Kabir has three fuel containers. One has a capacity of 7 litres,
one has a capacity of 4 litres and one has a capacity of 3 litres.
The 7 litre container is full, the other two containers are empty.
None of the containers has a measurement scale.
How can Kabir transfer the fuel so that two of the containers contain
a volume of 2 litres each, and the other contains a volume of 3 litres,
vithout having to estimate?

Answers

Answer 1

The solution is, the capacity of the largest container that can fill the tanks an exact number of times is, 44 litres.

What is CGF?

In mathematics, the greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted {\displaystyle \gcd}.

here, we have,

We subtract the remainders from the amounts.

447 - 7 = 440

577 - 5 = 572

669 - 9 = 660

Now we need the GCF of 440, 572, 660

440 = 2³ × 5 × 11

572 = 2² × 11 × 13

660 = 2² × 3 × 5 × 11

GCF = 2² × 11 = 44

The greatest common factor is 44.

Answer: 44

Check:

447/44 = 10 reminder 7

577/44 = 13 remainder 5

669/44 = 15 remainder 9

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Related Questions

3x-6y=9
2y=x-3

Solve by substitution

Answers

Answer:

It is impossible, because u can say x is 5 and y is 1 or x is 9 and y is 3

I need help with this please

Answers

Answer:

b

Step-by-step explanation:

349 visitors purchased no costume. 71 visitors purchased exactly one costume. 12 visitors purchased more than one costume. Based on these results, express the probability that the next person will purchase no costume as a percent to the nearest whole number.

Answers

The probability that the next person will purchase no costume is 80%.

What is the difference between a probability and an odds?

The possibility of an event occurring can be expressed using odds and probability, but they are computed and understood in different ways.

Probability, which is stated as a number between 0 and 1 (or between 0% and 100%), is the possibility that an event will occur. By dividing the number of positive possibilities by the total number of potential outcomes, the probability of an event happening is determined.

The possibility of an event happening is expressed differently by odds, which are expressed as a ratio of the number of favourable events to the number of negative outcomes. It is possible to state odds as "odds for" or "odds against."

Now,

The total number of visitors who purchased costumes is:

71 (exactly one) + 12 (more than one) = 83

The total number of visitors who did not purchase a costume is: 349

The probability that the next person will purchase no costume is:

349 / (349 + 83) = 349 / 432 ≈ 0.8079

Hence, the probability that the next person will purchase no costume is 80%.

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Given the formula y=12/x where y is mi/hr and x is hours find the speed (y) when x is 10 hours

Answers

Answer:

1.2 mi/hr

Step-by-step explanation:

y=12/x
y=12/10
y=1.2 mi/hr

Answer:

[tex]\huge\boxed{\sf y = 1.2 \ mph}[/tex]

Step-by-step explanation:

Given equation:

[tex]\displaystyle y=\frac{12}{x}[/tex]

Given that, x = 10

So,

[tex]\displaystyle y=\frac{12}{10} \\\\y = 1.2 \ mph\\\\\rule[225]{225}{2}[/tex]

It is estimated that 0.40 percent of the callers to the Customer Service department of Dell Incorporated will receive a busy signal. What is the probability that of today's 1,000 callers at least 5 received a busy signal?

Answers

The probability that at least 5 of the callers received a busy signal is given as follows:

0.3712 = 37.12%.

What is the binomial distribution formula?

The mass probability formula, giving the probability of x successes on n trials, is given by the equation presented as follows:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are listed as follows:

n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.

The parameter values for this problem are given as follows:

n = 1000, p = 0.004.

The probability of less than 5 busy signals is:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

P(X < 5) = 0.6288.

Hence the probability of at least 5 busy signals is of:

P(X >= 5) = 1 - P(X < 5)

P(X >= 5) = 1 - 0.6288

P(X >= 5) = 0.3712.

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What are the INEQUALITIES of these?

Answers

The evaluation of the inequalities are presented as follows;

2. x ≤ -5

3. x  ≤ -14

4. x ≤ 4

5. x < -10

What is an inequality?

An  inequality is an expression or comparison of two expressions that posses different values using an inequality sign.

