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2 years ago

A right-angled triangle has sides which are 5 inches and 12 inches. How long is the triangle's hypotenuse?

Mathematics

1 answer:

Andrew [12]2 years ago

4 0

Answer:

13 inches

Step-by-step explanation:

Use the Pythagorean Theorem:

a^2 + b^2 = c^2

(5)^2 + (12)^2 = c^2

c^2 = 169 in^2

c = 13 inches

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Use the Quotient Property to Simplify Square Roots Number 129

Inessa05 [86]

Using the quotient property we would have

$\begin{gathered} \sqrt{\frac{75r^9}{8^8}}=\frac{\sqrt{75r^9}}{\sqrt{8^8}} \\ \end{gathered}$

This follows the rule

$\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$

From the simplified expression as shown above

$\frac{\sqrt{75r^9}}{\sqrt{8^8}}=\frac{\sqrt{3\times25\times r^9}}{\sqrt{(2^3)^8}}$

Thus;

$\frac{\sqrt{3\times25r^9}}{\sqrt{(2^3)^8}}=\frac{\sqrt{25}\times\sqrt{3}\times\sqrt{r^9}}{\sqrt{2^{^3\times8}}}=\frac{5\sqrt{3r^9}}{\sqrt{2^{24}}}$

Therefore

$\begin{gathered} Using\text{ fraction index law we could simplify the denominator} \\ \frac{5\sqrt{3r^9}}{2^{\frac{24}{2}}}=\frac{5\sqrt{3r^9}}{2^{12}} \end{gathered}$

We can not simplify the 3 and the r raised to power of 9 as their power is not even, hence the final answer is given below

$\frac{5\sqrt{3r^9}}{2^{12}}=\frac{5\sqrt{3r^9}}{4096}$

The final answer is :

$\frac{5\sqrt{3r^9}}{4096}$

8 0

1 year ago

Nancy and Karen went on a trip to the mountain. Nancy started her trip 30 minutes later than Karen. They started from the same p

Katyanochek1 [597]

Distance = (rate)(time)
In this problem, note that both girls traveled the same distance.

Karens distance = r * 1.5 hrs we dont know her rate
Nancy distance = 50 * 1 hr we know she started 30 min later
but arrived at the same time

since the distances are equal
r*1.5 = 50 * 1 all you have to do is solve for r

1.5r = 50
r = 50/1.5
r = 33 1/3 miles per hour

3 0

3 years ago

A homeowner is building a circular fire pit in his backyard. He plans to outline the pit with bricks and cover the space inside

mash [69]

Answer:

------------feet--------

9.428571429 feet

9.4 feet

-----------------area--------

7.071428571 ft^2

7 ft^2

Step-by-step explanation:

tell me if i got it right

braniest?

4 0

3 years ago

A new movie came out in the theaters last weekend on Friday 3185 people saw the film on Saturday only 1294 people solid so how m

mote1985 [20]

Answer:

1891 people saw it more on Friday than Saturday

Step-by-step explanation:

3185-1294=1891

all you have to do is subtract

7 0

3 years ago

A submarine is exploring the Pacific Ocean. At 502.5 feet below sea level, the water temperature is 63 1/4 °F. The submarine div

Free_Kalibri [48]

Answer:

Step-by-step explanation:

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4 years ago