First setup the system of equations for the given case.
Let sandwich=x
and delivery fee =y
Equations are:
4x+y=33 Equation 1
8x+y=61 Equation 2
Subtract equation 1 from 2.
4x=28
x=7
Now substitute value of x in equation 1.
4(7)+y=33
28+y=33
y=5
So cost of single sandwich=$7 and Delivery fee=$5
Now cost of 12 sandwiches:
12x+y=85
Put y=5
12x+5=85
12x=80
x=6.67 which is less than 7. So, They are not able to get 12 sandwiches for $85.
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 !
You need to look at the question again, and notice the words "... did you ...".
From those words, it's clear that the question comes AFTER you have solved
several equations, and now, this question is asking you how you solved them.
The only way for YOU to answer this question is to solve the equations first.
And if you want someone ELSE to tell the math concepts and principles that
are used to solve them, then you have to show him what the equations are.
Answer:
A,B,and C
Step-by-step explanation:
Hopefully this helps!
3/4 is not P. Because 3 out of the 4 quadrants is not purple.
