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3 years ago

12

Find the value of x. If necessary, round your answer to the nearest tenth. O is the center of the circle.

1 answer:

hjlf3 years ago

6 0

Answer:

x = 9.8

Step-by-step explanation:

(please refer to attached)

after labeling the picture with all the known information, we can see that

OF = OR = Radius of the circle -----(eq 1)

Consider triangle OFP, by Pythagorean theorem,

OF² = PF²+OP²

r² = 11.5² + 11²

r² = 253.25 -----(eq 2)

Consider triangle ORQ, by Pythagorean theorem,

OR² = RQ²+OQ²

r² = 12.5² + x²

r² = 156.25 + x² ----(eq 3)

equating (eq 2) and (eq 3)

253.25 = 156.25 + x²

x² = 253.25 - 156.25

x² = 97

x = √97

x = 9.8 (nearest tenth)

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How do you simplify expressions with rational exponents

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Answer:

Step-by-step explanation:

Simplify expression with rational exponents can look like a huge thing when you first see them with those fractions sitting up there in the exponent but let's remember our properties for dealing with exponents. We can apply those with fractions as well.

Examples

(a) $(p^4)^{\dfrac{3}{2}}$

From above, we have a power to a power, so, we can think of multiplying the exponents.

i.e.

$(p^{^ {\dfrac{4}{1}}})^{\dfrac{3}{2}}$

$(p^{^ {\dfrac{12}{2}}})$

Let's recall that when we are dealing with exponents that are fractions, we can simplify them just like normal fractions.

SO;

$(p^{^ {\dfrac{12}{2}}})$

$= (p^{ 6})$

Let's take a look at another example

$\Bigg (27x^{^\Big{6}} \Bigg) ^{{\dfrac{5}{3}}}$

Here, we apply the $\dfrac{5}{3}$ to both 27 and $x^6$

$= \Bigg (27^{{\dfrac{5}{3}}} \times x^\Big{\dfrac{6}{1}\times {{\dfrac{5}{3}}} }\Bigg)$

$= \Bigg (27^{{\dfrac{5}{3}}} \times x^\Big{\dfrac{2}{1}\times {{\dfrac{5}{1}}} }\Bigg)$

Let us recall that in the rational exponent, the denominator is the root and the numerator is the exponent of such a particular number.

∴

$= \Bigg (\sqrt[3]{27}^{5} \times x^{10} }\Bigg)$

$= \Bigg (3^{5} \times x^{10} }\Bigg)$

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8 0

3 years ago

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Answer:

There is a 20% probablity that the marble will be green :)

Step-by-step explanation:

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3 years ago

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Answer:

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By-

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3 years ago

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jarptica [38.1K]

Answer:

See below.

Step-by-step explanation:

a.

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