X² <span>+ 11x + 7
because 7 is a prime number, this doesn't factor prettily. you'll want to use the quadratic formula; if you aren't familiar with it, i'd either research it or look it up in your textbook, because it's clunky and not easily understood in this format:
(-b </span>± √((b)² - 4ac))/(2a)
in your equation x² + 11x + 7 ... a = 1, b = 11, and c = 7. what you do is you take the coefficients of every term, then plug it into your equation:
(-11 ± √((11)² - 4(1)(7))/(2(1))
not pretty, i know. but, regardless, you can simplify it:
(-11 ± √((11)² - 4(1)(7))/(2(1))
(-11 ± √(121 - 28))/2
(-11 ± √93)/2
and you can't simplify it further. -11 isn't divisible by 2, and 93 doesn't have a perfect square that you can take out from beneath the radical. the ± plus/minus symbol indicates that you have 2 answers, so you can write them out separately:
(x - (-11 - √93)/2) and (x + (-11 - √93)/2)
they look confusing, but those are your two factors. they can be simplified just slightly by changing the signs in the middle due to the -11:
(x + (11 + √93)/2) (x - (11 - √93)/2)
and how these would read, just in case the formatting is too confusing for you: x plus the fraction 11 + root 93 divided by 2. the 11s and root 93s are your numerator, 2s are your denominator.
The third one would be the correct answer. I separately multiplied each number in the first section by each number in the second section. For instance, 0 x 2 is 0, 4 x 5 is 20, 5 x 3 is 15, and 2 x 0 is 0. All of these numbers are in the third answer.
Answer:
Step-by-step explanation:
I dont quite understand the problem but this is one way to solve it using completing the square:-
2x^2 + 8x - 12 = 0
2(x^2 + 4x) - 12 = 0
2((x + 2)^2 - 4) = 12
2(x + 2)^2 - 8 + 8 = 12 + 8
2(x + 2)^2 = 20
PEMDAS states that the value in the parenthesis should be evaluated first:
4(5*6)
4(30)
After just multiply the value in the parenthesis by the number outside of the parenthesis:
120
Answer:
Both of these triangles are congruent.
Step-by-step explanation:
All 3 angle measures of both of the triangles are equivalent and correlate to each other. This makes the triangles congruent.
