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Post by Laurie on May 2, 2019 18:05:48 GMT
I have been working on this problem with my dd and while I think I have the answer it is not factored. It is driving me crazy now not figuring this out. I said 24x=(12 square root of 3) squared. Which is 24x=432. X=18 How would we factor this? She said in the other review problems it was (square root + something)(square root + another #). I don’t remember anything from Geometry and it took me a lot of googling to even figure out how to go about this problem with her. Lol ETA: Ignore her 1.5 answer as she knew that was wrong.  Attachments:
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Post by stumpedagainof3 on May 2, 2019 18:15:41 GMT
I thought 1.5 was right, so I'm no help.
Sorry
Edited to add that my daughter thinks 1.5 is correct also. Haha
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Post by Laurie on May 2, 2019 18:24:53 GMT
I thought 1.5 was right, so I'm no help. Sorry Edited to add that my daughter thinks 1.5 is correct also. Haha I bet she is doubting herself because of my answer. Now that I look at it 1.5 would make more sense. My geometry googling has led me astray. |
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Jun 9, 2024 21:38:49 GMT
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Post by Deleted on May 2, 2019 18:37:35 GMT
I thought it's 1.5 as well.
3 x 3 = 9
Square root of 9 is 3
3 x 12 = 36
24x = 36
x = 36/24
x = 1.5
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Post by kmcginn on May 2, 2019 18:46:24 GMT
18 is correct.
(12 square root of 3) squared is (144 times 3) which equals 432. 24x = 432. 432 divided by 24 = 18. so x=18
ETA (square root of 3) squared is 3, not 9. 12 squared is 144. So 144 times 3 is 432. |
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Post by stumpedagainof3 on May 2, 2019 19:57:07 GMT
18 is correct.
(12 square root of 3) squared is (144 times 3) which equals 432. 24x = 432. 432 divided by 24 = 18. so x=18
ETA (square root of 3) squared is 3, not 9. 12 squared is 144. So 144 times 3 is 432. Just to debate this a little... I think the exponent only attaches to the square root of 3, not the 12. You would do the exponent first which would give you the 3. Then 12 × 3 is 36. 24x=36 X=36/24 I hope that makes sense. |
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Post by Darcy Collins on May 2, 2019 20:00:11 GMT
I'm not sure you set up the intersecting secant-tangent correctly - or I'm misinterpreting the figure. Assuming 24 is the distance within the circle and x is the distance outside the circle - it should be:
(24+x)*x=(12(sqrt 3))^2
Which would be x^2+24x-432=0
which would factor to 12 and negative 36
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Post by kmcginn on May 2, 2019 20:44:45 GMT
If the exponent is outside the parenthesis, then it applies to everything that's inside the parenthesis, so you have to square both the 12 and the square root of 3. It's hard to interpret without having a square root symbol to use while typing. Because in reality, the 12 is part of the expression so you have to square both.
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Post by Laurie on May 3, 2019 18:27:28 GMT
I think you are right Darcy Collins. I continued googling and came across a different formula that brought me to that same answer. X would have to be 12 because a line can't have a negative value. She won't get the assignment back until probably Tuesday (block scheduling here) so this is still unsolved in my mind and driving me crazy. FWIW, when I used photo math for the (12 square root of 3)^2 it came back with 432. LOL Given the formula that I was using I believe the 12 square root of 3 would be in parenthesis. I am so glad there is only 2 weeks of geometry left. I remember nothing from geometry years and years ago. HA! Thankfully next year is Algebra 2. I love algebra! |
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Post by kmcginn on May 3, 2019 20:51:48 GMT
My apologies! I didn't even see the attachment. I was going strictly by your typing of the problem.
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Post by mikewozowski on May 3, 2019 20:56:15 GMT
i don't think this is geometry.
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Post by missmiss on May 3, 2019 21:50:02 GMT
This is a tangent secant problem.
The equation is:
(tanget)^2 = (outside part of the secant)(the whole secant)
(12sqrt(3))^2 = (x)(x + 24)
432 = x^2 + 24x
0 = x^2 + 24x - 432
0 = (x + 36)(x - 12)
x = -36 or 12
since x can't be negative x = 12
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seaexplore
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Post by seaexplore on May 3, 2019 23:34:16 GMT
18 is correct.
