Answer: C
Step-by-step explanation:
Given 2 similar solids whose
ratio of sides = a : b, then
ratio of areas = a^2 : b^2 and
ratio of volumes = a^3 : b^3
Here the area ratio = 169 : 81, thus
side ratio = sqrt{169} : sqrt{81} = 13 : 9
Hence the volume ratio = 13^3 : 9^3
Using proportion then
frac{13^3}{9^3} = frac{124.92}{x} → C
Find the sum of -3a and 5a -3
-3a + (5a-3)
2a-3
Answer:
∠ N = 41°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 given angles and equate to 180, that is
6x + 1 + 3x - 10 + x + 19 = 180, simplifying
10x + 10 = 180 ( subtract 10 from both sides )
10x = 170 ( divide both sides by 10 )
x = 17
Thus
∠ N = 3x - 10 = 3(17) - 10 = 51 - 10 = 41°
When 40% is added, it becomes 140%
140% = 182
1% = 182 ÷ 140 = 1.3
100% = 1.3 x 100 =130
The number is 130
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.