Destinyyyy
  • Destinyyyy
Need help and a memory refresher on 8 problems.. Please do not give me answers. I want to remember how to solve them. This is my midterm review.
Mathematics
  • Stacey Warren - Expert brainly.com
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Destinyyyy
  • Destinyyyy
11. Perform the indicated operations and write in standard form. (-10 + square root -9) ^2
Destinyyyy
  • Destinyyyy
16. Solve the problem. A rain gutter is made from sheets of aluminum that are 24 inches wide. The edges are turned up to form right angles. Determine the depth of the gutter that will allow a cross-sectional area of 58 square inches. There are two solutions to this problem. Round to the nearest tenth of an inch.
Destinyyyy
  • Destinyyyy
21. Solve the linear inequality. Other than not solution sign, use interval notation to express the solution set and graph the solution set on a number line. x-1 over 16 >/ x-4 over 20 + 1 over 80

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Destinyyyy
  • Destinyyyy
@jim_thompson5910 @welshfella @Nnesha
Destinyyyy
  • Destinyyyy
Please help me finish. I still have a chapter test and midterm to do for another class. Im majorly behind since the system keeps glitching.
Destinyyyy
  • Destinyyyy
@IrishBoy123
jim_thompson5910
  • jim_thompson5910
Hopefully in your lesson somewhere you learned that \[\Large i = \sqrt{-1}\] ? or no?
Destinyyyy
  • Destinyyyy
Yes I did last term.
jim_thompson5910
  • jim_thompson5910
ok great
jim_thompson5910
  • jim_thompson5910
what we can do is rewrite -9 as -1*9 and simplify like this \[\Large \sqrt{-9} = \sqrt{-1*9}\] \[\Large \sqrt{-9} = \sqrt{-1}*\sqrt{9}\] \[\Large \sqrt{-9} = i*3\] \[\Large \sqrt{-9} = 3i\] make sense?
Destinyyyy
  • Destinyyyy
Yes!
jim_thompson5910
  • jim_thompson5910
\[\Large \left(-10+\sqrt{-9}\right)^2\] turns into \[\Large \left(-10+3i\right)^2\]
Destinyyyy
  • Destinyyyy
Yep I have that.
jim_thompson5910
  • jim_thompson5910
Next you'll use the box method or FOIL or the distributive property to expand out \[\Large \left(-10+3i\right)^2\]
jim_thompson5910
  • jim_thompson5910
personally I like the box method but you can choose which one you want to do
Destinyyyy
  • Destinyyyy
So.. (-10+3i)(-10+3i)
jim_thompson5910
  • jim_thompson5910
yes
jim_thompson5910
  • jim_thompson5910
keep going
Destinyyyy
  • Destinyyyy
I got.. 100-51i
jim_thompson5910
  • jim_thompson5910
incorrect
Destinyyyy
  • Destinyyyy
Yeah...
Destinyyyy
  • Destinyyyy
Not sure where im going wrong.. (-10+3i)(-10+3i) 100-30i-30i+9i 100-60i+9i 100-51i
jim_thompson5910
  • jim_thompson5910
3i times 3i = 9i^2 not just 9i
jim_thompson5910
  • jim_thompson5910
since i = sqrt(-1), squaring both sides gives i^2 = -1
Destinyyyy
  • Destinyyyy
Omg -.-
Destinyyyy
  • Destinyyyy
91-60i
jim_thompson5910
  • jim_thompson5910
perfect
Destinyyyy
  • Destinyyyy
Okay. For number 16. Solve the problem. A rain gutter is made from sheets of aluminum that are 24 inches wide. The edges are turned up to form right angles. Determine the depth of the gutter that will allow a cross-sectional area of 58 square inches. There are two solutions to this problem. Round to the nearest tenth of an inch. I got to -20+- square root 296 all over -4
Destinyyyy
  • Destinyyyy
the square root 296 can turn into 2 square root 74
Destinyyyy
  • Destinyyyy
-20 +- 2 square root 74 all over -4 Then I can -20 and -4 --> 5
Destinyyyy
  • Destinyyyy
I'm kinda stuck there.
jim_thompson5910
  • jim_thompson5910
I'm not sure how you got that. What quadratic equation did you get to?
Destinyyyy
  • Destinyyyy
Um.. -2x^2 +20x -13=0 -20+- square root (20)^2 -4(-2)(-13) all over 2(-2) Some girl earlier said to- 2x+y=20 y=20-2x x*y=13 x*(20-2x)=13
Destinyyyy
  • Destinyyyy
Im really not sure. I followed what she said. And I responded saying I was stuck and she didnt reply.
jim_thompson5910
  • jim_thompson5910
ok let's start with a 24 inch line |dw:1444423527504:dw|
jim_thompson5910
  • jim_thompson5910
we will bend this line into a partial rectangle like this |dw:1444423553539:dw| I can't do animations on here but hopefully you can picture what is going on
Destinyyyy
  • Destinyyyy
I can.
jim_thompson5910
  • jim_thompson5910
after the bending is done, we have this left over |dw:1444423623561:dw|
jim_thompson5910
  • jim_thompson5910
if we make x = depth, then we have this |dw:1444423774023:dw|
jim_thompson5910
  • jim_thompson5910
what is the length of the bottom side?
