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Levart [38]
3 years ago
7

Need help with questions 11&15

Mathematics
1 answer:
Paladinen [302]3 years ago
6 0

2000 (1 + .11 \times 72 \div 360)
= 2044
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Determine the next step for solving the quadratic equation by completing the square.
nexus9112 [7]

\qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2

the idea behind the completion of the square is simply using a perfect square trinomial,  hmmm usually we do that by using our very good friend Mr Zero, 0.

if we look at the 2nd step, we have a group as x² - x, hmmm so we need a third element, which will be squared.

keeping in mind that the middle term of the perfect square trinomial is simply the product of the roots of "a" and "b",  so in this case the middle term is "-x", and the 1st term is x², so we can say that

\stackrel{middle~term}{2(\sqrt{x^2})(\sqrt{b^2})~}~ = ~~\stackrel{middle~term}{-x}\implies 2xb~~ = ~~~~ = ~~-x \\\\\\ b=\cfrac{-x}{2x} \implies b=-\cfrac{1}{2}

so that means that our missing third term for a perfect square trinomial is simply 1/2, now we'll go to our good friend Mr Zero, if we add (1/2)², we have to also subtract (1/2)², because all we're really doing is borrowing from Zero, so we'll be including then +(1/2)² and -(1/2)², keeping in mind that 1/4 - 1/4 = 0, so let's do that.

-3~~ = ~~-2\left[ x^2-x+\left( \cfrac{1}{2} \right)^2 ~~ - ~~\left( \cfrac{1}{2} \right)^2\right]\implies -3=-2\left(x^2-x+\cfrac{1}{4}-\cfrac{1}{4} \right) \\\\\\ -3=-2\left(x^2-x+\cfrac{1}{4} \right)+(-2)-\cfrac{1}{4}\implies -3=-2\left(x^2-x+\cfrac{1}{4} \right)+\cfrac{1}{2} \\\\\\ -3-\cfrac{1}{2}=-2\left(x^2-x+\cfrac{1}{4} \right)\implies -\cfrac{7}{2}=-2\left(x-\cfrac{1}{2} \right)^2\implies \cfrac{7}{4}=\left(x-\cfrac{1}{2} \right)^2

~\dotfill\\\\ \pm\sqrt{\cfrac{7}{4}}=x-\cfrac{1}{2}\implies \cfrac{\pm\sqrt{7}}{2}=x-\cfrac{1}{2}\implies \cfrac{\pm\sqrt{7}}{2}+\cfrac{1}{2}=x \implies \cfrac{\pm\sqrt{7}+1}{2}=x

8 0
2 years ago
Help me please with 3 and 4
dezoksy [38]
X is equal to or greater than 3:

Plot x = 3 on the x-axis (horizontal axis).  Then, beginning at x = 3, draw an arrow from there to the right.  
8 0
3 years ago
use the following graph of the function of degree 9 to identify the zeros of function and their possible multiplicities
nexus9112 [7]

Answer:

d

Step-by-step explanation:

sd

7 0
3 years ago
-10x+x-76=149 what is x?
user100 [1]

Step-by-step explanation:

Add like terms: -10x and x which is equal to -9x. the equation is -9x-76=149 then add 76. the 76s cancel out. add 76 on the other side. it will be -9x=225. U then divide by -9. the -9s cancel out. on the other 225/-9=25. So x=-25 as the answer

4 0
4 years ago
The height of a baseball after being hit by a batter is given by h(t) = -16t^2 + 60t + 4 (where h(t) is the height and t is the
mr Goodwill [35]

Answer:

3.82 seconds only

Step-by-step explanation:

Time is only positive, therefore you should only use 3.82 seconds as your answer.

8 0
3 years ago
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