Maths-

General

Easy

Question

# For Christmas, Maryland purchased subscriptions to Xbox Live for her four children. Each subscription costs $5 per month plus a $15 sign-up fee. If she received a bill for $120, for how many months did she purchase subscriptions for her children?

## The correct answer is: x = 3

- Hint:

○ Form the eqaution using given information.

○ Take variable value as any alphabet.

○ Take terms with cofficient at one side and without cofficients at another side.

- Step by step explanation:

○ Given:

Sign up fee per subscription = $15.

Subscription cost per month = $5.

Total subscription purchased = 4

Total bill = $120.

○ Step 1:

Let Maryland purchase membership for x months.

So,

Bill for 1 month for 1 child = sign up fee + monthly cost

Bill for 1 month for 1 child = 15 + 5

Bill for x month for 1 child = 15 + 5x

Hence,

Bill for x month for 4 child = ( 15 + 5x ) 4

Bill for x month for 4 child = ( 60 + 20x )

○ Step 2:

○ As total bill is $120.

∴ 60 + 20x = 120

20x = 120 - 60

20x = 60

x =

x = 3

- Final Answer:

Hence, Maryland purchase 3 month subscription for childen.

### Related Questions to study

Maths-

### State the law of logic that is illustrated.

If 𝑥 + 2 = 4, then 𝑥 = 2.

If 𝑥 = 2, then 𝑥^{2} = 4.

If 𝑥+2=4, then 𝑥^{2} = 4

Hint:

Law of Syllogism states that:

Law of Syllogism states that:

1) if p q is true

2) If q r is true

then we can conclude that p r is also true.

Solution

It is given that: If 𝑥 + 2 = 4, then 𝑥 = 2, If 𝑥 = 2, then 𝑥

p: 𝑥 + 2 = 4

q: 𝑥 = 2

r: 𝑥

So can write the given statement “If 𝑥 + 2 = 4, then 𝑥 = 2” as p q and the statement “If 𝑥 = 2, then 𝑥

So we can see that we are given: p q is true

q r is true

p r is true

This statement resolves the law of syllogism which states that if p q is true and If q r is true then we can conclude that p r is also true

Final Answer:

Hence, the law of logic which is used in these statements is the law of syllogism

Law of Syllogism states that:

Law of Syllogism states that:

1) if p q is true

2) If q r is true

then we can conclude that p r is also true.

Solution

It is given that: If 𝑥 + 2 = 4, then 𝑥 = 2, If 𝑥 = 2, then 𝑥

^{2}= 4 and If 𝑥+2=4, then 𝑥^{2}=4. So if we takep: 𝑥 + 2 = 4

q: 𝑥 = 2

r: 𝑥

^{2}= 4So can write the given statement “If 𝑥 + 2 = 4, then 𝑥 = 2” as p q and the statement “If 𝑥 = 2, then 𝑥

^{2}= 4” can be written as q r and also the statement “If 𝑥+2=4, then 𝑥^{2}= 4” can be written as p r.So we can see that we are given: p q is true

q r is true

p r is true

This statement resolves the law of syllogism which states that if p q is true and If q r is true then we can conclude that p r is also true

Final Answer:

Hence, the law of logic which is used in these statements is the law of syllogism

### State the law of logic that is illustrated.

If 𝑥 + 2 = 4, then 𝑥 = 2.

If 𝑥 = 2, then 𝑥^{2} = 4.

If 𝑥+2=4, then 𝑥^{2} = 4

Maths-General

Hint:

Law of Syllogism states that:

Law of Syllogism states that:

1) if p q is true

2) If q r is true

then we can conclude that p r is also true.

