Calculate the average speed of a train that travels 500km in 4 hours

A line is a one-dimensional shape that is straight. The equation of the line that describes the shark's length is [tex]y = \frac{13}{3}x + 20\\[/tex].

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by:

[tex]y = mx + c[/tex]

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is constant.

Given when the shark was born the length of the shark was 20 inches, therefore, the coordinates can be written as (0,20).

Similarly, the length of the shark is 46 inches, while the age of the shark is 6 months. Therefore, the coordinates can be written as (6,46).

Now, the slope of the line can be written as,

m = (46-20)/(6-0) = 13/3

Now, the equation of the line can be written as  [tex]y = \frac{13}{3}x + c[/tex], further, substitute the value of any point in the equation of the line, therefore,

20=13/3(0)+c

c=20

Hence, the equation of the line that describes the shark's length is :

[tex]y = \frac{13}{3}x + 20\\[/tex].

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The ratio of unshaded squares to shaded squares is 15:10. This means that for every 15 unshaded squares, there are 10 shaded squares. This can also be simplified to 3:2, which means that for every 3 unshaded squares, there are 2 shaded squares.

It is important to keep in mind that the ratio is not equal to the fraction, it's just a way to express the relationship between the two.

Answer:

15:10

Step-by-step explanation:

15:10 which means that for every 15 unshaded squares there are 10 shaded squares which can also be simplified to 3:2 which means pretty much the same thing, for every 3 unshaded squares there will be 2 shaded ones. A ratio is not a fraction, so i advise not treating it like one.

The simplified expression of the given expression is 6x + (-21).

What is simplified expression?

Simplified expression is that expression which does not contains any like terms. When in an expression, all the like terms are combined and all of the specified brackets are solved, then only unlike terms are left in the simplified expression which cannot be further reduced.

We are given  expression as 6 + 2(x-8) + 3x -11 + x

Now, on simplifying the expression, we get

⇒ 6 + 2x - 16 + 3x - 11 + x

⇒ 6x - 21

⇒ 6x + (-21)

Hence, the simplified expression of the given expression is 6x + (-21).

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Since, there are multiple questions so the question I answered is attached below.

By evaluating and using the quadratic equation we will have:

1) 7 seconds.

2) Yes, it will pass.

3) 24.5 meters, after 3.5 seconds.

To find this, we need to solve the quadratic equation:

h = -2t^2 + 14t = 0

Taking t as a common factor we can write:

t*(-2t + 14) = 0

-2t +14 = 0

14 = 2t

14/2 = t

7 = t

The ball will be 7 seconds on the air.

2) To check this we need to evaluate the quadratic equation on t = 3

h = -2*3^2 + 14*3 = 24

The height is of the ball is larger than the height of the tree.

3) What is the maximum height of the ball?

This happens at the vertex of the quadratic equation:

h = -2t^2 + 14t

The two roots are t = 0 and t = 7, then the vertex is at t = (7 - 0)/2 = 3.5

And the maximum height is:

h = -2*3.5^2 + 14*3.5 = 24.5

The maximum height is 24.5 meters.

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The answers to each part is mentioned above.

Given is that Aiko works in the fish department of a pet store. She must drain, clean, and refill two reef tanks. The first tank hold 175 gallons of water and drains at a rate of 25 gallons per hour. The second tank holds 200 gallons of water and drains at a rate of 30 gallons per hour.

Equation for tank {1} -

y = 175 - 25x

Equation for tank {2} -

y = 200 - 30x

For the solution we can write -

175 - 25x = 200 - 30x

- 25x + 30x = 200 - 175

5x = 25

x = 5

and

y = 200 - 150

y = 50

For the same amount of water we can write -

175 - 25x = 200 - 30x

- 25x + 30x = 200 - 175

5x = 25

x = 5 hours

In tank (1), there is : 175 - 25 x 5 = 50 gallons

In tank (2), there is : 200 - 30 x 5 = 50 gallons

Therefore, the answers to each part is mentioned above.

