how do I determine what a function is for a line graph
​

The scale factor is: 1.8

because of :

\(\frac{36}{20}=1.8\\ \\\\\frac{25.2}{14}=1.8\)

Using the concept of ratio, the month of February had a better ratio in sales compared to January

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

This is the process of comparing two quantities against one another to determine their ratio against each other.

In the question given;

January = 10 minivans, 20 sedans

The ratio of minivans to sedan = 10 / 20 = 1/2

The ratio of minivans to sedan in January = 1/2

February = 15 minivans, 25 sedans

The ratio of minivans to sedans  = 15/25 = 3/5

The month of February has the highest ratio

Learn more on ratio here;

https://brainly.com/question/2328454

#SPJ1

The three solution of the equation are x= -5/2 or x = 1.25 -2.1651i or x = 1.25 + 2.165i

We have,

8x³ + 125 = 0

Now, simplifying for x we get

(2x)³ + (5)³ = 0

(2x+5) ( (2x)² - (2x)(5) + 5²)= 0

(2x + 5) (4x² - 10x + 25)=0

x = -5/2 or (4x² - 10x + 25)= 0

x= -5/2 or x = 1.25 -2.1651i or x = 1.25 + 2.165i

Learn more about Roots here:

https://brainly.com/question/12029673

#SPJ1

Answer:

396

Step-by-step explanation:

The solution is $ 36

The markup from the cost price to the sale price is $ 36

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the markup from the cost to the sale price be = A

Now , the equation will be

Let the initial selling price of an item be = $ 495

Now , it is marked down by 20 %

So ,

The new selling price after marked down = initial selling price of an item -
( 20 / 100 ) initial selling price of an item

Substituting the values in the equation , we get

The new selling price after marked down = 495 - ( 20/100 ) x 495

The new selling price after marked down = 495 - ( 0.2 x 495 )

The new selling price after marked down = 495 - 99

The new selling price after marked down = $ 396

The new selling price is marked up from the cost price of = $ 360

So , the equation will be

The markup from the cost to the sale price = new selling price after marked down - marked up from the cost price

Substituting the values in the equation , we get

The markup from the cost to the sale price = 396 - 360

The markup from the cost to the sale price = $ 36

Therefore , the value of A is $ 36

Hence , the markup from the cost price to the sale price is $ 36

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

Answer:

\(\frac{4}{7}\)

Step-by-step explanation:

A combination refers to the selection of objects such that order does not matter. A permutation refers to the arrangement of objects such that order do matter.

Number of bananas = 2

Number of apples = 5

One banana and two apples are chosen.

So,

probability that one banana and two apples are chosen = \(\frac{C(2,1)\,C(5,2)}{C(7,3)}\)

\(C(2,1)=\frac{2!}{1!(2-1)!}=2\)

\(C(5,2)=\frac{5!}{2!(5-2)!}=\frac{5!}{2!31} =10\)

\(C(7,3)=\frac{7!}{3!(7-3)!} =\frac{7!}{3!4!}=35\)

So,

Probability that one banana and two apples are chosen = \(\frac{2(10)}{35}=\frac{4}{7}\)

Answer:

Or 57.14%

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

If y is a function of x, then the equation for y would be y=Ix(+or-or*or%) to nI

For this specific event, the proper equation would be y=Ix-0.5I

Breaking down this equation, y equals the absolute value of x-0.5.

So if x was 2, it would go as y=I2-0.5I where y equals 1.5.

Answer:

56

hope it helpes if you could give me brainliest so i could level up

Where the above relations are given, note that Options A,  D, and E are the relations that represents a function. The others are just relations.

To distinguish a function from a relation, look to see if any of the x values are repeated; if not, the relationship is a function. If some x values are repeated but the accompanying y values differ, we have a relation rather than a function.

Note that where you are given domain and range, only the range is represented on the x-axis.

Some of the x values may be seen repeated in B, and C.

How is this so?

B) In a coordinate system, values are represented as (x, y). so

In relations, B 2 is repeated twice to in connection with -5, and -6. That is:

(2, -5) , (2, -6)

Since two is x, then its repetition nullified the relation as a function.

C) On table indicated on C, it is much easier to identify the x and y values. As is seen, -3 is repeated twice in connection with 4 and 2. Thus, its repetition nullified the relation as a function.

As a result, Options A,  D, and E are the relations that represent a function.

Learn more about function at:

https://brainly.com/question/30721594

#SPJ1

Answer:

a+b=(6,3)

6a+8b=(54,16)

a=(-3,4)

a-b=(-12,5)

Answer:

6\(\sqrt{17}\) or 24.738634

Step-by-step explanation:

We can use the Pythagorean theorem to find the length of the sides. We will only need to find the length of AB and AD, as AB = DC and AD = BC.