Solution

It is given that: If 𝑥 + 2 = 4, then 𝑥 = 2, If 𝑥 = 2, then 𝑥

p: 𝑥 + 2 = 4

q: 𝑥 = 2

r: 𝑥

So can write the given statement “If 𝑥 + 2 = 4, then 𝑥 = 2” as p q and the statement “If 𝑥 = 2, then 𝑥

So we can see that we are given: p q is true

q r is true

p r is true

This statement resolves the law of syllogism which states that if p q is true and If q r is true then we can conclude that p r is also true

Final Answer:

Hence, the law of logic which is used in these statements is the law of syllogism

Law of Syllogism states that:

Law of Syllogism states that:

1) if p q is true

2) If q r is true

then we can conclude that p r is also true.

Solution

It is given that: If 𝑥 + 2 = 4, then 𝑥 = 2, If 𝑥 = 2, then 𝑥

^{2}= 4 and If 𝑥+2=4, then 𝑥^{2}=4. So if we takep: 𝑥 + 2 = 4

q: 𝑥 = 2

r: 𝑥

^{2}= 4So can write the given statement “If 𝑥 + 2 = 4, then 𝑥 = 2” as p q and the statement “If 𝑥 = 2, then 𝑥

^{2}= 4” can be written as q r and also the statement “If 𝑥+2=4, then 𝑥^{2}= 4” can be written as p r.So we can see that we are given: p q is true

q r is true

p r is true

This statement resolves the law of syllogism which states that if p q is true and If q r is true then we can conclude that p r is also true

Final Answer:

Hence, the law of logic which is used in these statements is the law of syllogism

Maths-

### Show the conjecture is false by finding a counterexample. If A, B and C are collinear, then AB + BC = AC.

Hint:

Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

Counterexample: It is an example which shows that the conjecture is false.

Solution

In the given figure points A, B and C are collinear.

But here AC + CB = AB instead of AB + BC = AC. So the given conjecture is wrong.

Final Answer:

Hence, the counterexample for the given example i.e. “If A, B and C are collinear, then AB + BC = AC” is the above diagram.

Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

Counterexample: It is an example which shows that the conjecture is false.

Solution

In the given figure points A, B and C are collinear.

But here AC + CB = AB instead of AB + BC = AC. So the given conjecture is wrong.

Final Answer:

Hence, the counterexample for the given example i.e. “If A, B and C are collinear, then AB + BC = AC” is the above diagram.

### Show the conjecture is false by finding a counterexample. If A, B and C are collinear, then AB + BC = AC.

Maths-General

Hint:

Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

Counterexample: It is an example which shows that the conjecture is false.

Solution

In the given figure points A, B and C are collinear.

But here AC + CB = AB instead of AB + BC = AC. So the given conjecture is wrong.

Final Answer:

Hence, the counterexample for the given example i.e. “If A, B and C are collinear, then AB + BC = AC” is the above diagram.

Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

Counterexample: It is an example which shows that the conjecture is false.

Solution

In the given figure points A, B and C are collinear.

But here AC + CB = AB instead of AB + BC = AC. So the given conjecture is wrong.

Final Answer:

Hence, the counterexample for the given example i.e. “If A, B and C are collinear, then AB + BC = AC” is the above diagram.

Maths-

### After an oil pipeline burst one morning, gas prices went up by $2.20 per gallon. If that afternoon you bought 10 gallons of gas for $53.90, what was the price per gallon before the oil pipeline burst that morning?

- Hint:

○ Take variable value as any alphabet.

○ Take terms with cofficient at one side and without cofficients at another side.

- Step-by-step explanation:

Increase price per gallon = $2.20.

No of gallons of gas brought = 10.

Total money paid = $53.90.

○ Step 1:

Let the original price of one gallon of gas be x.

So,

Price of 1 gallon of gas after burst = original price + increase in price

Price of 1 gallon of gas after burst = x + 2.20

○ Step 2:

○ Total selling price.

Price of 1 gallon of gas after burst = x + 2.20

Price of 10 gallon of gas after burst = (x + 2.20) 10

10x + 22

As it is given total money paid is $53.90

∴ 10x + 22 = 53.90

10x = 53.90 - 22

10x = 31.90

x =

x = 3.190

- Final Answer:

### After an oil pipeline burst one morning, gas prices went up by $2.20 per gallon. If that afternoon you bought 10 gallons of gas for $53.90, what was the price per gallon before the oil pipeline burst that morning?