2. -14·x + 1 ≥ 71

-14·x + 1 - 1 ≥ 71 - 1

-14·x  ≥ 70

x ≤ 70/(-14) = -5

x ≤ -5

3. -3·x - 1 ≥ 41

-3·x - 1  + 1 ≥ 41 + 1 = 42

-3·x - 1  + 1 ≥ 42

-3·x  ≥ 42

x ≤ 42/(-3) = -14

x ≤ -14

4. (x/2) + 11 ≤ 13

(x/2) + 11  - 11 ≤ 13 - 11  = 2

x/2  ≤ 2

x ≤ 2 × 2

x ≤ 4

5. x/(10) - 6  < -7

x/(10)  - 6 < -7

x/(10) -6 + 6 < -7 + 6 = -1

x/(10) < -1

x  < -10

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The question is present in the image

Answers

The required values of exponent a, b, and c are 6, 8, and 9 respectively.

What is simplification?

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.

Here,
Given expression,
[tex][x^{24}y^{32}]^{1/4} \times (x^{-3}z^{27})^{1/5} = x^ay^bz^c[/tex]

We have to determine the value of a, b, and c in the exponents, so in order to get the solution we have to simplify the given expression.

[tex][x^{7}y^{8}] \times (x^{-1}z^{9}) = x^ay^bz^c\\x^{7 -1}y^8z^9 = x^ay^bz^c\\x^{6}y^8z^9 = x^ay^bz^c[/tex]

Comparing the exponent across the equal sign we get,
a = 6
b = 8
z = 9

Thus, the required value of exponent a, b, and c are 6, 8, and 9 respectively.

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(Plotting Ordered Pairs MC)
Which point represents the ordered pair (0, -3)?
-3
O Point D
E
O Point F
Previous Question
Point E
O Point G
-2
-1
3
29
1
O
-1
Ty
-2
?
H
G
D
LL
3
Question 1 (Not Answered) O
Next Question

Answers

A point that represents the ordered pair (0, -3) is: D. Point G.

What is an ordered pair?

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

Based on the ordered pair (0, -3), we can logically deduce that the coordinates would be located in quadrant IV as shown in the image attached below.

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is 5x=7y linear equation

Answers

Yes, 5x=7y is a linear equatiοn.

What is linear equatiοn?  

First οrder equatiοns include linear equatiοns. In the cοοrdinate system, the linear equatiοns are defined fοr lines. A linear equatiοn in οne variable is οne in which there is a hοmοgeneοus variable οf degree 1 (i.e., οnly οne variable). Multiple variables may be present in a linear equatiοn. Linear equatiοns in twο variables, fοr example, are used when a linear equatiοn cοntains twο variables.

Linear equatiοn is an algebraic equatiοn in οne οr mοre variables where the pοwer οf each variable is less than οr equal tο 1.

Fοr example,

y = mx + c , an equatiοn in this fοrm can be called as linear equatiοn.

Sο in equatiοn 5x = 7y

We can write this equatiοn as 7y = 5x + 0.

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Think a moment about factoring a polynomial by finding the GCF.

Explain the role of the GCF in factoring a polynomial.
Where is the GCF placed after factoring out the GCF?
How do you verify factoring is correct?

Answers

The role of GCF, its placement and verification has been explained below. The solution has been obtained by using the concept of Greatest Common Factor.

What is Greatest Common Factor?

The greatest common factor, or largest number, is the product of two or more numbers (GCF). The greatest number (factor) that separates them yields a natural number.

1. The GCF is a factor that all terms in a polynomial share.

For instance, if the polynomial has the form R * S + R * T, the GCF is R because both terms share the factor R.

2. The GCF is positioned in front of the remaining polynomials, outside of the parenthesis, once we have factored out the GCF.

R * S + R * T, given the prior example, is R (S + T).

3. By allocating the GCF to the polynomial enclosed in parenthesis, we can verify that our factoring is accurate.

Hence, the above stated is the role of GCF in factoring a polynomial.

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The square of the first of three consecutive integers is added to twice the sum of the second and third integers the result is 38. Find the integers.

I’m struggling to get the factors if someone could help. :)

Answers

The value of all the integers are,

4, 5, 6

or, - 8, - 7, - 6

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Let three consecutive numbers are, (x - 1) , x , (x + 1).