The picture shows the Pythagorean theorem being used to find AB and AD.

AB = \(\sqrt{17}\)

AD = \(\sqrt{68}\)

Now we can find the perimeter

2(\(\sqrt{17}\)) + 2(\(\sqrt{68}\)) = 6\(\sqrt{17}\)

The integral is ln|x + cos(x)| + C, where C represents the constant of integration.

To find the integral of the function 1/(x + cos(x)), we can employ a combination of algebraic manipulation and the use of standard integration techniques. Here's the solution:

First, let's rewrite the integral in a slightly different form to simplify the process:

∫(1/(x + cos(x))) dx

We notice that the denominator, x + cos(x), is not amenable to direct integration. To overcome this, we employ a substitution. Let's set u = x + cos(x). Now, differentiate u with respect to x: du/dx = 1 - sin(x).

Rearranging this equation, we get dx = du/(1 - sin(x)).

Substituting these values, the integral becomes:

∫(1/(u(1 - sin(x)))) du

Next, we simplify further by factoring out 1/(1 - sin(x)) from the integral:

∫(1/(u(1 - sin(x)))) du = ∫(1/u) du = ln|u| + C

Replacing u with its original expression, we have:

ln|x + cos(x)| + C

Therefore, the answer to the integral is ln|x + cos(x)| + C, where C represents the constant of integration.

For more questions on integral

https://brainly.com/question/30094386

#SPJ8

To prove that line segment a is parallel to line segment d, based on the given information, we can utilize the properties of perpendicular and parallel lines.

Given that a is perpendicular to b and b is perpendicular to c, we know that angles formed between a and b, as well as between b and c, are right angles. Let's denote these angles as ∠1 and ∠2, respectively.

Now, since c is parallel to d, we can conclude that the corresponding angles ∠2 and ∠3, formed between c and d, are congruent.Considering the fact that ∠2 is a right angle, it can be inferred that ∠3 is also a right angle.

By transitivity, if ∠1 is a right angle and ∠3 is a right angle, then ∠1 and ∠3 are congruent.Since corresponding angles are congruent, and ∠1 and ∠3 are congruent, we can deduce that line segment a is parallel to line segment d.

Thus, we have successfully proven that a is parallel to d based on the given information and the properties of perpendicular and parallel lines.

For more such questions on line segment

https://brainly.com/question/30756145

#SPJ8

a. In interval notation, Increasing intervals: (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm). Decreasing intervals: (8am, 9am) U (11am, 12pm). Constant intervals: (9am, 10am) U (10am, 11am)

b. The increase in cost between 12 noon and 3 pm is $2.

c. Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

Interval notation is used to represent continuous intervals of numbers or values, like ranges on a number line.

The graph shows that from 8-9am, and 11-12pm, the cost from Swift Ride decreases.

We can represent it as (8am, 9am) U (11am, 12pm).

It increases at these times (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm).

And stays constant at : (9am, 10am) U (10am, 11am)

We simply deduct the 12pm's cost from 3pm's cost.

So, we have

Cost increase = $3.5 - $1.5

Evaluate the difference

Cost increase = $2

Hence, the cost increase is $2

When you plot the points provided for Yellow cab, you'll notice that Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

Find more exercises on Interval notation;

https://brainly.com/question/17249352

#SPJ1

Answer:

392?

Step-by-step explanation:

Answer:

Step-by-step explanation:

The constant of proportionality is the same thing as the slope when the y intercept is 0.

y1 = 27.6

y2 = 82.8

x1 =2

x1 = 6

m = (y2 - y1)/(x2 - x1)

m = (82.8 - 27.6)/(6,2)

m = 55.2/4

m = 13.8

The constant of proportionality = 13.8

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2.

The five regular polyhedra, also known as the Platonic solids, are the only convex polyhedra where all faces are congruent regular polygons, and the same number of polygons meet at each vertex.

The five regular polyhedra are:

1. Tetrahedron: It has four triangular faces, and three triangles meet at each vertex.

2. Cube: It has six square faces, and three squares meet at each vertex.

3. Octahedron: It has eight triangular faces, and four triangles meet at each vertex.

4. Dodecahedron: It has twelve pentagonal faces, and three pentagons meet at each vertex.

5. Icosahedron: It has twenty triangular faces, and five triangles meet at each vertex.

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that:

"for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2".

