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love history [14]
3 years ago
11

Find the exact length of the third side.

Mathematics
2 answers:
KATRIN_1 [288]3 years ago
7 0

Answer:

The third side is sqrt(5)

Step-by-step explanation:

This is a right triangle so we can use the Pythagorean theorem

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

We know the legs are 1 and 2 and we are looking for the hypotenuse.

1^2+2^2 = c^2

1+4 = c^2

5 =c^2

Take the square root of each side

sqrt(5) = sqrt(c^2)

sqrt(5) =c

The third side is sqrt(5)

adell [148]3 years ago
6 0

Answer:

\sqrt{5} or 2.236

Step-by-step explanation:

The pythagorem theorm states that side 1^2 + side^2 = hypotenuse^2

2^2 + 1^2 = h^2

4+1 = h^2

5 = h^2

\sqrt{5} = \sqrt{h^{2} }

\sqrt{5} =h

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X over 2 - x over 3 = 4
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 x would equal 24 
24/2 - 24/3 = 4 
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Which number is composite<br> 5,2,9,11
horrorfan [7]

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9 number is composite is answer

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I hope this is helpful!

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3 years ago
Jane spent 3 hours exploring a mountain with a dirt bike. First, she rode 55 miles uphill. After she reached the peak she rode f
Neko [114]

Answer:

Her speed on the summit was 35 mph.

Step-by-step explanation:

Her speed on the summit was "x" mph while her speed while climbing was "x - 10" mph. The distance she rode uphill was 55 miles and on the summit it was 28 miles. The total time she explored the mountain was 3 hours. Therefore:

time uphill = distance uphill / speed uphill = 55 / (x - 10)

time summit = distance summit / speed summit = 28 / x

total time = time uphill + time summit

3 = [55 / (x - 10)] + 28 / x

3 = [55*x + 28*(x - 10)]/[x*(x - 10)]

3*x*(x - 10) = 55*x + 28*x - 280

3x² - 30*x = 83*x - 280

3x²  - 113*x + 280 = 0

x1 = {-(-113) + sqrt[(-113)² - 4*(3)*(280)]}/(2*3) = 35 mph

x2 = {-(-113) - sqrt[(-113)² - 4*(3)*(280)]}/(2*3) = 2.67 mph

Since her speed on the uphill couldn't be negative the speed on the summit can only be 35 mph.

6 0
3 years ago
A quality control engineer is testing the battery life of a new smartphone. The company is advertising that the
DIA [1.3K]

The question requires stating the Null and Alternative hypothesis for the scenario described :

Answer:

H0 : μ = 24

H1 : μ < 24

Step-by-step explanation:

The claim or hypothesis to be tested in a statistical problem or analysis is the alternative hypothesis. This is usually the opposite of the Null hypothesis which is the usually the initial truth until there is significant evidence provided using statistical test to prove otherwise.

The null hypothesis, H0 in the scenario above is :

H0 : μ = 24 ( average battery life is 24 hours)

The alternative hypothesis is the claim, that is. The mean battery life not up to 24 hours ;

H1 : μ < 24

4 0
2 years ago
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