Maths-General

- Hint:

○ Take variable value as any alphabet.

○ Take terms with cofficient at one side and without cofficients at another side.

- Step-by-step explanation:

Increase price per gallon = $2.20.

No of gallons of gas brought = 10.

Total money paid = $53.90.

○ Step 1:

Let the original price of one gallon of gas be x.

So,

Price of 1 gallon of gas after burst = original price + increase in price

Price of 1 gallon of gas after burst = x + 2.20

○ Step 2:

○ Total selling price.

Price of 1 gallon of gas after burst = x + 2.20

Price of 10 gallon of gas after burst = (x + 2.20) 10

10x + 22

As it is given total money paid is $53.90

∴ 10x + 22 = 53.90

10x = 53.90 - 22

10x = 31.90

x =

x = 3.190

- Final Answer:

Maths-

### Show the conjecture is false by finding a counterexample. Two supplementary angles form a linear pair.

Hint:

Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

Counterexample: It is an example which shows that the conjecture is false.

Solution

If we take a parallelogram

Here, we know that angles a and b are supplementary angles. But they are not linear.

So, the given conjecture is wrong.

Final Answer:

Hence, the counterexample of the given conjecture i.e. “Two supplementary angles form a linear pair.” is the adjacent angles of a parallelogram.

Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

Counterexample: It is an example which shows that the conjecture is false.

Solution

If we take a parallelogram

Here, we know that angles a and b are supplementary angles. But they are not linear.

So, the given conjecture is wrong.

Final Answer:

Hence, the counterexample of the given conjecture i.e. “Two supplementary angles form a linear pair.” is the adjacent angles of a parallelogram.

### Show the conjecture is false by finding a counterexample. Two supplementary angles form a linear pair.

Maths-General

Hint:

Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

Counterexample: It is an example which shows that the conjecture is false.

Solution

If we take a parallelogram

Here, we know that angles a and b are supplementary angles. But they are not linear.

So, the given conjecture is wrong.

Final Answer:

Hence, the counterexample of the given conjecture i.e. “Two supplementary angles form a linear pair.” is the adjacent angles of a parallelogram.

Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

Counterexample: It is an example which shows that the conjecture is false.

Solution

If we take a parallelogram

Here, we know that angles a and b are supplementary angles. But they are not linear.

So, the given conjecture is wrong.

Final Answer:

Hence, the counterexample of the given conjecture i.e. “Two supplementary angles form a linear pair.” is the adjacent angles of a parallelogram.

Maths-

### A store had homemade sweaters on sale for $20 off the original price. Aunt Ethel jumped at the bargain and bought a sweater for all 15 members of her family. If Aunt Ethel paid $375 for all the sweaters, what was the original price of each sweater?

- Hint:

○ Take variable value as any alphabet.

○ Take terms with cofficient at one side and without cofficients at another side.

- Step-by-step explanation:

Discount per sweater = $20.

No of sweaters brought = 15.

Total money paid = $375.

○ Step 1:

Let the original price of one sweater be x.

So,

Selling price of 1 sweater = original price - discount

Selling price of 1 sweater = x - 20

○ Step 2:

○ Total selling price.

As 1 sweater cost (x-20)

So, 15 sweater will cost

15(x - 20) = 15x - 300

As it is given total money paid is $375

∴ 15x - 300 = 375

15x = 375 + 300

15x = 675

x =

x = 45

- Final Answer:

### A store had homemade sweaters on sale for $20 off the original price. Aunt Ethel jumped at the bargain and bought a sweater for all 15 members of her family. If Aunt Ethel paid $375 for all the sweaters, what was the original price of each sweater?

Maths-General

- Hint:

○ Take variable value as any alphabet.

○ Take terms with cofficient at one side and without cofficients at another side.

- Step-by-step explanation:

Discount per sweater = $20.

