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djverab [1.8K]
3 years ago
9

Ashley has a rectangle made out of paper that is 8 cm by12 cm. She folds it in half twice, first vertically and then horizontall

y. The new rectangle looks just like the original rectangle but smaller. What is the area of the new smaller rectangle in square cm
Mathematics
1 answer:
Svetach [21]3 years ago
8 0

Answer:

Area =24cm^2

Step-by-step explanation:

Given

L = 8cm

W = 12cm

r = 2 -- folded twice

Required

The area of the new rectangle

When the length was folder, the new length is:

l = L/2 = 8cm/2 = 4cm

When the width was folder, the new width is:

w = W/2 = 12cm/2 = 6cm

So, the new area is:

Area =l * w

Area =4cm * 6cm

Area =24cm^2

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Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Salsk061 [2.6K]

When two lines intersect at 90° degrees angle, the lines are perpendicular to each other. Two perpendicular lines, their slope will give a product of -1

i.e. if the first's line slope is 5, then the second line's will be -1 ÷ 5 = -¹/₅

To find the slope of a line, we divide the vertical distance by the horizontal distance. 

We'll use the trial and error method to find the right pairing

Let's start with A(3, 3) and B(12, 6)

Vertical distance = 

Horizontal distance = 

The slope AB = ³/₉ = ¹/₃

We want BC to have a slope -1 ÷ ¹/₃ = -3

Try C(16, -6); check the slope with B(12, 6)

Vertical distance = 

Horizontal distance = 

Slope of BC = -12 ÷ 4 = -3

The slope BC = -3 is the value we want so, tile 1 pair with tile 4

-------------------------------------------------------------------------------------------------------------

Let's do A(-10, 5) and B(12, 16)

Vertical distance = 16 - 5 = 11

Horizontal distance = 12 - -10 = 22

Slope AB = ¹¹/₂₂ = ¹/₂

The perpendicular slope would be -1 ÷ ¹/₂ = -2

Try C(18, 4)  with B(12, 16)

Vertical distance = 16 - 4 = 12

Horizontal distance = 12 - 18 = -6

Slope BC = ¹²/₋₆ = -2

Slope BC and slope AB perpendicular, so tile 3 matches with tile 6

--------------------------------------------------------------------------------------------------------------

Let's try A(12, -14) and B(-16, 21)

Vertical distance = 21 - -14 = 35

Horizontal distance = -16 - 12 = -28

The slope AB = ³⁵/-₂₈ = ⁵/₋₄

We need the perpendicular slope to be -1 ÷ -⁵/₄ = ⁴/₅

Try C(-11, 25)

Vertical distance with B = 25 - 21 = 4

Horizontal distance with B = -11 - -16 = 5

The slope = ⁴/₅

Tile 7 matches tile 8

--------------------------------------------------------------------------------------------------------------

Take A(-12, -19) and B(20, 45)

Vertical distance = 45 - -19 = 64

Horizontal distance = 20 - -12 = 32

Slope AB = ⁶⁴/₃₂ = 2

We need the perpendicular slope to be -1 ÷ 2 = -¹/₂

We have C(6, 52) and checking the slope with B(20, 45)

Vertical distance = 45 - 52 = -7

Horizontal distance = 20 - 6 = 14

The slope is ⁻⁷/₁₄ = -¹/₂

Tile 9 pairs with tile 2

-----------------------------------------------------------------------------------------------------------

Conclusion

Tile 1 ⇒ Tile 4

Tile 3 ⇒ Tile 6

Tile 7 ⇒ Tile 8

Tile 9 ⇒ Tile 2

Tile 5 and Tile 10 do not have pairs

5 0
3 years ago
When in-person, I love celebrating holidays with my students, including Halloween and Valentine's Day. Valentine's Day, especial
Murljashka [212]

Answer:

5x +4(2y) = 50

i can only think of this but i have no idea if it's correct

Step-by-step explanation:

5 0
3 years ago
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Video Store A charges a $15.00 account
stepan [7]

Answer:

Step-by-step explanation:

video store A : 15 + 1.75m

video store B : 7.5 + 2.25m

15 + 1.75m = 7.5 + 2.25m

15 - 7.5 = 2.25m - 1.75m

7.5 = 0.50m

7.5 / 0.50 = m

15 = m <=== there would have to be 15 movie rentals to make them equal

check...

15 + 1.75m                      7.50 + 2.25m

15 + 1.75(15) =                 7.50 + 2.25(15) =

41.25                               41.25

yep...it checks out

4 0
3 years ago
Evaluate.
ohaa [14]

Step-by-step explanation:

\frac{9.2 \times  {10}^{ - 8} }{2.3 \times  {10}^{3} }  \\  = 4.0 \times  {10}^{ - 11}

8 0
3 years ago
Caleb borrowed $1500 from his aunt. He plans to pay his aunt back in 9 months. If he
sergeinik [125]

Answer:

A = $1,545.00

(I = A - P = $45.00)

Equation:

A = P(1 + rt)

Explanation:

First, converting R percent to r a decimal

r = R/100 = 4%/100 = 0.04 per year.

Putting time into years for simplicity,

9 months / 12 months/year = 0.75 years.

Solving our equation:

A = 1500(1 + (0.04 × 0.75)) = 1545

A = $1,545.00

The total amount accrued, principal plus interest, from simple interest on a principal of $1,500.00 at a rate of 4% per year for 0.75 years (9 months) is $1,545.00.

4 0
3 years ago
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