Answer:
first box: 12
second box: 5.5
the boxes in chart in order is 12, 17.5, 23, 39.5
Step-by-step explanation:
I've done this before
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:
In ∆ABC AND ∆DEF
ABC=DEF...........each 90°
SIDE AB =SIDE ED...........given
SIDE BC =SIDE EF............B-F-C and E-C-F
∆ABC =∆DEF....................by SAS test
Let
x be the price for a pound of ham
y the price for a pound of cheese
<span>1.3x +0.8y = 11.28 ....(1)
1.5x +1.2y = 14.76 ....(2)
Lets multiply (1) by -1.2
Lets multiply (2) by 0.8
-1.56x -0.96y = -13.536 .....(3)
</span> 1.2x + 0.96y = 11.808 .....(4)
If we add (3) and (4)
-0.36x = -1.728 ............> x = 4.8
We substitute in (1)
1.3(4.8) +0.8y = 11.28
y = 6.3
Price per pound of ham = x = 4.8
Price per pound of cheese = y = 6.3
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