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3 years ago

7. Phozia has three pieces of rope with lengths of 160 cm, 192 cm and

Mathematics

1 answer:

lianna [129]3 years ago

3 0

Answer:

a) 16 cm, b) 37 pieces

Step-by-step explanation:

Part a

Finding the largest divisor of 160, 192 and 240

160 divisors: 1, 2, 4, 5, 8, 10, 16, 32, 40, 80 and 160.

// You can alternatively find them by factor pairs, which are (1, 160), (2, 80), (4, 40), (5, 32), (8, 20) & (10, 16). This way is much more faster. Also, you can simply search them in metanumbers.com

192 divisors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96 and 192

240 divisors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120 and 240

The largest divider that they all have in common is 16.

So 16 cm is the largest possible length of each of the shorter pieces of

rope

Part b

Now we have to count how many 16 cm pieces of rope can we get from the large rope pieces, which lengths are 160 cm, 192 cm and 240 cm

160/16 + 192/16 + 240/16 = 10 + 12 + 15 = 37

The answer is 37 pieces

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Andrei [34K]

Answer:

Step-by-step explanation:

1. x+6=14

14-6=8

x=8

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15/3=x

x=5

3. 7*x=56

56/7=8

x=8

4. x^2-4=12

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5. 1/4x=10

x/4 = 10

x = 40

6. 3x-9=18

x=9

7. 1/2x-10=14

x/2-10=14

x=48

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x=72

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3 years ago

The temperature decreases by 0.5 degrees every hour.

UNO [17]

i think its the 2nd or 1st one

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8 0

3 years ago

The width of a container is 5 feet less than its height. Its length is 1 foot longer than its height. The volume of the containe

juin [17]

The height of container is 8 feet

Solution:

Let "w" be the width of container

Let "l" be the length of container

Let "h" be the height of container

The width of a container is 5 feet less than its height

Therefore,

width = height - 5

w = h - 5 ------ eqn 1

Its length is 1 foot longer than its height

length = 1 + height

l = 1 + h ---------- eqn 2

The volume of container is given as:

$v = length \times width \times height$

Given that volume of the container is 216 cubic feet

$216 = l \times w \times h$

Substitute eqn 1 and eqn 2 in above formula

$216 = (1 + h) \times (h-5) \times h\\\\216 = (h+h^2)(h-5)\\\\216 = h^2-5h+h^3-5h^2\\\\216 = h^3-4h^2-5h\\\\h^3-4h^2-5h-216 = 0$

Solve by factoring

$(h-8)(h^2+4h+27) = 0$

Use the zero factor principle

If ab = 0 then a = 0 or b = 0 ( or both a = 0 and b = 0)

Therefore,

$h - 8 = 0\\\\h = 8$

Also,

$h^2+4h+27 = 0$

Solve by quadratic equation formula

$\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

$\mathrm{For\:} a=1,\:b=4,\:c=27:\quad h=\frac{-4\pm \sqrt{4^2-4\cdot \:1\cdot \:27}}{2\cdot \:1}$

$h = \frac{-4+\sqrt{4^2-4\cdot \:1\cdot \:27}}{2}=\frac{-4+\sqrt{92}i}{2}$

Therefore, on solving we get,

$h=-2+\sqrt{23}i,\:h=-2-\sqrt{23}i$

Thus solutions of "h" are:

h = 8

$h=-2+\sqrt{23}i,\:h=-2-\sqrt{23}i$

"h" cannot be a imaginary value

Thus the solution is h = 8

Thus the height of container is 8 feet

8 0

3 years ago

A woman store sells the following categories of clothing for the following prices Blouse :¢14 each, skirt:¢16 each, Dress :¢25 e

eimsori [14]

Hello! What currency is this question in?

3 0

2 years ago

Point P is the center of the circle below. What is the exact area

Ber [7]

Answer:

192π unit²

Step-by-step explanation:

Given that :

Radius = 24

Area of circle = πr²

Area = π*24²

Area = 576π in²

The Shaded area is 120°

Entire Circumference = 360°

Hence, shaded area = 120°/ 360° = 1/ 3 of the area

1/3 * 576π in²

= 192π unit²

5 0

2 years ago