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Lana71 [14]
3 years ago
9

Which can be used to solved the expression (r^-4)^3

Mathematics
1 answer:
Oksana_A [137]3 years ago
3 0

Answer:

The expression is equal to 1 over 12 factors of r

Multiplying the exponents will create an equivalent expression.

Step-by-step explanation:

We are given the following in the question:

(r^-^4)^3

<h3>Properties of exponent: </h3>

(x^m)^n=x^m^n

x^-^a=\frac{1}{x^a}

Thus, we can simplify the given expression as:

(r^-^4)^3

= r^-^1^2

= \frac{1}{r^1^2}

Thus, the correct answer is:

Option 2) The expression is equal to 1 over 12 factors of r

Option 4) Multiplying the exponents will create an equivalent expression.

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Examine this system of equations. Which numbers can be multiplied by each equation so that when the two equations are added toge
WARRIOR [948]

You can use the fact that when coefficient of x variable are of equal magnitude but opposite sign, then adding them will make the coefficient 0, thus, making the x variable eliminated.

The numbers that can be multiplied by each equation so that when the two equations are added together, the x term is eliminated is given by

Option A: –10 times the first equation and 3 times the second equation

<h3>How does elimination works?</h3>

This method is actually called method of elimination to solve a system of linear equations.

We make one specific variable's coefficients of equal magnitude so that we can subtract or add the equations and eliminate that variable to make it easy to get the value of the other variable which will then help in getting the value of the first variable (if working in dual variable system).

If we have equations:

a_1x + b_1y  = c_1\\a_2x + b_2y = c_2

then, if we want to eliminate variable x, then we have to multiply equation 1 with

- \dfrac{a_2}{a_1}

which will make coefficient of x in first equation as

a_1 \times - \dfrac{a_2}{a_1} = -a_1

Then adding both equation will eliminate the variable x.

We could've skipped that -ve sign and at then end, instead of adding, we could've subtracted the equations.

<h3>What is magnitude and sign?</h3>

5 has 5 as magnitude, and sign isn't present which means its of positive (+) sign.

-5 has 5 as magnitude and sign is negative(-).

For this case, we're multiplying both the equations but the core concept or aim is same, ie, making the coefficients of equal magnitude but with opposite sign.

<h3>Using the above facts to get the numbers to multiply the equations of the given system</h3>

The given system of equations is

\dfrac{1}{5}x + \dfrac{3}{4}y = 9\\\\\dfrac{2}{3}x - \dfrac{5}{6}y = 8

Let two numbers be p,and q who multiply equation first and second respectively to make coefficient of x of equal magnitude but opposite sign.

We have

\text{Coefficient of x in first equation}= a_1 = \dfrac{1}{5}\\\\\text{Coefficient of x in second equation} = a_2 = \dfrac{2}{3}

Multiplying with p and q will give us

p\times a_1 = \dfrac{p}{5}\\\\q \times a_2 = \dfrac{2q}{3}

We need both resultant coefficient to add up to 0, or

p/5 + 2q/3 = 0\\p = -10q/3\\q = -3p/10

Now in options, we see first equation is either getting multiplied with -10, 10, or -3,3

If we put q = 3, we get p =  -10q/3=  -10

If we put q = -3, we get p = 10

If we put q = 5, we get p = -50/3

Thus only first choice is matching the correct pairs.

Thus,

The numbers that can be multiplied by each equation so that when the two equations are added together, the x term is eliminated is given by

Option A: –10 times the first equation and 3 times the second equation

Learn more about method of elimination here:

brainly.com/question/20385690

7 0
2 years ago
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Is a bachelor of finance degree ba or bs
Scrat [10]
A 4 year degree in finance is a BBA-
Bachelor's of Art.
4 0
3 years ago
The correct answer to the question *interquartile range
Vanyuwa [196]
The interquartile range (IQR) is 20

You find this by subtracting the values of Q3 and Q1
Q3 is the right most edge of the box which is 45
Q1 is the left most edge of the box which is 25

IQR = Q3 - Q1 = 45 - 25 = 20

Side Note: The median is not 45. The median is actually 40 since this is the middle line of the box, which is in between 35 and 45
7 0
3 years ago
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Writr the fractions which have been graphed on the number line. explanation also please
dexar [7]
4/10 the second one is 6/10 why because the number line goes by tens so ten is always under the fraction of the number line

8 0
3 years ago
How many repeating digits are in 0.ModifyingAbove 536 with bar? 1 2 3 4
Maksim231197 [3]

Answer:

3

Step-by-step explanation:

We want to determine the number of repeating digits in 0.\overline{536}

We can rewrite this number as: 0.\overline{536}=0.536536536536536536536...

Therefore the digits that are repeating are: 536.

Hence the number of digits repeating is 3.

The third choice is correct

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3 years ago
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