Hence, By given condition we get;

⇒ (x - 1)² + 2 (x + x + 1) = 38

⇒ x² - 2x + 1 + 4x + 2 = 38

⇒ x² + 2x - 35 = 0

⇒ x² + 7x - 5x - 35 = 0

⇒ x (x + 7) - 5 (x + 7) = 0

⇒ (x - 5) (x + 7) = 0

⇒ x = 5 or x = - 7

When, x = 5

All the integers are,

x - 1 = 5 - 1 = 4

x = 5

x + 1 = 5 + 1 = 6

When x = - 7

All the integers are,

x - 1 = - 7 - 1 = - 8

x = - 7

x + 1 = - 7 + 1 = - 6

Thus, The value of all the integers are,

4, 5, 6

or, - 8, - 7, - 6

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A bank is offering you a mortgage on a house that costs $250,000. The down payment is 3% of the purchase price and the closing costs are another 3%. The interest rate is 5.5% and the loan term is 30 years.
What amount of money do you need to save to purchase the home (down
payment + closing costs)?
What is the total amount the bank will be loaning you?
What do you expect your monthly payments to be?

Answers

Amount of money do you need to save to purchase the home is  $15,000. The total amount the bank will be loaning you is $235,000.  You can expect to pay around $1,332.29 per month.

Describe Down Payment?

A down payment is a payment made upfront when purchasing a large ticket item, such as a home or a car. It is a percentage of the total purchase price that the buyer pays out of their own pocket, with the remainder of the price financed through a loan.

To calculate the down payment, we need to multiply the purchase price by the percentage:

Down payment = 0.03 x $250,000 = $7,500

To calculate the closing costs, we also need to multiply the purchase price by the percentage:

Closing costs = 0.03 x $250,000 = $7,500

So the total amount of money needed to purchase the home is the sum of the down payment and the closing costs:

Total cost = $7,500 + $7,500 = $15,000

The amount the bank will be loaning you is the purchase price minus the down payment and the closing costs:

Loan amount = $250,000 - $15,000 = $235,000

To calculate the monthly payments, we need to use the formula for a fixed-rate mortgage:

M = P [ i(1 + i)ⁿ ] / [ (1 + i)ⁿ⁻¹]

where:

M = monthly payment

P = loan amount

i = monthly interest rate (5.5% / 12 = 0.0045833)

n = total number of payments (30 years x 12 months = 360)

Plugging in the numbers, we get:

M = $235,000 [ 0.0045833(1 + 0.0045833)³⁶⁰ ] / [ (1 + 0.0045833)³⁶⁰ – 1]

M ≈ $1,332.29

So you can expect to pay around $1,332.29 per month for 30 years to pay off the mortgage.

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What is the equation of a line perpendicular to y = 12
x + 3, which has an x-intercept 8 units greater than the x-intercept of y = 12
x + 3?

Answers

By analytic geometry, the equation of the line y = - (1 / 12) · x + 11 is perpendicular to the line y = 12 · x + 3.

How to derive the equation of a line perpendicular to another line

In accordance with analytic geometry, lines are described by algebraic equations of the form:

y = m · x + b

Where:

x - Independent variable.y - Dependent variable.m - Slopeb - Intercept

The relationship between the slopes of two perpendicular lines:

m · m' = - 1

First, write the original line:

y = 12 · x + 3

Second, write the slope and the intercept of the original line:

m = 12, b = 3

Third, the slope and the intercept of the perpendicular line:

m = - 1 / 12, b = 11

Fourth, write the equation of the perpendicular line:

y = - (1 / 12) · x + 11

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A city has 14200 people in a random sample of 80 people from the city 43 people say that have visited the city’s community garden which expression can you use to estimate the number of people in the city who have visited the city’s community garden

Answers

Answer:

we can estimate that about 7632 people in the city have visited the city's community garden.

Step-by-step explanation:

You can use a proportion to estimate the number of people in the city who have visited the city's community garden. The proportion is:

(Number of people in the city who have visited the community garden) / (Total number of people in the city) = (Number of people in the sample who have visited the community garden) / (Total number of people in the sample)

We can plug in the values given in the problem to get:

(x) / (14200) = (43) / (80)

To solve for x, we can cross-multiply and simplify:

80x = 14200 * 43

x = (14200 * 43) / 80

x ≈ 7632

Therefore, we can estimate that about 7632 people in the city have visited the city's community garden.

Consider the function y=z²+2x+3
Part A
What are the coordinates of the vertex of the given function? Show your work.
Part B
What is the function in vertex form? Pleaseee help!!!

Answers

Answer:

am not sure

Step-by-step explanation:

I will help you but yeh so y=20

How much would it cost to furnish a square room of 5m at N5.00 per square metre
(I need this answer before 6 march)

Answers

It would cost N125.00 to furnish a square room of 5m at N5.00 per square meter.