No of sweaters brought = 15.

Total money paid = $375.

○ Step 1:

Let the original price of one sweater be x.

So,

Selling price of 1 sweater = original price - discount

Selling price of 1 sweater = x - 20

○ Step 2:

○ Total selling price.

As 1 sweater cost (x-20)

So, 15 sweater will cost

15(x - 20) = 15x - 300

As it is given total money paid is $375

∴ 15x - 300 = 375

15x = 375 + 300

15x = 675

x =

x = 45

- Final Answer:

Maths-

### Gym charges a $50 activation fee and $17 per month for a membership. If you spend $356, for how many months do you have a gym membership?

- Hint:

○ Solve the equation.

○ Take terms with cofficient at one side and without cofficient at another side.

- Step by step explanation:

Activation fee for gym = $50.

Membership per month = $17.

Total money spent = $356.

○ Step 1:

Let you had membership for x months.

So,

Total amount paid for 1 month = activation fee + monthly membership

Total amount paid for 1 month = 50 + 17

Hence,

Total amount paid for x month = activation fee + membership for x month

Total amount paid for x month = 50 + 17x

○ Step 2:

○ As total amount paid is $356.

∴ 50 + 17x = 356

17x = 356 - 50

17x = 306

x =

x = 18

- Final Answer:

### Gym charges a $50 activation fee and $17 per month for a membership. If you spend $356, for how many months do you have a gym membership?

Maths-General

- Hint:

○ Solve the equation.

○ Take terms with cofficient at one side and without cofficient at another side.

- Step by step explanation:

Activation fee for gym = $50.

Membership per month = $17.

Total money spent = $356.

○ Step 1:

Let you had membership for x months.

So,

Total amount paid for 1 month = activation fee + monthly membership

Total amount paid for 1 month = 50 + 17

Hence,

Total amount paid for x month = activation fee + membership for x month

Total amount paid for x month = 50 + 17x

○ Step 2:

○ As total amount paid is $356.

∴ 50 + 17x = 356

17x = 356 - 50

17x = 306

x =

x = 18

- Final Answer:

Maths-

### State the law of logic that is illustrated.

If you score more than 75%, then you can go to the beach.

If you go to the beach, then you can surf.

If you score more than 75%. Then you can surf

Hint:

Law of Syllogism states that:

1) if p q is true

2) If q r is true

then we can conclude that p r is also true.

Solution

It is given that: If you score more than 75%, then you can go to the beach, If you go to the beach, then you can surf and If you score more than 75%. Then you can surf. So if we take

p = Score is more than 75%

q = You can go to the beach

r = You can surf

So can write the given statement “If you score more than 75%, then you can go to the beach” as

p q and the statement “If you go to the beach, then you can surf” can be written as q r and also the statement “If you score more than 75%. Then you can surf” can be written as p r.

So we can see that we are given: p q is true

q r is true

p r is true

This statement resolves the law of syllogism which states that if p q is true and If q r is true then we can conclude that p r is also true

Final Answer:

Hence, the law of logic which is used in these statements is the law of syllogism.

Law of Syllogism states that:

1) if p q is true

2) If q r is true

then we can conclude that p r is also true.

Solution

It is given that: If you score more than 75%, then you can go to the beach, If you go to the beach, then you can surf and If you score more than 75%. Then you can surf. So if we take

p = Score is more than 75%

q = You can go to the beach

r = You can surf

So can write the given statement “If you score more than 75%, then you can go to the beach” as

p q and the statement “If you go to the beach, then you can surf” can be written as q r and also the statement “If you score more than 75%. Then you can surf” can be written as p r.

So we can see that we are given: p q is true

q r is true

p r is true

This statement resolves the law of syllogism which states that if p q is true and If q r is true then we can conclude that p r is also true

Final Answer:

Hence, the law of logic which is used in these statements is the law of syllogism.

### State the law of logic that is illustrated.

If you score more than 75%, then you can go to the beach.

If you go to the beach, then you can surf.

