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2 years ago

If two solids are similar and have a linear ratio of 2:5, what is the ratio of the areas?

Mathematics

1 answer:

masya89 [10]2 years ago

4 0

Answer:

4 : 25

Step-by-step explanation:

given 2 similar figures with linear ratio a : b , then

ratio of areas = a² : b²

here the linear ratio = 2 : 5 , then

area ratio = 2² : 5² = 4 : 25

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A fisherman traveled in a boat from point N upstream. After having traveled 6 km, he stopped rowing and 2 hour 40 min after firs

Nat2105 [25]

Answer:

The speed of the river's current is 4.5 km/hr.

Step-by-step explanation:

Given : A fisherman traveled in a boat from point N upstream.

After having traveled 6 km, he stopped rowing and 2 hour 40 min after first leaving N, he was brought back to N by the current.

Knowing that the speed of the boat in still water is 9 km/hour

To find : The speed of the river’s current.

Solution :

Let the speed of current = x km/h

Speed of boat = 9 km/h

Thus, the speed in upstream = (9 - x) km/h

Also, the speed in downstream = x km/h (because the boat is stationary in downstream)

Total distance = 6 km ( from N to the point he reached )

Total time = 2 hours 40 minutes

$\text{2 hours 40 minutes}=2\frac{40}{60}=2 \frac{2}{3} \\\\\text{2 hours 40 minutes}=\frac{8}{3} \text{ hours}$

We know, $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$

According to the question,

$\frac{6}{9-x}+\frac{6}{x}=\frac{8}{3}$

Taking LCM and 6 common

$6[\frac{x+9-x}{(9-x)x}]=\frac{8}{3}$

Take 6 to another side,

$\frac{9}{9x-x^2}=\frac{8}{3\times 6}$

Cross multiply,

$9\times 18=8\times(9x-x^2)$

$162=72x-8x^2$

Taking 4 common and cancel out

$4x^2-36x+81=0$

Solve quadratic equation by middle term split,

$4x^2-18x-18x+81=0$

$2x(2x-9)-9(2x-9)=0$

$(2x-9)(2x-9)=0$

$\Rightarrow 2x-9=0$

$\Rightarrow x=\frac{9}{2}=4.5$

Therefore, The speed of the river's current is 4.5 km/hr.

6 0

3 years ago

How many solutions does a independent system of equations have?

Degger [83]

Answer:

one solution

An independent system of equations has exactly one solution (x,y) . An inconsistent system has no solution, and a dependent system has an infinite number of solutions.

Step-by-step explanation:

8 0

3 years ago

50(b+5) - 68 + 23 HELLPPP

lbvjy [14]

Answer:

50b+205

Step-by-step explanation:

Yes sir

6 0

3 years ago

Read 2 more answers

Rita makes and sells necklaces. The materials to make each necklace cost $2.75. Last week she made 8 necklaces and wants to make

Tresset [83]

Answer:

The error she made was that she was adding x and 2.75. She should subtract 2.75 from x.

Another mistake that she made was that she sold each for $7 assuming that she would make a profit of 78, but she should see each necklace for $12.5 so that she could make a profit of $78.

Step-by-step explanation:

The error she made was that she was adding x and 2.75.

She should write the equation as 8 (x - 2.75) = 78; as she spends $2.75 to make a necklace.

By using the correct equation: 8 (x - 2.75) = 78

=> 8x - 22 = 78

=> 8x = 78 + 22

=> 8x = 100

=> x = 100/8

=> x = 12.5

Another mistake that she made was that she sold each for $7 assuming that she would make a profit of 78, but she should see each necklace for $12.5 so that she could make a profit of $78.

Hope this helps you.

3 0

3 years ago

Use the Law of Sines to solve for x. Round to the nearest whole number.

bagirrra123 [75]

Answer:

12.94

Step-by-step explanation:

By the law of sines:

x / sin(35) = 7.9 / sin70

x = 7.9 * sin(70)/sin(35)

= 7.9 * 0.9397 / 0.5736

= 12.94

6 0

3 years ago