a graph shows a proportional relationship. what is the constant of proportionality

The domain and range of f(x) = |x| are Domain: (–∞, ∞ ) ; Range: [0, ∞)

f(x) = |x| is the absolute value function.

It always gives non-negative function values.

The absolute value function is defined as,

|x| = { x ; if x ≥ 0

      { -x ; if x < 0

So this definition says that if x is a non-negative real number, then the function gives the non-negative value itself.

Also if x is a negative real number, then -x is a positive real number which is the outcome from the absolute value function for negative real numbers.

This function is defined for all real numbers. Hence the domain is all the real numbers which is (–∞, ∞ ).

But the range of the function are only non-negative real numbers as absolute value function gives only non-negative values. So the range is    [0, ∞).

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The most appropriate choice for proportionality will be given by

When y = 24, x = 10

What is proportionality?

Any relationship which maintains the same ratio is known as proportionality.

Proportionality can be of two types-

Direct Proportion and inverse proportion

Direct proportion

Two quantities are said to be  directly proportional, if on increasing the value of one quantity, the value of other quantity also increases and vice versa

For Example- Cost of a commodity and quantity of a commodity are direct proportional.

Inverse proportion

Two quantities are said to be inversely proportion, if on increasing the value of one quantity, the value of other quantity decreases.

For Example- Number of men and time taken by those men to do a certain work are inversely proportional.

Here,

y is inversely proportional to x

[tex]y = k \times \frac{1}{x}[/tex], where [tex]k[/tex] is an arbitrary constant known as proportionality constant

when y = 80, x =3

Putting the value of y and x in the above equation,

[tex]80[/tex] = [tex]k \times \frac{1}{3}[/tex]

[tex]k = 80 \times 3\\k = 240[/tex]

So [tex]y = 240 \times \frac{1}{x}[/tex]

when [tex]y = 24[/tex]

[tex]24 = 240 \times \frac{1}{x}[/tex]

[tex]x = \frac{240}{24}[/tex]

[tex]x = 10[/tex]

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The distance between these two lines  y=1/2x+2 and x-2y=6 is 10/√5

Distance between two lines:

We know that, the parallel lines can be extended till infinity. The slopes of two parallel lines are equal.

Distance d between two parallel lines

y = mx + c1 and

y = mx + c2 is calculated by the

d = |C1–C2|/√(A² + B²)

Given,

Here we have the two line equation they are,

y=1/2x+2 and x-2y=6

And we need to find the distance between them.

To find the distance between the lines, then we ahve to make the equation into standard form, that is,

y = mx + c

Here the first equation is in standard form, so we have to convert the second one,

So, the second equation is written as,

x - 2y = 6

-2y = 6 - x

y = (6 - x)/-2

y = -3 + 1/2 x

y = 1/2 x - 3

Now, we have to derive the value of the following from the given equation, then we get,

Slopes are same m1 = m2 = 1/2 and c1 = 2 ,c2 = -3.

here a = 1/2, b = -1

Now, apply the values on the formula, then we get,

d = |2 - (-3)|/√(1/2)² + (-1)²

d = 5/√1/4 +1

d = 5/√5/4

d = 5/√5/2

d = 10/√5

Therefore, the distance between these two equation is 10/√5.

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Based on the dimensions of the rectangle, the number of square inches that are in the rectangle are 23,040 inches ²

x

First, convert the units of the rectangle from feet to inches so that it is easier to find the area.

Length of rectangle in inches:

= 16 x 12 inches per ft

= 192 inches

Width of rectangle:

= 10 x 12 inches per ft

= 120 inches

The area is:

= 192 x 120

= 23,040 inches ²

In conclusion, there are 23,040 square inches in the rectangle.

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Answer:

13 1/3 pages

Step-by-step explanation:

Unit rate = 5 p / 3 h

5p / 3 h  * 8h = 13 1/3 page

Answer:

F. -5

Step-by-step explanation:

R = {5, x, 3, 8}

Sum of R: x + 16

S = {6, y, 4, 1}

Sum of S: y + 11

The sums are equal.

x + 16 = y + 11

x - y = 11 - 16

x - y = -5

Answer: F. -5

Answer:

h = 2.5 cm

Step-by-step explanation:

the volume (V) of a triangular prism is calculated as

V = area of triangular end × length , that is

V = [tex]\frac{1}{2}[/tex] bh × l

given b = 4, l = 7 and V = 35 , then

[tex]\frac{1}{2}[/tex] × 4 × h × 7 = 35

14h = 35 ( divide both sides by 14 )

h = 2.5 cm

The model given is:

The term in the parentheses represents the change of rate of the model. If the number is the parentheses is less than 1, we call it exponential decay.

If the number in parentheses is bigger than 1, we call it exponential growth.

