<h3>
Answer: You have the correct answer. It's choice A. </h3>
Explanation:
You can verify this by plugging each root into the equation.
So for instance, plug in x = -2 and we get
f(x) = -3*(x+2)*(x-sqrt(3))*(x-4)
f(-2) = -3*(-2+2)*(-2-sqrt(3))*(-2-4)
f(-2) = -3*(0)*(-2-sqrt(3))*(-2-4)
f(-2) = 0
This verifies x = -2 is a root.
All that matters is that zero buried in there in the second to last step. Multiplying 0 by anything leads to 0. The other roots are verified in the same manner. The -3 out front is the leading coefficient.
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Extra info:
- Choice B is eliminated because (x+3) being a factor implies that x = -3 is a root. But this isn't listed in the instructions.
- Choice C is a similar story to choice B
- Choice D is eliminated since -sqrt(3) is not one of the listed roots, so (x+sqrt(3)) is not a factor.
Your answer is C) 2a² + 2b²
To find this we can just expand the brackets of (a - b)² and (a + b)², and then combine like terms:
(a - b)² = (a - b)(a - b) = a² - 2ab + b²
(a + b)² = (a + b)(a + b) = a² + 2ab + b²
Then when you combine like terms, you get (a² + a²) + (-2ab + 2ab) + (b² + b²), so the ab terms cancel out and you get left with 2a² + 2b².
I hope this helps!
The midpoint is calculated by averaging the coordinates of its endpoints:
Now we can use the usual distance formula to get the length of SM:
By drawing the hypotenuse of the shape.
Answer:
234 times
Step-by-step explanation:
<u>Number of times the number 7 appears in a hundred</u>
7 as units digit (07-17-27 ..... 97): 10 times
7 as tens digit (70-71-72..... 79): 10 times
20 times the digit 7 appears in first one hundred (0-100)
Let's calculate how many times 7 would be as units or tens in 7 hundreds
20X7 = 140 times digit 7 appears until number 699
<u>Now, from 700 to 777</u>
7 as hundreds digit (700-701-702 .... 777): 78 times
7 as tens digit (770-771-772 .... 777): 8 times
7 as units digit (707-717-727....777): 8 times
78 + 8 + 8 = 94 times the digit 7 appears in the range 700 - 777. Plus 140 times
140 + 94 = 234 times