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2 years ago

Mr. Pete just got a great deal at Lowe’s on tiles for his new patio. He wants to

Mathematics

1 answer:

sdas [7]2 years ago

8 0

Answer:

The fewest square tiles he can use without cutting any of them = 12 square tiles

Step-by-step explanation:

The given dimensions of Mr. Pete's rectangular patio = 108 inches by 144 inches

The area of the patio = 108 in. × 144 in. = 15,552 in.²

We note that when square tiles are used the must fit both the length and the with of the rectangular patio

Therefore, we have;

The dimensions of the square tiles that the fewest number of tiles is the highest common factor, HCF, of 108 inches and 144

The HCF of 108 and 144 are found from by the prime factors as follows;

108 = 2² × 3³ = 2² × 3² × 3

144 = 2⁴ × 3² = 2² × 3² × 4

From which we have;

The HCF of 108 and 144 = 2² × 3² = 36

Therefore, the size of the sides of the square tiles that will give the fewest number of tiles is 36 inches

The number of the 36 inches square tiles that fit into the length of the rectangular patio = 144 inches/(36 inches/tile) = 4 tiles

The number of the 36 inches square tiles that fit into the breadth of the rectangular patio = 108 inches/(36 inches/tile) = 3 tiles

The total number of tiles he will use = (4 × 3) tiles = 12 tiles = The fewest square tiles he can use without cutting any of them.

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What is the solution to the system? 1. x-y + 2 z = -7<br> 2. y + z =1<br> 3. x-2 y - 3 z = 0

kvv77 [185]

You'd find this problem easier to understand and do if you'd please list the defining equations vertically and line up variables:

1. x - 1y + 2 z = -7

2. y + 1z = 1

3. x - 2 y - 3 z = 0 Now eliminate the line numbers:

x - 1y + 2 z = -7

1y + 1 z = 1

x - 2 y - 3 z = 0

Let's use the elimination method to eliminate variable z: Seeing that z = 1 - y, we transform the first equation into 1x - 1y + 2(1-y) = -7

and the third into x - 2y - 3(1-y) = 0.

Simplifying 1x - 1y + 2(1-y) = -7

and x - 2y - 3(1-y) = 0,

we get

1x - 2y - 3 + 3y) = 0 and 1x - 1y + 2 - 2y = -7

which in turn simplify to

1x + y = 3 and 1x - 3y = -9

Having eliminated the variable z, we now focus on eliminating x. Mult. the 1st equation by -1, obtaining -1x - 1y = -3. Add this result to 1x - 3y = -9:

0 - 4y = -12, which tells us that y = 3. Subbing 3 for y in 1x + 1y = 3 tells us that x = 0.

All we have left to determine is the vaue of z.

Borrowing Equation 3, from above, we get x - 2 y - 3 z = 0, and into this equation we substitute x = 0 and y = 3: 0 -2(3) - 3z = 0.

Thus, -3z = 6, and z = -2.

The solution set is (0, 3, -2). You should check this by substitution.

3 0

3 years ago

I WILL AWARD BRAINLIEST!! PLEASE HELP!!!<br> Find the areas of the trapezoids.

Galina-37 [17]

Answer:

A = 12 units ^2

Step-by-step explanation:

The area of the trapezoid is found by

A = 1/2 (b1+b2)h

b1 = 2

b2 = 4

h = 4

I found these by looking at the graph

A = 1/2(2+4) 4

A = 1/2(6*4)

A = 12 units ^2

8 0

3 years ago

A model of a tractor trailer is shap d like a rectangular prism and has a width of 2 in. , a length of 11 in. , and a height of

Anna71 [15]

Answer:

Actual volume=3,773,000 in³

Step-by-step explanation:

Scale 1:35

Actual Width=Model Width×Scale factor=(2×35)=70 inches

Actual Length=Model Length×Scale factor=(11×35)=385 inches

Actual Height=Model Height×Scale factor=(4×35)=140 inches

Actual volume =(Base Area×Height)=Length×width×height=(385×70×140)=3,773,000 in³

Actual volume=3,773,000 in³

8 0

2 years ago

Please answer the following questions

shutvik [7]

Answer:

a) 8.8 square centimetres

b) 31.8 square centimetres

c) (3a + 12) square centimetres

d) Area = (2b + 2c + 4) square centimetres

Step-by-step explanation:

a) We have to split the diagram into three separate rectangles as shown below.

The area of A:

Area = 5.3 * 1 = 5.3 square centimetres

The area of B:

Area = 3.3 * 1 = 3.3 square centimetres

The area of C:

Area = 2 * 1 = 2 square centimetres

The area of the shape is the sum of the areas of the three shapes:

Area = 5.3 + 3.3 + 2 = 8.8 square centimetres

b) We have to split the diagram into two separate rectangles as shown below.

Note:(The diagram has conflicting values for 2.6 and 2.1 but I went with 2.6 as it seems more feasible in the diagram)

The area of A:

Area = 3 * 2.6 = 7.8 square centimetres

The area of B:

Area = 6 * 4 = 24 square centimetres

The area of the shape is the sum of the areas of the two shapes:

Area = 7.8 + 24 = 31.8 square centimetres

c) The shape is a rectangle and so its area is:

Area = 3 * (a + 4) = (3a + 12) square centimetres

d) The shape is a trapezium and so its area is:

Area = 0.5(A + B)H

where A = c cm

B = b + 2 cm

H = 4 cm

The area of the shape is therefore:

Area = 0.5 * (c + b + 2) * 4

Area = 2 * (b + c + 2)

Area = (2b + 2c + 4) square centimetres

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2 years ago