L=2w+6
260=lw
Substitute for l
260=w(2w+6)
260= 2w^2+6w
2w^2+6w-260=0
2(w^2+3w-130)
2(w+13)(w-10)
w=-13, w=10
Since width cannot be negative it must be 10
260=l(10)
26=l
Final answer: length-26 ft, width-10ft
Answer:
yes
Step-by-step explanation:
Given:
P: (2,0,5)
L: (0,6,4)+t(7,-1,5)
and required plane, Π , passes through P and perpendicular to L.
The direction vector of L is V=<7,-1,5>.
For Π to be perpendicular to V, Π has V as the normal vector.
The equation of a plane with normal vector <7,-1,5> passing through a given point P(xp,yp,zp) is
7(x-xp)-1(y-yp)+5(z-zp)=0
Thus the equation of plane Π passing through P(2,0,5) is
7(x-2)-y+5(z-5)=0
or alternatively,
7x-y+5z = 14+25
7x-y+5z = 39
Answer:
<h2> 105 tickets</h2>
Step-by-step explanation:
To solve this problem we need to model an equation to represent the situation first.
the goal is to archive $7500 in the even, bearing in mind that there is a cost of $375 fee for rent, we need to put this amount into consideration
let the number of tickets be x
so
75x-375>=7500--------1
Equation 1 above is a good model for the equation
we can now solve for x to determine the number of tickets to be sold to archive the aim
75x-375>=7500--------1
75x>=7500+375
75x>=7875
divide both sides by 75 we have
x>=7875/75
x>=105 tickets
so they must sell a total of 105 tickets and above to meet the target of $7500 with the rent inclusive
Answer:
we conclude that:
Hence, (1, 5) is the solution in interval notation.
Please also check the attached graph.
Step-by-step explanation:
Given the inequality expression
as
(x + 3)² = x² + 6x + 9
2(x² + 7) = 2x² + 14
so
rewriting in the standard form
Factor -x² + 6x - 5: - (x - 1) (x - 5)
Multiply both sides by -1 (reverse the inequality)
Simplify
so
Therefore, we conclude that:
Hence, (1, 5) is the solution in interval notation.
Please also check the attached graph.
