Maths-

General

Easy

Question

# Graph the following functions by filling out the X/Y chart using the given inputs

X | -7 | -6 | -3 | 2 | 9 |

Y |

Hint:

### First, we complete the table by calculating the values of y corresponding to each value of x from the given equation. To make the graph of the function, we draw perpendicular lines, x axis and y axis; then we plot the ordered points in the xy plane and join the points by a smooth curve to get the required graph.

## The correct answer is: 0,1,2,3,4

*Step by step solution:*

The given equation is

Putting x = -7 in the above equation, we get the value of y as

Similarly, putting x = -6, we get

Putting x = -3 we have

Putting x = 2 we have

Finally, putting x = 9, we have

Completing the table, we have

x

-7

-6

-3

2

9

y

0

1

2

3

4

We plot these points on the xy plane

After plotting the points, we join them with a smooth curve to get the graph of the equation.

We can find the tabular values for any points of x and then plot them on the graph. But we usually choose values for which calculating y is easier. Either way, we need points satisfying the equation to plot its graph.

### Related Questions to study

Maths-

### Make and test a conjecture about the square of even numbers.

SOLUTION:

HINT: Take general form and check.

Complete step by step solution:

The square of an even number is always an even number.

We know that the even number is always of the form 2n

Let some N = 2n

On squaring both the sides, we get

On taking common from RHS part, we get

So we get that the square of an even number is always even.

HINT: Take general form and check.

Complete step by step solution:

The square of an even number is always an even number.

We know that the even number is always of the form 2n

Let some N = 2n

On squaring both the sides, we get

On taking common from RHS part, we get

So we get that the square of an even number is always even.

### Make and test a conjecture about the square of even numbers.

Maths-General

SOLUTION:

HINT: Take general form and check.

Complete step by step solution:

The square of an even number is always an even number.

We know that the even number is always of the form 2n

Let some N = 2n

On squaring both the sides, we get

On taking common from RHS part, we get

So we get that the square of an even number is always even.

HINT: Take general form and check.

Complete step by step solution:

The square of an even number is always an even number.

We know that the even number is always of the form 2n

Let some N = 2n

On squaring both the sides, we get

On taking common from RHS part, we get

So we get that the square of an even number is always even.

Maths-

### Graph the following functions by filling out the X/Y chart using the given inputs

X | -9 | -8 | -5 | 0 | 7 |

Y |

*Step by step solution:*

The given equation is

Putting x = -9 in the above equation, we get the value of y as

Similarly, putting x = -8, we get

Putting x = -5 we have

Putting x = 0 we have

Finally, putting x = 7, we have

Completing the table, we have

x |
-9 |
-8 |
-5 |
0 |
7 |

y |
0 |
1 |
2 |
3 |
4 |

After plotting the points, we join them with a smooth curve to get the graph of the equation.

### Graph the following functions by filling out the X/Y chart using the given inputs

X | -9 | -8 | -5 | 0 | 7 |

Y |

Maths-General

*Step by step solution:*

The given equation is

Putting x = -9 in the above equation, we get the value of y as

Similarly, putting x = -8, we get

Putting x = -5 we have

Putting x = 0 we have

Finally, putting x = 7, we have

Completing the table, we have

x |
-9 |
-8 |
-5 |
0 |
7 |

y |
0 |
1 |
2 |
3 |
4 |

After plotting the points, we join them with a smooth curve to get the graph of the equation.

General

### Choose the synonym for 'Present’?

Correct answer a) Current.

Explanation- "Present - Existing or happening now”

Explanation- "Present - Existing or happening now”

### Choose the synonym for 'Present’?

GeneralGeneral

Correct answer a) Current.

Explanation- "Present - Existing or happening now”

Explanation- "Present - Existing or happening now”

Maths-

### Make and test a conjecture about the square of odd numbers.

HINT: Take general form and check.

Complete step by step solution:

The square of an odd number is always an odd number.

We know that the odd number is always of the form 2n+1

Let some N = 2n + 1

On squaring both the sides, we get

On taking common from RHS part, we get

So we get that the square of an odd number is always odd.

Note: We can take the form of N = 2n - 1 and then find the square and then also

we get that the square of an odd number is always odd.

Complete step by step solution:

The square of an odd number is always an odd number.

