Opening Exercise

X+2y=19 and x+y=13 in substitution methood

densk [106]

X=7, y=6. that’s your answer!

3 0

3 years ago

A change purse contains 16 coins. The coins are nickels, dimes, and quarters. The value of the change is $2.10. The number of di

elixir [45]

Taking into account the definition of a system of linear equations, there are 6 quarters in the change purse.

<h3>System of linear equations</h3>

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

<h3>Amount of quarters in the change purse</h3>

In this case, a system of linear equations must be proposed taking into account that:

N in the amount of nickels in the change purse.
D in the amount of dimes in the change purse.
Q in the amount of quarters in the change purse.

On the other hand, you know:

A change purse contains 16 coins.
The value of the change is $2.10.
The number of dimes is 4 fewer than the number of quarters.

The system of equations to be solved is

Equation 1: N + D + Q= 16

Equation 2: 0.05N + 0.10D + 0.25Q= 2.10

Equation 3: D= Q - 4

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

Substituting equation 3 into equation 1 you get:

N + Q - 4 + Q= 16 → N +2Q= 16 +4 → N + 2Q= 20

Isolating the variable N you get:

N= 20 - 2Q

Replacing this expression and equation 3 in equation 2 you get:

0.05×(20 -2Q) + 0.10×(Q -4) + 0.25Q= 2.10

Solving:

0.05×20 - 0.05×2Q + 0.10Q - 0.10×4 + 0.25Q= 2.10

1 - 0.10Q + 0.10Q - 0.40+ 0.25Q= 2.10

- 0.10Q + 0.10Q + 0.25Q= 2.10 -1 +0.40

0.25Q= 2.10 -1 +0.40

0.25Q= 1.50

Q= 1.50÷ 0.25

Finally, there are 6 quarters in the change purse.

Learn more about system of equations:

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#SPJ1

5 0

2 years ago

Find n please. I just forgot the simple theorem please someone andwrr

grigory [225]

Answer:

118 degrees

Step-by-step explanation:

m = 124 / 2 = 62

Sum of opposite angles m and n is supplementary,

m + n = 180

62 + n = 180

n = 180 - 62

n = 118 degrees

8 0

3 years ago

HELP asapppp!!!! I’ll mark you brilliant!!!! Thank you!!!!!

timurjin [86]

1.8 is your answer?

Step-by-step explanation:

so.. it would be $30.00x0.06 since 6% is 0.06 as a decimal

I think that is correct

4 0

3 years ago

Missing number in the series 9, ____, 6561, 43046721 is: 81 25 62 31 18 9. one number is 2 more than 3 times another. their sum

Nadusha1986 [10]

Alright, lets get started.

Missing number fom the series : 9, ..... , 6561, 43046721

43046721 is square of its previous number 6561, means

$6561^2 = 43046721$

It means the missing number will be square of its previous number

Means $9^2 = 81$ , so missing number is 81. : Answer

Next : one number is 2 more than 3 times another. their sum is 22. find the numbers.

Suppose one number is x and second number is y

As per given equation, $x = 3y + 2$ ......equation (1)

Their sum is 22 means, $x+y = 22$ .......equation (2)

Putting the value of x from equation1 into equation 2

$3y + 2 + y = 22$

$4y + 2 = 22$

Subtracting 2 in both sides

$4y + 2 - 2 = 22 - 2$

$4y = 20$

$y = 5$

$x = 22 - y = 22 - 5 = 17$

Means numbers are 17 and 5. : Answer

Next : the missing number in the series 1, 4, 27,____, 3125 is

1 could be written as 1

4 could be written as $2^2$

27 could be written as $3^3$

So , next number would be $4^4$

$4^4 = 256$

Next one is $5^5 = 3125$

So, the missing number is 256 : Answer

Next : the next number in the series 3, 4, 6, 7, 9, 10 is

After 3,4 (5) is mising, 6, 7 (8) is missing, 9, 10 (11) will be missing

So, next number will be 12. : Answer

Next : a farmer is planting a straight row of crops with 3 feet between each plant. if 23 are planted, what is the distance between the first and last plant?

Between 2 plants, the distance is = $3 * (2-1) = 3$

Between 3 plants, the distance is = $3 * (3-1) = 6$

So, between 23 plants, the distance is = $3 * (23-1) = 3 * 22 = 66$

hene the distance between first and last plant woule be 66 feet. : Answer

7 0

3 years ago