Maths-

General

Easy

Question

# Is the relation forms a linear function ?

Use the graph to support your answer.

Hint:

### An equation of the form y = f(x) is called a function if there is a unique value of y for every value of x. In other words, every value of x must have one value of y. We can check if the graph is a function by the vertical line test. A graph represents a function if any vertical line in the xy plane cuts the graph at maximum one point. A function is linear if the graph of the function is a straight line.

## The correct answer is: function is linear

*Step by step solution:*

Let us denote the week by x.

Let us denote the number of students by y.

The given table is

x

0

1

2

3

4

5

y

300

250

200

150

100

50

We draw a graph from the above table.

From the graph, we can observe that, the curve drawn is a straight line.

Hence the function is linear.

There are other ways to determine whether a function is linear or not, like, checking if the slope is equal between each of the points or if the equation can be written in the form of y = ax + b, where a and b are constants.

### Related Questions to study

Maths-

### Solve 2x-5<5x-22, then graph the solution

Hint:

Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .

We are asked to solve the inequality and graph the solution.

Step 1 of 2:

Rearrange and solve the inequality,

Step 2 of 2:

Graph the inequality using the solution;

Note:

Whenever we use the inequality symbol < or> we do not include the end point.

Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .

We are asked to solve the inequality and graph the solution.

Step 1 of 2:

Rearrange and solve the inequality,

Step 2 of 2:

Graph the inequality using the solution;

Note:

Whenever we use the inequality symbol < or> we do not include the end point.

### Solve 2x-5<5x-22, then graph the solution

Maths-General

Hint:

Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .

We are asked to solve the inequality and graph the solution.

Step 1 of 2:

Rearrange and solve the inequality,

Step 2 of 2:

Graph the inequality using the solution;

Note:

Whenever we use the inequality symbol < or> we do not include the end point.

Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .

We are asked to solve the inequality and graph the solution.

Step 1 of 2:

Rearrange and solve the inequality,

Step 2 of 2:

Graph the inequality using the solution;

Note:

Whenever we use the inequality symbol < or> we do not include the end point.

Maths-

### Write the solutions to the given equation.

Rewrite them as the linear-quadratic system of equations and graph them to solve.

Hint:

A quadratic equation is when the polynomial has a degree two. A graph is a geometrical representation of an equation.

We are asked to solve the equation graphically by arranging them in a linear-quadratic equation.

Step 1 of 2:

The given equation is .

Re arranging them, we get:

Here, once we rearrange it, we multiply the equation with ten to remove the decimal. Then, take out five to factorize into the simplest form.

Step 2 of 2:

Graph the equation to get the solution:

.

Thus, the solution of the equation is:

.

Note:

A lot of the quadratic equations can be solved using identities and factorization. You would get a maximum of two solutions for each quadratic equation.

A quadratic equation is when the polynomial has a degree two. A graph is a geometrical representation of an equation.

We are asked to solve the equation graphically by arranging them in a linear-quadratic equation.

Step 1 of 2:

The given equation is .

Re arranging them, we get:

Here, once we rearrange it, we multiply the equation with ten to remove the decimal. Then, take out five to factorize into the simplest form.

Step 2 of 2:

Graph the equation to get the solution:

.

Thus, the solution of the equation is:

.

Note:

A lot of the quadratic equations can be solved using identities and factorization. You would get a maximum of two solutions for each quadratic equation.

### Write the solutions to the given equation.

Rewrite them as the linear-quadratic system of equations and graph them to solve.

Maths-General

Hint:

A quadratic equation is when the polynomial has a degree two. A graph is a geometrical representation of an equation.

We are asked to solve the equation graphically by arranging them in a linear-quadratic equation.

Step 1 of 2:

The given equation is .

Re arranging them, we get:

Here, once we rearrange it, we multiply the equation with ten to remove the decimal. Then, take out five to factorize into the simplest form.

Step 2 of 2:

Graph the equation to get the solution:

.

Thus, the solution of the equation is:

.

Note:

A lot of the quadratic equations can be solved using identities and factorization. You would get a maximum of two solutions for each quadratic equation.

A quadratic equation is when the polynomial has a degree two. A graph is a geometrical representation of an equation.

We are asked to solve the equation graphically by arranging them in a linear-quadratic equation.

Step 1 of 2:

The given equation is .

Re arranging them, we get:

Here, once we rearrange it, we multiply the equation with ten to remove the decimal. Then, take out five to factorize into the simplest form.

Step 2 of 2:

Graph the equation to get the solution:

.

Thus, the solution of the equation is:

.

Note:

A lot of the quadratic equations can be solved using identities and factorization. You would get a maximum of two solutions for each quadratic equation.

Maths-

### Prove the following statement.

The length of any one median of a triangle is less than half the perimeter of the triangle.

