Answer:
The inequality x3 − 14x2 + 48x − 1,680 ≤ 0 can be used to find pool’s length.
⇒The water level in the pool cannot exceed 14 feet.
Step-by-step explanation:
The question is on inequalities
Given;
Length= x ft
depth= x-6 ft
Width= x-8 ft
volume ≤ 1680 ft³
Forming the inequality to find length x of the pool
Volume= base area × depth
base area × depth ≤ volume
x(x-8) × (x-6) = 1680
(x²-8x )(x-6) = 1680
x(x²-8x) -6 (x²-8x)=1680
x³-8x²-6x²+48x=1680
x³-14x²+48x=1680
x³-14x²+48x-1680 ≤ 0
⇒The water level in the pool cannot exceed 14 feet...why?
taking the value of x at maximum to be 17 according to the graph, then maximum depth will be;
d=x-6 = 17-6=11 ft
⇒11 ft is less than 14ft
Answer:
No solution
Step-by-step explanation:
Lets start by simplifying everything out, and then try to get all of the x's on one side of the equation.
1/2x + 1/3x - 4 = 5/6(x+6)
Simplify and distributive property
5/6x - 4 = 5/6x + 5
Lets subtract 5/6x from both sides to try and get rid of the x from the right side of the equation. (Now, as you may already see, is we try to get all of the x's on one side of the equation, the x's will cancel out, and we will be left with no solution.)
5/6x - 4 - 5/6x = 5/6x + 5 - 5/6x
Simplify
-4 = 5
Because we ended up with something in the form a = b and a ≠ b, there is no solution. (If a = b, then there would be an infinite number of solutions.)
I hope you find this helpful. Let me know if anything in my answer confuses you. Happy studying.
Answer:
x=50
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
It crosses the y-axis at y=1 so the y-intercept is b=1.
The slope is count straight up from (-5,-2) to you are on the same horizontal level as (5,4). The rise is 6
Once you get the same horizontal level as (5,4), you will count straight over to you get to (5,4). The run is 10.
Slope=rise/run=6/10=3/5.
Or you could find slope by using the slope formula. I like to line up two pairs of points and subtract then put 2nd difference over first difference. Like so,
(5,4)
-(-5,-2)
----------
10 6
So the slope is 6/10 or 3/5 after reducing.
Slope-intercept form of a line is y=mx+b
Plug in m=3/5 and b=1
y=3/5 x +1
So the answer is D.
since the triangles are similar
angle DEC = 60 degrees
3 angles inside a triangle equal 180 degrees
BAC = DCE = 64
CBA = EDC = 56
DEC = 180 -56 -64 = 60 degrees
used angle-angle theorem