9514 1404 393
Answer:
m^2 = 35/9
Step-by-step explanation:
The line will be tangent to the ellipse where there is one point of intersection between the line and the ellipse. We can find that case by looking at the discriminant of the quadratic.
x^2 +9(mx +2)^2 = 1
x^2 +9(m^2x^2 +4mx +4) = 1
(9m^2 +1)x^2+36mx +35 = 0 . . . . subtract 1, collect terms
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Then the discriminant is ...
(36m)^2 -4(9m^2 +1)(35)
We want it to be zero, so we have ...
1296m^2 -1260m^2 -140 = 0 . . . . eliminate parentheses
36m^2 = 140 . . . . . . . . . . . . . . . add 140
m^2 = 140/36 . . . . . . . . . . . . divide by 36
m^2 = 35/9
Answer:
x = 1/5
Step-by-step explanation:
Step 1: Write equation
-5x - (-7 - 4x) = -2(3x - 4)
Step 2: Solve for <em>x</em>
- <u>Distribute:</u> -5x + 7 + 4x = -6x + 8
- <u>Combine like terms:</u> -x + 7 = -6x + 8
- <u>Add 6x to both sides:</u> 5x + 7 = 8
- <u>Subtract 7 on both sides:</u> 5x = 1
- <u>Divide by 5 on both sides:</u> x = 1/5
Step 3: Check
<em>Plug in x to verify it's a solution.</em>
-5(1/5) - (-7 - 4(1/5)) = -2(3(1/5) - 4)
-1 - (-7 - 4/5) = -2(3/5 - 4)
-1 - (-39/5) = -2(-17/5)
-1 + 39/5 = 34/5
34/5 = 34/5
When expanding number, we should separate the numbers according to the places like the number 275 written in expanded form 200+70+5. So, in this question we must likely done like this. The number is 39,005 the sum that is written on expanded form is 30,000+9,000+5.
Answer:
-.5
Step-by-step explanation:
I believe if I’m not wrong the answer should be B 1/6
