000\\\\x=\frac{48,000*6,50,000}{8,00,000} =39,000[/tex]

Commission for the house 2 = $39,000

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The average rainfall for the rest of the year need to be per month is 1.31 inches per month.

According to the statement

We have to find that the average rainfall for the rest of the year.

So, For this purpose, we know that the

The average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.

From the given information:

an average monthly rainfall of 0.87 inches per month. and the average rainfall for the first three months was 2.02 inches per month and that the average rainfall for the next 7 months was 0.25 inches.

Then

An average monthly rainfall per month = 0.87 inches

An average monthly rainfall per year = 0.87 *12

An average monthly rainfall per year = 10.44 inches

Then

The average rainfall for the first three months was 2.02 inches per month

The average rainfall for the first three months = 2.02 *3

The average rainfall for the first three months = 6.06

And

The average rainfall for the next seven months = 0.25*7

The average rainfall for the next seven months = 1.75

Then

The remaining average rainfall in one year = average monthly rainfall per year - (average rainfall for the first three months + average rainfall for the next seven)

The remaining average rainfall in one year = 10.44  - (6.06 + 1.75)

The remaining average rainfall in one year = 10.44  - (7.81)

The remaining average rainfall in one year = 2.63

And then

The remaining average rainfall in 2 months = 2.63

The remaining average rainfall in 2 months per month = 2.63/2

The remaining average rainfall in 2 months per month = 1.31.

So, The average rainfall for the rest of the year need to be per month is 1.31 inches per month.

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Answer:

109 x 3 = 327

Step-by-step explanation:

Polygon Q is a scaled replica of Polygon P with a factor of half. The area of Polygon Q is a proportion of the area of Polygon P= 1/4

A polygon is a plane figure characterized by a fixed amount of straight-line segments joined to form a closed polygonal chain. A polygon is a bounded plane region, a bounding circuit, or both. The segments of such a polygonal circuit are referred to as its edges or sides.

Polygons are made up of triangles, hexagons, pentagons, and quadrilaterals. The name indicates how many sides the form has. A triangle, for example, has three sides, whereas a quadrilateral has four.

We are aware of this.

If the areas of two figures were similar, the ratio of their areas equals the scale factor squared.

Let

z → the scale factor

x → polygon q’s area

y → polygon p’s area

So,

Z² = x/y

Z is given as  = 1/2

Putting value we get:

(1/2)² = x/y

(1/4) = x/y

x = 1/4(y)

The  fraction of Polygon P's area = 1/4

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Answer:

⬤ = 8

⬛ = 6

Step-by-step explanation:

⬤ = x

⬛ = y

x + y = 14

x - y = 2

add the numbers on top of each other together:

add x to x = 2x , y + -y = 0 , 14 + 2 = 16

2x = 16

divide both sides by 2

x = 8, plug this back into the equation

8 + y = 14

8 - y = 14

y = 6

The line l which is perpendicular to line k has an x intercept of -3.

An equation is an expression that shows the relationship between two or more numbers and variables.

The standard equation of a line is:

y = mx + b

where m is the slope and b is the y intercept.

Line k passes through the points (-12, 10) and (6, 1), hence:

Slope = (1 - 10) / (6 - (-12)) = -1/2

Two lines are perpendicular if the product of their slopes is -1. Line L is perpendicular to line k, with y-intercept 6. hence:

Slope of line l = 2

Equation of line l is:

y = 2x + 6

At y = 0:

0 = 2x + 6

x = -3

The line l which is perpendicular to line k has an x intercept of -3.

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y = x² , y = 2 x are  the region enclosed by the given equations is revolved about the y -axis.

What exactly is a closed area?

All space between a floor and ceiling that is enclosed on all sides by solid walls or windows, except doors that stretch from the floor to the ceiling, is referred to as an enclosed area.

What do you mean by the region that a closed curve encloses?

The sum of all infinitely thin rectangles with height f(x), enclosed by the curve y=f(x), and the x-axis between x=a and x=b, is what we mean when we write baf(x)dx.

Whether contained or not?

The graph is attached in equation y = x² , y = 2 x

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The equation of the circle x^2 + y^2 - 6x - 2y + 4 = 0 has a radius of √6 and a center located at (3 , 1).

The standard form of the equation of  circle is given by

(x - h)^2 + (y - k)^2 = r^2

where (h , k) is the location of the center and r is the radius of the circle.

On the other hand, the general form of the equation of  circle is given by

x^2 + y^2 + Dx + Ey + F = 0

where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.

If the equation of the circle in general form is x^2 + y^2 - 6x - 2y + 4 = 0, then the coefficients are:

D = -6

E = -2

F = 4

If D = -2h and D = -6, then

-6 = -2h

h = 3

If E = -2k and E = -2, then

-2 = -2k

k = 1

If F = h^2 + k^2 -r^2 and F = 4, then

4 = 3^2 + (1)^2 - r^2

r^2 = 9 + 1 - 4

r^2 = 6

r = √6

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Answer:

Image result for what is a voronoi diagram in SIMPLE terms please help!