Destinyyyy
  • Destinyyyy
What do you mean? As in y?
jim_thompson5910
  • jim_thompson5910
hint: |dw:1444423922673:dw|
jim_thompson5910
  • jim_thompson5910
replace the question marks with some expression in terms of x
Destinyyyy
  • Destinyyyy
I understand what your saying but I keep thinking Y. Unless its 58?
jim_thompson5910
  • jim_thompson5910
|dw:1444424117414:dw|
Destinyyyy
  • Destinyyyy
Or is it still 24 even though the edges have been bent.
Destinyyyy
  • Destinyyyy
Oh..
jim_thompson5910
  • jim_thompson5910
there are 2 xs being subtracted off, so that's how I got 24-2x
jim_thompson5910
  • jim_thompson5910
|dw:1444424187334:dw|
Destinyyyy
  • Destinyyyy
Yes I understand now.
jim_thompson5910
  • jim_thompson5910
Area = Length * Width 58 = (24 - 2x) * x 58 = 24x - 2x^2 -2x^2 + 24x - 58 = 0 solve for x using the quadratic formula
Destinyyyy
  • Destinyyyy
Okay. Im at.. -24 +- 4 square root 65 over -4
jim_thompson5910
  • jim_thompson5910
you made an error somewhere
Destinyyyy
  • Destinyyyy
-24 +- square root 576 +464 over -4
jim_thompson5910
  • jim_thompson5910
it should be -464 not +464
jim_thompson5910
  • jim_thompson5910
b^2 - 4ac (24)^2 - 4*(-2)*(-58) 576 - 464
Destinyyyy
  • Destinyyyy
Oops I put a + in front of the 4...
Destinyyyy
  • Destinyyyy
Now I have.. 6+- -1 square root 7
jim_thompson5910
  • jim_thompson5910
good, \[\Large x = 6 \pm \sqrt{7}\]
Destinyyyy
  • Destinyyyy
Answer-> 3.4 and 8.6
jim_thompson5910
  • jim_thompson5910
both are correct
Destinyyyy
  • Destinyyyy
Okay thank you.. 6 left.. 21. Solve the linear inequality. Other than not solution sign, use interval notation to express the solution set and graph the solution set on a number line. x-1 over 16 >/ x-4 over 20 + 1 over 80
jim_thompson5910
  • jim_thompson5910
This? \[\Large \frac{x-1}{16} \ge \frac{x-4}{20} + \frac{1}{80}\]
Destinyyyy
  • Destinyyyy
I know the answer is -10.. Its the only option.. My first attempt I canceled out the fractions by using 4... Yes thats it.
jim_thompson5910
  • jim_thompson5910
I would use 80 instead
Destinyyyy
  • Destinyyyy
True..
jim_thompson5910
  • jim_thompson5910
Multiply every term by the LCD 80 to clear out the fractions \[\Large \frac{x-1}{16} \ge \frac{x-4}{20} + \frac{1}{80}\] \[\Large 80*\frac{x-1}{16} \ge 80*\frac{x-4}{20} + 80*\frac{1}{80}\] \[\Large 5(x-1) \ge 4(x-4) + 1\]
Destinyyyy
  • Destinyyyy
Yep.. Should of figured that out :/ ... x
jim_thompson5910
  • jim_thompson5910
correct
Destinyyyy
  • Destinyyyy
Its [-10, infinity) correct?
jim_thompson5910
  • jim_thompson5910
yes, sorry I misread your first inequality it should be \(\Large x \ge -10\) which turns into `[-10, infinity)`
Destinyyyy
  • Destinyyyy
Okay. Sorry typed the wrong one.
Destinyyyy
  • Destinyyyy
Next problem.. 24. Determine whether the equation defines y as a function of x. xy + 5y = 1
Destinyyyy
  • Destinyyyy
I don't remember doing any problems like this. And I couldn't find any examples from my notes.
jim_thompson5910
  • jim_thompson5910
We solve for y to get xy + 5y = 1 y(x + 5) = 1 y = 1/(x + 5) which is definitely a function. You can graph to verify that it passes the vertical line test. Any given input (x) produces EXACTLY ONE output (y)
Destinyyyy
  • Destinyyyy
Okay!
Destinyyyy
  • Destinyyyy
26. Evaluate the function at the given value of the independent variable and simplify. f(x) = 3x2 - 4x + 4; f(x - 1)
Destinyyyy
  • Destinyyyy
I'm not sure on this one either.. I was thinking plug (x-1) in for the x's but im not sure. If you want me to post in a new question I can.
jim_thompson5910
  • jim_thompson5910
You're right. Replace each x with x-1 and simplify \[\Large f(x) = 3x^2 - 4x + 4\] \[\Large f(\color{red}{x}) = 3(\color{red}{x})^2 - 4(\color{red}{x}) + 4\] \[\Large f(\color{red}{x-1}) = 3(\color{red}{x-1})^2 - 4(\color{red}{x-1}) + 4\] now simplify the right hand side
jim_thompson5910
  • jim_thompson5910
` If you want me to post in a new question I can. ` yes please. It's getting laggy with all of these questions. It's a good idea to have one question per post to avoid clutter and lag
Destinyyyy
  • Destinyyyy
Okay Ill do it now..

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