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The prime numbers of 36 are 2 and 3 and the Prime factorization expression of 36 is equals to 2 × 2 × 3 × 3.

Prime factorization is a method of representing a number as a product of prime factors. A prime factor of a number is a factor that is prime. The numbers are called factors of 36 that divide 36 evenly. In other words, if we multiply two numbers and get the result equals to 36. So, factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Steps for Prime Factorization of 36 :

Step 1: In first step, divide the number i.e., 36 by its smallest prime factor. So, by divisibility rules, 2 is the smallest prime factor of 36. So, we get, 36 ÷ 2 = 18

Step 2: Here need repeatedly divide the quotient by 2 until we get a number that is no more divisible by 2. So, we divide 18 again by 2 which is 18 ÷ 2 = 9.

Step 3 : Now, 9 is not completely divisible by 2, so, we proceed with the next prime factor of 36, which is 3. That is 9 ÷ 3 = 3

Step 5: Divide the quotient by 3 again which is 3 ÷ 3 = 1. Now, we need not proceed further as we have obtained 1 as our quotient. Therefore, the prime factorization of 36 is expressed as 2 × 2 × 3 × 3 = 2² × 3²; where 2 and 3 are prime numbers and the prime factors of 36.

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The expressions that could be equivalent to x^2+bx-36 where b is negative is option 1: (x + 3)(x - 12) and option 5: (x - 9)(x + 4).

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The given expression is - x² + bx - 36

The first expression is - (x + 3)(x - 12)

Solve using the multiplication property -

= (x + 3)(x – 12)

= x(x - 12) + 3(x - 12)

= x² - 12x + 3x - 36

= x² - 9x - 36

The second expression is - (x - 2)(x + 18)

Solve using the multiplication property -

= (x - 2)(x + 18)

= x(x + 18) - 2(x + 18)

= x² + 18x - 2x - 36

= x² + 16x - 36

The third expression is - (x - 13)(x - 3)

Solve using the multiplication property -

= (x - 13)(x - 3)

= x(x - 3) - 13(x - 3)

= x² - 3x - 13x + 39

= x² - 16x + 39

The fourth expression is - (x + 4)(x + 9)

Solve using the multiplication property -

= (x + 4)(x + 9)

= x(x + 9) + 4(x + 9)

= x² + 9x + 4x + 36

= x² + 13x + 36

The fifth expression is - (x - 9)(x + 4)

Solve using the multiplication property -

= (x - 9)(x + 4)

= x(x + 4) - 9(x + 4)

= x² + 4x - 9x - 36

= x² - 5x - 36

Therefore, the choices for b being negative is x² - 5x - 36, and x² - 9x - 36.

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Select all expressions that could be equivalent to x^2+bx-36 where b is negative.

(x + 3)(x - 12)

(x - 2)(x + 18)

(x - 13)(x - 3)

(x + 4)(x + 9)

(x - 9)(x + 4)

Answer: 24.2

Step-by-step explanation: Use the Pythagorean Theorem:

10^2 + 22^2 = x^2

100 + 484 = x^2

x^2 = 584

x = 24.16609..

which is close to 24.2

Answer: 24.2

Step-by-step explanation:

Use the Pythagorean Theorem.

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

We already know a and b.

We can plug it in into the theorem.

[tex]10^2 + 22^2 = c^2[/tex]

[tex]584 = c^2[/tex]

Then, take the square root of 584.

[tex]\sqrt{584}[/tex] ≈ 24.2 (24.16 rounded up is 24.2)

The inverse of the function f(x) and its domain include the following: D. f⁻¹(x) = (x + 4)²; x ≥ 0.

In order to determine an inverse function or the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;

f(x) = √x - 4

y = √x - 4

x = √y - 4

√y = x + 4

Taking the square of both sides of this inverse function, we have:

f⁻¹(x) = (x + 4)²

For the domain of this function, we have the following:

f(x) = √x - 4

When x= 0, we have:

f(0) = √0 - 4

f(0) = 0.

