Respond

1. Describe a real-life situation that can be modeled by a function (a relation in which every input
value corresponds to only one output value). The situation must be different from the examples
provided in the reading and in the homework. Identify the input value and the output value of the function, and provide justification that your
relation does, in fact, represent a function.


2. Create a function in the form y = f(x) that models the relation described. You may choose variables in place of y or x that better represent the relation, as seen in the provided example.


3. Identify the domain and range of your function, using proper mathematical notation.


4. Cite any sources you may have used in
formulating your response.

Equation to represent the given situation :

7(19.70 + 1.97 + m X 0.05) = 180.39,

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Given that:

Total cost for 7 month =$180.39

Let m be the average number of minutes  that exceeds 700 minutes each month.

Equation :

7(19.70 + 1.97 + m X 0.05) = 180.39,

or,  7(19.70 + 1.97 + m X 0.05) = 180.39,

or, 21.67 + 0.05m = 180.39/ 7,

or, 0.05m = 25.77 – 21.67,

0.05m = 4.1

m= 82

Hence,  equation to represent the given situation : 7(19.70 + 1.97 + m X 0.05) = 180.39.

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Answer:

Domain: [tex]\displaystyle (-\infty,-3)\cup(-3,6)\cup(6,\infty)[/tex]

Range: [tex](-\infty,0)\cup(0,\frac{1}{9})\cup(\frac{1}{9},\infty)[/tex]

Step-by-step explanation:

Factor the numerator and denominator

[tex]\displaystyle f(x)=\frac{x-6}{x^2-3x-18}\\ \\f(x)=\frac{x-6}{(x-6)(x+3)}\\\\f(x)=\frac{1}{x+3}[/tex]

Because the factor [tex]x-6[/tex] exists in both the numerator and denominator, then there is a hole at [tex]x=6[/tex] because the function is not continuous there. Additionally, because the denominator cannot be 0, [tex]x\neq-3[/tex], and there will be a vertical asymptote at the line [tex]x=-3[/tex].

Thus, the domain of the function is [tex]\displaystyle (-\infty,-3)\cup(-3,6)\cup(6,\infty)[/tex].

Also, notice that because [tex]x\neq6[/tex], as the function gets closer to [tex]x=6[/tex], the function gets closer to [tex]\displaystyle f(6)=\frac{1}{6+3}=\frac{1}{9}[/tex], so [tex]\displaystyle y=\frac{1}{9}[/tex] is not included in the range.

Thus, the range is [tex](-\infty,0)\cup(0,\frac{1}{9})\cup(\frac{1}{9},\infty)[/tex].

[tex]\large \boxed{\sf y = (x - 2)^2 - 4}[/tex]

[tex]\large \boxed{\sf Quadratic \ Function}[/tex]

A linear function shall increase linearly. Here due to mass differences between points, it is visible that it is not a linear function.

There is a better way to understand what type of equation it is after plotting the coordinates on the graph.

After looking so, we can determine this as quadratic function.

** Not a exponential, inverse, linear function **

Quadratic function: y = a(x - h)² + k

Locate (h, k) = (2, -4)

Take any other suitable point for example = (0, 0)

Insert values to find (a),

a(0 - 2)² - 4 = 0

4a = 4

a = 1

Now Join together: y = 1(x - 2)² - 4   --- Quadratic Equation

Exponential

It should be a parabola

The best shortcut trick is the fact about the parabola is that parabola is symmetric and axis of symmetry goes through vertex

So on both sides of vertex i e same distance on x from vertex the two x values have same y value .

Observe the table and find similar y values

FIND midpoint of x which is axis of symmetry

We have been sured axis of symmetry is at x=2

Form equation

Put (5,5)

Final equation

Answer:

308

Step-by-step explanation:

so to find how much a rectangular prisim is by

length * with* height

11* 7 * 12

= 924 cubic feet

and then we just divid by 3

=308

If the area of the square is 36 square units. Then the area of the circle will be 28.26 square units.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The area of the square will be given as 36 square units.

