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(x^2) <64 => (x^2) -64 < 64-64 => (x^2) - 64 < 0 64= 8^2 so (x^2) - (8^2) < 0 To solve the inequality we first find the roots (values of x that make (x^2) - (8^2) = 0 ) Note that if we can express (x^2) - (y^2) as (x-y)* (x+y) You can work backwards and verify this is true. so let's set (x^2) - (8^2) equal to zero to find the roots: (x^2) - (8^2) = 0 => (x-8)*(x+8) = 0 if x-8 = 0 => x=8 and if x+8 = 0 => x=-8 So x= +/-8 are the roots of x^2) - (8^2)Now you need to pick any x values less than -8 (the smaller root) , one x value between -8 and +8 (the two roots), and one x value greater than 8 (the greater root) and see if the sign is positive or negative. 1) Let's pick -10 (which is smaller than -8). If x=-10, then (x^2) - (8^2) = 100-64 = 36>0 so it is positive
2) Let's pick 0 (which is greater than -8, larger than 8). If x=0, then (x^2) - (8^2) = 0-64 = -64 <0 so it is negative3) Let's pick +10 (which is greater than 10). If x=-10, then (x^2) - (8^2) = 100-64 = 36>0 so it is positive Since we are interested in (x^2) - 64 < 0, then x should be between -8 and positive 8. So -8<x<8 Note: If you choose any number outside this range for x, and square it it will be greater than 64 and so it is not valid.
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Answer:
1st answer: 52 serves
2nd answer: $8.40
Step-by-step explanation:
1st: 80 times 65 equals 5,200 divided by 100 equals 52
2nd: 42 times 0.20 equals 8.4 or 8.40
your answer is right since your going to the right +3 and decreasing -9 units
Answer:
sqrt(54) is between 7 and 8
Step-by-step explanation:
Lets look at integers that are squared
1^2 = 1
2^2 = 2
3^2 = 9
4^2 = 16
5^2= 25
6^2 = 36
7^2 = 49
6^2 =64
54- 49 = 5 and 64 - 54 = 10
So 54 is closer to 49
so sqrt(54) is closer to the sqrt(49) = 7
sqrt(54) is between 7 and 8
Answer:
V≈12308.8
Step-by-step explanation:
V=πr2h
V=(3.14)(14)2(20)
R=14cm
H=20cm
π=3.14
