10.2L/100km = ______/480 km

How man litres of fuel would the car use if it travels 480 km?

Express your answer to the nearest tenth of a litre.

10.2L/100 km = 49.0L/480

480 litres of fuel is being used for 480 km.

1. A car uses fuel at a rate of 10.2L/100 km while travelling at 90 km/h. At this rate of fuel consumption, how many litres of fuel would the car use if it travels 480 km? Express your answer to the nearest tenth of a litre.

10.2L/100km = ______/480 km

How man litres of fuel would the car use if it travels 480 km?

10.2L/100km = ______/480 km

How man litres of fuel would the car use if it travels 480 km?

Express your answer to the nearest tenth of a litre.

10.2L/100 km = 49.0L/480

480 litres of fuel is being used for 480 km.

Its how many times a shape/image rotates before it finishes
a rotation.

360° / 4 = 90°

360° / 2 = 180°

90° angle turns = order of rotation 4

180° _________ =
________ 2

If you divide 360° by the Order of Rotation, we get the angle at which we
made our turns.

It’s the minimum
degree of the angle of our turns in one full rotation.

It has to have a center of rotation

When you turn/
rotate the image, at least part of the image has to fit on top of another part.

It has to have an order of rotation greater than 1.

Center of the image or shape that the image or shape has to
rotate around.

The number of times an image reflects upon itself by
rotating, before finishing one full rotation.

The hypotenuse of an isosceles right triangle has a length of 20cm. What is the length of each leg of the triangle? Provide your answer to the nearest tenth of a centimeter.

The side length of each leg of the triangle is 14.1 cm.

A baseball diamond is square area of about 750m2.

what is the distance from first to second base. Give

your answer to the nearest tenth of a metre.

The distance from first base to second base is 27.4m.

32. The total area of the shape is 52 centimetres squared. What is it's perimeter?

- I found the answer by dividing 52 by 2, which gets me 26. I did this to put the two squares at the side away to let me see the rectangle in the middle.

- I know that the rectangle's perimeter is 10, so I finish the equation by adding ten, getting me to 36, which is the answer.

- I found the answer by dividing 52 by 2, which gets me 26. I did this to put the two squares at the side away to let me see the rectangle in the middle.

- I know that the rectangle's perimeter is 10, so I finish the equation by adding ten, getting me to 36, which is the answer.

16 a) The label on a 1-L can of paint states that the paint will cover an area of 10m². What is the length of the largest square area that the paint will cover? Express your answer to the nearest hundredth of a metre.

You just squareroot using a calculator

√10m²= 3.16227766

= 3.16m

Round of to the nearest hundredth of a metre.

b) what is the side length of the largest square area that a 3.79-L can of the same paint will cover? Express your answer to the nearest hundredth of a metre.

First off I rounded 3.79 to 3.80.

Then multiply 3.80 by 10

3.80x10 = 38

√38 = 6.164414003 round of to the nearest hundredth

= 6.16m

c) Nadia is applying two coats of paint to an area that is 4.6m by 4.6m. How much paint will she use if she applies the same amount of paint for each coat? Express your answer to the nearest tenth of a litre.

4.6x4.6= 21.16

21.16x2 = 42.32

42.32 ÷ 10 = 4.232 round to the nearest tenth of a litre

= 4.2L

You just squareroot using a calculator

√10m²= 3.16227766

= 3.16m

Round of to the nearest hundredth of a metre.

b) what is the side length of the largest square area that a 3.79-L can of the same paint will cover? Express your answer to the nearest hundredth of a metre.

First off I rounded 3.79 to 3.80.

Then multiply 3.80 by 10

3.80x10 = 38

√38 = 6.164414003 round of to the nearest hundredth

= 6.16m

c) Nadia is applying two coats of paint to an area that is 4.6m by 4.6m. How much paint will she use if she applies the same amount of paint for each coat? Express your answer to the nearest tenth of a litre.

4.6x4.6= 21.16

21.16x2 = 42.32

42.32 ÷ 10 = 4.232 round to the nearest tenth of a litre

= 4.2L

A square field has an area of 1000 m2. Laura wants to walk from one corner of the field to the opposite corner. If she walks at 1.5 m/s, how much time can she save by walking diagonally instead of walking along two adjacent sides? Express your answer to the nearest tenth of a second.

