2. Given two consecutive positive EVEN integers, the square of the largest minus
10 times the smaller is 76. What is the sum of the two integers?

26

Step-by-step explanation:

2. Given two consecutive positive EVEN integers, the square of the largest minus 10 times the smaller is 76. What is the sum of the two integers?

I'll call the two integers a and b.    a=b+2

a² - 10b = 76

(b+2)² - 10b =76

(b+2)(b+2) -10b = 76

b² +2b + 2b +4  -10b = 76

b² +4b + 4  -10b  = 76

b² -6b + 4 =76  subtract 76 from both sides to get the right side equal to zero

b² -6b +4 -76 = 0

b² -6b - 72 = 0  what factors of -72 add up to -6? The two that work are -12, 6

(b-12)(b+6) = 0   so  b-12  = 0   or b+6  =  0

                                 +12  +12         -6     -6

                                  b = 12      or     b = -6  but b must be positive so b=12, a=14  

a+b= 14+12 = 26

d.) yes, because the volume of the cone is greater than the volume of the sphere

step-by-step explanation:

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