First, "boxes of two sizes" means we can assign variables: Let x = number of large boxes y = number of small boxes "There are 115 boxes in all" means x + y = 115 [eq1] Now, the pounds for each kind of box is: (pounds per box)*(number of boxes) So, pounds for large boxes + pounds for small boxes = 4125 pounds "the truck is carrying a total of 4125 pounds in boxes" (50)*(x) + (25)*(y) = 4125 [eq2] It is important to find two equations so we can solve for two variables. Solve for one of the variables in eq1 then replace (substitute) the expression for that variable in eq2. Let's solve for x: x = 115 - y [from eq1] 50(115-y) + 25y = 4125 [from eq2] 5750 - 50y + 25y = 4125 [distribute] 5750 - 25y = 4125 -25y = -1625 y = 65 [divide both sides by (-25)] There are 65 small boxes. Put that value into either equation (now, which is easier?) to solve for x: x = 115 - y x = 115 - 65 x = 50 There are 50 large boxes.
We either need to see a picture of this and/or get more information about the measurements of the triangle. In general, the area outside of the triangle will be the area of the semi-circle minus the area of the triangle itself, or: 1/2*49*3.14 - 1/2 b*h of the triangle. That first part, which is the area of the semi-circle, works out to 76.93 So based on the info we have, it becomes 76.93 - 1/2*b*h of the triangle = area outside of triangle.
The nature of the roots can be determined by the determinant of the equation. The determinant is:
b² - 4ac
If this is positive, there are two roots
If this is 0, there is only one root
If this is negative, there are complex roots
Hello there.^••^
−7w+8(w+1)=w−7
w+8=w−7
w+8−w=w−7−w8=−7
8−8=−7−80=−15
No solutions.
Answer:
New area: 12ft^2
Step-by-step explanation:
1/3 of 9 is 3
1/3 of 12 is 4
Area = l x w
so 3 x 4 = 12
