Answer:
Width is 12 inches and height is 4 inches.
Step-by-step explanation:
Let the width of the piece of cardboard be = w inches
Then length is = 
inches
As given, 4 inch squares are cut from each corner;
So, the width is = 
inches
Length is = 
inches
When we are folding the cut portion, that gives the height as = 4 inches
The volume is given by : length x width x height
And volume is given as 256 cubic inches
So, 
=> 
=> 
=> 
or 
=> 
=> 
We get , 
; w = -8(neglect the negative value)
; w = 12 inches
And length = 
inches
Hence, dimensions are : L = 24 inches ; w = 12 inches and h = 4 inches
We can check by putting these values in equation :
=> 
=> 
Part 1:
Proportion: $7 every 2 days
Solve: He will earn 98 dollars if he does his chores every day for 2 weeks.
Solution as a sentence: To find the answer, you need to multiply seven, by fourteen.
Part 2:
Proportion: 2 bags last 5 days.
Solve: 8 bags of feed will last 20 days.
Solution in a sentence: To solve the problem, divide eight by two. Then multiply five by four.
Part 3:
Proportion: 3 eggs for every 4 hens.
Solve: 24 hens will lay 18 eggs.
Solution in a Sentence: If you divide twenty four by four, then multiply the answer by three, you will get your answer of eighteen eggs total.
Hope this helps you out. :)
Answer:
f(2) = 12
f(x) = 7, x = -3, 1
Step-by-step explanation:
<u>a)</u>
plug in x as 2
f(x) = 2^2 + 2(2) + 4
f(x) = 4 + 4 + 4
f(x) = 12
<u>b)</u>
replace f(x) with 7
7 = x^2 + 2x + 4
x^2 + 2x - 3 (move 7 to other side)
Factor
ac: -3x^2
b: 2x
split b into 3x, -x
(x^2 -x) + (3x - 3)
↓ ↓
x(x-1) + 3(x-1)
Factor: (x-1)(x+3) = 0
Solve using Zero Product Property:
x - 1 = 0, x + 3 = 0
x = 1, x = -3
F = 2t - 3
f = 2(7) - 3
f = 14 - 3
f = 11
