When you simplify the expressionIon -11 (-5) the result Is

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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5 0

2 years ago

Can someone pls help me

Sophie [7]

Answer:

e

Step-by-step explanation:

If you divide 36 by 12, you get 3.

For this to work, whatever the white wax is, it needs to be 3 times as more as 5.

5x3=15

5 0

3 years ago

Read 2 more answers

How to do question 27

GenaCL600 [577]

1/(sin(90 + θ)cos(360 - θ)) - tan²(-θ)

Note:

sin(90 + θ) = cosθ Cosine and Sine are complementary.

cos(360 - θ) = cosθ Cosine positive in 4th quadrant.

tan(-θ) = -tanθ Negative angle concept.

1/(sin(90 + θ)cos(360 - θ)) - tan²(-θ) = 1/(cosθcosθ) - (-tanθ)²

   = 1/(cos²θ) -       tan²θ

      = (1/cosθ)² -       tan²θ
Note: 1/cosθ = secθ

   = (secθ)² -       tan²θ

      = sec²θ -       tan²θ

      = 1

Note that 1+ tan²θ = sec²θ is a Trigonometric identity.

That means: sec²θ -       tan²θ = 1

Hope this explains it.

5 0

3 years ago

Please I have my final now can someone help me with this fast

Mariana [72]

Answer:

option B

Step-by-step explanation:

Given :

$y = \frac{2}{3}x + 3\\\\y = \frac{5}{2}x + \frac{7}{2}\\\\$

Step 1 : simplify the equation :

$3y = 2x + 9\\\\2y = 5x + 7\\$

Step 2: Arrange the terms :

$2x - 3y = - 9\\\\5x -2 y = -7$

Step 3 : Solve for x and y :

2x - 3y = - 9 ------ ( 1 )

5x - 2y = - 7 --------- ( 2 )

_____________________

( 1 ) x 5 => 10x - 15y = - 45 ---------- (3 )

( 2) x 2 => 10x - 4y = - 14 ----------- (4 )

_______________________

( 3 ) - ( 4 ) => 0x - 11y = - 31

- 11 y = - 31

$y = \frac{31}{11}$

Substitute y in ( 1 ) :

2x - 3y = - 9

$2x - 3 (\frac{31}{11}) = - 9\\\\2x = -9 + 3(\frac{31}{11})\\\\2x = - 9 + \frac{93}{11}\\\\2x = \frac{-99 + 93}{11} \\\\2x = \frac{-6}{11} \\\\x = \frac{-6}{2 \times 11} = -\frac{3}{11}$

Therefore the solution to the sytem is $( - \frac{3}{11} , \frac{31}{11})$

The solution of the system of equation is a point which lies

on the both the lines.

Option A : False , It says the solution lies above one of the given line.

But the solution of the system of equation always lies on

both the line.

Option B : True , says the solution is a point on the coordinate plane.

Option C : False, because if the solution is on the x-axis , then

the y coordinate in the solution would be zero.

But it is not zero.

Option D : False , the solution is the point where both the lines intersect.

8 0

3 years ago

Sara is making a key chain using the bead design shown. What fraction of the beads in her design are either blue or red?

klio [65]

You can make a ratio of red to overall colors and then that will give you the fraction, you might have to simplify it

4 0

3 years ago