First you would find what the side length of the square is:

Now that you know its 63.24 s walking along the two sides you need to find the diagonal way.

Now you subtract both of them so you can find the difference. Then you have to divide 18.53 by 1.5

which is

12.353 because you know Laura walks 1.5 m/s.

The answer is:

If Laura walks diagonally instead of walking the two whole sides, she saves 12.3 s

7.74 x 4 = 30.96

30.96 x 80 = 2476.8

And because we are finding the area of

20. Leon's rectangular living room is 8.2 m by the 4.5 m. A square rug covers 2/5 of the area of the floor. What is the side length of the rug, to the nearest tenth of a metre.

I first find the area of the living room.

A= l x w

A = 8.2 (4.5)

A= 36.9

Then, I find 40% of the area of the living room (36.9m). I got 40% because 2/5 is equivalent to 40%. 40% of the area of the living room is 14.7. I got to this answer by:

0.40 x 36.9= 14.7

I then find the side length of the rug by getting the square root of 14.7 which equals 3.82.

A= l x w

√14.7 = 3.82

The side length of the rug is 3.82 m.

Heron's formula is A=√

2

Determine the area of each triangle with the following side lengths.

Express each area to the nearest tenth of a square centimetre.

For this question I had to find the distance of how much a person can see across the ocean to the horizon. I know that in order to find the distance you have to find the square root of 12.74 x

~First I re - wrote the formula.

~Then I found out the height of how much meters Adele's eyes are above the water which was 4.1 m.

~Next I multiplied 12.74 x 41. Then I got the answer of 52.234.

~Lastly now I have to find the square root of 52.234, so I got the answer of around 7.2273 km. Then I rounded my answer to 7.20 km.

In this question it is very similar to the first one. The only thing different I have to do in convert the height which was 165 cm into m. I did this by dividing 165 by 100 because there is 100 cm in 1 meter.

First I re - wrote the formula.

Then I found the height that Brian was above the water, which was 165 cm then converted in 1.65 m.

Then I finally multiplied 12.74 by 1.65 and got the answer of 21.021.

Lastly I found the square root of 21.021 and I got around 4.5848 km, and rounded this answer to 4.6 km.

In this question I converted the height of Yvonne's eyes above the water into meters by multiplying 5 ( The height in km. ) by 1000 because there is 1000 meters in 1 kilometer.

First I re - wrote the formula.

Then I found the height that Yvonne's eyes were above the water, which was 5 km then I converted it to 5000 m.

Then I multiplied 12.74 by 5000 and got a product of 63700.

Lastly I found the square root of 63700 and got an answer of around 252.2885 km and then I rounded it to 252.4 km.

A square picture with an area of 100cm² is mounted on a square piece of matting. The matting has 2.5 times the area of the picture. If the picture is centered on the matting, what width of matting is visible around the outside of the picture. Give your answer to the nearest tenth of a centimeter.

So we know that the picture in the middle is 100cm²

So I if we find out what 100cm² x 2.5 is we get 250. Now we need to find the square root of 250 which we get 15.8cm.

The space between the 10cm and 15.8cm line is 5.8cm

if we move the square in the middle to the very center, that is like splitting that space in half, so 5.8÷2 you get 2.9cm

So we know that the picture in the middle is 100cm²

So I if we find out what 100cm² x 2.5 is we get 250. Now we need to find the square root of 250 which we get 15.8cm.

The space between the 10cm and 15.8cm line is 5.8cm

if we move the square in the middle to the very center, that is like splitting that space in half, so 5.8÷2 you get 2.9cm

You would replace 't' by 30 and (-20) and solve such as the following:

Then you would find the difference:

In today's Math class we found out how square roots work.

Examples that was given by Mr. Backe are:

√121=11 √81 =9 √36=6

√12.1 ≠1.1 because if you use a calculator the answer will be 3.48. But if you estimate it, the easy way to figure it out is to find the closest perfect square in this case √12.1 is close to √9 and √16. Then you find out the distance between √9 and √16 and it will be 7 so the answer will be close to 3 and 3/7. Which is 3.428.

