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2 years ago

Look at this system of equations. 4x+3y=33 2x+3y=21 What is the value of x+y?

Mathematics

1 answer:

Maurinko [17]2 years ago

3 0

Answer:

x = 6

y = 3

x + y = 9

Step-by-step explanation:

(Step 1)

Isolate one of the variables in one of the equations. This will allow you to solve by substitution in the following steps.

2x + 3y = 21 <----- Original equation

3y = -2x + 21 <----- Subtract 2x from both sides

y = (-2/3)x + 7 <----- Divide all terms by 3

(Step 2)

Substitute the new equation into the untouched equation and isolate the "x" variable.

4x + 3y = 33 <----- Original equation

4x + 3((-2/3)x + 7) = 33 <------ Substitute manipulated equation

4x - 2x + 21 = 33 <------ Multiply 3 by terms in parentheses

2x + 21 = 33 <------ Subtract terms with variables

2x = 12 <----- Subtract 21 from both sides

x = 6 <----- Divide both sides by 2

(Step 3)

Plug the value of "x" into one of the equations to find the value of "y".

4x + 3y = 33 <----- Original equation

4(6) + 3y = 33 <----- Plug 6 in for "x"

24 + 3y = 33 <----- Multiply

3y = 9 <----- Subtract 24 from both sides

y = 3 <----- Divide both sides by 3

(Step 4)

Since you now know the value of both variables, you can add them together to find your final answer.

x = 6

y = 3

x + y = ?

6 + 3 = ?

9 = ?

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3 years ago

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A marketing research company needs to estimate the average total compensation of CEOs in the service industry. Data were randoml

mezya [45]

SOLUTION:

Step 1 :

In this question, we are told that a marketing research company needs to estimate the average total compensation of CEOs in the service industry.

We also have that: Data were randomly collected from 38 CEOs and the 98% confidence interval was calculated to be ($2,181,260, $5,836,180).

Then, we are asked to find the margin error for the confidence interval.

Step 2:

We need to recall that:

$\text{Higher Confidence Interval, CI}_{H\text{ = }}X\text{ + }\frac{Z\sigma}{\sqrt[]{n}}$ $\text{Lower Confidence Interval , CI}_{L\text{ }}=\text{ X - }\frac{Z\sigma}{\sqrt[]{n}}$

It means that:

$\vec{}X\text{ = }\frac{CI_{H\text{ }}+CI_L}{2}$ $\text{Margin of error, }\frac{Z\sigma}{\sqrt[]{n}\text{ }}\text{ = }\frac{CI_{H\text{ - }}CI_L}{2}$

where,

$CI_H\text{ = }$$5,836,180$\text{ }$$$$ $CI_{L\text{ }}=\text{ }2,181,260$

putting the values into the equation for the margin of error, we have that:

$\text{Margin of error,}\frac{Z\sigma}{\sqrt[]{n}\text{ }}\text{ = }\frac{5,836,180\text{ - }2,181,260\text{ }}{2}$ $\begin{gathered} =\text{ }\frac{3654920}{2} \\ =1,\text{ 827, 460} \end{gathered}$

CONCLUSION:

The margin error for the confidence interval is 1, 827, 460

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1 year ago

What are the greatest common divisors of these pairs of integers?a. 3⁷. 5³. 7³,2ⁱⁱ.3⁵.5⁹b. 11.13.17, 2⁹.3⁷.5⁵.7³c. 23³ⁱ,23ⁱ⁷d. 4

KatRina [158]

Answer:

a) 3⁵5³.

b) 1

c) 23³

d) 41·43·53

e) 1

f) 1111

Step-by-step explanation:

The greatest common divisor of two integers is the product of their common powers of primes with greatest exponent.

For example, to find gcd of 2⁵3⁴5⁸ and 3⁶5²7⁹ we first identify the common powers of primes, these are powers of 3 and powers of 5. The greatest power of 3 that divides both integers is 3⁴ and the greatest power if 5 that divides both integers is 5², then the gcd is 3⁴5².

a) The greatest common prime powers of 3⁷5³7³ and 2²3⁵5⁹ are 3⁵ and 5³ so their gcd is 3⁵5³.

b) 11·13·17 and 2⁹3⁷5⁵7³ have no common prime powers so their gcd is 1

c) The only greatest common power of 23³ and 23⁷ is 23³, so 23³ is the gcd.

d) The numbers 41·43·53 and 41·43·53 are equal. They both divide themselves (and the greatest divisor of a positive integer is itself) then the gcd is 41·43·53

e) 3³5⁷ and 2²7² have no common prime divisors, so their gcd is 1.

f) 0 is divisible by any integer, in particular, 1111 divides 0 (1111·0=0). Then 1111 is the gcd

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3 years ago

A group of 12 students goes on a school field trip, 6 are in third grade. which fraction is equivalent to 6 12

Elis [28]

The fraction which is equivalent to 6/12 is 1/2

What does a fraction mean?

In the first place, fraction is a numerical quantity or relationship where one number is expressed in terms of another.

In order to determine the equivalence of 6/12 in fraction , we need reduce 6/12 to the lowest term, since 6 is common to 6 and 12 and that 6 divided by gives 1 and 12/6 gives 2, which means that we are left 1/2

The correct fraction which is equivalent to 6/12 is 1/2

Find out more about fraction on:brainly.com/question/5243429

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Full question:

A group of 12 students goes on a school field trip, 6 are in third grade. which fraction is equivalent to 6/12?

(A) 1/3

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2 years ago

The algebraic expression for "the quotient of 73 and x" is

lyudmila [28]

Answer

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Step-by-step explanation:

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3 years ago