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hram777 [196]
3 years ago
15

The longer leg of a right triangle is 4cm longer than the shorter leg. the hypotenuse is 8cm longer than the shorter leg. find t

he side lengths of the triangle
Mathematics
1 answer:
Alexeev081 [22]3 years ago
8 0
Longer leg = x + 4

Shorter leg = x

Hypotenuse = x + 8


Using Pythagorean Theorem:

a^2 + b^2 = c^2

(x + 4)^2 + x^2 = (x + 8)^2

x^2 + 8x + 16 + x^2 = x^2 + 16x + 64

2x^2 + 8x + 16 = x^2 + 16x + 64

2x^2 +8x = x^2 + 16x + 48

2x^2 - 8x = x^2 + 48

x^2 - 8x = 48

x^2 - 8x - 48 = 0

You can complete the square from here or use the quadratic formula.

Completing the square:

x^2 - 8x = 48

x^2 - 8x + (-8/2)^2 = 48 + (-8/2)^2

x^2 - 8x + 16 = 48 + 16

(x - 4)(x - 4) = 64 or (x - 4)^2 = 64

x - 4 = +√64 OR x - 4 = -√64

x - 4 = +8 OR x - 4 = -8

x = 12 OR x = -4

However, you can't use negative 4 as a length because your length needs to be a positive.

So x will be 12.


Shorter leg: 12

Longer leg: 12 + 4

Hypotenuse: 12 + 8

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Answer:

$9,979,032,100 or $9.979 billion

Step-by-step explanation:

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All of the calculations bellow assume that the volume of the bills would not be an issue and only concerns weight.

1 pound is equivalent to approximately 453.59237 grams.

The weight in grams that the Big Falcon Rocket can carry is:

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Since each bill weighs 1 gram, the number of bills it could carry, rounded to nearest whole bill is 99,790,321. The total amount it could carry is:

A=99,790,321*\$100=\$9,979,032,100

4 0
3 years ago
What is the anwer of 40+678​
dsp73

Answer:

718

Step-by-step explanation:

just add the two numbers

6 0
2 years ago
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Aleena has a savings account that gives 5% annual interest. She deposits $200 that she received on her birthday. Write an equati
ANTONII [103]

Answer:the equation is 200 + 10x

Step-by-step explanation:

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal or initial amount deposited into the account.

R represents interest rate on the principal

T represents time in years

I = interest after t years

From the information given

T = x years

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R = 5%

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3 years ago
A couple quick algebra 1 questions for 50 points!
kkurt [141]

Answer:

Question 6) Neither (Not an inverse variation)

Question 7) Inverse variation

Question 8) Inverse variation

Step-by-step explanation:

These are the two formulas we need to know prior to solving the question.

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Inverse variation: c times 1/x --> c/x

- Here, c is the constant

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This is neither. It is not in the form of a direct, or inverse variation, so it does not belong in any category.

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This equation is an inverse variation.

xy = 14

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14 is the constant, and the format is the same as for an inverse variation.

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This equation is an inverse variation.

yx = -8

y = -8/x

-8 is the constant, and the format is the same as for an inverse variation.

So we can conclude that questions 7 and 8 is an inverse variations, while question 6 isn't.

6 0
1 year ago
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Step-by-step explanation:

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So the equation in y int form is

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This when convert to stardard form is

x + y = 5

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