Here is one way to solve for x.
Step 1) 2x^2-7=9
Step 2) 2x^2-7+7=9+7
Step 3) 2x^2=16
Step 4) (2x^2)/2=16/2
Step 5) x^2=8
Step 6) sqrt(x^2)=sqrt(8)
Step 7) |x|=sqrt(8)
Step 8) x=sqrt(8) or x=-sqrt(8)
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Below are explanations/reasons to each of the steps above.
Step 1) Original equation
Step 2) Add 7 to both sides
Step 3) Combine like terms
Step 4) Divide both sides by 2
Step 5) Simplify
Step 6) Apply the square root to both sides. The notation "sqrt" is shorthand for "square root"
Step 7) Use the rule that sqrt(x^2) = |x| for all real numbers x
Step 8) Use the rule that if |x| = k then x = k or x = -k for some fixed number k.
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The two solutions are
x = sqrt(8) or x = -sqrt(8)
Answer:
y= 1/2 x +7
the slope is 1/2 since hwne it's perpendicular, it's reciprocal and the sign also changes
Step-by-step explanation:
3= -4 +b
b= 7
Answer:
Some number or variable less than 5.
Step-by-step explanation:
Answer:
Proofs are in the explantion.
Step-by-step explanation:
We are given the following:
1) 
for integer 
.
1) 
for integer 
.
a)
Proof:
We want to show 
.
So we have the two equations:
a-b=kn and c-d=mn and we want to show for some integer r that we have
(a+c)-(b+d)=rn. If we do that we would have shown that .
kn+mn = (a-b)+(c-d)
(k+m)n = a-b+ c-d
(k+m)n = (a+c)+(-b-d)
(k+m)n = (a+c)-(b+d)
k+m is is just an integer
So we found integer r such that (a+c)-(b+d)=rn.
Therefore, .
//
b) Proof:
We want to show 
.
So we have the two equations:
a-b=kn and c-d=mn and we want to show for some integer r that we have
(ac)-(bd)=tn. If we do that we would have shown that .
If a-b=kn, then a=b+kn.
If c-d=mn, then c=d+mn.
ac-bd = (b+kn)(d+mn)-bd
= bd+bmn+dkn+kmn^2-bd
= bmn+dkn+kmn^2
= n(bm+dk+kmn)
So the integer t such that (ac)-(bd)=tn is bm+dk+kmn.
Therefore, .
//
Answer:
B) No
Step-by-step explanation:
the expressions are not equivalent
