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geniusboy [140]
4 years ago
5

Which expression(s) are equivalent to (5^1/8•5^3/8)^3

Mathematics
2 answers:
german4 years ago
7 0

Answer:

The answer is the first and third option.

Marina CMI [18]4 years ago
6 0

Answer:

\sqrt{5^3}

Step-by-step explanation:

  1. To reduce the expression, we should start looking inside the parenthesis.
  2. Let's look at (5^{\frac{1}{8}}\times5^{\frac{3}{8}}): there is a power property ("Power of a product property ") that says that when the bases of the products are equal,  the following stands: (5^{\frac{1}{8}}\times5^{\frac{3}{8}})=5^{(\frac{1}{8}+\frac{3}{8})} =5^{(\frac{4}{8})}=5^{(\frac{1}{2})}.
  3. Now, we have to look at the resulting expression: (5^{\frac{1}{2}})^3. Because of the "Power of a power property", we can reduce this into 5^{\frac{3}{2}} (just by multiplying the powers).
  4. The last expression is equivalent to \sqrt{5^3}, because when any number is rise at a certain fraction, the numerator of the fraction equals the  power of the number, and the numerator of the fractiontells us the root index of the number (this means that, if you have a number "a" risen at a power "x/y" you can express it in two ways: a^{\frac{x}{y}} or \sqrt[y]{a^x})
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timurjin [86]
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8 0
4 years ago
6. The angle of elevation from a small boat to the top of a lighthouse is 25°. If the top of the lighthouse is 150
Anna007 [38]

Answer:

321.68feet

Step-by-step explanation:

Given the following

Top of the house above the sea level  = 150feet = opposite

Angle of elevation = 25°

Required

Distance from the boat to the base of the house(adjacent)

Using the SOH CAH TOA identity

tan theta = opp/adj

tan 25 = 150/d

d = 150/tan25

d = 150/0.4663

d = 321.68

Hence the required distance is  321.68feet

3 0
3 years ago
The angle of elevation from a boat to the top of a lighthouse is 22°. The lighthouse is 32 meters tall.
Nimfa-mama [501]
Look at this like a right triangle with a height of 32 M and the angle at the base of 22 degrees
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to find the base given the height and angle given the formula is

x = height /  tan(angle)

x = 32 / tan(22)

x = 79.2 Meters


5 0
3 years ago
Explain the relationship between the measure of the inscribed angle and measure of the arc subtends it.​
Fantom [35]

—The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.

The measure of an inscribed angle is half the measure of the intercepted arc. That is, m∠ABC=12m∠AOC. This leads to the corollary that in a circle any two inscribed angles with the same intercepted arcs are congruent.

8 0
2 years ago
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Zielflug [23.3K]

Answer:

B and E

Step-by-step explanation:

Subtract the area of the rug from the bedroom floor.

3 0
4 years ago
Read 2 more answers
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