Using the law of cosines:
The grocery store to the school:
Distance = √(7^2 + 10^2 - 2*7*10*cos(100)
Distance = 13.16 miles
The movie store to the school:
Distance = √(7^2 + 10^2 - 2*7*10*cos(120)
Distance = 14.80 miles
The friend is further away.
Answer:
Step-by-step explanation:
A quadratic in factored form is usually expressed as: 
where the sign of a and b depends on the sign of the zero. And I said "usually" since sometimes the x will have a coefficient. Anyways in the quadratic there are two zeroes at x=-1 and x=3. This can be written as: 
. Notice how the signs are different? This is because when you plug in -1 as x you get a factor of (-1+1) which becomes 0 and it makes the entire thing zero since when you multiply by 0, you get 0. Same thing for the x-3 if you plug in x=3. Now a is in front and it can influence the stretch/compression. To find the value of a, you can take any point (except for the zeroes, because it will make the entire thing zero, and you can technically input anything in as a)
I'll use the point (1, -4) the vertex
-4 = a(1+1)(1-3)
-4 = a(2)(-2)
-4 = -4a
1 = a. So yeah the value of a is 1
So the equation is just:
Answer:
Quadrilaterals
Step-by-step explanation:
One number (a) exceeds another number (b) by 11 so
a = b+11
a + b = 77
Substitute the equation for a into the second equation
(b+11) + b = 77
multiply each side by 1 to remove parentheses
b + 11 + b = 77
Combine like terms
2b + 11 = 77
Isolate the variable
2b = 77-11
Simplify
2b = 66
Divide by 2
b = 33
Now substitute b back into the initial equation for a
a = (33) + 11
a = 44
Check your work by substituting both values into the second equation
44 + 33 = 77
This is true, so 44 and 33 are solutions