If you score more than 75%. Then you can surf

Maths-General

Hint:

Law of Syllogism states that:

1) if p q is true

2) If q r is true

then we can conclude that p r is also true.

Solution

It is given that: If you score more than 75%, then you can go to the beach, If you go to the beach, then you can surf and If you score more than 75%. Then you can surf. So if we take

p = Score is more than 75%

q = You can go to the beach

r = You can surf

So can write the given statement “If you score more than 75%, then you can go to the beach” as

p q and the statement “If you go to the beach, then you can surf” can be written as q r and also the statement “If you score more than 75%. Then you can surf” can be written as p r.

So we can see that we are given: p q is true

q r is true

p r is true

This statement resolves the law of syllogism which states that if p q is true and If q r is true then we can conclude that p r is also true

Final Answer:

Hence, the law of logic which is used in these statements is the law of syllogism.

Law of Syllogism states that:

1) if p q is true

2) If q r is true

then we can conclude that p r is also true.

Solution

It is given that: If you score more than 75%, then you can go to the beach, If you go to the beach, then you can surf and If you score more than 75%. Then you can surf. So if we take

p = Score is more than 75%

q = You can go to the beach

r = You can surf

So can write the given statement “If you score more than 75%, then you can go to the beach” as

p q and the statement “If you go to the beach, then you can surf” can be written as q r and also the statement “If you score more than 75%. Then you can surf” can be written as p r.

So we can see that we are given: p q is true

q r is true

p r is true

This statement resolves the law of syllogism which states that if p q is true and If q r is true then we can conclude that p r is also true

Final Answer:

Hence, the law of logic which is used in these statements is the law of syllogism.

Maths-

### Show the conjecture is false by finding a counterexample. Two adjacent angles always form a linear pair.

Hint:

Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

Counterexample: It is an example which shows that the conjecture is false.

Solution

Linear pairs are always supplementary but adjacent angles may not be. It can be shown by the following

diagram:

Here, we can see that the sum of adjacent angles will be definitely less than 180

Final Answer:

Hence, the counterexample for the given conjecture is the above figure.

Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

Counterexample: It is an example which shows that the conjecture is false.

Solution

Linear pairs are always supplementary but adjacent angles may not be. It can be shown by the following

diagram:

Here, we can see that the sum of adjacent angles will be definitely less than 180

^{o}. So, the given conjecture is wrong.Final Answer:

Hence, the counterexample for the given conjecture is the above figure.

### Show the conjecture is false by finding a counterexample. Two adjacent angles always form a linear pair.

Maths-General

Hint:

Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

Counterexample: It is an example which shows that the conjecture is false.

Solution

Linear pairs are always supplementary but adjacent angles may not be. It can be shown by the following

diagram:

Here, we can see that the sum of adjacent angles will be definitely less than 180

Final Answer:

Hence, the counterexample for the given conjecture is the above figure.

Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

Counterexample: It is an example which shows that the conjecture is false.

Solution

Linear pairs are always supplementary but adjacent angles may not be. It can be shown by the following

diagram:

Here, we can see that the sum of adjacent angles will be definitely less than 180

^{o}. So, the given conjecture is wrong.Final Answer:

Hence, the counterexample for the given conjecture is the above figure.

Maths-

### Prove that ∠ ABC ≅ ∠ ADC

Complete step by step solution:

From the figure,

In △ABC and △CDA, we have

AB = CD (given)

AD = CB (given)

AC = AC (common side)

Hence △ABC⩭ △CDA by SSS congruence rule.

⇒ ∠ ABC ≅ ∠ CDA (corresponding parts of congruent triangles)

From the figure,

In △ABC and △CDA, we have

AB = CD (given)

AD = CB (given)

AC = AC (common side)

Hence △ABC⩭ △CDA by SSS congruence rule.

