Answer:
-1772
Step-by-step explanation:
The nth term of an arithmetic sequence is expressed as;
Tn = a+(n-1)d
a is the first term
n is the number of terms
d is the common difference
From the sequence
a = 28
d = 8-28 = -12-8 = -20
n =91(since we are looking for the 91st term)
Substrate
T91 = 28+(91-1)(-20)
T91 = 28+90(-20)
T91 = 28-1800
T91 = -1772
Hence the 91st term is -1772
Answer:
-33
Step-by-step explanation:
well you can use mid point formula and solve for x
or count how many it takes to get from -3 to 27 and add that to -3 the other direction
Answer:
1428 in³
Step-by-step explanation:
To find the volume of this figure, we will need to use two formulas. The volume of a Rectangular Prism (
) and volume of a triangular prism. 
If we look at the Rectangular Prism, we can find that l = 17, w = 8, and h = 5. Multiply these to find the volume:
17 × 8 × 5 = 680 in³.
Solving for the triangular prism gives us:
A = 1/2 (11 × 8 × 17)
A = 748.
Add these two volumes to find the volume of the composite figure:
748 + 680 = 1428 in³
Answer:
Step-by-step explanation:
This is a quadratic expression. Use the quadratic formula to find the roots, and then once you have the roots, write the corresponding factors.
The coefficients of this quadratic expression are a = 7, b = 5 and c = -3
The discriminant is b^2 - 4ac, or 5^ - 4(7)(-3), or 25 + 84 = 109. Because this is positive, we know that the expression has two unequal, real roots.
Using the quadratic formula, we now find these roots:
-b ± √(discriminant)
x = -------------------------------- which here is:
2a
-5 ± √109
x = -----------------
14
The factors can be found from these two roots. The first one is
-5 - √109 5 + √109
(x - ---------------- ) = (x + ---------------- )
14 14
and the second is
5 - √109
(x + ---------------- )
14