In conclusion, the domain of this function cannot be equal to -4 because it is impossible to find the square root of a negative number.

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The equation in the said case is 10x + 5 = 35

Tickets bought = 10

Parking fee paid = $5

Money spent on seeing the show = $35

Determining the equation in the given case -

10x + 5 = 35

Where x is the cost of each ticket, and 10x represents the total cost of the tickets.

The equation states that the total cost of the tickets which is 10x plus the cost of the parking fee which is $5 is equal to the total amount spent by Kate which will be 35$.

This equation can be further used to find the cost of each ticket by isolating x:

10x + 5 = 35

10x = 30

x = 3

Therefore, each ticket cost $3.

Complete Question:

kate buys 10 tickets to the show. She also pays a 5$ parking fee. she spent $35 to see the show. What equation is this

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The lower limit of a modal can be calculated by determining the lowest frequency interval having a smallest value.

In mathematics, limits are the points at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend heavily on limits, which are required to determine integrals, derivatives, and continuity. It is applied during the analysis process and always focuses on the function's behavior at a certain time.

Let the least term 'h' of a sequence be a term which is smaller than all but a finite number of the terms which are equal to 'h'. Then 'h' is called the lower limit of the sequence.

A lower limit of a series,

lower[tex]\lim_{n \to \infty} S_n = \lim_{n \to \infty} S_n = h[/tex]

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Step-by-step explanation:

16x - 4y = 12

4x - y = 3

4x = 3+y

x= 3+y/4

for y = 1

x= 3+1/4 = 1

y = 2

x=3+2/4 = 5/4 = 1.25

y = 3

x = 3+3/4 = 6/4 = 1.5

Answer: 62.5%.

hope this helped

The range of a negative function are those which lies in the intervals where the function is below the x-axis.

The range function can be positive or negative because the range formula substracts the lowest number from the highest number. A negative function has all negative values. The negative function has values that are all negative. The domain of the function can be positive. Every output must be less than zero. A negative function has values that are negative for all arguments of its domain. The function values can be positive or negative. They can increase or decrease as the input increases.

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4t + 0.2 = 6(t+x) this system of equations can be used to find when Carson catches up with Arturo.

What is a system of equations?

A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously. In order to solve a system of equations, one must find all the sets of values of the variables that constitute solutions of the system.

The system of equations that can be used to find when Carson catches up with Arturo is:

distance = speed x time

For Arturo:

distance = 4t + 0.2

For Carson:

distance = 6(t+x)

where t is the time in hours that Arturo has been walking, x is the time in hours that Carson has been jogging, and distance is measured in miles.

Equating the two equations to find when they meet:

4t + 0.2 = 6(t+x)

And solving for x, the time in hours that Carson has been jogging.

x = (4t + 0.2 - 4t)/6 = 0.2/6 = 1/30

This is the time in hours that Carson has been jogging when he catches up with Arturo.

Hence, 4t + 0.2 = 6(t+x) this system of equations can be used to find when Carson catches up with Arturo.

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The lowest positive whole number that should replace the question mark on the pinner such that the probability of pinning an odd number greater than 6 is 1/4 is 9.

It could be determined by calculating the probability of pinning an odd number greater than 6 out of the total number of possible outcomes.

If we consider the lowest positive whole number greater than 6 is 7, then we have 7,9,11,13,15,17,19,21,23,25 and so on.

Out of these numbers, 1/4 are odd numbers greater than 6. So the lowest whole number that could replace the question mark on the pinner is 9.

This is applicable for any situation where the probability of an event occurring out of a set of possible outcomes needs to be determined, and the lowest value for which that probability is a certain ratio needs to be found. In this case, the event is pinning an odd number greater than 6, and the set of possible outcomes is all positive whole numbers greater than 6. The probability being considered is 1/4, and the question is what is the lowest value that can replace the question mark on the pinner such that this probability is achieved.

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The complete factor 3x² 6x or 3x² - 6x are 3x and (x-2) and the factor form can be written as 3x( x - 2).