In this case, the correct option is "decaying"

The number in parentheses let's call it R, is:

Where r is the rate of change. To find it:

To convert to percentage, we convert by multiplying by 100::

The second answer is 0.45%

And since t is the time passed in hours, and has a "60" multiplying it, the last answer is: Every 60 hours

The final answer is:

The function is exponentially decaying at a rate of 0.45% evary 60 hours.

Answer:C

Step-by-step explanation:

The image and preimage coincide when reflecting a figure in a line or a point. Every point of a figure is translated to an image across a fixed line via a reflection. The fixed line is referred to as the reflection line

An image can be produced by the reflection of a shape along a line of reflection. The mirror line is another name for the reflection line.

Reflections move each shape's points down a line known as the line of reflection (sometimes informally called the mirror line). The distance between a point and its matching point in the image is the same.

Consider the case when the point (6, 7) is reflected across the line y = x. The reflected point's coordinates are (7, 6). Similar to reflections across

y = -x, reflections across y = -x involve not only reversing the order of the coordinates but also their signs. For instance, when reflected over the line y = -x, (8, -2) becomes (2, -8)

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Answer:

y-y1=m(x-x1)

y+1=-2(x-7)

y+1=-2x+14

-1           -1

y=-2x+13

Step-by-step explanation:

Answer:

first way: 2 Angles and one side

second way: 2 sides and one angle

Answer:

Step-by-step explanation:

congruent triangles

how to tell if triangles are congruent using SSS, SAS, ASA, and AAS rules

why AAA and SSA do not work as congruence shortcuts

the Hypotenuse Leg Rule for right triangles

how to use CPCTC (corresponding parts of congruent triangles are congruent)

If Johny receives £x, then Sara will receive £4x (Given ratio is 1:4).

In mathematics, a ratio shows how many times one number is contained in another.

For instance, if there are eight oranges and six lemons in a fruit plate, the orange to lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).

Similarly, the ratio of oranges to total fruit is 8:14, while the ratio of lemons to oranges is 6:8 (or 3:4). (or 4:7). Numbers in a ratio can represent any quantity, including counts of people or objects, weights, lengths, times, and so on. Most of the time, both numbers have to be positive.

If Johny receives £x, then Sara will receive £4x (Given ratio is 1:4).

assumable, 4x - x = £69

or, 3x = 69

or, x = 69/3 = £21

Then Johny receives £21 and Sara receives £84 (4x£21).

Becky receives £(138-(21+84)) = £33 as well.

Her proportion in the ratio is equal to (33/138) x 100% (23.91%).

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Answer:

[tex] {x}^{2} + 6x - 27 = (x + 9)(x - 3)[/tex]

Answer:

Step-by-step explanation:

the total amount is 9000

Answer:

1 ⅜

Step-by-step explanation:

⅝ + ¾ = 11/8 or 1 ⅜

Answer:

0.3016

Step-by-step explanation:

If we have an 8 letter code word...

Total number of possible letters = 26

The number of letters possible = 8

So...

26 ^ 8 = 0.3016

Hope this helps!

Answer:

[tex]\approx 0.30164[/tex]

Step-by-step explanation:

The Alphabet contains 26 characters, and to better understand this probability, let's do each letter one step at a time.

Any letter being chosen should have an equal probability of: [tex]\frac{1}{26}[/tex], and for the first letter we don't really have to worry about choosing a non-repeated letter, since it's impossible to have a non-repeated letter on the first letter... since it's the first letter, so no other letter has been chosen.

This means we have a probability of: 1 to get a non-repeated letter when we choose the first letter.

The probability when we choose the 2nd letter is different, since there is a possibility of choosing a repeated letter. As stated above, the probability of choosing any one letter should be equal for each letter and is: [tex]\frac{1}{26}[/tex]

Since we want to avoid this one letter we choose in the beginning, the probability of choosing it is: [tex]\frac{1}{26}[/tex], which means the probability of not choosing it is: [tex]\frac{25}{26}[/tex]

For the 3rd letter it follows the same pattern, assuming we have two non-repeated letters, the probability of choosing a repeated letter from the previous two is there combined probabilities of: [tex]\frac{1}{26} + \frac{1}{26} = \frac{2}{26}[/tex]. Since we want a non-repeated letter, we subtract this probability from one, because the entire probability will equal one.

This gives us a probability of: [tex]\frac{24}{26}[/tex] of choosing a non-repeated letter.

You'll notice a pattern, the numerator is decreasing by one! This makes sense since each time we choose a non-repeated letter, well the number of non-repeated letters will decrease by one.