Then the side length of the square will be

36 = a²

 a = 6 units

Then the diameter of the circle and side length of the square are equal. Then we have

a = d = 6 units

Then the radius of the circle will be

2r = d

2r = 6

 r = 3 units

Then the area of the circle will be

Area of circle = πr²

Area of circle = 3.14 x 3²

Area of circle = 28.26 square units.

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Answer:

<HAD

Step-by-step explanation:

take two points

Slope

Answer:

[tex]m=\dfrac{7}{5}[/tex]

Step-by-step explanation:

To find the slope of a line, find two points on the line and define them as follows:

[tex]\textsf{let}\:(x_1,y_1)=(-3,-3)[/tex]

[tex]\textsf{let}\:(x_2,y_2)=(2,4)[/tex]

Substitute the points in the slope formula and solve for m:

[tex]\begin{aligned}\textsf{slope}\:(m) & =\dfrac{y_2-y_1}{x_2-x_1}\\\\ & =\dfrac{4-(-3)}{2-(-3)}\\\\ & = \dfrac{4+3}{2+3}\\\\ & = \dfrac{7}{5}\end{aligned}[/tex]

Therefore, the slope of the given line is [tex]\dfrac{7}{5}[/tex]

Step-by-step explanation:

Radio=

Normal Price = K48.

Discount 20%

Selling Price

Answer:

Here!! Hope i helped.

Answer:

A dot plot is like a histogram but it uses dots instead of bars. Like histogram, a dot plot also presents the frequency of data points. The dot plot as described by the problem is shown in the picture. A bell shape is drawn for a symmetrical data. From the choices, the answer is: It is symmetric and has no gaps. The other statements are wrong because the peak is at $5 or $6.

Answer:

A dot plot is like a histogram but it uses dots instead of bars. Like histogram, a dot plot also presents the frequency of data points. The dot plot as described by the problem is shown in the picture. A bell shape is drawn for a symmetrical data. From the choices, the answer is: It is symmetric and has no gaps. The other statements are wrong because the peak is at $5 or $6.

Step-by-step explanation:

A dot plot is like a histogram but it uses dots instead of bars. Like histogram, a dot plot also presents the frequency of data points. The dot plot as described by the problem is shown in the picture. A bell shape is drawn for a symmetrical data. From the choices, the answer is: It is symmetric and has no gaps. The other statements are wrong because the peak is at $5 or $6.

Answer:

1)  N/A

2) ( -0.714, 3.857)

Step-by-step explanation:

for question 1 since the slope is the same, they will never intersect

for question 2 they intersect at (-0.714, 3.857)

1) as for the coordinates, for y=3x+2 it is (0,2) (-2/3, 0) it's an upward slope

y=3x-5 coordinates are (0, -5) (1.667, 0) it's an upward slope

2) 4x+y=1 coordinates are (0,1) (1/2, 0) it's a downwards slope

y=3x+6 coordinates are (-2, 0) (0,6) it's a upward slope

Based on the percentage coverage for personal property, the amount of coverage for Melissa's personal property is $50,760.

This can be found by the formula:

= Replacement value x Percentage of personal property coverage

Solving gives:

= 84,600 x 60%

= $50,760

In conclusion, Melissa's personal property coverage is $50,760.

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The area of triangle FGH that is similar to triangle ABC is: 8 square feet.

If two shapes are similar, the ratio of their areas equals the ratio of the square of their corresponding sides.

Therefore:

area of triangle EFG / area of triangle ABC = FG²/BC²

Plug in the values

area of triangle EFG / 18 = 2²/3²

area of triangle EFG / 18 = 4/9

area of triangle EFG = (18×4)/9

area of triangle EFG = 8 sq. ft.

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Step-by-step explanation:

well don't breath just collect like terms and booom

Answer:

The diameter divides a circle into fourths. (False)

The diameter is twice the length of the radius. (True)

The diameter is the distance around the circle. (True)

The diameter is a chord. (True)

The diameter passes through the center of a circle. (True)

The diameter is about three times larger that the circumference. (I don't really know this from the top of my head. Sorry!