We know that the odd number is always of the form 2n+1

Let some N = 2n + 1

On squaring both the sides, we get

On taking common from RHS part, we get

So we get that the square of an odd number is always odd.

Note: We can take the form of N = 2n - 1 and then find the square and then also

we get that the square of an odd number is always odd.

### Make and test a conjecture about the square of odd numbers.

Maths-General

HINT: Take general form and check.

Complete step by step solution:

The square of an odd number is always an odd number.

We know that the odd number is always of the form 2n+1

Let some N = 2n + 1

On squaring both the sides, we get

On taking common from RHS part, we get

So we get that the square of an odd number is always odd.

Note: We can take the form of N = 2n - 1 and then find the square and then also

we get that the square of an odd number is always odd.

Complete step by step solution:

The square of an odd number is always an odd number.

We know that the odd number is always of the form 2n+1

Let some N = 2n + 1

On squaring both the sides, we get

On taking common from RHS part, we get

So we get that the square of an odd number is always odd.

Note: We can take the form of N = 2n - 1 and then find the square and then also

we get that the square of an odd number is always odd.

General

### Complete the sentences with a subordinating cogs Rehire, at trough once. since

### Complete the sentences with a subordinating cogs Rehire, at trough once. since

GeneralGeneral

Maths-

### Graph the following functions by filling out the X/Y chart using the given inputs

X | -6 | -3 | 0 | 3 | 6 |

Y |

*Step by step solution:*

The given equation is

Putting X = -6 in the above equation, we get the value of y as

Similarly, putting X = -3 we get

Putting X = 0 in the above equation, we have

Putting X = 3 in the above equation, we have

Finally, putting X = 6 in the above equation, we have

Completing the table, we get

x |
-6 |
-3 |
0 |
3 |
6 |

y |
0 |
1 |
2 |
3 |
4 |

After plotting the points, we join them with a line to get the graph of the equation.

### Graph the following functions by filling out the X/Y chart using the given inputs

X | -6 | -3 | 0 | 3 | 6 |

Y |

Maths-General

*Step by step solution:*

The given equation is

Putting X = -6 in the above equation, we get the value of y as

Similarly, putting X = -3 we get

Putting X = 0 in the above equation, we have

Putting X = 3 in the above equation, we have

Finally, putting X = 6 in the above equation, we have

Completing the table, we get

x |
-6 |
-3 |
0 |
3 |
6 |

y |
0 |
1 |
2 |
3 |
4 |

After plotting the points, we join them with a line to get the graph of the equation.

Maths-

### Make and test a conjecture about the sign of the product of any two negative integers.

SOLUTION:

HINT: Use an example to prove it.

Complete step by step solution:

Take 2 negative numbers to be -3 and -4

So, product of - 3 and - 4 = - 3×- 4 = 12

We get that, the product of 2 negative numbers is always a positive number.

HINT: Use an example to prove it.

Complete step by step solution:

Take 2 negative numbers to be -3 and -4

So, product of - 3 and - 4 = - 3×- 4 = 12

We get that, the product of 2 negative numbers is always a positive number.

### Make and test a conjecture about the sign of the product of any two negative integers.

Maths-General

SOLUTION:

HINT: Use an example to prove it.

Complete step by step solution:

Take 2 negative numbers to be -3 and -4

So, product of - 3 and - 4 = - 3×- 4 = 12

We get that, the product of 2 negative numbers is always a positive number.

HINT: Use an example to prove it.

Complete step by step solution:

Take 2 negative numbers to be -3 and -4

So, product of - 3 and - 4 = - 3×- 4 = 12

We get that, the product of 2 negative numbers is always a positive number.

General

### Choose whether the following is a simile or a metaphor

"Busy as a bee"?

Correct answer a) Simile

Explanation - Simile- Compares two different things. Something is like or as something else

Example - She swam like a fish.

Metaphor - Compares two different things. Something is something else

Example- Time is money.

Explanation - Simile- Compares two different things. Something is like or as something else

Example - She swam like a fish.

Metaphor - Compares two different things. Something is something else

Example- Time is money.

### Choose whether the following is a simile or a metaphor

"Busy as a bee"?

GeneralGeneral

Correct answer a) Simile

Explanation - Simile- Compares two different things. Something is like or as something else

Example - She swam like a fish.