In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators)

Step-by-step explanation:yes

A consistent system of equations has at least one solution.

A consistent system is considered to be an independent system if it has a single solution, such as the example we just explored. The two lines have different slopes and intersect at one point in the plane.

A consistent system is considered to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide so the equations represent the same line. Every point on the line represents a coordinate pair that satisfies the system. Thus, there are an infinite number of solutions.

Another type of system of linear equations is an inconsistent system, which is one in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no points common to both lines; hence, there is no solution to the system.

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The common ratio of a geometric series with  a₂ = 2/5 and a₅ = 16/135  is r = 2/3 (B)

The formula for the nth term of a geometric series is given by:

a(n) = a(1) . rⁿ⁻¹

Where:

a(1) = first term

r = common ratio

Parameters given:

a(2) = 2/5

a(5) = 16/135

Note that:

a(2) = a.r

a(5) = a.r⁴

Divide a(5) by a(2)

a.r⁴ : a.r = 16/135 : 2/5

r³ = 8/27

r = 2/3     (B)

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Answer:

What do you mean by that?

Step-by-step explanation:

Answer:

Here, at Brainly!!

Step-by-step explanation:

Here, we can solve any questions or problems that you have! We'll always keep you updated, and make sure that all your questions are answered! If you have any questions, try asking questions, and be ready to receive and answer soon!!!

Thank You,

I really hope this helps

Answer:

1

Step-by-step explanation:

It is a linear equation, so it has 0 or 1 solution (or infinitely many).

You could view this one as the intersection of line y=3(x-7)+4 and the line y=x-1. There is one intersection, and it is at x=8.

Answer:

C = 32 - F

Step-by-step explanation:

that is the solution above

Given set of numbers 7, 24, 25 represent a right triangle.

By the  triangle inequality theorem , the sum of the lengths of any two sides should be greater than the length of the third side.

Since the sum of the lengths of any two sides is greater than that of the third side, the set of numbers are the measures of a triangle.

Now we find the type of triangle.

We find the sum of the squares of the two smaller sides, and compare the sum to the square of the largest side.

the sum of the squares of the two smaller sides is,

= 7² + 24²

= 49 + 576

= 625

= 25²

Since the sum of the squares of the two smaller sides is equal to the square of the largest side, by Pythagoras theorem the triangle must be right triangle.

Therefore, given set of numbers 7, 24, 25 represent a right triangle.

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The coordinate of the point L is such that ΔL K L is an isosceles triangle that will be either (0,y) or (2a,y).

It is given that in ΔL K L , J has coordinates (0,0) and K has coordinates (2 a, 2 b) .

We have to find the coordinates of point L so that , ΔL K L is an isosceles triangle.

What is a triangle ?

A triangle is a 3-sided shape. There are three sides and three angles in every triangle, some of which may be the same.

As per the question ;

The ΔL K L is an isosceles triangle,

J has coordinates (0,0)

K has coordinates (2 a, 2 b) .

The possible coordinate of the point L will be (0,y) or (2a,y).

Let's check it.

Using the distance formula ;

JK = [tex]\sqrt{(2a-0)^2 + (2b -0)^2}[/tex]

JK = [tex]\sqrt{(4a^2 + 4b^2)}[/tex]

JK = [tex]2\sqrt{a^2 + b^2}[/tex]

Similarly ;

JL = [tex]\sqrt{0^2 + y^2}[/tex]

JL = y

And

KL = [tex]\sqrt{4a^2 + (2b - y)^2}[/tex]

Let's say two sides JK and KL are equal at any value of a , b and y.

Then ;

The two sides are of equal length , so , we can conclude that this is an isosceles triangle.

Thus , the coordinate of the point L is such that ΔL K L is an isosceles triangle that will be either (0,y) or (2a,y).

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Answer:

22.8 blocks

Step-by-step explanation:

We can think of your path as traveling on a coordinate plane. You start by walking 6 units in the positive y direction, then 22 units in the negative x direction, then walking from this point (-22, 6) back to (0, 0)

This path draws a right triangle. The shorter leg is 6 units long, and the longer end is 22 units long. You want to find the hypotenuse of this triangle.

The hypotenuse is found using the Pythagorean theorem:

[tex]a^2+b^2=c^2[/tex]

A and B represent the sides of the triangle, and c represents the hypotenuse!

Before plugging in the functions, isolate c, since that's the answer we're looking for:

[tex]a^2+b^2=c^2\\c=\sqrt{a^2+b^2}[/tex]

Now, plug in the side lengths of the triangle:

[tex]c=\sqrt{6^2+22^2}[/tex]

Now simplify!

[tex]c=\sqrt{36+484} \\x=\sqrt{520} x=22.8[/tex]

It is 22.8 blocks back to your house! Hope this helps!