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1 year ago

Which of the following is equal to the fraction below?

Mathematics

2 answers:

Nesterboy [21]1 year ago

7 0

<h3>Answer: Choice B</h3>

Reason:

We apply the exponent 8 to each term inside. Think of it like the distribution rule in a way.

The rule is $\displaystyle \left(\frac{a}{b}\right)^c = \frac{a^c}{b^{c}}$

So $\displaystyle \left(\frac{5}{9}\right)^8 = \frac{5^8}{9^{8}}$

The reason this works is because we have 8 copies of (5/9), so we'll have 8 copies of "5" in the numerator multiplied together. Also, we'll have 8 copies of "9" in the denominator multiplied together.

S_A_V [24]1 year ago

7 0

Answer:

(5/9)^8 = 5^8/9^8

answer; B

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The fare for a taxi cab is $2.50 per passenger and $0.75 for each mile. A group of friends has $22.00

xeze [42]

For this case we have to:

x: Let the variable representing the number of people to travel in the group

y: Let the variable representing the number of miles traveled.

If friends only have $22 then we have the following inequality:

$2.50x + 0.75y \leq22$

Now, if there are three people in the group we have that $x = 3.$

$2.50 (3) + 0.75y \leq22\\7.5 + 0.75y \leq22\\0.75y \leq22-7.5\\0.75y \leq14.5\\y\leq \frac {14.5} {0.75}\\y\leq19.33$

The taxi can travel a maximum of 19.33 miles.

On the other hand, if the group wants to travel 10 miles then we have to y = 10.

$2.50x + 0.75 (10) \leq22\\2.50x + 7.5 \leq22\\2.50x \leq22-7.5\\2.50x \leq14.5\\x\leq \frac {14.5} {2.50}\\x \leq5.8$

Thus, they could travel a maximum of 5 people.

ANswer:

$2.50x + 0.75y \leq22$

Traveling 3 people, the taxi can travel a maximum of 19.33 miles

Traveling 10 miles, a maximum of 5 people can travel

7 0

3 years ago

A coordinate plane. Which expression could help you find the distance between (10, 4) and (–6, 4)?

nirvana33 [79]

Answer:

d=16

Step-by-step explanation:

d: distance (10,4),(-6,4)

d=√(x2-x1)^2+(y2-y1)^2

d=√(-6-10)^2+(4-4)^2

d=√16^2

d=16

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3 years ago

Select all the correct answers.

Vlad1618 [11]

Answer:

The measure of reference angle is $30^{\circ}$ .
$\cos \theta=\frac{\sqrt{3}}{2}$

Step-by-step explanation:

Converting $\theta$ to degrees,

$\theta=\left(\frac{11\pi}{6} \right) \left(\frac{180}{\pi} \right)=330^{\circ}$

This means $\theta$ lies in Quadrant 4, and thus its reference angle is $360^{\circ}-330^{\circ}=\boxed{30^{\circ}}$

Since $\theta$ lies in the fourth quadrant, $\sin \theta$ and $\tan \theta$ are negative.

Since $\theta$ lies in the fourth quadrant, $\cos \theta$ is positive, and is equal to $\cos (30^{\circ})=\boxed{\frac{\sqrt{3}}{2}}$

3 0

2 years ago

What is the explicit rule for the geometric sequence? 4.05,1.35,0.45,0.15,...

Anastaziya [24]

Step-by-step explanation:

Since the above sequence is a geometric sequence

For an nth term in a geometric sequence

That's

$A(n) = a( {r})^{n - 1}$

where

r is the common ratio

a is the first term

n is the number of terms

From the question

a = 4.05

r = 1.35 / 4.05 = 0.33

Substitute the values into the above formula

We have

$A(n) = 4.05( {0.33})^{n - 1}$

Hope this helps you

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3 years ago

A water tank has a capacity of 6.25 kilolitres.

Troyanec [42]

Whenever you're dealing with units of measure,
the prefix "kilo..." always means " 1,000 ".

6.25 kiloliters = (6.25) x (1,000 liters) = <u>6,250 liters</u> .

3 0

3 years ago