For regular polyhedra, each face has the same number of sides (n) and each vertex is the meeting point of the same number of edges (k). Therefore, we can rewrite Euler's formula for regular polyhedra as:

V - E + F = 2  

=>  kV/2 - kE/2 + F = 2  

=>  k(V/2 - E/2) + F = 2

Since each face has n sides, the total number of edges can be calculated as E = (nF)/2, as each edge is shared by two faces. Substituting this into the equation:

k(V/2 - (nF)/2) + F = 2  

=>  (kV - knF + 2F)/2 = 2  

=>  kV - knF + 2F = 4

Now, we need to consider the conditions for a valid polyhedron:

1. The number of faces (F), edges (E), and vertices (V) must be positive integers.

2. The number of sides on each face (n) and the number of edges meeting at each vertex (k) must be positive integers.

Given these conditions, we can analyze the possibilities for different values of n and k. By exploring various combinations, it can be proven that the only valid solutions satisfying the conditions are:

(n, k) pairs:

(3, 3) - Tetrahedron

(4, 3) - Cube

(3, 4) - Octahedron

(5, 3) - Dodecahedron

(3, 5) - Icosahedron

Therefore, there exist only five regular polyhedra.

Learn more about regular polyhedron here:

https://brainly.com/question/29134238

#SPJ1

Approximately 99.7% of scores lie in the shaded region.

We have,

The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.

According to this rule:

Approximately 68% of scores lie within 1 standard deviation of the mean.

Approximately 95% of scores lie within 2 standard deviations of the mean.

Approximately 99.7% of scores lie within 3 standard deviations of the mean.

Now,

In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.

This encompasses the area within 3 standard deviations of the mean.

And,

Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.

Therefore,

Approximately 99.7% of scores lie in the shaded region.

Learn more about normal distribution here:

https://brainly.com/question/31327019

#SPJ1

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

For more such questions on graph

https://brainly.com/question/19040584

#SPJ8

The area of the figure in the image is 800 square centimeters.

Here we have a square of sidelength of 30cm, such that in each corner we removed little squares of sidelength of 5cm.

Then the area of the figure will be the difference between the area of the first square and 4 times the area of the smaller square,

The area of a square of sidelength of 30 cm is:

A = 30cm*30cm = 900cm^2

The area of a square of sidelength of 5 cm is:

a = 5cm*5cm = 25cm^2

Then the area of the figure is:

area = A - 4a = 900cm^2 - 4*25cm^2 = 800cm^2

if you want to learn more about areas:

https://brainly.com/question/24487155

#SPJ1

Answer:

The range of values from one job is between $50 and $650.

Step-by-step explanation:

An electrician charges y amount to work x hours on a job. The electrician charges a $50 service fee and $30 per hour.

This means that his earnings in a job can be modeled by the following function:

\(y = 30x + 50\)

The electrician works maximum of 20 hours on any job. What is the range of values for one job?

Minimum, he works 0 hours, and earns:

\(y(0) = 30(0) + 50 = 50\)

Maximum, he works 20 hours, and earns:

\(y(20) = 30(20) + 50 = 650\)

The range of values from one job is between $50 and $650.

Answer:

One solution

BRAINLIEST, PLEASE!

Step-by-step explanation:

2y - x = 6

2y = x + 6

y = x/2 + 3

y = 2x + 7

After graphing, they have one solution at (-2.667, 1.667).

We want to find the answer of the following polynomial:

We can see that the last term is -72

We want to find all the possible numbers that can divide it. Those are:

{±1, ±2, ±3, ±4, ±6, ±8, ±9, ±12, ±18, ±36, ±72}

We want to factor this polynomial in order to find all the possible x-values. In order to factor it we will have to find some binomials that can divide it using the set of divisors of -72.

We know that if

(x - z) is a divisor of this polynomial then z might be a divisor of the last term -72.

We will verify which is a divisor using synthetic division. If it is a divisor then we can factor using it:

Let's begin with

(x-z) = (x - 1)

We want to divide

Using synthetic division we have that if the remainder is 0 it will be a factor

We can find the remainder by replacing x = z in the polynomial, when it is divided by (x - z). It is to say, that if we want to know if (x -1) is a factor of the polynomial we just need to replace x by 1, and see the result:

If the result is 0 it is a factor

If it is different to 0 it is not a factor

Replacing x = 1

If we replace x = 1, we will have that:

Then the remainder is not 0, then (x - 1) is not a factor.

Similarly we are going to apply this until we find factors:

(x - z) = (x + 1)

We replace x by -1:

Then, (x + 1) is a factor.

Using synthetic division we have that:

Then:

Now, we want to factor the 4th grade polynomial.

Let's remember our possibilities:

{±1, ±2, ±3, ±4, ±6, ±8, ±9, ±12, ±18, ±36, ±72}

Since we verified ±1, let's try with ±2 as we did before.

(x - z) = (x - 2)

We want to divide:

We replace x by z = 2:

Then (x - 2) is a factor. Let's do the synthetic division:

Then,

Then, our original polynomial is:

Now, let's prove if (x +2) is a factor, using the new 3th grade polynomial.

(x - z) = (x + 2)

We replace x by z = -2:

Since the remainder is not 0, (x +2) is not a factor.

