Subtract 5/6 - 7/12 Simplify your answer.

You can use the distance formula, which is Distance = Speed x Time, to determine the bus's speed. In this instance, the trip is 54 kilometers long and takes 90 minutes.

 To answer a problem quickly, rearrange the formula as follows:

     Speed = Distance / Time

 Therefore, you must convert time from minutes to hours in order to determine the speed. 90 minutes are equal to 1.5 hours because there are 60 minutes in an hour.

After that, you may enter the formula with the known values for time and distance:

54 km travelled in 1.5 hours equals 36 km/h.

therefore , the bus travels at a 36 km/h speed.

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The two equations represent the same line.

Here we have the two linear equations below:

y = (1/6)*x + 5

y - (1/6)*x = 5

Remember that:

Two linear equations are parallel if the slope is equal and the y-intercept is different, and two linear equations are perpendicular if the product between the slopes is -1.

Now we can rewrite the second equation just by adding (1/6)x in both sides:

y = (1/6)*x + 5

y = (1/6)*x + 5

So both equations are equal, then the equation represent the same line.

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The solution to the equation "5*2-3^2 / (3^2-(-2))^2" after solving it is 1/121

To solve the equation 5*2-3^2 / (3^2-(-2))^2, we need to simplify the numerator and the denominator. This will give us this:

5*2-3^2 / (3^2-(-2))^2 =

= 10 - 9 / (9 - (-2))^2

Simplify further to make the number reduced

10 - 9 / (9 - (-2))^2

After the subtraction at the numerator level, the denominator figures have two minus signs which becomes a plus. As a result, we realize the value below

= 1 / (11)^2

In order to remove the bracket in the denominator, it implies that the number in bracket will be multiplied by itself since it is in the superscript of 2 which means 11 multiply by 11 or (11 x 11)

= 1/121

Therefore, to solve the equation 5*2-3^2 / (3^2-(-2))^2, one needs to simplify the equation and do the subtraction and addition from the numerator and the denominator respectively to realize the answer which is 1/121

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Answer: 1/121

Step-by-step explanation:

( 5 * 2 - 3^2 )/[ 3^2 - (-2)] ^ 2

= (10 - 9)/(9+2)^2

= 1 / 11^2

= 1/121

Answer:

a₅ = 141

Step-by-step explanation:

using the recursive rule [tex]a_{n+1}[/tex] = - 3[tex]a_{n}[/tex] - 3 and a₁ = 1

the recursive rule allows a term in the sequence to be found by multiplying the previous term by - 3 and then subtracting 3 , that ia

a₁ = 1

a₂ = - 3a₁ - 3 = - 3(1) - 3 = - 3 - 3 = - 6

a₃ = - 3a₂ - 3 = - 3(- 6) - 3 = 18 - 3 = 15

a₄ = - 3a₃ - 3 = - 3(15) - 3 = - 45 - 3 = - 48

a₅ = - 3a₄ - 3 = - 3(- 48) - 3 = 144 - 3 = 141

The requried days over which the mass of the kitten gets doubled is 9 days.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

here,
Let the number of days be x,
According to the quesiton,
2×90 = 90 + 10x
180 - 90 = 10x
x = 9 days

Thus, the requried days over which the mass of the kitten gets doubled is 9 days.

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Answer:

√((x2-x1)^2 + (y2-y1)^2)

Step-by-step explanation:

To find the distance between two points in fractions, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

To use the Pythagorean theorem to find the distance between two points, you can think of the two points as the endpoints of one of the legs of the right triangle. Let the two points be (x1, y1) and (x2, y2). The distance between the two points is the length of the hypotenuse of the right triangle formed by the two points and the origin. The distance can be computed using the formula:

distance = √((x2-x1)^2 + (y2-y1)^2)

This will give you the distance between the two points in whatever unit you are using for x and y.

The shortest possible distance between Trae and Katrina is 6 feet.

Since Yana, Josh, and Katrina are standing at the vertices of a right triangle, the distance between Yana and Josh is the hypotenuse of the triangle and the other two sides are the legs.

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

Using the Pythagorean theorem, we can calculate that the distance between Yana and Katrina is 15 feet.

