V=LWH=20
L is 5 more than W
V=5+W
H is 1 less than W
H=-1+W
easy, sub 5+W for L and -1+W for H in LWH=V=20
20=(5+W)(W)(-1+W)
expand
20=W^3+4W^2-5W
minus 20 both sides
W^3+4W^2-5W-20=0
either factor or graph to find the possible values for W
(W+4)(W^2-5)=0
set each to zero
W+4=0
W=-4
impossible, measures cannot be negative
W^2-5=0
add 5
W^2=5
sqrt both sides
W=√5
sub back
L=5+W
L=5+√5
aprox
7.24 rounded
H=-1+W
H=-1+√5
aprox
1.24 rounded
the dimentions are
√5 by (5+√5) by (-1+√5) or aprox
2.24in by 7.24in by 1.24in
7 1/4 - 5 3/4= 1 1/2 because you can either 1) change it into decimals: 7.25-5.75 and do simple subtraction or... 2) u can change the 7 to a 6 and add 4 to the numerator of 1/4 making the equation 6 5/4 - 5 3/4 = 1 2/4 which simplified to 1 1/2 I hope I didn’t confuse you! :))
Answer:
I think there must be g(x) instead of 8(x) in the question. You can look the solution but i have corrected it and then solved it.
First, find the eq'n of the line connecting (7,8) and (9,0). The slope of this line is m = rise / run = (0-8) / (9-7), or m = -8/2, or m = -4. Thus, the equation of this line is y-0 = -4(x-9), or y = -4x + 36.
We must now solve simultaneously the system y = -4x + 36, y = 2x - 10. Let's equate these to one another: -4x + 36 = 2x - 10. Thus, 46=6x, or 3x=23, or
x = 23/3. Subbing this value for x into y = 2x - 10 results in y = 2(23/3) - 30/3, or
y = 16/3. Thus, the solution is (23/3, 16/3). a=23/3 and b=16/3.
We are to compute a+b. This is a+b = 23/3 + 16/3, or 39/3, or 13 (answer).