Select ALL the correct answers. MORE THAN ONE ANSWER!!
Which situations can be represented by the given quadratic equation?

x^2+8x=384

A. A printed place mat has a yellow border and an inside area with a floral design. The inside area of the place mat is 384 square inches, and the area of the border is one-eighth of the inside area.
B. Jack's plot of land has an area of 384 square yards. The cultivated area is 8 times larger than the uncultivated area.
C. The layout of a kitchen is in the shape of an L and has a total area of 384 square feet. One part of the kitchen is a square, and the other part is a rectangle that has a length equal to one side of the square and a width of 8 feet.
D. Ann's yard has an area of 384 square feet. She builds a small rabbit hutch that takes up 8 square feet of the yard.
E. The length of a shipping box is 8 inches more than its width. The area of the base of the box is 384 square inches.

b,c

Step-by-step explanation:

they are the only two tha tproperly use the equation

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

b. x + 1

step-by-step explanation:

i'am smart