Polynomial factorization represents a polynomial with coefficients in a given field, or an integer as a product of irreducible factors with coefficients in the same domain. Full factoring is a three step process :

2. Factor a Trinomial, if possible.

Example: x² – 2x – 3 factored into

(x + 1)(x – 3).

3. Factor a difference between two

Squares as many times as possible.

Example: y²– 9 factored into

(y + 3)(y – 3).

We have, a polynomial (binomial) say, p(x) = 3x² - 6x , and we have to complete factorize it. Follows the steps,

=> 3x( x - 2 ) , (irreducible factors). Therefore, the 3x is a common factor that we can be factored out and keeping the x minus sign 2 .

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Answer:

10.35

Step-by-step explanation:

Add 10.25+14.35+15.45+9.60= 49.60

60-49.65=10.35

An

Answer:

11 months

Step-by-step explanation:

It looks like you are trying to create a function that represents the number of members the fitness club has over time, assuming that each month they add 25 new members to the club.

You can use the function f(x) = 225 + 25x, where x represents the number of months from the current time.

The function starts with an initial value of 225 members, which represents the number of members the club already has. Then, for each additional month represented by x, the function adds 25 new members to the total, represented by 25x.

So, if the fitness club wants 500 members in 9 months, you can set f(9) = 500 and solve for x

f(9) = 225 + 25x = 500

25x = 500 - 225

25x = 275

x = 11

So, the club will reach 500 members in 11 months if they continue to add 25 members per month

Answer: Slope = - 1/3, the y-intercept = -4

Step-by-step explanation:

Pick two coordinates: (-1, -1), (2, -2)

Find the slope: y2 -y1 / x2 - x1  

                         -2 - (-1) / 2 - (-1) = - 1/3

Slope intercept form: y = mx + b

Substitute in what you know to find b:

-1 = -1/3 (-1) + b           substitution property

-1 = 1/3 + b                 distributive property

-3 = 1 + b                    multiplication property

-4 = b                         subtraction property

Regular dodecagons have internal angles that are the same size and have equal length sides and the interior angles of the dodecagon total 1800 degrees.

A regular dodecagon is a shape with equal-length sides and equal-sized internal angles.

It features rotational symmetry of order 12 and twelve reflected symmetry lines.

The Schläfli symbol for a regular dodecagon is 12, and it can be formed from a truncated hexagon (t6) or twice-truncated triangle (tt3).

In a regular dodecagon, the internal angle at each vertex is 150°.

The dodecagon's internal angles add up to 1800 degrees.

A 12-sided polygon is called a dodecagon.

The illustrations above show several unique varieties of dodecagons.

A regular polygon known as a regular dodecagon is a dodecagon with vertices evenly placed around a circle and all sides having the same length.

Therefore, the interior angles of the dodecagon total 1800 degrees.

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Answer:

Hugo earns $11.50 per hour

Step-by-step explanation:

57.50/5 = 11.50

Answer:$11.5 per hour

Step-by-step explanation: $57.50 / 5 hour shift = $11.5 per hour

The two column proof showing that ΔKLG ≅ ΔMLG is as detailed below.

A two-column proof is defined as a geometric proof consists of a list of statements, and the reasons for which we know those statements to be true.

Statement 1: GL ⊥ KM

Reason 1: Given

Statement 2: KG  ≅ MG

Reason 2: Given

Statement 3: ∠GLK and ∠GLM are right angles

Reason 3: Definition of right angles

Statement 4: GL ≅ GL

Reason 4: Reflexive Property

Statement 5: ΔKLG and ΔMLG are right triangles

Reason 5: definition of right triangles

Statement 6: ΔKLG ≅ ΔMLG

Reason 6: HL Congruency postulate

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Answer:11 miles

Step-by-step explanation:

so, no matter what you pay $5, and each mile is $4, so you pay $49 dollars. First do 49 - 5, which equals 44, and 44 ÷ 4 = 11, so the answer is 11 miles

To find the discriminant and nature of the roots of a quadratic equation, you can use the quadratic formula.

