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2 years ago

Simplify the expression. Write answer using only positive exponents. (1/3a^3)^-4

Mathematics

2 answers:

Fantom [35]2 years ago

8 0

Answer:

81/a^16

Step-by-step explanation:

(1/3a^3)^-4

1/3^-4a^-16

3^4 x 1/a^16

81/a^16

Artemon [7]2 years ago

3 0

Answer:

81/a^12

Step-by-step explanation:

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Four out of 32 students in Mr. Lee’s class speak 3 languages. Which decimal represents the number of students who speak 3 langua

viva [34]

Answer:

.125

Step-by-step explanation:

4 is one-eighth (1/8) of 32, which would be represented by the decimal .125 or 0.125

4 0

2 years ago

Jesse is playing a game with a number cube with faces numbered 1 through 6. What is the probability of rolling a number that is

lana [24]

Answer:

The probability of rolling a number that is even and a multiple of 3 is $\frac{1}{6}$

Step-by-step explanation:

The total possible outcomes of cube = { 1, 2, 3 , 4 , 5 , 6}

Now, let E: Event of getting an even number and a multiple of 3

So, out of all the outcomes, {6) is the ONLY possible favorable outcome.

$\textrm{P(E)} =\frac{\textrm{Number of favorable outcomes }}{\textrm{Total number of outcomes}}$

or, $P(E) = \frac{1}{6}$

Hence, the probability of rolling a number that is even and a multiple of 3 is $\frac{1}{6}$

8 0

2 years ago

Write an equation of a circle that has the center at the origin and goes through (-3,-6)

dexar [7]

Answer:

$x^{2} +y^{2} = 45$

Step-by-step explanation:

General Equation of circle is

$(x-x_1)^{2} +(y-y_1)^{2} = r^{2}$ ----------- (1)

Here

$(x_1, y_1)= (0, 0)$

Radius r is distance from origin (x1, y1) to point (x2, y2)=(-3, -6)

$r=\sqrt{(x_2-x_1)^{2} + (y_2-y_1)^{2} }$

$r= \sqrt{(-3-0)^{2} + (-6-0)^{2} }$

$r= \sqrt{9+36}$

$r=\sqrt{45}$

Substituting values in equation (1)

$(x-0)^{2} +(y-0)^{2} =( \sqrt{45})^{2}$

$x^{2} +y^{2} = 45$

6 0

2 years ago

If f(x)=3^x+10x and g(x)=4x-2, find (f+g)(x)

Vikentia [17]

Hi there!

First we need to remember the following.
$(f + g)(x) = f(x) + g(x)$

Now substitute both of the formulas.
$(f + g)(x) = ({3}^{x} + 10x)+ (4x - 2)$

Work out the parenthesis.
$(f + g)(x) = {3}^{x} + 10x + 4x - 2$

And finally collect terms.
$(f + g)(x) = {3}^{x} + 14x - 2$

~ Hope this helps you!

3 0

2 years ago

Read 2 more answers

A farmer plans to fence a rectangular corral. The diagonal distance from one corner of the corral to the opposite corner is five

garik1379 [7]

Answer:

Length of diagonal is 7.3 yards.

Step-by-step explanation:

Given: The diagonal distance from one corner of the corral to the opposite corner is five yards longer than the width of the corral. The length of the corral is three times the width.

To find: The length of the diagonal of the corral.

Solution: Let the width of the rectangular garden be <em>x</em> yards.

So, the length of the diagonal is $x+5$