Metaphor - Compares two different things. Something is something else

Example- Time is money.

Explanation - Simile- Compares two different things. Something is like or as something else

Example - She swam like a fish.

Metaphor - Compares two different things. Something is something else

Example- Time is money.

Maths-

### Mark has 100 gift card to buy apps for his smart phone .Each week he buys one new app for 4.99

a) Write an equation that relates the amount left on the card ,y , over time x.

b) Make a graph of the function

*Step by step solution:*

Let the amount left on the gift card be denoted by y.

Let the time (in weeks) be denoted by x.

The initial amount on the gift card = $100

Amount spent each week = $4.99

Thus, we can say that

Rate of change of amount left in the gift card with respect to time (in weeks), m = - 4.99

The value is negative as the amount is decreasing.

Initial value, c = 100

Using the slope intercept form of an equation

y = mx + c

We get

y = -4.99x + 100

The above equation relates the amount left on the card over time

Next, we construct a table with different values of x and corresponding values of y.

Putting x = 0 in the above equation, we will get, y = 100

Similarly, putting x = 1, in the above equation, we get y = 95.01

Continuing this way, we have

For x = 2, we get y = 90.02

For x = 3, we get y = 85.03

For x = 4, we get y = 80.04

Making a table of all these points, we have

x |
0 |
1 |
2 |
3 |
4 |

y |
100 |
95.01 |
90.02 |
85.03 |
80.04 |

This is the required graph.

### Mark has 100 gift card to buy apps for his smart phone .Each week he buys one new app for 4.99

a) Write an equation that relates the amount left on the card ,y , over time x.

b) Make a graph of the function

Maths-General

*Step by step solution:*

Let the amount left on the gift card be denoted by y.

Let the time (in weeks) be denoted by x.

The initial amount on the gift card = $100

Amount spent each week = $4.99

Thus, we can say that

Rate of change of amount left in the gift card with respect to time (in weeks), m = - 4.99

The value is negative as the amount is decreasing.

Initial value, c = 100

Using the slope intercept form of an equation

y = mx + c

We get

y = -4.99x + 100

The above equation relates the amount left on the card over time

Next, we construct a table with different values of x and corresponding values of y.

Putting x = 0 in the above equation, we will get, y = 100

Similarly, putting x = 1, in the above equation, we get y = 95.01

Continuing this way, we have

For x = 2, we get y = 90.02

For x = 3, we get y = 85.03

For x = 4, we get y = 80.04

Making a table of all these points, we have

x |
0 |
1 |
2 |
3 |
4 |

y |
100 |
95.01 |
90.02 |
85.03 |
80.04 |

This is the required graph.

General

### Chore the correct synonym for the word 'text'.

Correct answer a) words

Explanation - text the words of something writer

Explanation - text the words of something writer

### Chore the correct synonym for the word 'text'.

GeneralGeneral

Correct answer a) words

Explanation - text the words of something writer

Explanation - text the words of something writer

General

### Choose the synonym for "Jumped”

Correct answer a) leaped

Explanation - to push yourself suddenly off the ground into and go over something.

Explanation - to push yourself suddenly off the ground into and go over something.

### Choose the synonym for "Jumped”

GeneralGeneral

Correct answer a) leaped

Explanation - to push yourself suddenly off the ground into and go over something.

Explanation - to push yourself suddenly off the ground into and go over something.

Maths-

### Use the function Y = 1.5X + 3 to complete the table of values.

X | ||||

Y | 9 | 6 | 0 | -3 |

*Step by step solution:*

The given equation is

Y = 1.5x + 3

We rewrite this equation with ‘x’ on one side of the equation so that it is easy to find its value.

Using , we get

Now, we calculate x for the given values of y.

Putting y = 9, in the above equation, we get,

Similarly, putting y = 6 in the above equation,

Putting y = 0 in the above equation,

Finally, putting y = -3, we get

Thus, we complete the table as

X |
4 |
2 |
-2 |
-4 |

y |
9 |
6 |
0 |
-3 |

### Use the function Y = 1.5X + 3 to complete the table of values.

X | ||||

Y | 9 | 6 | 0 | -3 |

Maths-General

*Step by step solution:*

The given equation is

Y = 1.5x + 3

We rewrite this equation with ‘x’ on one side of the equation so that it is easy to find its value.