Answer:

c < a + b

solution:

Side AB = a

Side BC = b

Side AC = c

And median AM be M

AM is median so M is midpoint of BC

BM =

So, according to triangle inequality theorem,

M

In △ACM,

AM is median so M is midpoint of BC

MC =

So, according to triangle inequality theorem,

M

Add eq. 1 and eq. 2.

M

2M

M

- Hints:
- Triangle inequality theorem
- According to this theorem, in any triangle, sum of two sides is greater than third side,
- a < b + c

c < a + b

- The line segment which joins the vertex of triangle to midpoint of opposite side is called the ‘median’.
- Perimeter of triangle is sum of sides.
- Perimeter = a + b + c
- To prove:
- The length of any one median of a triangle is less than half the perimeter of the triangle.

solution:

- Step 1:

Side AB = a

Side BC = b

Side AC = c

And median AM be M

_{a}- Step 2:

AM is median so M is midpoint of BC

BM =

So, according to triangle inequality theorem,

M

_{a}< a + ---- eq. 1In △ACM,

AM is median so M is midpoint of BC

MC =

So, according to triangle inequality theorem,

M

_{a}< c + ---- eq. 2Add eq. 1 and eq. 2.

M

_{a}+ M_{a}< a + + c +2M

_{a}< a + b + cM

_{a}<- Final Answer:

### Prove the following statement.

The length of any one median of a triangle is less than half the perimeter of the triangle.

Maths-General

Answer:

c < a + b

solution:

Side AB = a

Side BC = b

Side AC = c

And median AM be M

AM is median so M is midpoint of BC

BM =

So, according to triangle inequality theorem,

M

In △ACM,

AM is median so M is midpoint of BC

MC =

So, according to triangle inequality theorem,

M

Add eq. 1 and eq. 2.

M

2M

M

- Hints:
- Triangle inequality theorem
- According to this theorem, in any triangle, sum of two sides is greater than third side,
- a < b + c

c < a + b

- The line segment which joins the vertex of triangle to midpoint of opposite side is called the ‘median’.
- Perimeter of triangle is sum of sides.
- Perimeter = a + b + c
- To prove:
- The length of any one median of a triangle is less than half the perimeter of the triangle.

solution:

- Step 1:

Side AB = a

Side BC = b

Side AC = c

And median AM be M

_{a}- Step 2:

AM is median so M is midpoint of BC

BM =

So, according to triangle inequality theorem,

M

_{a}< a + ---- eq. 1In △ACM,

AM is median so M is midpoint of BC

MC =

So, according to triangle inequality theorem,

M

_{a}< c + ---- eq. 2Add eq. 1 and eq. 2.

M

_{a}+ M_{a}< a + + c +2M

_{a}< a + b + cM

_{a}<- Final Answer:

General

### Select the three most common text features

Correct answer a) Title, 6) Table of Content d) Picture of and Captions

Explanations - Text features refer to parts of a text but don't necessarily appear directly within the main body

Explanations - Text features refer to parts of a text but don't necessarily appear directly within the main body

### Select the three most common text features

GeneralGeneral

Correct answer a) Title, 6) Table of Content d) Picture of and Captions

Explanations - Text features refer to parts of a text but don't necessarily appear directly within the main body

Explanations - Text features refer to parts of a text but don't necessarily appear directly within the main body

Maths-

### Solve 3.5x+19≥1.5x-7

Hint:

Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .

We are asked to solve the inequality.

Step 1 of 1:

Rearrange and solve the inequality,

Note:

Whenever we use the symbol ≤ or ≥ , we use the endpoint as well. We could also solve the inequality by graphing it.

Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .

We are asked to solve the inequality.

Step 1 of 1:

Rearrange and solve the inequality,

Note:

Whenever we use the symbol ≤ or ≥ , we use the endpoint as well. We could also solve the inequality by graphing it.

### Solve 3.5x+19≥1.5x-7

Maths-General

Hint:

Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .

We are asked to solve the inequality.

Step 1 of 1:

Rearrange and solve the inequality,

Note:

Whenever we use the symbol ≤ or ≥ , we use the endpoint as well. We could also solve the inequality by graphing it.

Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .

We are asked to solve the inequality.

Step 1 of 1:

Rearrange and solve the inequality,

Note:

Whenever we use the symbol ≤ or ≥ , we use the endpoint as well. We could also solve the inequality by graphing it.

Maths-

### Determine whether each graph represents a function ?

*Step by step solution:*

We consider the first graph.

We can observe that any vertical line drawn on the graph cuts the line at exactly one point

Hence, this graph represents a function.

The second graph is

Again, we can observe that any vertical line drawn cuts the graph at exactly one point.

Hence, this graph is also a function.

Finally, consider the third graph.

If we draw a vertical line at the origin, that is, the y-axis, we can see that it cuts the graph at two points.

Thus, this graph is not a function.

### Determine whether each graph represents a function ?

Maths-General

*Step by step solution:*

We consider the first graph.