Answer: 10, 11, & 12
<u>Step-by-step explanation:</u>
Let x represent the age of the youngest child.  
Their ages are consecutive so,
Youngest: x
Middle: x + 1
Oldest: x + 2
The age of the Youngest squared (x²) equals 8 times the Oldest [8(x + 2)] plus 4.
x² = 8(x + 2) + 4
x² = 8x + 16 + 4
x² = 8x + 20
x² - 8x - 20 = 0
(x - 10)(x + 2) = 0
x - 10 = 0     or      x + 2 = 0
   x = 10       or          x = -2
Since age cannot be negative, x = -2 is not valid
So, the Youngest (x) is 10
the Middle (x + 1) is 11
and the Oldest (x + 2) is 12
 
        
             
        
        
        
<u>Answer:</u><u> </u><u>3</u><u>4</u><u> </u><u>m</u><u>o</u><u>r</u><u>e</u><u> </u><u>p</u><u>o</u><u>u</u><u>c</u><u>h</u><u>e</u><u>s</u>
7 boxes - fish food; 1 box contained 6 pouches
Total amount of fish food is 7 × 6 = 42 pouches of fish food
2 packets - cat food; 1 packet contained 4 pouches
Total amount of cat food is 2 × 4 = 8 pouches
How many more pouches of fish food than cat food did Shelly buy? 
42 pouches - 8 pouches = 34 pouches
Therefore there was 34 more pouches of fish food than cat food
 
        
             
        
        
        
Because if you rotate an object 360 degrees it’s like the object never moved because the object would still be in the same spot as if you didn’t move it
        
             
        
        
        
<u>Given</u>:
The sides of the base of the triangle are 8, 15 and 17.
The height of the prism is 15 units.
We need to determine the volume of the right triangular prism.
<u>Area of the base of the triangle:</u>
The area of the base of the triangle can be determined using the Heron's formula.

Substituting a = 8, b = 15 and c = 17. Thus, we have;


Using Heron's formula, we have;





Thus, the area of the base of the right triangular prism is 36 square units.
<u>Volume of the right triangular prism:</u>
The volume of the right triangular prism can be determined using the formula,

where  is the area of the base of the prism and h is the height of the prism.
 is the area of the base of the prism and h is the height of the prism.
Substituting the values, we have;


Thus, the volume of the right triangular prism is 450 cubic units.