( 18^2 + 12^2 = 15^2)

Since Trae is standing between Josh and Katrina, the shortest possible distance between Trae and Katrina is half of the distance between Josh and Katrina, which is 6 feet.

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The inverse of the function f(x) = 2x - 1  is f(x) = 1/2(x + 1)

An inverse of a function is a function that cancels the action of the given function.

The inverse of a function is obtained by reversing the given function.

In the problem, the function is  f(x) = 2x - 1. Hence,

y = f(x) = 2x - 1

Add  both sides with 1:

y + 1 = 2x -1 + 1

2x = y + 1

Divide both sides by 2:

x = 1/2 (y + 1)

Replace y with x

f(x) = 1/2 (x + 1)

Hence, the inverse function of f(x) = 2x - 1 is f(x) = 1/2 (x + 1)

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The given expression if 23+37=60 does 23+37+9=60+97 is not true.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

23 + 37 = 60 ____(1)

Now,

From (1),

23 + 37 + 9 = 60 + 97

23 + 37 + 9 = 157

60 + 9 = 157

69 ≠ 157

This is not true.

Thus,

The given expression is not true.

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Answer:

the answer is c, I took the test and it's C

The first three terms of the given sequence are -17, -27 and -37

A sequence is an ordered list of objects. Like a set, it contains elements. The number of ordered elements (possibly infinite) is called the length of the sequence.

Given that, an arithmetic sequence formula an = -10n - 7

We are asked to find the first three terms of this sequence.

Therefore,

Put n = 1 for first term,

a₁ = -10(1)-7

a₁ = -17

Put n = 2 for second term,

a₂ = -10(2)-7

a₂ = -27

Put n = 3 for third term,

a₃ = -10(3)-7

a₃ = -37

Hence, the first three terms are -17, -27 and -37

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option A is correct, 5+0.5n=11 is the equation and value of n is 12.

Two or more expressions with an Equal sign is called as Equation.

Given sentence is  5 increased by half a number is 11.

In the sentence increases means added and half means 1/2 of a number.

Here the unknown number is n.

5+n/2=11

5+0.5n=11

Subtract 5  on both sides

0.5n=6

Divide both sides by 0.5

n=12

Hence, option A is correct, 5+0.5n=11 is the equation and value of n is 12.

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Answer: 17

Step-by-step explanation:

in the screenshot, b=y

The required way to write logarithmic function is [tex]\log_{b}({b^x})=x[/tex]

A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number. If bx = n, then x is the logarithm of n to the base b, which is expressed mathematically as x = logb n. For instance, 23 = 8; hence, 3 is the base-2 logarithm of 8 or 3 = log2 8.

The formula for the logarithmic function is f(x) = log base b of x. The base 10 is used for the common log.

The base used by the natural log is e, an irrational integer with the value 2.71828.

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The difference in the means is about 4.3 to 10.5 times the MAD.

Statistics is the study of mathematics that deals with relations between comprehensive data.

Here,
volleyball: mean = 86, MAD = 19.6
basketball: mean = 185, MAD = 17.7
The difference in volleyball the means to MAD is given as,
= 86 / 19.6

= 4.3  

The difference in basketball the means to MAD is given as,
= 185 / 17.7

= 10.5

Thus, the difference in the means is about 4.3 to 10.5 times the MAD.

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The leap pattern of the frog is up 2 steps then back 1 step. To reach 10th step she have to take 9 leaps up.

Let represent leaps up with positive number and leaps back with negative number.

Hence, the movement of the little green frog can be written as:

2 - 1 + 2 - 1 + 2 - 1 + ....

Notice, that every 4 leaps (both up and back) she reaches 2 steps.

2 - 1 + 2 - 1  = 2

Hence, after 4 x 4 = 16 leaps she will reach the 8th steps. The last leap in this instant is leap back. Hence, the next leap will be leaps up 2 steps, and she reaches the 10th steps.

In every 4 leaps there are 2 leaps up.

Therefore, she have to leaps up 2 x 4 + 1 = 9 leaps up.