Describe the square meter.

A square meter is a unit of measurement that denotes the surface area of a two-dimensional object or surface that is one metre long and one meter broad. It is frequently used to determine the dimensions of rooms, structures, and other areas as well as the surface area of land or other objects. The imperial method of measurement converts one square metre into 10.764 square feet. Science, engineering, and other fields frequently utilise the square metre, a core unit of the International System of Units (SI).

The area of the room is:

Area = 5m x 5m = 25 square meters

Then, we multiply the area by the cost per square meter:

Cost = 25 square meters x N5.00 per square meter = N125.00

Hence, it would cost N125.00 to furnish a square room of 5m at N5.00 per square meter.

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[tex]\int\limits^3_2 2{x} \, dx* \frac{3x}{2}[/tex]

Answers

Answer:

We can solve this integral using the u-substitution method.

Let u = 3x, then du/dx = 3 and dx = du/3.

Substituting these values, we get:

∫2x * 2/3x dx = ∫4/3 du

Integrating, we get:

= (4/3)u + C

Substituting back u = 3x, we get:

= (4/3)(3x) + C

= 4x + C

Therefore, the solution to the integral ∫2x * 2/3x dx is 4x + C.

QUESTION 13
Consider the following argument: If virtual reality video games are perfected in the 21st century, video games will become
the dominant entertainment industry. If video games become the dominant entertainment industry, Hollywood will go
bankrupt and California will lose much of its annual revenue. So, if virtual reality video games are perfected in the 21st
century, Hollywood will go bankrupt and California will lose much of its annual revenue. What is the logical form of this
argument?
O a. Disjunctive Syllogism
O b. Affirming a disjunct
O c. Affirming the consequent
O d. Denying the antecedent
O e. Hypothetical Syllogism

Answers

Disjunctive Syllogism is the logical form of the given argument. Therefore, the correct option is option A.

What is argument?

An argument seems to be a statement or set of claims, known as premises, that seeks to assess the plausibility or acceptance of a conclusion. The logical, dialectical, and rhetorical perspectives are the three basic areas of study for arguments.

An argument in logic can be defined as a collection of propositions whereby a single one is tried to claim to follow the rest through deductively obtain reasonable that maintain truth from either the premises towards the conclusion. Disjunctive Syllogism is the logical form of the given argument.

Therefore, the correct option is option A.

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HELP!!!! LIMITED TIME PLEASE!!!!!
What is the domain of the function shown on the graph below?
(Photo of graph is added)

Select one,
(-3, -2,-1,0}
(-3,-2,2,3}
(-3,-2,-1,-0]
(-3, -2,-2,-3)

Answers

Answer:

(-3,-2,2,3}

that is the answer

Find the area of a trapezoid that is 12in. and 5in. in length and 4in. in width.

Answers

To find the area of a trapezoid, you can use the formula:

Area = (base1 + base2) * height / 2

where base1 and base2 are the lengths of the two parallel sides of the trapezoid, and height is the perpendicular distance between the two bases.

In this case, we are given that the length of the trapezoid is 12 inches and 5 inches, and the width is 4 inches. Since the width is not the height of the trapezoid, we need to find the height before we can calculate the area.

To find the height, we can use the Pythagorean theorem, since the trapezoid is a right trapezoid (i.e., one of its angles is a right angle). The height will be the shorter leg of the right triangle, and the longer leg will be the difference between the lengths of the two parallel sides:

height^2 + (base2 - base1/2)^2 = width^2

height^2 + (5-12/2)^2 = 4^2

height^2 + (-1.5)^2 = 16

height^2 = 16 + 2.25

height^2 = 18.25

height ≈ 4.27 inches (rounded to two decimal places)

Now that we have the height, we can plug in the values for the bases and height into the formula for the area:

Area = (base1 + base2) * height / 2
= (12 + 5) * 4.27 / 2
= 62.79 square inches

Therefore, the area of the trapezoid is approximately 62.79 square inches.

Numbers multiply to seven and add to -8

Answers

Answer:

-7 and -1

Step-by-step explanation:

Remember, a negative times a negative equals a positive

Three girls share R12000 in the ratio 2:3:7 calculate how much each girl will get show calculations

Answers

According to the ratio , the three girls shares are R2000,R3000 and R7000.

What is ratio?