(12 square root of 3) squared is (144 times 3) which equals 432. 24x = 432. 432 divided by 24 = 18. so x=18
ETA (square root of 3) squared is 3, not 9. 12 squared is 144. So 144 times 3 is 432. Just to debate this a little... I think the exponent only attaches to the square root of 3, not the 12. You would do the exponent first which would give you the 3. Then 12 × 3 is 36. 24x=36 X=36/24 I hope that makes sense. Yep. I teach middle school mat and I’m in the 1.5 camp. The way it is written, the squared is only on the root of 3. They are opposite operations so they cancel out. 12*3=36. 36/24=1.5 |
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Post by seaexplore on May 3, 2019 23:35:17 GMT
I'm not sure you set up the intersecting secant-tangent correctly - or I'm misinterpreting the figure. Assuming 24 is the distance within the circle and x is the distance outside the circle - it should be: (24+x)*x=(12(sqrt 3))^2 Which would be x^2+24x-432=0 which would factor to 12 and negative 36 Yep. If it’s written correctly like you’ve said here. |
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Post by missmiss on May 3, 2019 23:46:38 GMT
Just to debate this a little... I think the exponent only attaches to the square root of 3, not the 12. You would do the exponent first which would give you the 3. Then 12 × 3 is 36. 24x=36 X=36/24 I hope that makes sense. Yep. I teach middle school mat and I’m in the 1.5 camp. The way it is written, the squared is only on the root of 3. They are opposite operations so they cancel out. 12*3=36. 36/24=1.5 The way the student (her daughter) did the problem is incorrect. 12sqrt(3) is the exact value for the tangent length which means you have to square all of it not just the sqrt(3). If it was 24x = 12 * sqrt(3)^2 then 1.5 would be correct but the student's equation does not properly use the formula correctly. www.dummies.com/education/math/geometry/how-to-use-the-tangent-secant-power-theorem/High School Math Teacher for 14 years. |
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Post by seaexplore on May 4, 2019 0:30:03 GMT
Yep. I teach middle school mat and I’m in the 1.5 camp. The way it is written, the squared is only on the root of 3. They are opposite operations so they cancel out. 12*3=36. 36/24=1.5 The way the student (her daughter) did the problem is incorrect. 12sqrt(3) is the exact value for the tangent length which means you have to square all of it not just the sqrt(3). If it was 24x = 12 * sqrt(3)^2 then 1.5 would be correct but the student's equation does not properly use the formula correctly. www.dummies.com/education/math/geometry/how-to-use-the-tangent-secant-power-theorem/High School Math Teacher for 14 years. Yep. I was looking at it originally as the part her kiddo wrote was given by the teacher. Once I saw the other explanation of it, it makes sense. The drawing made no sense to me but I did get that it was something to do with tangent. I totally suck at geometry. Hence the teaching of middle school math. Lol |
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Post by missmiss on May 4, 2019 0:41:00 GMT
The way the student (her daughter) did the problem is incorrect. 12sqrt(3) is the exact value for the tangent length which means you have to square all of it not just the sqrt(3). If it was 24x = 12 * sqrt(3)^2 then 1.5 would be correct but the student's equation does not properly use the formula correctly. www.dummies.com/education/math/geometry/how-to-use-the-tangent-secant-power-theorem/High School Math Teacher for 14 years. Yep. I was looking at it originally as the part her kiddo wrote was given by the teacher. Once I saw the other explanation of it, it makes sense. The drawing made no sense to me but I did get that it was something to do with tangent. I totally suck at geometry. Hence the teaching of middle school math. Lol I didn't want to teach Geometry but 4 years ago my boss decided to have me teach it all day. The only thing I don't like teaching in Geometry is proofs. Everything else to me is fun. |
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Post by seaexplore on May 4, 2019 0:45:18 GMT
Yep. I was looking at it originally as the part her kiddo wrote was given by the teacher. Once I saw the other explanation of it, it makes sense. The drawing made no sense to me but I did get that it was something to do with tangent. I totally suck at geometry. Hence the teaching of middle school math. Lol I didn't want to teach Geometry but 4 years ago my boss decided to have me teach it all day. The only thing I don't like teaching in Geometry is proofs. Everything else to me is fun. I have advanced 8th grade math kids who come to me after taking 0 period math at the high school. They were doing proofs and asked me for help. I handed them a chromebook and directed them to Khan Academy. I DETEST proofs! I teach the VERY beginnings of them in my regular 8th Math class. Ick! My least favorite section after the hell of surface area and volume! |
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