Answer:
A function can have many x values for a given y value and still be a function but it cannot have many y values for a given x value. You can easily test this by graphing the equation and doing the vertical line test by seeing if a vertical line will intersect the graph only once at all x values, if it passes it is a function. In short what you have here is a function
Step-by-step explanation:
Answer:3x < 8x - 3
Step-by-step explanation:
Assume that the length of the rectangle is "l" and that the width is "w".
We are given that:
(1) The length is one more than twice the base. This means that:
l = 2w + 1 .......> equation I
(2) The perimeter is 92 cm. This means that:
92 = 2(l+w) ...........> equation II
Substitute with equation I in equation II to get the width as follows:
92 = 2(l+w)
92 = 2(2w+1+w)
92/2 = 3w + 1
46 = 3w + 1
3w = 46-1 = 45
w = 45/3
w = 15
Substitute with w in equation I to get the length as follows:
l = 2w + 1
l = 2(15) + 1
l = 30 + 1 = 31
Based on the above calculations:
length of base = 31 cm
width of base = 15 cm
Hey there! :)
Answer:
C(-1) = -5.
Step-by-step explanation:
C(x) = -4x² + 4x + 3
Plug in -1 for x to solve for C(-1):
C(-1) = -4(-1)² + 4(-1) + 3
Simplify:
C(-1) = -4 + (-4) + 3
C(-1) = -5
Answer:
5
Step-by-step explanation:
The general term of an arithmetic progression is ...
an = a1 +d(n -1)
where a1 is the first term and d is the common difference.
Here we are given that ...
a5 = 3×a2
a5 +a6 +a7 +a8 = 240
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In terms of a1 and d, these tell us ...
a1 +d(5 -1) = 3(a1 +d(2 -1))
a1 +4d = 3a1 +3d . . . . . eliminate parentheses
d = 2a1 . . . . . . . . . . . subtract a1+3d
and ...
(a1 +4d) +(a1 +5d) +(a1 +6d) +(a1 +7d) = 240
4a1 +22d = 240
Substituting for d, we have ...
4a1 +22(2a1) = 240
48a1 = 240
a1 = 240/48 = 5
The first term is 5.
