25% of 176 is what number in equation forms

Give a geometric description of the following system of equations.a. 2x−4y=12 −3x+6y=−15.b. 2x−4y=12 −5x+3y=10.a. 2x−4y=12 −3x+6

Reptile [31]

Answer:

a. No solution, parallel lines.

b. One solution.

Step-by-step explanation:

Given the system of equations:

a. $2x-4y=12$

$-3x+6y=-15$

b. $2x-4y=12$

$-5x+3y=10$

To give a geometric description of the given system of equations.

The geometric description of a system of equations in 2 variables mean the system of equations will represent the number of lines equal to the number of equations in the system given.

i.e.

Number of planes = Number of variables

Number of lines = Number of equations in the system.

Here, we are given 2 variables and 2 equation in each system.

So, they can be represented in the xy-coordinates plane.

And the number of solutions to the system depends on the following condition.

Let the system of equations be:

$A_1x+B_1y+C_1=0\\A_2x+B_2y+C_2=0$

1. One solution:

There will be one solution to the system of equations, If we have:

$\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}$

2. Infinitely Many Solutions: (Identical lines in the system)

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}= \dfrac{C_1}{C_2}$

3. No Solution:(Parallel lines)

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}$

Now, let us discuss the system of equations one by one:

a. $2x-4y=12$ OR $2x-4y-12=0$

$-3x+6y=-15$ OR $-3x+6y+15=0$

$A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -3, B_2 = 6, C_2= 15$

Here, the ratio:

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2} = -\dfrac{2}{3}\\\dfrac{C_1}{C_2} = -\dfrac{4}{5}$

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}$

Therefore, no solution i.e. parallel lines.

b. $2x-4y=12$ OR $2x-4y-12=0$

$-5x+3y=10$ OR $-5x+3y-10=0$

$A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -5, B_2 = 3, C_2 = -10$

$\dfrac{A_1}{A_2}= -\dfrac{2}{5}\\\dfrac{B_1}{B_2} = -\dfrac{4}{3}\\\dfrac{C_1}{C_2} = -\dfrac{6}{5}$

$\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}$

So, one solution.

Kindly refer to the images attached for the graphical representation of the given system of equations.

6 0

3 years ago

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Eva8 [605]

The answer is negative twenty five. By the way, if that is you in the picture, you are beautiful.

5 0

3 years ago

YALL PLEASE HELP FRFR

Arturiano [62]

First of all, let's note the sales tax rates in each town. In Washington, we know it's 6%. In the town in Virginia, it's 5%. In the town in Maryland, it's 9%.

Let's figure out the total taxes in every town by applying the sales tax rate for each town.

To add percents to a whole number, we always multiply using 0.XX (example: to add 1% to a the number 100, we would multiply 100*0.01 and get the answer 1. We'd then add the 1 to the original number, 100, and get 101.)

In this case, we need to multiply the $1000 by the sales tax in Washington, 6%.

1000 x 0.06 = 60. Now, we add the 60 to the original number (1000), and get 1060. Now we know the total tax in Washington on the computer will be $60, and the total price we will pay is $1060.00

For Virginia, the sales tax is 5%. Let's add the 5% using the same method we used in the equation above.

1000 x 0.05 = 50. Now, add the 50 to the original 1000, and we get 1050. Now we know that the total tax in Virginia is going to be $50, and the total price that we'll pay in Virginia is $1050.00.

On to the final town, Maryland. In Maryland, the sales tax rate is 9%. Let's use the same formula again.

1000 * 0.09 = 90. Now that we have the 90, we add it to the original 1000, and we get 1090. In Maryland the total sales tax will be $90, and the total price we'll pay is $1090.00.

Now, let's complete the question by answering the 3 parts.

To spend the least amount total Amir should buy the computer in Virginia ($1050.00).

Amir would pay the most sales tax in Maryland ($90.00).

Amir would pay $60 sales tax in Washington, DC.

I hope this answer was in depth enough to help you out so that you can do this on your own in the future. :)

3 0

3 years ago

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