The same thing will happen for √8.1 and √3.6. But √8.1 ≠0.9 and √3.6 ≠0.6, and √3.6 equal to 1.897 and √8.1 equals to 2.846

Here are the other examples:

√1.21=1.1 √0.81=0.9 √0.36=1.6

√0.121=0.348 √0.081=0.2846 √0.036=0.1847

√0.0121=0.11 √0.0081=0.09 √0.0036=0.06

√0.00121=0.0348

You might realize that there is a pattern. And the pattern is that even amount of even numbers are perfect squares and the ones that have odd amount of decimals are surds. They move one place value.

11²= 11x11=121

1.1²= 1.1x1.1= 1.21

0.11²= 0.11x0.11= 0.0121

Those are perfect squares.

Another thing we learned is to know how to square root a fraction.

√__25__= √__25 __= __5__

49 √49 7

√__64__ = __ 8__

81 9

√__36__ = 2 √__36__ = √4=2

9 9

Homework:

Textbook: pg 72-77

Do Practise: 6,7,9,10,11,13,14

Apply: 15,16,17,18,19,20,22,24,25,27,28,30,31

Extend Any 2 plus 36

Examples that was given by Mr. Backe are:

√121=11 √81 =9 √36=6

√12.1 ≠1.1 because if you use a calculator the answer will be 3.48. But if you estimate it, the easy way to figure it out is to find the closest perfect square in this case √12.1 is close to √9 and √16. Then you find out the distance between √9 and √16 and it will be 7 so the answer will be close to 3 and 3/7. Which is 3.428.

The same thing will happen for √8.1 and √3.6. But √8.1 ≠0.9 and √3.6 ≠0.6, and √3.6 equal to 1.897 and √8.1 equals to 2.846

Here are the other examples:

√1.21=1.1 √0.81=0.9 √0.36=1.6

√0.121=0.348 √0.081=0.2846 √0.036=0.1847

√0.0121=0.11 √0.0081=0.09 √0.0036=0.06

√0.00121=0.0348

You might realize that there is a pattern. And the pattern is that even amount of even numbers are perfect squares and the ones that have odd amount of decimals are surds. They move one place value.

11²= 11x11=121

1.1²= 1.1x1.1= 1.21

0.11²= 0.11x0.11= 0.0121

Those are perfect squares.

Another thing we learned is to know how to square root a fraction.

√

49 √49 7

√

81 9

√

9 9

Homework:

Textbook: pg 72-77

Do Practise: 6,7,9,10,11,13,14

Apply: 15,16,17,18,19,20,22,24,25,27,28,30,31

Extend Any 2 plus 36

A frame measures 30 cm by 20 cm. Can you mount a sqaure picture with an area of 500 cm² in the frame? Explain.

√500 = 22.36 cm

Picture = 22.36 cm

Frame = 30 cm x 20cm

No you cannot mount a square picture on the frame because one side of the picture is too big for the frame so it won't fit.
√65 536 is a perfect square because when you multiply 256 x 256, it equals 65 536.

√65 536 = 256 x 256

√256 is a perfect square because when you multiply 16 x 16, it equals to 256.

√256 = 16 x 16

√16 is a perfect square because when you multiply 4 x 4, it equals to 16.

√16 = 4 x 4

- Since there are three square root signs (radicals), that means you keep square rooting the given number three times.
**The final answer of √√√65 536 should be 4.**

Here is a picture of perfect squares:

21.6 cm² = 466.56

778.41 cm² + 466.56 cm² = 1,244.97

√1,244.97 = 35.28 cm

35.28 cm rounded to the nearest centimeter would be 35.3 cm.

14. Given the area of square, determine its side length. Express your answer to the nearest hundredth of a unit.

a) 0.85 m² b) 60 cm²

a) 0.85 m² b) 60 cm²

So, the dimensions of a square that 3/4 of a bag of fertilizer will cover are 12.2m by 12.2m.

Length = √area of square

L = √1.69 m

L = 1.3 m

= 1.69 m

Question: Li and Ray shared a vegetarian pizza which was cut into eight equal pieces and the Hawaiian pizza into six equal pieces. Li ate two slices of vegetarian pizza and one slice of Hawaiian pizza. Ray ate two slice of Hawaiian pizza and one slice of vegetarian pizza.

