The answer is 12.4071769563
Answer: n = 1, n = -1/3
<u>Step-by-step explanation:</u>
(3n - 1)² = 12n + 8
9n² - 6n + 1 = 12n + 8
9n² - 18n - 7 = 0
Substitute -18n with 3n - 21n and find the common factor of each side:
9n² + 3n -21n - 7 = 0
3n(<u>3n + 1</u>) -3(<u>3n + 1</u>) = 0
(3n - 3) (3n + 1) = 0
Solve for each factor:
3n - 3 = 0 3n + 1 = 0
3n = 3 3n = -1
n = 1 n = -1/3
If there are x $13 each books and y $17 each books, then we can build the following equations:
x + y = 8 (or y = 8 - x)
13x + 17y = 128 (or y = 128/17 - 13x/17)
:)
Answers:
(a) BC = 40
(b) GF = 15
(c) CD = 45
(d) KM = 37.5
=========================================================
Explanations:
Part (a)
GF is a midsegment of triangle ABC, so GF is half that of the parallel base AC
AC = 30 so GF = (1/2)*AC = 0.5*30 = 15
--------------------------
Part (b)
For similar reasons as part (a), FB if half that of BC. This leads to FB = FC
FB = FC
FC = 20
since FB = 20
Now use the segment addition postulate
BC = BF + FC
BC = 20 + 20
BC = 40
Note: FB is the same as BF. The order of the letters does not matter.
--------------------------
Part (c)
GF = AD are the same length because of the single tickmark
GF = 15 so AD = 15
use the segment addition postulate
CD = CA + AD
CD = 30 + 15
CD = 45
--------------------------
Part (d)
EG = 15 since GF = 15 (and EG = GF by the single tickmark)
use the segment addition postulate
EF = EG + GF
EF = 15 + 15
EF = 30
The length of KM is the average of the base lengths EF and DC, since KM is a midsegment of the trapezoid
KM = (EF+DC)/2
KM = (30+45)/2
KM = (75)/2
KM = 37.5