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2 years ago

How can I express this as a single power with positive exponents?

Mathematics

1 answer:

Tamiku [17]2 years ago

3 0

Answer:

5^1

Step-by-step explanation:

$\sqrt{5} =5^{\frac{1}{2} }$ (law of indices - fractional powers)

after converting all the numbers to this form:

$\frac{5^{{\frac{2}{3} } } * 5^{\frac{1}{2} } }{5^{\frac{1}{6} } } \\$

combine using law of indices:

5^(2/3+1/2-1/6) = 5^1

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3 years ago

Express 0.032 as a fraction in lowest terms

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Step-by-step explanation:

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2 years ago

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For the following right triangle, find the side length of x. round your answer to the nearest hundredth.

tatyana61 [14]

Answer:

14.87 units

Step-by-step explanation:

The sides of all right triangles share the same relationship known as the Pythagorean Theorem a² + b² = c². Substitute the lengths of the triangle into the theorem and solve for the unknown side. Since the problem does have an attached a picture, assume that a = 10, b = 11, and c = x.

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2 years ago

For each of the following, state the equation of a perpendicular line that passes through (0, 0). Then using the slope of the ne

SVEN [57.7K]

Answer:

The answer is below

Step-by-step explanation:

a) y=3x-1

The standard equation of a line is given by:

y = mx + c

Where m is the slope of the line and c is the intercept on the y axis.

Given that y=3x-1, comparing with the standard equation of a line, the slope (m) = 3, Two lines with slope a and b are perpendicular if the product of their slope is -1 i.e. ab = -1. Let the line perpendicular to y=3x-1 be d, to get the slope of the perpendicular line, we use:

3 × d = -1

d = -1/3

To find the equation of the perpendicular line passing through (0,0), we use:

$y-y_1=d(x-x_1)\\d\ is\ the \ slope:\\y-0=-\frac{1}{3} (x-0)\\y=-\frac{1}{3}x$

To find x if the point P(x, 4) lies on the new line, insert y = 4 and find x:

$y=-\frac{1}{3}x\\ 4=-\frac{1}{3}x\\-x=12\\x=-12$

b) y=1/4 x+2

Given that y=1/4 x+2, comparing with the standard equation of a line, the slope (m) = 1/4. Let the line perpendicular to y=1/4 x+2 be f, to get the slope of the perpendicular line, we use:

1/4 × f = -1

f = -4

To find the equation of the perpendicular line passing through (0,0), we use:

$y-y_1=f(x-x_1)\\f\ is\ the \ slope:\\y-0=-4 (x-0)\\y=-4x$