An 8-pack of juice boxes costs $5. How much do 32 juice boxes cost?

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

The sum of interior angles in a triangle are 180 degrees. Angle B and C are congruent. Angle B is twenty less than angle A. Writ

Margarita [4]

Answer:

A = 73.33

B = 53.33

C = 53.33

Step-by-step explanation:

Mathematically, adding the 3 angles would equal 180

Thus;

A + B + C = 180 •••••(i)

Since B and C are congruent, that means they are equal ( we are looking at isosceles triangle)

B = C •••••••••(ii)

Lastly;

B = A -20 ••••••••(iii)

Make a substitution in equation 1;

A + A -20 + A -20 = 180

Since B = C ; C also is A-20

3A -40 = 180

3A = 220

A = 220/3 = 73.33

B = C = A -20 = 73.33 -20 = 53.33

6 0

3 years ago

Which of the following is true for the relation f(x) = x2 + 8? Only the inverse is a function. Both the equation and its inverse

Alchen [17]

<u>ANSWER</u>

Only the equation is a function

<u>EXPLANATION</u>

$f(x)=x^2+8$ is graphed above with its inverse $f^{-1}(x)=\pm \sqrt{x-8}$ .

We perform the vertical line test for both the equation and its inverse.

The equation $f(x)=x^2+8$ passed the vertical line hence it is a function.

However, $f^{-1}(x)=\pm \sqrt{x-8}$ failed the vertical line test, hence it is not a function.

3 0

3 years ago

thirteen of 50 states in the united states do not touch the ocean. write 13/50 as a decimal and percent

SOVA2 [1]

To find decimal, divide 13/50= 0.26

To find percent divide decimal above by 100 (or move decimal place to the right two places).

0.26/100= 26%

Hope this helps! :)

8 0

3 years ago

What is the halving and doubling strategy

malfutka [58]

Halving-reduce by half or think what is fifty% of the number or divide by two
doubling-add the number you got to the same number or multiply by two

Halving Ex.:6/2=3

Doubling ex.: 9+9=18 or 6*2=12

6 0

3 years ago