Which functions are increasing?
Select all answers that are correct.

To simplify the fraction 10/30, divide both the numerator and the denominator by their greatest common divisor, which is 10, resulting in the simplified fraction 1/3.

Simplifying the Fraction 10/30

To simplify the fraction 10/30, we want to find the greatest common divisor (GCD) that both the numerator (10) and the denominator (30) share. In this case, both numbers are divisible by 10. So, we divide both parts of the fraction by 10 to find the simplest form.

Step 1: Divide the numerator by 10.
10 / 10 = 1

Step 2: Divide the denominator by 10.
30 / 10 = 3

Therefore, the simplified form of the fraction 10/30 is 1/3. As we recall from our Algebra classes, this is a legal maneuver because multiplying or dividing by a fraction equivalent to 1 (like 10/10) does not change the value of the original fraction. It only simplifies it. So, the simplified fraction of 10/30 is indeed 1/3.

Final answer:

To evaluate 5/9(f-32) when f=50, substitute 50 into the expression, simplify the bracket (50 - 32 = 18), and then multiply the result by 5/9. This simplifies to 18/9 (which is 2), and then 2 x 5, yielding a final answer of 10 degrees Celsius.

Explanation:

To evaluate the expression 5/9(f-32) when f=50, you need to plug the value of f into the expression and then simplify it.

Here are the steps:

Substitute 50 for f in the expression: (5/9) × (50 - 32).

Calculate the bracket first: 50 - 32 = 18.

Multiply the result by 5/9: (5/9) × 18.

Divide 18 by 9, which gives you 2.

Finally, multiply 2 by 5, which gives you 10.

Therefore, 5/9(f-32) evaluated at f=50 is 10 degrees Celsius.

The slope in the equation y = 15x + 25 represents the rate at which Aaron's earnings increase per lawn mowed, which is $15 for each additional lawn.

In the equation y = 15x + 25, the slope is represented by the coefficient of x, which is 15. The slope indicates the rate at which Aaron's total earnings increase for each additional lawn he mows. Specifically, the slope value of 15 means that Aaron earns $15 for each lawn he mows. The y-intercept of the equation is 25, which represents a starting value or a fixed amount that does not depend on the number of lawns mowed. This indicates that Aaron might have a base charge or initial fee of $25 before he starts mowing any lawns.

The slope in the equation y = 15x + 25 indicates Aaron earns $15 for each lawn he mows. The slope is the rate of change between lawns mowed (independent variable) and money earned (dependent variable).

The slope in the equation y = 15x + 25 represents the amount of money Aaron earns per lawn he mows. In this equation, the slope is 15, which means that Aaron earns $15 for each lawn he mows. The y-intercept in this context is 25, which typically would represent an initial fee or starting amount, but since it relates to lawns mowed, it may not have a contextually relevant interpretation without additional information. In general, the slope in a linear equation like this contextualizes the rate of change between the independent variable (lawns mowed) and the dependent variable (total money earned).

Answer:

If you graph the data points and the points lie along a straight line then the data is linear.

Answer: C.2

Step-by-step explanation:

Given: Independent variable= Number of sides

To check how many of the remaining three columns represent a linear relationship, we need to check the rate of change of the three columns with respect to dependent variable.

For number of diagonals

The rate of change of diagonals w.r.t number of sides is constant and that is 1.

For Sum of all interior angles (degrees)

The rate of change of  Sum of all interior angles w.r.t number of sides is constant and that is 180°.

For measure of each angle (degrees)

The rate of change of  measure of each angle w.r.t number of sides is not constant and that is 180°.

Since for vertices 3 , measure of angle=60

vertices 4 , measure of angle=90

From vertices 3 to 4 change in measure of angle is 30

vertices 5 , measure of angle=108

From vertices 4 to 5 change in measure of angle is 18

Thus number of diagonals and Sum of all interior angles are the columns represent a linear relationship when compared with the independent variable.

Therefore there are 2 columns represent a linear relationship when compared with the independent variable.

Solution:

The equation of linear relationship is , y= k x

That is, [tex]\frac{y-value}{x-value}=k({\text{a constant})[/tex]

As, you can see that , ratio of

1.

[tex]\frac{\text{Sum of interior angles of a regular polygon}}{\text{number of sides of that polygon}}={\text{Measure of each interior angle of regular polygon}}[/tex]

2. Also, as number of sides increases, the smallest regular polygon is equilateral triangle(3 sides) , having 0, diagonal, the number of diagonal increases by 1.

→→Regular polygon having sides , n≥3=k, where k is number of diagonals=0,1,2,3,4,[ For example, for, n=3,k=1,n=4, k=2,...]

Column (2)

[tex]C_{4}-C_{3}=C_{3}-C_{2}=C_{2}-C_{1}=1[/tex]

Column (4)

[tex]C_{2}-C_{1}=90-60=30\\\\ C_{3}-C_{2}=108-90=18\\\\ C_{4}-C_{3}=120-108=12[/tex]

Column (3)

[tex]C_{4}-C_{3}=720-540=180\\\\ C_{3}-C_{2}=540-360=180\\\\ C_{2}-C_{1}=360-180=180[/tex]

In, Column (2) and Column(3) the difference between two consecutive values is same, while in column (4) difference between two consecutive values is not same.So, C(2) and C(3) shows linear relationship, column (4) do not.

Option (C) 2 is Right choice.

Answer:

Negative Slope

Step-by-step explanation:

The slope is the ratio of Change in height to the change in horizontal distance. It can also be define as tangent of angle made by that line and it is find by formula, [tex]slope (m)= \frac{y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]

The slope is said to be a positive slope when a line is moving from left to right, the line rises.

The slope is said to be a negative slope when a line is moving from left to right, the line falls.

Here, Let the student earns be y marks in test

and let incorrect question be x

then y₁ = 98 , y₂ = 90 and x₁ = 1 , x₂ = 5

then [tex]slope (m)= \frac{y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]

[tex]slope (m)= \frac{90 - 98}{5 - 1} [/tex]

⇒ m = -2

Hence, it has negative slope.

The required expression is  x + 2y = 2 (3/2 + y) that gives the value 3.

An algebraic expression is consists of variables, numbers with various mathematical operations,

To write the algebraic expression with variable x that has a value of 3.

Let x is a variable and y is another variable,

The expression for the x equal to 3 can be written as,

x + 2y = 2 (3/2 + y)

The expression x + 2y = 2 (3/2 + y) gives the value 3.

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Answer:

k/2 − 3/5

Step-by-step explanation:

To simplify the expression 2/5k - 3/5k + 1/10k, we combine the like terms and simplify the fractions. The simplified expression is -1/10k.

To simplify the expression 2/5k - 3/5k + 1/10k, we can combine like terms. Like terms have the same variable raised to the same power. In this case, the variable is 'k'. So, combining the fractions, we get:

(2/5 - 3/5 + 1/10)k

Now, let's simplify the fractions:

Therefore, the simplified expression is -1/10k.

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