Complete the steps in solving the quadratic function 7x – 9 = 7x2 – 49x by completing the square.

–9 = 7x2 –
x

–9 +
= 7(x2 – 8x +
)

  x = 4 ± (1/7)√721

Step-by-step explanation:

7x – 9 = 7x^2 – 49

-9 = 7x^2 -56x . . . . . . . . subtract 7x

-9 = 7(x^2 -8x) . . . . . . . . factor out leading coefficient

-9 +7(16) = 7(x^2 -8x +16) . . . . . add the square of (-8/2) inside parentheses

103 = 7(x -4)^2 . . . . . collect terms, write as a square

103/7 = (x -4)^2 . . . . divide by the leading coefficient

±√(103/7) = x -4 . . . . . take the square root

x = 4 ± (1/7)√721 . . . . add 4, rationalize the denominator

___

You "complete the square" by making sure the constant in the quadratic is the square of half the x-term coefficient. If changes are made on one side of the equation, the same changes need to be made on the other side of the equation. Here, we added 7(16) to complete the square.

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

the most boring ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.