You can also write all her leaps to reach the 10th steps:

2 - 1 + 2 - 1 +    2 - 1 + 2 - 1  +    2 - 1 + 2 - 1  +   2 - 1 + 2 - 1   + 2

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[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{S varies inversely with }F^2}{S = \cfrac{k}{F^2}}\hspace{5em}\textit{we also know that} \begin{cases} F=8\\ S=125 \end{cases} \\\\\\ 125=\cfrac{k}{8}\implies (125)(8)=k\implies 1000=k~\hfill \boxed{S=\cfrac{1000}{F^2}} \\\\\\ \textit{when F=4, what is "S"?}\qquad S=\cfrac{1000}{4^2}\implies S=\cfrac{125}{2}[/tex]

The domain of f(x) =7 is all real numbers and the range of f(x)= 7 is 7.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

This is a function f(x)=7 defined for all real arguments x, so its domain is all real numbers (−∞,+∞).

Since for any value of an argument the function takes a value of 7, its range is one and only one real number y=7.

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Linear functions are those whose graph is a straight line.

If you have a table to look at instead of a graph, you should look at the rate of change. If the rate of change in the input to the rate of change in the output is the same at all points in the table, the table represents a linear function. Linear functions have a straight line as their graph. There is one independent variable and one dependent variable in a linear function. X is the independent variable, while y is the dependent variable.

Check to verify if the function has a constant rate of change to determine whether it is linear or nonlinear.

Choose any two rows from the database and compute the rate of change between them.

Now choose a different

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The area of the border between the two rectangles is 40 units^2

The new rectangle will have the dimensions  of (7 + 2) x (11 + 2)  =  9 x 13

So....the area between them is just  

The equation for calculating a rectangle's area. Rectangle's surface area. A = l × b. Once the length and breadth of a rectangle are known, its area may be computed.

The area of the rectangle is obtained in a square-unit dimension by multiplying length and width.

( 9 * 13) - (11 * 7 )  =

117 - 77 =

40 units^2

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Five points are located on a line. The value of K is 12.

We would first draw the number line and, by trial and error, add some of the above-mentioned numbers to identify the missing number.

The range of the numbers would be 0 to 19. This is so because the ten values listed represent the least to maximum distances between pairs of points.

That is, in order to receive 2, the point pairs would need to be between 0 and 2, and in order to get 19, they would need to be between 0 and 19.

Place the following numbers on the first number line we will create 0, 2, and 19.

The pairs could be 0 and 7 or 8 and 15 in order to have a distance of 7.

This would be shown on the number line.

From the arrows drawn, we can see we have distances: 2, 7, 15, 19, 5, 13, 17, 8, 12, 4

The number available in this list but not specified in the ten-distance list in the question is 12.

Therefore, the value of k = 12

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A production possibility chart is a graphical representation of the maximum amount of a good or service that can be produced using a given amount of resources.

A production possibility chart is a graphical representation of the maximum amount of a good or service that can be produced using a given amount of resources. It provides a visual representation of the tradeoffs between two or more different types of production that must be made when allocating finite resources. The production possibility chart illustrates the concept of opportunity cost, which is the cost of a particular decision in terms of the next best alternative. By plotting the various production possibilities, it is easy to see the possible outcomes of different combinations of resources. For example, a production possibility chart can be used to illustrate the tradeoff between producing more of one good and less of another in order to maximize efficiency.

A production possibility chart is a graphical representation of the maximum amount of a good or service that can be produced using a given amount of resources. It illustrates the concept of opportunity cost and the tradeoffs between different types of production that must be made when allocating finite resources. It is used to show the possible outcomes of different combinations of resources and to maximize efficiency.

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Answer is attached here.

Answer:

5

Step-by-step explanation:

slope = rise/run or y-value/x-value

point=(10,50)

50/10=5

slope=5

The answer is 4-9 is the expression is equivalent to (4−3)−6.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

the expression is,

(4-3)-6

= 1-6

= -5

so,

4-9 = -5

Hence, The answer is 4-9.

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Answer:

The rate of speed is 1,066

Step-by-step explanation:

If you see it as a fraction: 5/410 and 13/?

You can multiply 13 and 410 together and divide that quotient by 5 to find the rate.