⇒ ∠ ABC ≅ ∠ CDA (corresponding parts of congruent triangles)

### Prove that ∠ ABC ≅ ∠ ADC

Maths-General

Complete step by step solution:

From the figure,

In △ABC and △CDA, we have

AB = CD (given)

AD = CB (given)

AC = AC (common side)

Hence △ABC⩭ △CDA by SSS congruence rule.

⇒ ∠ ABC ≅ ∠ CDA (corresponding parts of congruent triangles)

From the figure,

In △ABC and △CDA, we have

AB = CD (given)

AD = CB (given)

AC = AC (common side)

Hence △ABC⩭ △CDA by SSS congruence rule.

⇒ ∠ ABC ≅ ∠ CDA (corresponding parts of congruent triangles)

Maths-

### A man bought 4 cups of coffee and left a $7 tip. A woman bought 8 cups of coffee and only left a $2 tip. If they paid the same amount, how much was each cup of coffee?

- Hint:

○ Take terms with cofficient at one side and without cofficient at another side.

- Step by step explanation:

A man bought 4 cups of coffee and left a $7 tip.

A woman bought 8 cups of coffee and only left a $2 tip.

Amount paid by both is same.

○ Step 1:

Let the price of 1 cup of coffee be x.

So, in case of man,

Total amount paid = 4x + 7 { %7 is tip }

In case of women,

Total amount paid = 8x + 2 { %2 is tip }

○ Step 2:

○ As amount paid by both of them is same.

∴ 4x + 7 = 8x + 2

7 - 2 = 8x - 4x

5 = 4x

x =

x = 1.25

- Final Answer:

### A man bought 4 cups of coffee and left a $7 tip. A woman bought 8 cups of coffee and only left a $2 tip. If they paid the same amount, how much was each cup of coffee?

Maths-General

- Hint:

○ Take terms with cofficient at one side and without cofficient at another side.

- Step by step explanation:

A man bought 4 cups of coffee and left a $7 tip.

A woman bought 8 cups of coffee and only left a $2 tip.

Amount paid by both is same.

○ Step 1:

Let the price of 1 cup of coffee be x.

So, in case of man,

Total amount paid = 4x + 7 { %7 is tip }

In case of women,

Total amount paid = 8x + 2 { %2 is tip }

○ Step 2:

○ As amount paid by both of them is same.

∴ 4x + 7 = 8x + 2

7 - 2 = 8x - 4x

5 = 4x

x =

x = 1.25

- Final Answer:

Maths-

### Prove that ∠ ABC ≅ ∠ PQR

Complete step by step solution:

Consider 2 triangles, and

From the figure, we have

∠ BAC = ∠ QPR (given)

∠ BCA = ∠ QRP (given)

By angle sum property

We have, ∠ ABC = ∠ PQR

Ie, ∠ ABC = 180°- (∠ BAC + ∠ BCA) and

∠ PQR = 180°- (∠ QPR + ∠ QRP) = 180° - (∠ BAC + ∠ BCA)

So, ⇒ ∠ ABC ≅ ∠ PQR

Consider 2 triangles, and

From the figure, we have

∠ BAC = ∠ QPR (given)

∠ BCA = ∠ QRP (given)

By angle sum property

We have, ∠ ABC = ∠ PQR

Ie, ∠ ABC = 180°- (∠ BAC + ∠ BCA) and

∠ PQR = 180°- (∠ QPR + ∠ QRP) = 180° - (∠ BAC + ∠ BCA)

So, ⇒ ∠ ABC ≅ ∠ PQR

### Prove that ∠ ABC ≅ ∠ PQR

Maths-General

Complete step by step solution:

Consider 2 triangles, and

From the figure, we have

∠ BAC = ∠ QPR (given)

∠ BCA = ∠ QRP (given)

By angle sum property

We have, ∠ ABC = ∠ PQR

Ie, ∠ ABC = 180°- (∠ BAC + ∠ BCA) and

∠ PQR = 180°- (∠ QPR + ∠ QRP) = 180° - (∠ BAC + ∠ BCA)