Write the quadratic equation in the form of ax² + bx + c = 0, where a, b, and c are constants, and x is the variable.

Calculate the discriminant using the formula

b² - 4ac.

Use the discriminant to determine the nature of the roots:

If the discriminant is greater than 0, the roots are real and distinct.

If the discriminant is equal to 0, the roots are real and identical (i.e., the equation has only one root).

If the discriminant is less than 0, the roots are complex and not real numbers.

To find the roots of the quadratic equation, you can use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. The plus-minus sign indicates that there are two possible solutions, and the square root of the discriminant is used to find them.

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Step-by-step explanation:

the arc angle KLI = 142°.

that means that the arc angle KJI = 360 - 142 = 218°.

this is twice the inscribed opposite angle on the arc (L).

so,

(a)

angle KLI = 218/2 = 109°

(b)

for the same reason

angle LKJ is half of the arc angle LIJ.

arc angle LIJ = 2× angle LKJ = 2×66 = 132°

that means

arc angle LKJ = 360 - 132 = 228°

angle LIJ = half of arc angle LKH = 228/2 = 114°

FYI for such an inscribed quadrilateral there is Akari the rule that the sum of opposite angles have to be 180°.

so, angle LIJ is opposite of angle LKJ.

angle LIJ = 180 - angle LKJ = 180 - 66 = 114°

A function is decreasing on some interval of its domain if f(a) < f(b) for all a, b in that interval such that a > b.

A function f(x) decreases on an interval I if f(b)<=f(a) for all b>a, where a,b in I. If f(b)<f(a) for all b>a, the function is said to be strictly decreasing. Conversely, a function f(x) increases on an interval I if f(b)>=f(a) for all b>a with a,b in I. If f(b)>f(a) for all b>a, the function is said to be strictly increasing. If the derivative f^'(x) of a continuous function f(x) satisfies f^'(x)<0 on an open interval (a,b), then f(x) is decreasing on (a,b). However, a function may decrease on an interval without having a derivative defined at all points. For example, the function -x^(1/3) is decreasing everywhere, including the origin x=0, despite the fact that the derivative is not defined at that point.

A function is increasing on some interval of its domain if f(a) > f(b) for all a, b in that interval such that a > b. A function is decreasing on some interval of its domain if f(a) < f(b) for all a, b in that interval such that a > b. More casually put: a function is increasing if the graph rises to the right. It is decreasing if the graph falls to the right.

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We can rewrite the given linear equation to have the different numbers of solutions as:

a) 3x + 8 = 3x + 4

b) 3x + 8 = 3x + 8

c) 3x + 8 = 3x +x

Here we have the linear equation:

3x + 8 = 3x + ?

Notice that the first term (the one that depends of x) is equal in both sides, so the equation will not be true only if the second term is a constant and is different to 8, so for example we could write:

3x + 8 = 3x + 4

b) Infinite solutions means that we have the same thing in both sides, so here we can add 8

3x + 8 = 3x + 8

Is true for all values of x, thus, it has infinite solutions.

c) The equation will have one solution only if the coefficients of the variable x are different in both sides, then here we can add "x"

3x + 8 = 3x +x

3x + 8 = 4x

That equation has a single solution:

8 = 4x - 3x

8 = x

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The equivalence class of a is [a] = {x ∈ A: (a, x) ∈ R}. This includes all elements of A that are related to 'a'.

An equivalence class is the name we give to the subset S that includes all elements that are equivalent to each other. If there is an equivalence relation between any two elements, they are called equivalent.

Equivalence class properties : The relation ~ is an equivalence relation if and only if:

When our relation ~ satisfies the above three properties, we can write the definition of an element equivalence class as follows [a] = { x ∈ X | and ~ x}. Consider an example, If X were the set of all polygons and the equivalence relation ~ was defined as "having the same number of sides", the set of all triangles, the set of all quadrilaterals, the set of all pentagons, etc., are represents the equivalence classes.

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Complete question:

What is equivalence class ?