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crimeas [40]
1 year ago
9

Find the value of x in a triangle . If the hypotenuse of the triangle is 10 , the opposite is x+2 and the adjacent is x.​

Mathematics
1 answer:
Sauron [17]1 year ago
8 0

Answer:

x = 6

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

x² + (x + 2)² = 10² ← expand parenthesis on left side and simplify

x² + x² + 4x + 4 = 100 ( subtract 100 from both sides )

2x² + 4x - 96 = 0 ( divide through by 2 )

x² + 2x - 48 = 0

(x + 8)(x - 6) = 0 ← in factored form

equate each factor to zero and solve for x

x + 8 = 0 ⇒ x = - 8

x - 6 = 0 ⇒ x = 6

however, x > 0 , then x = 6

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2 years ago
Please help can you also explain how you got it please
miss Akunina [59]

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Step-by-step explanation:

-14 + 2x + 3 = 4x - 13 - 7x

We can first add the numbers and coefficients on either side:

2x - 11 = -3x - 13

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Lastly, we can divide both sides by 5

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4 0
3 years ago
Read 2 more answers
Pls help so I did tournament with my friend the placement is 1st-1250th and we got top 27% what does that mean-
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Step-by-step explanation:

Hope this helps! Have a great day

6 0
3 years ago
A population of bacteria is initially 6000. After three hours the population is 3000. If this rate of decay continues, find the
serious [3.7K]

Answer:

The equation is A=6000e^{-0.23t}  at a rate of -23%.

Step-by-step explanation:

Decay can be represented by the equation A=A_0e^{rt}. We can find the rate at which it decays by using t=3 hours and A=3000. This means A_0=6000 in this context.

A=A_0e^{rt}\\3000=6000e^{r(3)}

0.5=e^{(24.5)r}

After substituting, we divided by 6000 to each side to get 0.5 on the left. Now to solve for r, we will take the natural log of both sides and use log rules to isolate r.

ln 0.5=ln e^{(3)r}\\ln 0.5=3r (ln e)\\\frac{ln0.5}{3} =r

We know lne=1 so we were able to cancel it out and divide both sides by 3.

We solve with a calculator \frac{ln0.5}{3} =r\\-0.23=r

We change -0.23 into a percent by multiplying by 100 to get -23% as the rate.

The equation is A=6000e^{-0.23t}


5 0
3 years ago
The population of Oak Forest is increasing at a rate of 4% per year. If the population is 74,145 today, what will it be in three
Shtirlitz [24]

Answer:

83,403

Step-by-step explanation: Take 74,145 and multiply it by 4%. Then take that number and add it to the 74,145 and that'll give you year one. For year 2 you'll take your total from year 1 and multiply it by the 4% growth rate then you'll add the 4% to what your ending from year 1 and that'll give you your total growth after 2 years. Then you'll take your ending total from year 2 and multiply it by 4% and then you'll add that 4% to the total end from year 2 and that'll give you your total growth of 4% every year for 3 consecutive years.

Hope this helps!

4 0
3 years ago
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