Answer:
9
Step-by-step explanation:
The first sentence of the problem can be interpreted two ways. The way that makes the second sentence work out correctly is ...
'a larger number is 5 less than 3 times a smaller number'
Using x for the smaller number, the two equations that can be written are ...
Adding 4 times the first equation to the second, we get ...
4(3x -y) + (x +4y) = 4(5) +(97)
13x = 117 . . . . . simplify
x = 9 . . . . . . . . divide by 13
The smaller number is 9.
9514 1404 393
Answer:
10,450 cm³
Step-by-step explanation:
The volume is the product of the area of the facing face and the depth of the figure. The area of the facing face is the sum of the areas of a rectangle and a triangle. The relevant area formulas are ...
A = bh . . . . . area of rectangle with base b and height h
A = 1/2bh . . . area of triangle with base b and height h
Here the rectangle and triangle have the same base, 19 cm. Then the sum of the areas is ...
Atot = (19 cm)(18 cm) + 1/2(19 cm)(14 cm)
Atot = (19 cm)(18 cm +1/2×14 cm) = (19 cm)(25 cm) = 475 cm².
Then the volume of the figure is ...
V = Bh = (475 cm²)(22 cm) = 10,450 cm³
_____
<em>Additional comment</em>
Effectively, this is the volume of a cuboid whose height is that of the bottom rectangular prism (18 cm) plus half the height of the triangular prism on top (1/2×14 cm = 7 cm). (18+7=25) The volume is essentially 19 cm × 25 cm × 22 cm. This recognition can serve to simplify the work or to act as a check on the work done some other way.
41 because if you separate the parts the square and the triangle then you would have a square that is 16 sq in diameter and a triangle that is 25sq in diameter
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