So, ⇒ ∠ ABC ≅ ∠ PQR

Consider 2 triangles, and

From the figure, we have

∠ BAC = ∠ QPR (given)

∠ BCA = ∠ QRP (given)

By angle sum property

We have, ∠ ABC = ∠ PQR

Ie, ∠ ABC = 180°- (∠ BAC + ∠ BCA) and

∠ PQR = 180°- (∠ QPR + ∠ QRP) = 180° - (∠ BAC + ∠ BCA)

So, ⇒ ∠ ABC ≅ ∠ PQR

Maths-

### Show the conjecture is false by finding a counterexample. If ≅ , then point B is the midpoint of AB.

Hint:

Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

Counterexample: It is an example which shows that the conjecture is false.

Solution

In the above diagram we can see that AB = BC, but point B is not on AC.

So the conjunction is false

Final Answer:

Hence, the diagram is the counterexample of the given conjecture.

Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

Counterexample: It is an example which shows that the conjecture is false.

Solution

In the above diagram we can see that AB = BC, but point B is not on AC.

So the conjunction is false

Final Answer:

Hence, the diagram is the counterexample of the given conjecture.

### Show the conjecture is false by finding a counterexample. If ≅ , then point B is the midpoint of AB.

Maths-General

Hint:

Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

Counterexample: It is an example which shows that the conjecture is false.

Solution

In the above diagram we can see that AB = BC, but point B is not on AC.

So the conjunction is false

Final Answer:

Hence, the diagram is the counterexample of the given conjecture.

Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

Counterexample: It is an example which shows that the conjecture is false.

Solution

In the above diagram we can see that AB = BC, but point B is not on AC.

So the conjunction is false

Final Answer:

Hence, the diagram is the counterexample of the given conjecture.

Maths-

### A store discounted the price of Doritos $0.35 and then a man bought 5 bags. If he paid a total of $12.70 for the bags of chips, how much was each bag originally?

○ Given:

Discount on 1 pack of Doritos = $.0.35.

Total pack brought = 5.

Total money paid = $12.70.

○ Step 1:

○ Total discount;

Discount on 1 pack of Doritos= $.0.35

So,

Discount on 5 pack of Doritos= $.0.35 5 = $ 1.75

○ Step 2:

○ Original price of 5 bags Doritos:

It is given that price of 5 bags after discount is $12.70

So, original price of 5 bags = 12.70 + 1.75 = 14.45

○ Step 3:

○ Original price of 1 bag:

original price of 5 bags = $ 14.45

original price of 1 bags = $ = 2.89

Discount on 1 pack of Doritos = $.0.35.

Total pack brought = 5.

Total money paid = $12.70.

○ Step 1:

○ Total discount;

Discount on 1 pack of Doritos= $.0.35

So,

Discount on 5 pack of Doritos= $.0.35 5 = $ 1.75

○ Step 2:

○ Original price of 5 bags Doritos:

It is given that price of 5 bags after discount is $12.70

So, original price of 5 bags = 12.70 + 1.75 = 14.45

○ Step 3:

○ Original price of 1 bag:

original price of 5 bags = $ 14.45

original price of 1 bags = $ = 2.89

- Final Answer:

### A store discounted the price of Doritos $0.35 and then a man bought 5 bags. If he paid a total of $12.70 for the bags of chips, how much was each bag originally?

Maths-General

○ Given:

Discount on 1 pack of Doritos = $.0.35.

Total pack brought = 5.

Total money paid = $12.70.

○ Step 1:

○ Total discount;

Discount on 1 pack of Doritos= $.0.35

So,

Discount on 5 pack of Doritos= $.0.35 5 = $ 1.75

○ Step 2:

○ Original price of 5 bags Doritos:

It is given that price of 5 bags after discount is $12.70

So, original price of 5 bags = 12.70 + 1.75 = 14.45

○ Step 3:

○ Original price of 1 bag:

original price of 5 bags = $ 14.45

original price of 1 bags = $ = 2.89

Discount on 1 pack of Doritos = $.0.35.