Using , we get

Now, we calculate x for the given values of y.

Putting y = 9, in the above equation, we get,

Similarly, putting y = 6 in the above equation,

Putting y = 0 in the above equation,

Finally, putting y = -3, we get

Thus, we complete the table as

X |
4 |
2 |
-2 |
-4 |

y |
9 |
6 |
0 |
-3 |

General

### Rewrite the sentences using possessive nouns

Explanation 7

Possessive Nouns - A noun that possesses something. has something. In most cases, a possessive known is formed by adding an apostrophe to the noun the noun is plural and already and already exists ends in S, only an apes trope needs be added.

Possessive Nouns - A noun that possesses something. has something. In most cases, a possessive known is formed by adding an apostrophe to the noun the noun is plural and already and already exists ends in S, only an apes trope needs be added.

### Rewrite the sentences using possessive nouns

GeneralGeneral

Explanation 7

Possessive Nouns - A noun that possesses something. has something. In most cases, a possessive known is formed by adding an apostrophe to the noun the noun is plural and already and already exists ends in S, only an apes trope needs be added.

Possessive Nouns - A noun that possesses something. has something. In most cases, a possessive known is formed by adding an apostrophe to the noun the noun is plural and already and already exists ends in S, only an apes trope needs be added.

General

### Choose the synonym 6 ‘auditory'

Correct answer a) acoustic

Explanation - relating to the sense of hearing.

Explanation - relating to the sense of hearing.

### Choose the synonym 6 ‘auditory'

GeneralGeneral

Correct answer a) acoustic

Explanation - relating to the sense of hearing.

Explanation - relating to the sense of hearing.

Maths-

### You have an ant form with 22 ants. The population of ants in your farm doubles every 3 months.

a) Complete the table .

b) Is the relation forms a function ? If so , is it a linear function or non linear function ? Explain.

*Step by step solution:*

Given,

Population of the ant farm initially = 22

The population doubles every 3 months.

Rate at which the population of the ant farm increases per month =

We know, the slope intercept form of the equation is y = mx + c, where m is the slope and c is the y intercept.

Here, m = = 1.5 and c=22

Thus, the equation representing the relationship between the ant population with respect to the number of months is

y = 1.5x + 22

We use this equation to complete the table.

We can see that for x = 0, we get y = 22

Putting x = 3 in the above equation, we get

y = 1.5 3 + 22 = 4.5 + 22 = 26.5

Similarly, putting in the above equation, we get

y = 15 6 + 22 = 9 + 22 = 31

Finally, putting in the above equation, we have

y = 1.5 9 + 22 = 13.5 + 22 = 35.5

Putting these values in the table, we have

No. of months (x) |
0 |
3 |
6 |
9 |

Ant population (y) |
22 |
26.5 |
31 |
35.5 |

It is also a linear function as the rate of change of ant population or the slope of the equation is a constant value 1.5.

### You have an ant form with 22 ants. The population of ants in your farm doubles every 3 months.

a) Complete the table .

b) Is the relation forms a function ? If so , is it a linear function or non linear function ? Explain.

Maths-General

*Step by step solution:*

Given,

Population of the ant farm initially = 22

The population doubles every 3 months.

Rate at which the population of the ant farm increases per month =

We know, the slope intercept form of the equation is y = mx + c, where m is the slope and c is the y intercept.

Here, m = = 1.5 and c=22

Thus, the equation representing the relationship between the ant population with respect to the number of months is

y = 1.5x + 22

We use this equation to complete the table.

We can see that for x = 0, we get y = 22

Putting x = 3 in the above equation, we get

y = 1.5 3 + 22 = 4.5 + 22 = 26.5

Similarly, putting in the above equation, we get

y = 15 6 + 22 = 9 + 22 = 31

Finally, putting in the above equation, we have

y = 1.5 9 + 22 = 13.5 + 22 = 35.5

Putting these values in the table, we have

No. of months (x) |
0 |
3 |
6 |
9 |

Ant population (y) |
22 |
26.5 |
31 |
35.5 |

It is also a linear function as the rate of change of ant population or the slope of the equation is a constant value 1.5.