Answer:
Step-by-step explanation:
i put this in a desmos graphing calculator
Answer:
Step-by-step explanation:
Answer:
- 5(x +1.5)^2
- 10(x +1)^2
- 1/4(x +2)^2
- 3(x +5/6)^2
Step-by-step explanation:
When your desired form is expanded, it becomes ...
a(x +b)^2 = a(x^2 +2bx +b^2) = ax^2 +2abx +ab^2
This tells you the overall factor (a) is the leading coefficient of the given trinomial. Factoring that out, you can find b as the root of the remaining constant.
a) 5x^2 +15x +11.25 = 5(x^2 +3x +2.25) = 5(x +1.5)^2
b) 10x^2 +20x +10 = 10(x^2 +2x +1) = 10(x +1)^2
c) 1/4x^2 +x +1 = 1/4(x^2 +4x +4) = 1/4(x +2)^2
d) 3x^2 +5x +25/12 = 3(x^2 +5/3x +25/36) = 3(x +5/6)^2
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<em>Additional comment</em>
If you know beforehand that the expressions can be factored this way, finding the two constants (a, b) is an almost trivial exercise. It gets trickier when you're trying to write a general expression in vertex form (this form with an added constant). For that, you must develop the value of b from the coefficient of the linear term inside parentheses.
Answer:
The first step is to replace the y in y-x=15 with 7x (we can do this because the first equation tells us that they're equal)
solve and get
(2.5,17.5)
or x= 2.5 y=17.5
Step-by-step explanation:
The first step is to recognize that y=7x which means that we can just replace the y in the second equation with 7x
7x-x=15
6x=15
x=2.5
Then we can solve for y
y=7(2.5)
y=17.5
Note that 60 minutes is 1 standard deviation away from the mean and from recalling the 68-95-99.7 rule, the area that will remain is (100 - 68) = 32%. However, we only want the leftmost portion of this area, so the answer is 32%/2 = 16%.
<span>Choose D.</span>