**A) Who ate more pizza?**

Ray ate more because:

Li: Veggie pizza- 2/8 and Hawaiian pizza 1/6

Ray: VP- 1/8 and Hawaiian pizza 2/6

I found the lowest common denominator for 6 and 8. Which was 24.

Then also multiplied the numerator with the same number which I multiplied with the denominator.

Li: VP 2/8 x 3/3 = 6/24

HP 1/6 x 4/4 = 4/24

4/24 + 6/24= 10/24

Ray: VP 1/8 x 3/3= 3/24

HP 2/6 x 4/4 = 8/24

3/24+ 8/24= 11/24

Also 6ths are much bigger pieces than 8ths so if you had more sixths you probably had more pizza because they were bigger pieces.

**B) How much more pizza did that person eat?**

1/24

**C) How much pizza was left over?**

13/24 or 5/8 of veggie pizza and 3/6 of Hawaiian pizza.

Ray ate more because:

Li: Veggie pizza- 2/8 and Hawaiian pizza 1/6

Ray: VP- 1/8 and Hawaiian pizza 2/6

I found the lowest common denominator for 6 and 8. Which was 24.

Then also multiplied the numerator with the same number which I multiplied with the denominator.

Li: VP 2/8 x 3/3 = 6/24

HP 1/6 x 4/4 = 4/24

4/24 + 6/24= 10/24

Ray: VP 1/8 x 3/3= 3/24

HP 2/6 x 4/4 = 8/24

3/24+ 8/24= 11/24

Also 6ths are much bigger pieces than 8ths so if you had more sixths you probably had more pizza because they were bigger pieces.

1/24

13/24 or 5/8 of veggie pizza and 3/6 of Hawaiian pizza.

22. Taj has three scoops for measuring flour. The largest scoop hold 2 1/2 times as much as the smallest one. The middle scoop holds 1 3/4 as much as the smallest one.

Describe two different ways in which Taj could measure each of the following quantities. He can use full scoops only.

a) 3 1/4 times as much as the smallest scoop holds

b) 1/2 as much as the smallest scoop holds

__ __

Before we can find out what what the other cups are we need to find out what the smallest cup is.

Smallest cup =*X*.... So 2 1/2 ÷ *X = *2 1/2 or 1 3/4 ÷ *X* = 1 3/4.

*X = *1

Smallest cup = 1

Large cup = 2 1/2 or 5/2

Medium cup = 1 3/4 or 7/4

**ANSWER**..

a) First way: 1 large scoop + 1 medium scoop - 1 small scoop

Second way: 2 large scoop - 1 medium

**ANSWER**

b) First Way: 1 large scoop - 2 small scoop

Second Way: 2 medium scoops - 3 small scoop

Describe two different ways in which Taj could measure each of the following quantities. He can use full scoops only.

a) 3 1/4 times as much as the smallest scoop holds

b) 1/2 as much as the smallest scoop holds

Before we can find out what what the other cups are we need to find out what the smallest cup is.

Smallest cup =

Smallest cup = 1

Large cup = 2 1/2 or 5/2

Medium cup = 1 3/4 or 7/4

a) First way: 1 large scoop + 1 medium scoop - 1 small scoop

Second way: 2 large scoop - 1 medium

b) First Way: 1 large scoop - 2 small scoop

Second Way: 2 medium scoops - 3 small scoop

18. Determine the mean of each set of numbers. Express your answer to the nearest hundredth, if necessary.

a) 0, -4.5, -8.2, 0.4, -7.6, 3.5, -0.2

To determine the mean, I first add all the numbers together:

0 + -4.5 + -8.2 + 0.4 + -7.6 + 3.5 + -0.2= -16.6

I then divide the sum with how many numbers I used to add it with.

-16.6/7= -2.37

b) 6.3, -2.2, 14.9, -4.8, -5.3, 1.6

6.3 + -2.2 + 14.9 + -4.8 + -5.3 + 1.6= 10.5

10.5/6= 1.75

12. A pelican dives vertically from a height of 3.8 m above the water. It then catches a fish 2.3 m underwater.

a) Write an expression using rational numbers to represent the length of the pelican's dive.

