Question

Help with loooonggg question

Answer 1

A. original length is already given (6 inches)
B. two pieces (already given in diagram)
C. write an expression that describes

original length - 2*length of each piece

but translated to the numbers/variables given in the problem

Answer 2

2*4*6

Answer 3

the length of each cut-off piece is x

the original length is 6

write an expression that describes:

original length - 2*length of cut-off piece

Answer 4

6-2*x

Answer 5

good, that's C

we can follow a similar process for DEF

Answer 6

4-2*x

Answer 7

good

D = 4 inches (given)
E = 2 pieces (given in diagram)
F = 4 - 2x

Answer 8

for part IIA, it is simply asking for the new dimensions (which is just 4 - 2x and 6 - 2x from parts C/F)

for part IIB, A(x) = area = length * width, so

multiply new length * new width = (4-2x)(6-2x) not sure what form they want, I guess you could leave it like this

Answer 9

okay now for part III

Answer 10

"set the equation from part II equal to 16 and solve"

so (4-2x)(6-2x) = 16

solve for x using the quadratic formula

first step: use foil to distribute the left hand side

Answer 11

x=5+sqrt17 all over2

Answer 12

x=5-qrt17 all over2

Answer 13

good. that's A.

for part B we must consider the limits of the original notecard. since the x-pieces are cut from the notecard, we cannot cut more than the notecard size allows

the shorter side of the notecard is (4-2x)

4 - 2x must be greater than 0

4 - 2x > 0

this means x < 2

so using the two x solutions, select the answer where x is less than 2

Answer 14

(for this one just convert the two solutions to decimal form and see which one is < 2)

Answer 15

4 - 2x > 0

Answer 16

your two solutions are:

x=5+sqrt17 all over2
x=5-sqrt17 all over2

select the answer that is less than 2.

Answer 17

x=5-sqrt17 all over2

Answer 18

good, that is the correct answer for B