As soon as I read this, the words "law of cosines" popped
into my head. I don't have a good intuitive feeling for the
law of cosines, but I went and looked it up (you probably
could have done that), and I found that it's exactly what
you need for this problem.
The "law of cosines" relates the lengths of the sides of any
triangle to the cosine of one of its angles ... just what we need,
since we know all the sides, and we want to find one of the angles.
To find angle-B, the law of cosines says
b² = a² + c² - 2 a c cosine(B)
B = angle-B
b = the side opposite angle-B = 1.4
a, c = the other 2 sides = 1 and 1.9
(1.4)² = (1)² + (1.9)² - (2 x 1 x 1.9) cos(B)
1.96 = (1) + (3.61) - (3.8) cos(B)
Add 3.8 cos(B) from each side:
1.96 + 3.8 cos(B) = 4.61
Subtract 1.96 from each side:
3.8 cos(B) = 2.65
Divide each side by 3.8 :
cos(B) = 0.69737 (rounded)
Whipping out the
trusty calculator:
B = the angle whose cosine is 0.69737
= 45.784° .
Now, for the first time, I'll take a deep breath, then hold it
while I look back at the question and see whether this is
anywhere near one of the choices ...
By gosh ! Choice 'B' is 45.8° ! yay !
I'll bet that's it !
Answer:
234
Step-by-step explanation:
We want to find the summation from n = 2 to n = 10 of the equation -4 + 5n.
We can use the summation formula:
, where a1 is the first term, 
is the last term, and n is the number of terms
Here, we can say the first term occurs when n = 2:
-4 + 5n
-4 + 5 * 2 = -4 + 10 = 6
The last term will be when n = 10:
-4 + 5n
-4 + 5 * 10 = -4 + 50 = 46
The number of terms is just 10 - 2 + 1 = 9 terms.
Substitute these in:
Thus, the answer is 234.
Answer:
Step-by-step explanation:
It’s c believe me
Given triangle ABC with coordinates A(−6, 4), B(−6, 1), and C(−8, 0), and its image A′B′C′ with A′(−2, 0), B′(−5, 0), and C′(−6,
Zinaida [17]
Answer:
The line of reflection is at y = x+6.
Step-by-step explanation:
The perpendicular bisector of AA' is a line with slope 1 through the midpoint of AA', which is (-4, 2). In point-slope form, the equation is ...
y = 1(x +4) +2
y = x + 6 . . . . . . . line of reflection
Answer:
6.2 kilograms/ deciliters
Step-by-step explanation:
megagrams to kilograms
1 megagram = 1000 kilograms
hectoliter to deciliter
1 hectoliter = 1000 deciliter
Using conversion factors
6.2megagrams 1000 kilgrams 1 hectoliter
---------------------- * ----------------------- * -------------------------
hectoliter 1 megagram 1000 deciliters
Canceling like terms
6.2 kilograms/ deciliters