- 3.8 - ( -2.3) because 3.8 represents the height above the water the pelican is at and 2.3 represents how deep the the fish underwater is.

b) How long is the pelican's dive?

- The pelican's dive is 6.1 m because you add the two numbers together (3.8 and 2.3), which is the pelican's dive altogether (it dove 3.8 above water and 2.3 underwater).

a) Write an expression using rational numbers to represent the length of the pelican's dive.

- 3.8 - ( -2.3) because 3.8 represents the height above the water the pelican is at and 2.3 represents how deep the the fish underwater is.

b) How long is the pelican's dive?

- The pelican's dive is 6.1 m because you add the two numbers together (3.8 and 2.3), which is the pelican's dive altogether (it dove 3.8 above water and 2.3 underwater).

In everyday speech,* in a jiffy* means in a very short time. In science, a specific value sometimes assigned to a jiffy is 1/100 s.

Naima can type at 50 words/min. On average, how many jiffies does she take to type each word.

She takes up to 120 jiffies to type each word.

Please make any suggestions. This was kind of rushed.

Naima can type at 50 words/min. On average, how many jiffies does she take to type each word.

She takes up to 120 jiffies to type each word.

Please make any suggestions. This was kind of rushed.

15) Predict the next three numbers in each pattern.

A) -1 1/2, -7/8, -1/4, 3/8, 1, 1 5/8, 2 1/4, 2 7/8

B) 1 1/3, -2/3, 1/3, -1/6, 1/12, -1/24, 1/48, -1/96

A) -1 1/2, -7/8, -1/4, 3/8, 1, 1 5/8, 2 1/4, 2 7/8

B) 1 1/3, -2/3, 1/3, -1/6, 1/12, -1/24, 1/48, -1/96

12. In the table, a positive number shows how many hours the time in a location is ahead of the time in London, England. A negative number shows how many hoursthe time is behind the time in London.

A) How many hours is the time in St. John's ahead of the time in Brandon

St. John's: -3 1/2

Brandon: -6

-3.5 - (-6) = 2.5 hours

B) How many hours is the time in Victoria behind the time in Mumbai?

Victoria: -8

Mumbai: +5 1/2

+5.5 - (-8) = 13.5 hours

C) Determine and interpret the time difference between Tokyo and and Kathmandu.

Tokyo: +9

Kathmandu: +5 3/4

+9 - (+5.75) = 3.25

Tokyo is 3.25 hours ahead of Kathmandu.

D) Determine and interpret the time difference between Chatham Islands and St. John's.

Chatham Islands: +12 3/4

St. John's: -3 1/2

+12.75 - (-3.5) = 16.25

Chatham Islands is 16.25 hours ahead of St. John's.

E) In which location is the time exactly halfway between the times in Istanbul and Alice Springs?

Istanbul: +2

Alice Springs: +9 1/2

9.5 + 2 = 11.5

11.5 / 2 = 5.75

Kathmandu: +5 3/4

Kathmandu is location with the time that is exactly halfway between istanbul and Alice Springs.

A) How many hours is the time in St. John's ahead of the time in Brandon

St. John's: -3 1/2

Brandon: -6

-3.5 - (-6) = 2.5 hours

B) How many hours is the time in Victoria behind the time in Mumbai?

Victoria: -8

Mumbai: +5 1/2

+5.5 - (-8) = 13.5 hours

C) Determine and interpret the time difference between Tokyo and and Kathmandu.

Tokyo: +9

Kathmandu: +5 3/4

+9 - (+5.75) = 3.25

Tokyo is 3.25 hours ahead of Kathmandu.

D) Determine and interpret the time difference between Chatham Islands and St. John's.

Chatham Islands: +12 3/4

St. John's: -3 1/2

+12.75 - (-3.5) = 16.25

Chatham Islands is 16.25 hours ahead of St. John's.

E) In which location is the time exactly halfway between the times in Istanbul and Alice Springs?

Istanbul: +2

Alice Springs: +9 1/2

9.5 + 2 = 11.5

11.5 / 2 = 5.75

Kathmandu: +5 3/4

Kathmandu is location with the time that is exactly halfway between istanbul and Alice Springs.

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