How much will you pay when a $54 shirt has a 5% tax?

Drag the tiles to the correct boxes to complete the pairs not all tiles will be used match the system of equations with their so

allochka39001 [22]

Answer:

Part 1) solution {(-5,8),(3,0)} ----> $y+12=x^{2}+x$ and $x+y=3$

Part 2) No solutions ----> $y-15=x^{2}+4x$ and $x-y=1$

Part 3) solution [(-2,5),(3,-5)] ---> $y+5=x^{2}-3x$ and $2x+y=1$

Part 4) No solutions ---> $y-6=x^{2}-3x$ and $x+2y=2$

Part 5) solution [(2,3),(8,9)] ---> $y-17=x^{2}-9x$ and $-x+y=1$

Part 6) solution [(-2,3),(7,-6)] ---> $y-15=-x^{2}+4x$ and $x+y=1$

Step-by-step explanation:

Part 1) we have

$y+12=x^{2}+x$ ----> equation A

$x+y=3$ ----> equation B

Solve by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution are the points (-5,8) and (3,0)

see the attached figure N 1

Part 2) we have

$y-15=x^{2}+4x$ ----> equation A

$x-y=1$ ----> equation B

Solve by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The system has no solutions, because there is no point of intersection between the two graphs

see the attached figure N 2

Part 3) we have

$y+5=x^{2}-3x$ ----> equation A

$2x+y=1$ ----> equation B

Solve by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution are the points (-2,5) and (3,-5)

see the attached figure N 3

Part 4) we have

$y-6=x^{2}-3x$ ----> equation A

$x+2y=2$ ----> equation B

Solve by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The system has no solutions, because there is no point of intersection between the two graphs

see the attached figure N 4

Part 5) we have

$y-17=x^{2}-9x$ ----> equation A

$-x+y=1$ ----> equation B

Solve by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution are the points (2,3) and (8,9)

see the attached figure N 5

Part 6) we have

$y-15=-x^{2}+4x$ ----> equation A

$x+y=1$ ----> equation B

Solve by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution are the points (-2,3) and (7,-6)

see the attached figure N 6

5 0

3 years ago

R(-5, 5) S(1, 7) T(2, 4) U(-4, 2)

natali 33 [55]

Would you like to solve this problem or give you the description of it

4 0

3 years ago

Solve equation. Show steps 8+x=4x+2

statuscvo [17]

Answer:

x=2

Step-by-step explanation:

8 + x = 4x +2

Subtract 4x from both sides:

8 + x - 4x = 4x + 2 - 4x

Group like terms:

x - 4x + 8 = 4x + 2 -4x

Simplify the arithmetic:

-3x + 8 = 4x + 2 -4x

Group like terms:

-3 + 8 = 4x - 4x + 2

Simplify the arithmetic:

-3x + 8 = 2

8 0

2 years ago

Patrick has just finished building a pen for his new dog. The pen is 3 feet wider than it is long. He also built a doghouse to p

zalisa [80]

General Idea:

(i) Assign variable for the unknown that we need to find

(ii) Sketch a diagram to help us visualize the problem

(iii) Write the mathematical equation representing the description given.

(iv) Solve the equation by substitution method. Solving means finding the values of the variables which will make both the equation TRUE

Applying the concept:

Given: x represents the length of the pen and y represents the area of the doghouse

Statement 1: "The pen is 3 feet wider than it is long"

$Length \; of\; the \; pen = x\\ Width \; of\; the\; pen=x+3$

------

Statement 2: "He also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base"

$Area \; of\; the\; Dog \; house=y\\ Perimeter \; of\; Dog\; house=y$

------

Statement 3: "After putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen."

$Area \; of \; the\; Pen - Area \;of \;the\;Dog \;House=\;Space\;inside\;Pen\\ \\ x \cdot (x+3)-y=178\\ Distributing \;x\;in\;the\;left\;side\;of\;the\;equation\\ \\ x^2+3x-y=178\Rightarrow\; 1^{st}\; Equation\\$

------

Statement 4: "The perimeter of the pen is 3 times greater than the perimeter of the doghouse."

$Perimeter\; of\; the\; Pen=3\; \cdot \; Perimeter\; of\; the\; Dog\; House\\ \\ 2(x \; + \; x+3)=3 \cdot y\\ Combine\; like\; terms\; inside\; the\; parenthesis\\ \\ 2(2x+3)=3y\\ Distribute\; 2\; in\; the\; left\; side\; of\; the\; equation\\ \\ 4x+6=3y\\ Subtract \; 6\; and \; 3y\; on\; both\; sides\; of\; the\; equation\\ \\ 4x+6-3y-6=3y-3y-6\\ Combine\; like\; terms\\ \\ 4x-3y=-6 \Rightarrow \; \; 2^{nd}\; Equation\\$