All the possible cases are:

{±1, ±2, ±3, ±4, ±6, ±8, ±9, ±12, ±18, ±36, ±72}

let's prove with +4

(x - z) = (x + 4)

We want to divide:

Let's replace x by z = -4 in order to find the remainder:

Then (x + 4) is a factor. Let's do the synthetic division:

Then,

Since

x² + 9 cannot be factor, we have completed our factoring:

Now, we have the following expression:

Then, we have five posibilities:

(x - 1) = 0

or (x - 2) = 0

or (x + 4) = 0

or (x² + 9) = 0

Then, we have five solutions;

x - 1 = 0 → x₁ = 1

x - 2 = 0 → x₂ = 2

x + 4 = 0 → x₃ = -4

x² + 9 = 0 → x² = -9 → x = ±√-9 = ±√9√-1 = ±3i

→ x₄ = 3i

→ x₅ = -3i

Answer:

m  =  7 /2

Step-by-step explanation:

Answer:

Step-by-step explanation:

(1,12)(-5,-9)

m=7/2

Answer: \(45^{\circ}\)

Step-by-step explanation:

\(\angle ABC\) is formed by \(\overline{AB}\) and \(\overline{BC}\), so we can begin by finding their slopes.

\(m_{\overline{AB}}=\frac{2-5}{4-7}=-1\\m_{\overline{BC}}=\frac{2-2}{9-4}=0\)

This means that:

\(\tan \left(\angle ABC \right)=\left| \frac{-1-0}{1-(0)(-1)} \right|\\\tan \left(\angle ABC \right)=1\)

As \(\angle ABC\) is acute, this means \(m\angle ABC=\boxed{45^{\circ}}\)

Answer:

Kindly check table below :

Step-by-step explanation:

Given :

Ages of Best Actors Age %

26-35 30

36-45 35

46-55 25

56-65 4

66-75 3

76-85 3

The class width = difference between the intervals = (35 - 26) = 10

Class midpoint = (sum of interval) / 2 = (26 + 35) / 2 = 61 / 2 = 30.5

The class boundaries :

Lower - 0.5 = 26 - 0.5 = 25.5

Upper + 0.5 = 35 + 0.5 = 35.5

Ages _ F ___Class Bound.__ classW__midpoint

26-35 _ 30 _ 25.5-35.5 ____ 10 _____ 30.5

36-45 _ 35 _ 35.5-45.5 ____ 10 _____ 40.5

46-55 _ 25 _ 45.5-55.5 ____ 10 _____ 50.5

56-65 _ 4 __ 55.5-65.5 ____ 10 _____ 60.5

66-75 _ 3 __ 65.5-75.5 _____10 _____ 70.5

76-85 _ 3 __ 75.5-85.5 _____ 10 _____ 80.5

Point H is the ortho-center of our given triangle and option c is the correct choice.

We have been given an image of a triangle. We are asked to find the term that describes point H.

We can see that point H is the point, where, all the altitudes of our given triangle EFF are intersecting.

We know that ortho-center of a triangle is the point, where all altitudes of triangle intersect. Therefore, point H is the ortho-center of our given triangle and option c is the correct choice.

for such more question on ortho-center

https://brainly.com/question/7552525

#SPJ8

Question:

What is the elevation of the deck where Winston ate dinner?

Answer:

The surf shop was higher and the distance would be 12.8 feet above the oceans surface.

12.8

Step-by-step explanation:

The freighter is approximately 164.33 miles from the city.

We can use the Law of Cosines to solve this problem. Let's label the distances as follows:

d: distance between the city and the freighter

x: distance between the city and the island

y: distance between the island and the freighter

First, we need to find x using the given coordinates:

N23°38'W is equivalent to S23°38'E, so we have:

cos(23°38') = x/48

x = 48cos(23°38') ≈ 42.67 miles

Next, we can use the coordinates of the freighter to find y:

N11°26'E is equivalent to E11°26'N, and N12°16'W is equivalent to S12°16'E. This means that the angle between the island and the freighter is:

23°38' + 11°26' + 12°16' = 47°20'

cos(47°20') = y/d

We can rearrange this equation to solve for y:

y = dcos(47°20')

Now we can use the Law of Cosines to solve for d:

d² = x² + y² - 2xy cos(90° - 47°20')

d² = 42.67² + (d cos(47°20'))² - 2(42.67)(d cos(47°20')) sin(47°20')

d² = 1822.44 + d² cos²(47°20') - 2(42.67)(d cos(47°20')) sin(47°20')

d² - d² cos²(47°20') = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')

d² (1 - cos²(47°20')) = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')

d² sin²(47°20') = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')

d² = (1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')) / sin²(47°20')

d ≈ 164.33 miles

Therefore, the freighter is approximately 164.33 miles from the city.

Learn more about  Law of Cosines at https://brainly.com/question/30766161

#SPJ1