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tekilochka [14]
3 years ago
14

What is the length of the hypotenuse? If necessary, round to the nearest tenth.

Mathematics
2 answers:
worty [1.4K]3 years ago
7 0

Answer:

The length of the hypotenuse is 9.4

Step-by-step explanation:

The Pythagorean theorem states a^2 + b^2 = c^2. So, we can do8.4^2 + 4.3^2= 89.05. Take the square root of that, and you get 9.4.

soldier1979 [14.2K]3 years ago
6 0

<u>Answer:</u>

  • c = 9.4

<u>Step-by-step explanation:</u>

<u>Let's find 'c' using Pythagoras theorem.</u>

  • => c² = 8.4² + 4.3²
  • => c² = 70.56 + 18.49
  • => c² = 89.05
  • => c = √89.05
  • => c = 9.437 = 9.4 (Estimated)

Hoped this helped.

BrainiacUser1357

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Answer:

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Step-by-step explanation:

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3 years ago
Barbara made a bad investment. Rather than earning interest, her money is decreasing in value by 11% each week! After just one w
pochemuha

Answer: She started with $160.

It will take 6 weeks before she has less than half of what she originally invested.

Step-by-step explanation:

If her money is decreasing in value by 11% each week, it means that the rate at which it is decreasing is exponential.

We would apply the formula for exponential decay which is expressed as

A = P(1 - r)^t

Where

A represents the value of the investment after t weeks.

t represents the number of weeks.

P represents the initial value of the investment.

r represents rate of depreciation.

From the information given,

A = $142.40

r = 11% = 11/100 = 0.11

t = 1

Therefore

142.40 = P(1 - 0.11)^1

142.40 = P(0.89)

P = 142.4/0.89

P = 160

For her to have half of what she invested originally, then

80 = 160(0.89)^t

80/160 = (0.89)^t

0.5 = (0.89)^t

Taking log of both sides to base 10

Log 0.5 = log0.89^t = tlog0.89

- 0.3010 = - 0.051t

t = - 0.3010/- 0.051

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3 years ago
An observer on top of a 50-foot tall lighthouse sees a boat at a 7° angle of depression. To the nearest foot, how far is the boa
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Answer:

407.22 foot is the boat from the base of the lighthouse

Step-by-step explanation:

Given the statement: An observer on top of a 50-foot tall lighthouse sees a boat at a 7° angle of depression.

Let x foot be the distance of the object(boat) from the base of the lighthouse

Angle of depression = 7^{\circ}

\angle CAB = \angle DCA = 7^{\circ}       [Alternate angle]

In triangle CAB:

To find AB = x foot.

Using tangent ratio:

\tan (\theta) = \frac{Opposite side}{Adjacent Base}

\tan (\angle CAB) = \frac{BC}{AB}

Here, BC = 50 foot and \angle CAB =7^{\circ}

then;

\tan (7^{\circ}) = \frac{50}{x}

or

x = \frac{50}{\tan 7^{\circ}}

x = \frac{50}{0.1227845609}

Simplify:

AB = x = 407.217321 foot

Therefore, the boat from the base of the light house is, 407.22'





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3 years ago
A scientist needs 10 L of a solution that is 60% acid. She has a 50% acid solution and a 90% acid solution she can mix together
dybincka [34]

Allegation is a method to find the ratio in which two or more indignant are mixed to produce a mixture or solution.

The equation represents the total liters of acid that are needed is,

0.5x+0.9y=6

Thus the option 3 is the correct option.

<h3>What is allegation?</h3>

Allegation is a method to find the ratio in which two or more indignant are mixed to produce a mixture or solution.

Given information-

A scientist needs 10 L of a solution that is 60% acid.

The percentage of two acid solution are 50% and 90%.

Variable<em> x</em><em> </em>represent the number of liters of the 50% solution.

Variable<em> y </em>represent the number of liters of the 90% solution.

Quantity of acid from 50% solution is 0.5x liters, and quantity of acid from 90% solution is 0.9x liters.

As the scientist needs 10 L of a solution that is 60% acid. Therefore the quantity of acid in 60 percent acid solution is,

a=10\times\dfrac{60}{100} \\a=6

Thus 6 liters of acid required by the scientist. As to get the 6 liters of acid from 50% and 90 percent solution, we need to add the amount of acid in these solutions.Thus,

0.5x+0.9y=6

This is the required equation.

Hence the equation represents the total liters of acid that are needed is,

0.5x+0.9y=6

Thus the option 3 is the correct option.

Learn more about the mixture and allegation  here;

brainly.com/question/24372098

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2 years ago
Why is it necessary to learn how to factor if you can just use the quadratic formula to solve quadratic equations?
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