A ,
B
and
C
form a triangle where
∠
B
A
C
=
90
∘
.
A
B
=
13.1
mm and
B
C
=
23.7
mm.
Find the length of
A
C
, giving your answer rounded to 1 decimal place.

y=3n + 1

step-by-step explanation:

this is wrong because it says the second number is one less and i added one instead

step-by-step explanation:

given that ab is divided into equal parts as

ac, cd, de, ef, fg, gh, hi, ib.

from this we find that f is the midpoint of ab.

so using mid point formula we find

f = (3,7)

similarly considering fb, we get

h = mid point of fb = ((6,6) and g, mid point of fh is

g = (9/2, 13/2)

i is mid point of hb

so i =(15/2,11/2)

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.

presumably all methods would give the same solution; for each choice we just try x=-4, y=2 and see if it checks.

a.

3x+13y=3(-4)+13(2)=-12 + 26 = 14   that checks

6x+11y=6(-4)+11(2)=-24 + 22 = -2 that checks too

b.  

4x + 5y =4(-4)+5(2)=-16 + 10 = 6   nope

c.

5x+4y = 5(-4)+4(2)=-20 + 8= -12 nope

d.

10x+3y = 10(-4)+3(2)=-40 + 6 = -34 nope

answer: a (the first one) is correct