Step-by-step explanation:

Hope this helps!

From your neighborhood softie. :)

Answer:

19.8 rounded to 20m

Step-by-step explanation:

reason;

Area=1/2 x perimeter x apothem

27=1/2 x p x 2.726

Divide both sides by 1/2

54= p x 2.726

Now divide both sides by 2.726 to isolate p

Answer p=19.8

Answer:

horizontal line

Step-by-step explanation:

The slope formula is m=(y2-y1)/(x2-x1)

-6+6/-4-1

y2-y1 = 0

Answer:

Domain: all real numbers (all reals)

Range: y> OR EQUAL TO -2

Step-by-step explanation:

Hope this helps! ;-)

Answer:

Yes, no is correct

Step-by-step explanation:

This is because you only add up the outside sides of the polygon to find the perimeter. None of the inside sides. Hope this makes sense and hope it helps.

Answer:

No, because the friend counted a length that is inside of the polygon, which you don't need for finding the perimeter, since the perimeter is the sum of the outside lengths of the polygon.

[tex](2x + 1)(x + 1)[/tex]

•Distribute

[tex](2x + 1)(x + )[/tex]

[tex]2x(x + 1) + 1( x + 1)[/tex]

•Distribute

[tex]2x(x + 1) + 1(x + 1)[/tex]

[tex]2x² + 2x1(x + 1)[/tex]

•Multiply

[tex]2x² + 2x + 1(x + 1)[/tex]

[tex]2x² + 2x + x + 1[/tex]

•Combine like terms

[tex]2x² + x + x + 1[/tex]

[tex]2x²+ 3x + 1[/tex]

Solution:

[tex]2x² + 3x + 1[/tex]

Explanation:

see the graph

Answer: C)

Step-by-step explanation:

Answer:

In romania I was doing this in the 6th grade

Step-by-step explanation:

5.

A B and D C are parallel lines.

"slope" means inclination. and as you can imagine, parallel lines must have the same inclination, or they would not be parallel.

so, the slope of D C must be also 2/7.

4.

same thing as with 5.

both lines are parallel and must therefore have the same slope.

so, the slope of D C is also 3/4. and the first answer is correct.

Answer:

Step-by-step explanation:

6z² + 12z +1 8​

= 6(z^2 + 2z + 3).

That's it.

Answer:

It is in vertex form so:

(x-h) + k --> (x-(-5)) + 8 = (x + 5) + 8

(h,k)

(-5, 8)

This equation turns out to be linear. So it would be an absolute maximum probably since negative values of x are greater than positive values of x.

okay,here is about a formula.

n=2x

where x is the numbers.

n=2×3

n=6.

therefore the three digit numbers which can be obtained is 6.

The reason that best supports statement 3 in the given proof is the substitution property of equality. The correct option is - D. Substitution

The substitution property of equality states that, if m = n, then m can be substituted in for n in any equation, and vice versa.

From the question, we are to determine the reason that best supports Statement 3

In the diagram, statement 3 is

m∠A ÷ 5 = 20°

From the given expressions,

m∠A ÷ 5 = m∠B and m∠B = 20°

By the substitution property, we can substitute 20° for m∠B in the first expression

That is,

m∠A ÷ 5 = m∠B  becomes

m∠A ÷ 5 = 20°

Hence, the reason that best supports statement 3 in the given proof is the substitution property of equality. The correct option is - D. Substitution

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Answer:

It's 90 if you go through k12 :]

Step-by-step explanation:

The number of ways to choose a combo meal is 24.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

2 drinks, 4 main dishes, and 3 desserts

Now,

To find the number of different combo meals possible, we can use the fundamental counting principle. This states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things.

2 ways to choose a drink

4 ways to choose a main dish

3 ways to choose a dessert

2×4×3=24

Therefore, by algebra the answer will be 24.

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Step-by-step explanation:

all the pink area above the blue line (above means ">", and the blue line is -1/2 x), and not including the line.