Step-by-step explanation:
y > -15
y is bigger than -15
= -14 , -13 , -12 , -11 , -10 , etc . . .
NOT MY WORDS TAKEN FROM A SOURCE!
(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.
Hope this helped!
:)
Answer:
53, 55, 57, and 59
Step-by-step explanation:
Let the numbers be
x, x +2, x +4, and x+6. Then
x + x+2 + x +4 + x + 6 = 224 Combine like terms
4x + 12 = 224 Subtract 12 from each side
4x = 212 Divide each side by 4
x = 53
The four consecutive integers are 53, 55, 57, and 59.
<em>Check:
</em>
53 + 55 + 57 + 59 =224
Answer: Around 2,000 words.
(a)6x-28=4x+18
2x=46
x=23
(b)75=11x-2
77=11x
7=x
(c)x+139=132
x=-7
