Answer:
x = 4 ± √13
Step-by-step explanation:
x² − 8x + 3 = 0
Complete the square. (-8/2)² = 16.
x² − 8x + 16 − 13 = 0
(x − 4)² − 13 = 0
(x − 4)² = 13
x − 4 = ±√13
x = 4 ± √13
Answer:
yes. it would technically be -1
Step-by-step explanation:
Because fractions are technically division, 6 ÷-6 = -1
Answer:
No it doesn't
Step-by-step explanation:
It doesn't because the numbers are not the same.
<h3>
Answer: D) 5</h3>
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Work Shown:
We use the intersecting chords theorem
(AH)*(HG) = (FH)*(HB)
(x-2)*(x+7) = (2x-1)*(4)
x*(x+7) - 2(x+7) = 4(2x-1)
x^2+7x - 2x - 14 = 8x - 4
x^2 + 7x - 2x - 14 - 8x + 4 = 0
x^2 - 3x - 10 = 0
(x - 5)(x + 2) = 0
x-5 = 0 or x+2 = 0
x = 5 or x = -2
If x = -2, then AH = x-2 = -2-2 = -4, but having a negative segment length is not possible. Lengths must be positive. So we ignore x = -2
If x = 5, then we find the following lengths
- AH = x-2 = 5-2 = 3
- HG = x+7 = 5+7 = 12
- FH = 2x-1 = 2*5-1 = 9
Then note how AH*HG = 3*12 = 36 while FH*HB = 9*4 = 36. This confirms that (AH)*(HG) = (FH)*(HB) is a true equation and confirms we have the correct x value.
<u>ANSWER: </u>
The length and breadth of the rectangle are 18 m and 12 m.
<u>SOLUTION:
</u>
Let the length and breadth of a rectangle be "l" and "b"
Given,length and breadth of the rectangle are in ratio 3 : 2
Then, length : breadth :: 3 : 2
-- eqn 1
After changing the length and breadth by 1 meter on both sides, length and breadth becomes L+2 and b+2
Now, the ratio of length to breadth is 10 : 7
Length : breadth :: 10 : 7
7l + 14 = 10b + 20
10b – 7l + 20 -14 = 0
10b – 7l + 6 =0 -- eqn (2)
Now, substitute “l” value in (2)
20b – 21b + 12 = 0
-b + 12 = 0
b = 12.
Substitute b value in (2)
10(12) – 7l + 6 = 0
120 + 6 = 7l
7l = 126
l = 18
hence, the length and breadth of the rectangle are 18 m and 12 m.