When two numbers are compared, the ratio between them shows how often the first number contains the second. As an illustration, the ratio of oranges to lemons in a dish of fruit is 8:6 if there are 8 oranges and 6 lemons present.

Here the given total share amount is R12000.

Now the ratio for three girls is 2:3:7.

Total = 2+3+7=12

Now the share amounts are,

=> [tex]\frac{2}{12}\times 12000[/tex] = [tex]2\times1000=R2000.\\[/tex]

=> [tex]\frac{3}{12}\times=3\times1000=R3000[/tex]

=> [tex]\frac{7}{12}\times12000=7\times1000=R7000[/tex]

Hence the three girls shares are R2000,R3000 and R7000.

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The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate.
Principal $6500
Rate. 2%
Compounded. quarterly
Time. 3 years

A. Find how much money there will be in the account after the given number of years.
B. Find the interest earned.

Answers

Answer:

A. After 3 years, the amount in the account will be $6730.40.

B. The interest earned will be $230.40.

Step-by-step explanation:

x, y, z – natural numbers.
[tex] {3}^{x} + {5}^{y} + {7}^{z} [/tex] is divisible by 105.
Find the smallest possible value of x+y+z

Answers

The smallest possible value of x+y+z such that 3^x+5^y+7^z is divisible by 105 is 11.

What are Natural Numbers?

Natural numbers are a set of positive integers that are used for counting and ordering. In other words, natural numbers are the set of numbers that are used to represent the quantity of objects, such as 1, 2, 3, 4, 5, 6, and so on. Some definitions include zero as a natural number, while others define natural numbers to start from 1. In mathematics, natural numbers are denoted by the symbol "N" or "N+", and are sometimes referred to as counting numbers.

What are whole numbers?

Whole numbers are a set of non-negative integers that include all natural numbers (positive integers) and zero. Whole numbers are used to represent quantities that cannot be divided into smaller parts, such as the number of people in a room, the number of apples in a basket, or the number of books on a shelf.

In the given question,

We know that 105 is a multiple of 3, 5, and 7. Therefore, if 3^x+5^y+7^z is divisible by 105, it must also be divisible by 3, 5, and 7.

If 3^x+5^y+7^z is divisible by 3, then 3^x ≡ 0 (mod 3), which means x ≥ 1.

If 3^x+5^y+7^z is divisible by 5, then 5^y ≡ 0 (mod 5), which means y ≥ 1.

If 3^x+5^y+7^z is divisible by 7, then 7^z ≡ 0 (mod 7), which means z ≥ 1.

Therefore, we have x+y+z ≥ 3.

We also know that 105 is the smallest multiple of 3, 5, and 7. Therefore, we want to find the smallest values of x, y, and z that will make 3^x+5^y+7^z divisible by 105.

If we want 3^x+5^y+7^z to be divisible by 105, we need x, y, and z to be multiples of 4, 4, and 3, respectively.

The smallest such values are x=4, y=4, and z=3. Therefore, the smallest possible value of x+y+z is 4+4+3=11.

So, the smallest possible value of x+y+z such that 3^x+5^y+7^z is divisible by 105 is 11.

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I’ll give more points!! A
C
Find the mAB
1040
1260
B
D

Answers

Answer:I’ll give more points!! A

Step-by-step explanation:I’ll give more points!! A

C

Find the mAB

NO LINKS!!!! URGENT HELP PLEASE!!!!

Please help me with #1 and #2

Answers

Answer:

1a. Decay

1b. r = 0.43

1c. a = 35

1d. y = 6.481755

2a. Growth

2b. r = 2.23

2c. a = 225

2d. y = 340.4025

Step-to-Step Explanation:

1.

  (a)Decay

  (b) [tex]y=a(1-r)^{x}[/tex]

       r = rate of decay, a is the initial value

       1-r=0.57 = r=1-0.57 = r = 0.43

  (c) a = 35

  (d) [tex]y=35(0.57)^{3}\\\\y=35(0.185193)\\y=6.481755[/tex]

2.

   (a) Growth

   (b)[tex]y=a(1+r)^{x} \\[/tex]

        r = rate of growth, a is the initial value

         1+r=1.23 = r=1+1.23 = r = 2.23

   (c) a = 225

   (d) [tex]y=225(1.23)^{2} \\y=225(1.5129)\\y=340.4025[/tex]

Problem 1

Set the base of the exponent equal to 1+r and solve for r.

