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zheka24 [161]
3 years ago
6

Harry the hippo is munching on the lily pads in his pond. When he arrived at the pond, there were 20 lily pads, but he is eating

4 lily pads an hour. Heinrick the hungrier hippo found a better pond with 29 lily pads! He eats 7 lily pads every hour.
Part A.) If Harry and Heinrick start eating at the same time, when will their ponds have the same number of lily pads remaining?

(PLEASE ANSWER THIS ONE)


Part B.) How many lily pads will be left in each pond at the same time.
Mathematics
1 answer:
Lisa [10]3 years ago
4 0

Answer:

After the 3rd hour

8 lily pads

Step-by-step explanation:

This is quite straight forward and require no deep mathematics.

Harry has 20 lily pads to eat and he eats 4 per hour. After the first hour, he eats 4 and he has 16 left. After second hour, he eats another 4 and he has 12 left. After third hour, he eats four and has eight left.

For Hennrick, he has 29 lily pads and he eats 7 per hour. After first hour, he has 22 left. After second hour, he eats another 7 and have 15 left. After 3rd hour, he eats another 7 and has just 8 left.

8 lily pads will be left at the same time

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Answered below

Step-by-step explanation:

<u>Sheet 1: Question 3</u>

<em>Vertically opposite angles are equal so you will equate the angles given,</em>

∠LPN = ∠OPM

7 + 13x = -20 + 16x

27 = 3x

x = 9

<u>Sheet 1: Question 4</u>

<em>Vertically opposite angles are equal so you will equate the angles given,</em>

∠ABD = ∠EBC

2x + 20 = 3x + 15

-x = -5

x = 5

<u>Sheet 1: Question 5</u>

<u>Step 1: Find the value of x</u>

<em>Vertically opposite angles are equal so you will equate the angles given,</em>

∠SOP = ∠ROQ

5x = 4x + 10

x = 10

<u>Step 2: Find angles</u>

Angle SOP = 5x = 5(10) = 50°

Angle ROQ = 50° <em>(because it is vertically opposite to angle SOP)</em>

Angle SOR = 180 - 50 <em>(because all angles on a straight line are equal to 180°)</em>

Angle SOR = 130°

Angle POQ = 130° <em>(because it is vertically opposite to angle SOR)</em>

<u>Sheet 1: Question 6</u>

Angle 1 = 72° <em>(because vertically opposite angles)</em>

∠4 + ∠1 + 41 = 180° <em>(because all angles on a straight line are equal to 180°)</em>

∠4 + 72 + 41 = 180

∠4 = 67°

∠3 = 41° <em>(because vertically opposite angles)</em>

∠2 = 67° <em>(because vertically opposite angles)</em>

<u>Sheet 2: Question 3</u>

Step 1: Find the value of x

<em>Sum of complementary angles is equal to 90°</em>

Angle A + Angle B = 90°

7x + 4 + 4x + 9 = 90°

11x = 90 - 13

11x = 77

x = 7

<u>Step 2: Find angle A and angle B using x</u>

Angle A: 7x + 4

7(7) + 4

Angle A = 53°

Angle B: 4x + 9

4(7) + 9

Angle B = 37°

<u>Sheet 3: Question 3</u>

<u>Step 1: Find the value of x</u>

<em>Sum of supplementary angles is equal to 180°.</em>

Angle A + Angle B = 180°

3x - 7 + 2x + 2 = 180°

5x = 185

x = 37

<u>Step 2: Find angle A and angle B using x</u>

Angle A: 3x - 7

3(37)-7

Angle A = 104°

Angle B: 2x + 2

2(37) + 2

Angle B = 76°

<u>Sheet 3: Question 4</u>

<em>Sum of supplementary angles is equal to 180°.</em>

<u>Step 1: Find x</u>

1/4(36x-8) + 1/2(6x-20) = 180°

Take LCM

[36x - 8 + 2(6x - 20)]/4 = 180°

36x - 8 +12x - 40 = 180 x 4

48x - 48 = 720

48x = 768

x = 16

<em>Step 2: Find both angles with the help of x</em>

Angle 1: 1/4(36x-8)

1/4[36(16)-8] = 568/4

Angle 1 = 142°

Angle 2: 1/2(6x-20)

1/2[6(16)-20] = 76/2

Angle 2 = 38°

<u>Sheet 4: Question 1</u>

<em>All angles on a straight line are equal to 180°</em>

Angle z + 138° = 180°

Angle z = 180 - 138

Angle z = 42°

<u>Sheet 4: Question 2</u>

Linear pair 1: 5 and 7 <em>(because both angles are on a straight line and are equal to 180°)</em>

Linear pair 2: 6 and 8<em> (because both angles are on a straight line and are equal to 180°)</em>

<u>Sheet 4: Question 3</u>

<u>Step 1: Find the value of x</u>

<em>All angles on a straight line are equal to 180° or linear pairs are equal to 180°</em>

Angle LMO + Angle OMN = 180°

7x + 20 + 10 + 5x = 180°

12x = 180 - 30

x = 150/12

x = 12.5

<em>Step 2: Find angles using the value of x</em>

Angle LMO: 7x + 20

7(12.5) + 20

Angle LMO = 107.5°

Angle OMN: 10 + 5x

10 + 5(12.5)

Angle OMN = 72.5°

<u>Sheet 4: Question 4</u>

<em>Linear pairs are equal to 180°.</em>

Angle 1 + Angle 2 = 180°

1/3(27x-6) + 1/2(6x-20) = 180°

<em>Take LCM = 6</em>

[2(27x-6) + 3(6x-20)]/6 = 180

54x - 12 + 18x - 60 = 1080

72x - 72 = 1080

72x = 1152

x = 16

!!

7 0
3 years ago
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