In order to complete the square, the leading coefficient has to be a positive 1, which it is. Now we will set the polynomial equal to 0 and move the 2 over by subtraction to isolate the x terms.
. The rule now is to take half the linear term, square it, and then add it in to both sides. Our linear term is 6. Half of 6 is 3, and 3 squared is 9, so we add 9 to both sides.
. Simplifying we have
. During this process, and the reason for it, was to create a perfect square binomial on the left which will give us the x coordinate (or the h) for our vertex. That perfect square binomial is
. Now we will move the 7 over by subtraction and set the polynomial back equal to y to get
. Our vertex, then, is (3, -7) and this is a min value since our parabola is positive and opens up like a cup that has a bottom instead of mountain that has a top. And there you go! Your answer is C
Answer:
a) I used the equation x=-5; f(x)=-11 and x=-4; f(x)=-3. We get the range = -3-(-11)=8
b) I used the equation x=-5; f(x)=-11 and x=-3; f(x)=5. We get the range = 5-(-11)=16
c) I used the equation x=-5; f(x)=-11 and x=-2; f(x)=13. We get the range = 13-(-11)=24
d) Range of input is equal with the ratios of the output. You can find the pattern of output above 8,16,and 24 can divided by 8 and give the result 1,2 and 3
Part A: The algebraic equation for the situation is 2x - 3 = 5
Part B: Bob has 4 brand new music CD's
Step-by-step explanation:
Translate the situation into an algebraic equation:
- Ann has 5 brand new music CD’s, which is 3 less than twice the amount that Bob (x) has
- Find the value of x (the number of brand new CD's Bob has)
Part A:
∵ Bob has x brand new CD's
∵ Ann has 5 brand new music CD’s, which is 3 less than twice
the amount that Bob has
- That means multiply x by 2 and then subtract 3 from the product
and equate the answer by 5
∵ Twice x 2x
∵ 3 less than twice x = 2x - 3
∴ 2x - 3 = 5
The algebraic equation for the situation is 2x - 3 = 5
Part B:
Let us solve the equation to find the value of x
∵ 2x - 3 = 5
- Add 3 to both sides
∴ 2x = 8
- Divide both sides by 2
∴ x = 4
Bob has 4 brand new music CD's
Learn more:
You can learn more about the algebraic expressions in brainly.com/question/1600376
#LearnwithBrainly
Answer:
20, 000
Step-by-step explanation:
For a duration of 50 years, the consumption will be equal to the product of annual consumption and the number of years hence 800*50=40, 000 barrels.
Since 20, 000 barrels are unknown and they are part if consumption in the next 50 years, then the known or proven reserves will be given by getting the difference between total consumption and unknown reserve, expressed as 40, 000-20, 000=20, 000 barrels.