1+r = 0.57

r = 0.57-1

r = -0.43

The result is negative, which tells us we have exponential decay. Notice that b = 0.57 fits the interval 0 < b < 1.

The rate of decay is 43%

The initial value is a = 35 since this is the first value mentioned in the equation. Plugging x = 0 into the equation will lead to y = 35.

Let's now plug in x = 3

y = 35*(0.57)^x

y = 35*(0.57)^3

y = 35*0.185193

y = 6.481755

-----------------------------

Answers in bold:1a. Decay1b. 43% decay rate1c. 351d. 6.481755

======================================================

Problem 2

We'll follow similar steps as problem 1.

1+r = 1.23

r = 1.23-1

r = 0.23

The r value is positive, so we have growth this time. Notice that b = 1.23 fits the interval b > 1.

The growth rate is 23% since r = 0.23 converts to this.

The initial value is a = 225. Compare y = a(1+r)^x to y = 225(1.23)^x to see how the terms match up. If you want you can think of it like y = 225(1+0.23)^x. Plugging x = 0 into the equation will lead to y = 225.

Let's plug in x = 2.

y = 225*(1.23)^x

y = 225*(1.23)^2

y = 225*1.5129

y = 340.4025

-----------------------------

Answers in bold:2a. Growth2b. Growth rate is 23%2c. 2252d. 340.4025

Find the value of each variable proofs needed

Answers

The value of the variables are as follows:

z = 39√2y = 13√3x = 26√3

What are the values of the variables?

The value of the variables is given as follows:

sin 45° = 39/z

z = 39/sin 45°

sin 45° = 1/√2

z = 39 / 1/√2

z = 39√2

Let the height of the triangle be h;

cos 45 = h/39√2

cos 45 = 1/√2

h = 39√2 * 1/√2

h = 39

tan 60° = 39/y

tan 60° = √3

y = 39/√3

y = 13√3

sin 60° = 39/x

x = 39 / sin 60°

sin 60° = √3/2

x = 39 /√3/2

x = 26√3

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This question is from my linear algebra class:
Suppose u and w are unital orthogonal vectors. Show that || u - w || = [tex]\sqrt{2}[/tex]

Answers

Step-by-step explanation:

Since u and w are orthogonal, their dot product is 0. Thus,

u · w = 0

Using the Pythagorean Theorem,

||u - w||^2 = ||u||^2 + ||w||^2 - 2(u · w)

Since u and w are unital (i.e., their lengths are 1), we have

||u||^2 = ||w||^2 = 1

Substituting these values and u · w = 0, we get

||u - w||^2 = 1 + 1 - 0 = 2

Taking the square root of both sides, we get

||u - w|| = √2

Therefore, we have shown that if u and w are unital orthogonal vectors, then ||u - w|| = √2.

A company has 20 employees. Each employee earns the same salary. If the company pays a total of $730,000 in salaries, how much does each employee earn?

Answers

Answer:

$36,500 per employee

Step-by-step explanation:

$730,000/20 employees

Follow the directions to solve the system of equations by elimination.

8x + 7y = 39

4x – 14y = –68

Multiply the first equation to enable the elimination of the y-term.
Add the equations to eliminate the y-terms.
Solve the new equation for the x-value.
Substitute the x-value back into either original equation to find the y-value.
Check the solution.
The solution to the system of equations is (
,
).

Answers

The solution to the system of equations is (1/2, 5).

Describe Elimination Method?

The elimination method involves manipulating these equations to eliminate one of the variables. This is done by multiplying one or both of the equations by a constant so that the coefficients of one of the variables are equal in both equations, but with opposite signs. The equations are then added or subtracted, depending on the signs, to eliminate one of the variables.

To solve the system of equations by elimination, we can follow these steps:

Multiply the first equation by 2 to get rid of the y-term:

16x + 14y = 78

Add the second equation to the new equation to eliminate the y-terms:

16x + 14y + 4x - 14y = 78 - 68

20x = 10

Solve for x:

x = 1/2

Substitute x = 1/2 into the first equation to solve for y:

8(1/2) + 7y = 39

4 + 7y = 39

7y = 35

y = 5

Check the solution by substituting both x = 1/2 and y = 5 into both original equations:

8(1/2) + 7(5) = 39 (true)

4(1/2) - 14(5) = -68 (true)

Therefore, the solution to the system of equations is (1/2, 5).

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