13 x 410 is 5,330 and 5,330 divided by 5 is 1,066.

A right angle is one that is 90 degrees in length.

When two rays intersect and form a 90˚ angle or are perpendicular to each other at the intersection, they are said to form a right angle. It is the most frequently encountered angle in our daily lives. It can be noticed in room corners, box edges, mobile phone screens, and so on.

A square's and a rectangle's sides always make a right angle with each other. It is represented in radians as /2.

The angle formed by two lines that are perpendicular to each other is called a right angle. A right angle is equal to 90° and is in the shape of the letter "L". In the following figure, ray AB and BC form a right angle ABC.

Thus, A right angle is one that is 90 degrees in length.

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The time required for the population to triple is nearly 8 years if the population of a community is known to increase at a rate proportional to the number of people present at time t and an initial population p0 has doubled in 5 years.

Given that the population is increasing at a rate proportional to the number of people present at time t.

the population growth is modeled by the following differential equation:

[tex]\frac{dP(t)}{dt} = kP(t)[/tex]

P(t) = Po[tex]e^{kt}[/tex]           ..(1)

Initially given that population doubled in five years

i.e. P(5) = 2Po

Putting it in equation(1)

2Po = Po[tex]e^{5k}[/tex]

taking logs is both sides

ln 2 = 5k

k = ln2/5 = 0.1386

therefore, P(t) = Po[tex]e^{0.1386t}[/tex]

Now, the time required for the population to triple or P(t) 3Po

3Po = Po[tex]e^{0.1386t}[/tex]

ln3 = 0.1386t

or t = 7.9265 = 7.9

Therefore, the time required for the population to triple is nearly 8 years.

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A: The range of the function f(x) is (-3,∞).

B: The horizontal asymptote for y=2^(x+1)−3 is y=-3, the vertical and horizontal asymptote for y=10/x is x=0 and y=0 respectively.

C: The end behaviour of y=2^(x+1)−3 is [x→∞,x→-∞] = [f(x)→∞,f(x)→-3] and the end behaviour of y=10/x is [x→∞,x→-∞] = [f(x)→0,f(x)→0].

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The set of values of the dependent variable for which a function is defined is known as the range of the function.

The range of an exponential function of the form c·n^(ax+b) + k is f(x) > k.

So, the range of function {2^(x+1)}-3 is f(x)>-3.

The range of function 10/x is (-∞,+∞).

So, the range for system of function becomes (-3,+∞).

The line x=L is a vertical asymptote of the function y=2^(x+1)−3, if the limit of the function (one-sided) at this point is infinite.

In other words, it means that possible points are points where the denominator equals 0 or doesn't exist.

So, find the points where the denominator equals 0 and check them.

As it can be seen, there are no such points, so this function doesn't have vertical asymptotes.

Line y=L is a horizontal asymptote of the function y=f(x), if either limx→∞f(x)=L or limx→−∞f(x)=L, and L is finite.

Calculate the limits -

limx→∞(2x+1−3)=∞

limx→−∞(2x+1−3)=−3

Thus, the horizontal asymptote is y=−3.

The line x=L is a vertical asymptote of the function y=10x, if the limit of the function (one-sided) at this point is infinite.

In other words, it means that possible points are points where the denominator equals 0 or doesn't exist.

So, find the points where the denominator equals 0 and check them.

x=0, check:

limx→0+(10x)=∞

Since the limit is infinite, then x=0 is a vertical asymptote.

Line y=L is a horizontal asymptote of the function y=f(x), if either limx→∞f(x)=L or limx→−∞f(x)=L, and L is finite.

Calculate the limits:

limx→∞(10x)=0

limx→−∞(10x)=0

Thus, the horizontal asymptote is y=0.

The end behaviour of a function f(x) describes the behaviour of the function as x approaches +∞ and x approaches -∞.

The end behaviour of y=2^(x+1)−3 is as x approaches +∞, f(x) approaches +∞ and x approaches -∞, f(x) approaches -3.

The end behaviour of y=10/x is as x approaches +∞, f(x) approaches 0 and x approaches -∞, f(x) approaches 0.

Therefore, the range, asymptotes and end behaviour is found.

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