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:
1.
hours / views
1. / 125
2. / 250
3. / 375
4. / 500
5. / 625
2.
f(x)= 125 x views=125.hours
The slope of the function equals the visits of each hour.
3. (1;125) (2;250) (3;375) (4;500) (5;625)
4. "views as a function of hours"
5. in 12 hours the website will have f(12)=125 . 12 = 1500 views.
we can see in the plot that the line gets to that number for 8
Week 15 they'll both weigh 181 lbs
Lowest common denominator for 3,4,6 is 12
5/6 = 10/12
1/4 = 3/12
2/3 = 8/12
a)
10/12 + 3/12 = 13/12 = 1 1/12
So you need to use first and second cables
b)
3/12 + 8/12 = 11/12
To reach 1 yard Carl need 1/12 yard cable
Hello there!
To find the increasing intervals for this graph just based on the equation, we should find the turning points first.
Take the derivative of f(x)...
f(x)=-x²+3x+8
f'(x)=-2x+3
Set f'(x) equal to 0...
0=-2x+3
-3=-2x
3/2=x
This means that the x-value of our turning point is 3/2. Now we need to analyze the equation to figure out the end behavior of this graph as x approaches infinity and negative infinity.
Since the leading coefficient is -1, as x approaches ∞, f(x) approaches -∞ Because the exponent of the leading term is even, the end behavior of f(x) as x approaches -∞ is also -∞.
This means that the interval by which this parabola is increasing is...
(-∞,3/2)
PLEASE DON'T include 3/2 on the increasing interval because it's a turning point. The slope of the tangent line to the turning point is 0 so the graph isn't increasing OR decreasing at this point.
I really hope this helps!
Best wishes :)
