Answer:
x = 4 + sqrt(73) or x = 4 - sqrt(73)
Step-by-step explanation by completing the square:
Solve for x:
(x - 12) (x + 4) = 9
Expand out terms of the left hand side:
x^2 - 8 x - 48 = 9
Add 48 to both sides:
x^2 - 8 x = 57
Add 16 to both sides:
x^2 - 8 x + 16 = 73
Write the left hand side as a square:
(x - 4)^2 = 73
Take the square root of both sides:
x - 4 = sqrt(73) or x - 4 = -sqrt(73)
Add 4 to both sides:
x = 4 + sqrt(73) or x - 4 = -sqrt(73)
Add 4 to both sides:
Answer: x = 4 + sqrt(73) or x = 4 - sqrt(73)
Answer:
13 and 16
Step-by-step explanation:
let the 2 parts be x and y, then
x + y = 29 → (1) and
x² + y² = 425 → (2)
From (1) → x = 29 - y → (3)
substitute x = 29 - y into (2)
(29 - y)² + y² = 425 ( expand factor )
841 - 58y + y² + y² = 425 ( rearrange into standard form )
2y² - 58y + 416 = 0 ← in standard quadratic form
divide all terms by 2
y² - 29y + 208 = 0
Consider the factors of 208 which sum to - 29
These are - 13 and - 16, hence
(y - 13)(y - 16) = 0
equate each factor to zero and solve for y
y - 13 = 0 ⇒ y = 13
y - 16 = 0 ⇒ y = 16
substitute these values into (3)
x = 29 - 13 = 16 and x = 29 - 16 = 13
The 2 parts are 13 and 16
Answer:
D. 15°
Step-by-step explanation:
EGF and HGF are equal and 75°
since JGH is 90° we can say JGI is 90 - 75 = 15°
Area = πr²
50 = πr²
r = √50/π
so diameter = 2√50/π
which is = 7.98m to 3sf
Probability helps us to know the chances of an event occurring. The probability being a Sophomore given she is a girl is 1/3.
<h3>What is Probability?</h3>
Probability helps us to know the chances of an event occurring.
The probability of being a girl and Sophomore is 9/37. While the probability of being a girl is 27/37. Therefore, the probability being a Sophomore given she is a girl is,
P(Girl l Sophomores) = P(Girl and Sophomore)/ P(Girl)
= (9/37) / (27/37)
= 9 / 27
= 1/3
Hence, the probability being a Sophomore given she is a girl is 1/3.
Learn more about Probability:
brainly.com/question/795909
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