Answer:
a = 2, b = -9, c = 3
Step-by-step explanation:
Replacing x, y values of the points in the equation y = a*x^2 + b*x +c give the following:
(-1,14)
14 = a*(-1)^2 + b*(-1) + c
(2,-7)
-7 = a*2^2 + b*2 + c
(5, 8)
8 = a*5^2 + b*5 + c
Rearranging:
a - b + c = 14
4*a + 2*b + c = -7
25*a + 5*b + c = 8
This is a linear system of equations with 3 equations and 3 unknows. In matrix notation the system is A*x = b whith:
A =
1 -1 1
4 2 1
25 5 1
x =
a
b
c
b =
14
-7
8
Solving A*x = b gives x = Inv(A)*b, where Inv(A) is the inverse matrix of A. From calculation software (I used Excel) you get:
inv(A) =
0.055555556 -0.111111111 0.055555556
-0.388888889 0.444444444 -0.055555556
0.555555556 0.555555556 -0.111111111
inv(A)*b
2
-9
3
So, a = 2, b = -9, c = 3
Answer:
what are the answer choicesss
Step-by-step explanation:
First, all the heights have to be converted to similar units, say feet.
Therefore,
Building= 20 feet
Tree = 252*0.083333 = 21 feet
Flagpole = 6*3 = 18 feet
The tallest of the three is the tree and thus should cast the longest shadow. However, it should be noted that at exactly noon when the sun is overhead, all the three will have equal length of shadow (that is, 0 feet long).
Answer:
2.4 hours
Step-by-step explanation:
Let total work = X
Rate of work done = X ÷ time
Rate of A = X/4
Rate of B = X/6
If they work together, rate is the sum of their individual rates, i.e.
X/4 + X/6
= (3X + 2X)/12 (taking LCM)
=5X/12
Rate = X/time
5X/12 = X/time
time = X÷(5X/12)
time = X × 12/(5X)
time = 2.4 hours
Shortcut:
Product of individual times/sum of individual times
= (4×6)/(4+6)
=24/10
=2.4 hours
The distributive property is a(b + c) = ab + ac