Total pack brought = 5.

Total money paid = $12.70.

○ Step 1:

○ Total discount;

Discount on 1 pack of Doritos= $.0.35

So,

Discount on 5 pack of Doritos= $.0.35 5 = $ 1.75

○ Step 2:

○ Original price of 5 bags Doritos:

It is given that price of 5 bags after discount is $12.70

So, original price of 5 bags = 12.70 + 1.75 = 14.45

○ Step 3:

○ Original price of 1 bag:

original price of 5 bags = $ 14.45

original price of 1 bags = $ = 2.89

- Final Answer:

Maths-

### Use the Law of Detachment to make a valid conclusion in the true situation.

If the measure of an angle is less than 90°, then it is an acute angle.

Hint:

Law of Detachment states that if p q is true and it is given that p is true then we can conclude

that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: The measure of an angle is less than 90°

q: The angle is an acute angle.

So we can write the given statement “If the measure of an angle is less than 90°, then it is an acute angle” as:

It is given that

𝑚∠𝑄 = 165°

Angle Q is greater than 90

Final Answer:

Hence, we are unable to conclude anything.

Law of Detachment states that if p q is true and it is given that p is true then we can conclude

that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: The measure of an angle is less than 90°

q: The angle is an acute angle.

So we can write the given statement “If the measure of an angle is less than 90°, then it is an acute angle” as:

It is given that

𝑚∠𝑄 = 165°

Angle Q is greater than 90

^{o}which means the p statement is false and hence we cannot conclude anything.Final Answer:

Hence, we are unable to conclude anything.

### Use the Law of Detachment to make a valid conclusion in the true situation.

If the measure of an angle is less than 90°, then it is an acute angle.

Maths-General

Hint:

Law of Detachment states that if p q is true and it is given that p is true then we can conclude

that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: The measure of an angle is less than 90°

q: The angle is an acute angle.

So we can write the given statement “If the measure of an angle is less than 90°, then it is an acute angle” as:

It is given that

𝑚∠𝑄 = 165°

Angle Q is greater than 90

Final Answer:

Hence, we are unable to conclude anything.

Law of Detachment states that if p q is true and it is given that p is true then we can conclude

that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: The measure of an angle is less than 90°

q: The angle is an acute angle.

So we can write the given statement “If the measure of an angle is less than 90°, then it is an acute angle” as:

It is given that

𝑚∠𝑄 = 165°

Angle Q is greater than 90

^{o}which means the p statement is false and hence we cannot conclude anything.Final Answer:

Hence, we are unable to conclude anything.

Maths-

### Find JK

Complete step by step solution:

Consider 2 triangles, and

From the figure, we have

JL = OQ = 5 (given)

∠ JLK = ∠ OQP (given)

KL = PQ = 7 (given)

∴ △ KJL ⩭ △ POQ by SAS congruence rule.

⇒ JK = OP (corresponding parts of congruent triangles)

⇒ JK = 8

Consider 2 triangles, and

From the figure, we have

JL = OQ = 5 (given)

∠ JLK = ∠ OQP (given)

KL = PQ = 7 (given)

∴ △ KJL ⩭ △ POQ by SAS congruence rule.

⇒ JK = OP (corresponding parts of congruent triangles)

⇒ JK = 8

### Find JK

Maths-General

Complete step by step solution:

Consider 2 triangles, and

From the figure, we have

JL = OQ = 5 (given)

∠ JLK = ∠ OQP (given)

KL = PQ = 7 (given)

∴ △ KJL ⩭ △ POQ by SAS congruence rule.

⇒ JK = OP (corresponding parts of congruent triangles)

⇒ JK = 8

Consider 2 triangles, and

From the figure, we have

JL = OQ = 5 (given)

∠ JLK = ∠ OQP (given)

KL = PQ = 7 (given)

∴ △ KJL ⩭ △ POQ by SAS congruence rule.

⇒ JK = OP (corresponding parts of congruent triangles)

⇒ JK = 8