This gives us the probability for each letter up to eight letters

[tex]\frac{26}{26}, \frac{25}{26}, \frac{24}{26}, \frac{23}{26}, \frac{22}{26}, \frac{21}{26}, \frac{20}{26}, \frac{19}{26}[/tex]

To get an eight letter code that has no no repeated letters, all these events have to occur. To find the collective probabilities of all these events happening, we simply multiply them, assuming they're independent which we have no reason to believe they aren't independent.

This gives us a total probability of approximately: [tex]0.30164[/tex]

Answer:

No solution

Step-by-step explanation:

The method that will use is substitution

ill use the equation 5x+2y=10 and substitute into the other one

5x+2y=10

2y=10-5x

y=5-2.5x

Now we must insert this equation into another

5x + 2(5-2.5x) = 20

5x+10-5x = 20

10=20

10 does not equal to 20 so it has no solution

Please mark as brainliest

Answer:

See below

Step-by-step explanation:

well, is simply the price plus tax, so

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5.65\% of 15.99}}{\left( \cfrac{5.65}{100} \right)15.99} ~~ \approx ~~ 0.90~\hfill \underset{total~cost}{\stackrel{15.99~~ + ~~0.90}{\approx\text{\LARGE 16.89}}}[/tex]

EXPLANATION

Given the equation 8x -4y

When x=2 and y=3 the resulting expression would be as follows:

8*2 -4*3=

=16 - 12

= 4

The answer is 4

Answer:

J

Step-by-step explanation:

the magnitude of a vector (a, b ) is

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

then magnitude of vector v = (4, 3 ) is

| v | = [tex]\sqrt{4^2+3^2}[/tex] = [tex]\sqrt{16+9}[/tex] = [tex]\sqrt{25}[/tex] = 5

Step-by-step explanation:

...............

............

Step-by-step explanation:

(9)

9x + 5y = 35

-2x - 5y = 0

---------------------

7x 0 = 35

(10)

7x = 35

x = 5

(11)

we pick one of the 2 equations, e.g.

-2x - 5y = 0

-2×5 - 5y = 0

-10 - 5y = 0

-10 = 5y

y = -10/5 = -2

The  number of visits thay Liam can make to earn his first free movie ticket is 9 visit.

Let x represent the number of visits

Since he receives 50 rewards points just for signing up and earns 12.5 points for each visit to the movie theater. This will be illustrated as:

50 + 12.5x >= 160

12.5x >= 160 - 50

12.5x >= 110

Divide

x >= 110/12.5

x >= 8.8

Therefore, he will need at least 9 visit.

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Liam has a points card for a movie theater.

He receives 50 rewards points just for signing up.

He earns 12.5 points for each visit to the movie theater.

He needs at least 160 points for a free movie ticket.

Write and solve an inequality which can be used to determine xx, the number of visits Liam can make to earn his first free movie ticket.

Answer:

$45.70

Step-by-step explanation:

$9.40 four times and $8.10 1 time so 9.40 x 4 = 37.6 + 8.10 = 45.70

The given ant can only go up or right here in every turn and as there is a 50% chance for either of

them, therefore each of the paths in 12 moves would be equally likely here.

As for each of the 12 steps here, there are 2 ways that the ant can move, therefore total number of

paths in 12 moves is computed as:

= 2^12 here.

We use the multiplication rule for independent events here to get the total number of outcomes here

by getting the product of the number of outcomes for each of those independent events.

Total number of 12 move paths such that we reach 4, 8 here is computed as the number of

permutation of 12 moves with 4 rights and 8 up points here. This is computed here as:

12!/(8!4!) = 495

Therefore, the probability that the ant is located at (4, 8) here is computed as:

=

495/(2^12)

= 0.1208

Therefore, 0.1208 is the required probability here

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The proof that shows that triangles PQR and TSR are similar by AA similarity theorem is explained below.

The AA similarity theorem proves that two triangles are similar if we can show that two of its corresponding angles are congruent to each other.

Therefore, for triangles PQR and TSR to be similar by the AA similarity theorem, they must have two corresponding congruent angles.

The proof below shows the triangles, ΔPQR ~ ΔTSR are similar to each other:

Statement                                             Reasons                                              

1. QR ⊥ PT                                             1. Given

2. ∠QRP and ∠SRT are right angles   2. Def. of perpendicular

3. ∠QRP ≅ ∠SRT                                  3. All right angles are ≅

4. ∠QPR ≅ ∠STR                                  4. Given

5. ΔPQR ~ ΔTSR                                   5. AA similarity theorem

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Answer:

I don't know about this b

Answer:

possible value would be 28

Step-by-step explanation:

an acute angle is an angle less then 90° , that is

3x + 12 < 90 ( subtract 12 from both sides )

3x < 78 ( divide both sides by 3 )

x < 26

thus any value of x greater than 26 is not possible

so x = 28 is a possible value of x