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katrin2010 [14]
3 years ago
10

Akshat lost 14 baseball cards from his card collection. He realized that he has lost 28 % of his cards. How many cards were in h

is card collection initially?
Mathematics
1 answer:
rodikova [14]3 years ago
4 0

Answer:

50 cards

Step-by-step explanation:

We can start by saying that his total card collection has x cards in it, meaning that 28% or 28/100 of his total cards, x, is equal to 14. Next, we can divide by 28/100 on both sides, and dividing is the same as multiplying by the reciprocal. The reciprocal of 28/100 is 100/28, so 14 * 100/28 is equal to 100/2, which is 50. We can say that 50 cards were in his card collection initially.

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A source of laser light sends rays AB and AC toward two opposite walls of a hall. The light rays strike the walls at points B an
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Answer:

The distance between the walls is 70 m.

Step-by-step explanation:

Given: A source of laser light is at point A on the ground between two parallel walls BE and CD . The walls are perpendicular to the ground that is

BE ⊥ ED and CD ⊥ ED

AB is a ray of light which strikes the wall on the left at point B which is 30 meters above the ground. that is BE = 30 m

AC is a ray of light which strikes the wall on the right at point C. The length of AC = 80 meters.

The ray AB makes an angle of 45 degrees with the ground that is m∠BAE = 45°

The ray AC makes an angle of 60 degrees with the ground that is m∠CAD = 60°

As shown is figure attached below.

WE have to find the distance between the walls that is Length of ED

Length of ED = EA + AD

Consider the Δ AEB,

Using trigonometric ratio,

\tan\theta=\frac{perpendicular}{base}

Here \theta=45^{\circ} , perpendicular = 30 m  and base we can find.

thus,

\tan 45^{\circ}=\frac{30}{EA}

We know \tan 45^{\circ}=1

thus, EA =  30 m

Consider the Δ AEB,

Using trigonometric ratio,

\cos\theta=\frac{base}{hypotenuse}

Here \theta=60^{\circ} , hypotenuse = 80 m  and base we can find.

thus, \cos 60^{\circ}=\frac{base}{80}

We know, \cos 60^{\circ}=\frac{1}{2}

thus, Base = 40 m

AD = 40 m

Thus, the distance between the walls that is the length of ED = 30 + 40 = 70 m

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Step-by-step explanation:

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