Let the five terms be: a, a + d, a + 2d, a + 3d, a + 4d, then
a + a + d + a + 2d + a + 3d + a + 4d = 5a + 15d = 40
i.e. a + 3d = 8
Also, (a + 2d)(a + 3d)(a + 4d) = 224
(a + 3d - d)(a + 3d)(a + 3d + d) = 224
(8 - d)(8)(8 + d) = 224
(8 - d)(8 + d) = 224/8 = 28
64 - d^2 = 28
d^2 = 64 - 28 = 36
d = sqrt(36) = 6
But a + 3d = 8
a + 3(6) = 8
a = 8 - 18 = -10
Therefore, the term of the sequence is: -10, -10 + 6, -10 + 2(6), -10 + 3(6), -10 + 4(6)
= -10, -4, -10 + 12, -10 + 18, -10 + 24
= -10, -4, 2, 8, 14
Answer:
72 cm³ (see below)
Step-by-step explanation:
First, refer to the volume formula:
V = l · w · h
If you plug in all of your values and simplify, you'll get the volume:
l = 6 cm
w = 3 cm
h = 4 cm
V = (6) (3) (4)
V = 18 (4)
V = 72 cm³
Because this is volume, the measurements are units cubed, meaning it's cm³.
c
All the information you need is in the quadratic trinomial ... Read from right to left:
Find factors of 49 which ADD (+) to give 14.
These will be 7
and
7 because:
7
×
7
=
49
and
7
+
7
=
14
The + sign shows that the signs in the brackets will be the SAME, the minus (-) shows that they will be negative:
(
x
−
7
)
(
x
−
7
)
=
(
x
−
7
)
2
The answer is highlighted and I put the work for checking the answer at the bottom
I believe that the answer is c but if you wanted to make sure you could figure out the correlation on a graphing calculator.
