Need help checking my answers

D

droptimus

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I got this "take-home" test in math and I don't know anyone IRL that I can ask for help.. I'd just like to make sure they are all correct since this is a "take-home"

1) g(x) = 2x - 11, find g^-1(x)

My answer: g^-1(x) = (x+11)/2

2) Given f(x) = (1/2)x² + x - 5 , answer the following below:

a) Which way does the graph open?

My answer: up

b) Find the vertex (nearest hundredth)

My answer: (-1,-5.5)

c) Find the y-intercept

My answer: (0,-5)

d) x-intercepts (nearest hundredth)

My answer: (-4.32,0) (2.32,0)

e) What is the domain of this function?

My answer: all real numbers

f) range of this function?

My answer: y is greater than or equal to -5.5

g) Find axis of symmetry

My answer: x=-1

h) Find f(12)

My answer: f(12) = 79

4) Find the vertex of f(x) = 5x² - 5x + 1 algebraically.

My answer: x = 1/2

5) The height, h, (in feet) of a baseball that is popped into the air is a quadratic function of time, t, (in seconds) since it was hit. The following function represents this relationship: h(t) = 4 + 60t - 16t²

a) How high is the ball when it strikes the bat?

My answer: 4 feet

b) What is the max height the ball reaches?

My answer: 60.25 feet

c) when will the ball reach its max height?

My answer: 1.88 seconds

d) When does the baseball hit the ground?

My answer: 3.76 seconds

6) Solve for all x in the equations below

a) (x - 5)² - 3 = 0

My answer: x = 5 ± √3

b) (x + 2)² + 50 = 0

My answer: x = -2 ± 5i√2

7) Perform the indicated operations on the complex numbers below and simplify (a + bi form)

a) (-5 - 3i) + (5 - 6i)

My answer: -9i

b) (2 - 3i) - (-4 + 3i)

My answer: 6 - 6i

c) (2 + 7i)(3 - 2i)

My answer: 20 + 17i

d) (2 + 3i)/(5 - i)

My answer: (6 + 17i)/26

8) Solve the quadratic equation, x² - 8x - 2 = 0 by completing the square

My answer: x = 4 ± 3√2

9) Solve the following quadratics for all x by using the quadratic formula

a) 2x² + 6x = 3

My answer: x = (-6 ± 2√15)/4

b) x² + 2x + 8 = 0

My answer: x = -1 ± 2i√7

10) Solve the following 3X3 system of linear equations by finding the ordered triple:

2x + 4y - z = -2
x - 2y + z = -5
-2x + y + 2z = 7

My answer: x = -8.2, y = 5.8, z = 8.8
 
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5d) did you include the final 4 feet from bat-height to the ground?

7d) typo?

8,9) would have to see the steps to know you used the proper methods

10) very suspicious of that one.
 
droptimus said:
I got this "take-home" test in math and I don't know anyone IRL that I can ask for help.. I'd just like to make sure they are all correct since this is a "take-home"




10) Solve the following 3X3 system of linear equations by finding the ordered triple:

2x + 4y - z = -2
x - 2y + z = -5
-2x + y + 2z = 7

My answer: x = -8.2, y = 5.8, z = 8.8
Click to expand...

You can check your answer by inserting the calculated values in the given equations:

2*(-8.2) + 4*(5.8) - (8.8) = ??

(-8.2) - 2*(5.8) + (8.8) = ??

-2*(-8.2) + (5.8) + 2*(8.8) = ??

If all three answers are correct - you are most probably correct!!
 
DrPhil said:
5d) did you include the final 4 feet from bat-height to the ground?

7d) typo?

8,9) would have to see the steps to know you used the proper methods

10) very suspicious of that one.
Click to expand...


5d is asking how long does it take for the baseball to hit the ground after its struck by the bat

7d was a typo, sorry. I fixed it in the original post, the denominator was actually (5 - i) and not (5 - 1)

8,9 i used the methods given, im just wondering if i got the correct answers

and 10 I checked myself by plugging them back into the equation and they all worked out

can anyone confirm the answers as being correct?
 
droptimus said:
5d is asking how long does it take for the baseball to hit the ground after its struck by the bat

7d was a typo, sorry. I fixed it in the original post, the denominator was actually (5 - i) and not (5 - 1)

8,9 i used the methods given, im just wondering if i got the correct answers

and 10 I checked myself by plugging them back into the equation and they all worked out

can anyone confirm the answers as being correct?
Click to expand...

Your answers are not correct.
 
droptimus said:
I got this "take-home" test in math and I don't know anyone IRL that I can ask for help.. I'd just like to make sure they are all correct since this is a "take-home"

1) g(x) = 2x - 11, find g^-1(x)

My answer: g^-1(x) = (x+11)/2 . . . . . . Yes.

2) Given f(x) = (1/2)x² + x - 5 , answer the following below:

a) Which way does the graph open?

My answer: up . . . . . . Yes.

b) Find the vertex (nearest hundredth)

My answer: (-1,-5.5) . . . . . Yes.

c) Find the y-intercept

My answer: (0,-5) . . . . . . . Yes.

d) x-intercepts (nearest hundredth)

My answer: (-4.32,0) (2.32,0) . . . . . . Yes.

e) What is the domain of this function?

My answer: all real numbers . . . . . . Yes.

f) range of this function?

My answer: y is greater than or equal to -5.5 . . . . . . . Yes.

g) Find axis of symmetry

My answer: x = -1 . . . . . . Yes.

h) Find f(12)

My answer: f(12) = 79 . . . . . . Yes.

4) Find the vertex of f(x) = 5x² - 5x + 1 algebraically.

My answer: x = 1/2 . . . . . Incorrect. It is incomplete. You only have the x-value instead of the vertex.

5) The height, h, (in feet) of a baseball that is popped into the air is a quadratic function of time, t, (in seconds) since it was hit. The following function represents this relationship: h(t) = 4 + 60t - 16t²

a) How high is the ball when it strikes the bat?

My answer: 4 feet . . . . . . Yes.

b) What is the max height the ball reaches?

My answer: 60.25 feet . . . . . . Yes, when using the exact time of 1.875 seconds

c) when will the ball reach its max height?

My answer: 1.88 seconds . . . . . . . Yes, when rounded to the hundredths place

d) When does the baseball hit the ground?

My answer: 3.76 seconds . . . . . . Incorrect. You need to solve (or do another attempt at solving) the equation \(\displaystyle \ 0 \ = \ 4 + 60t - 16t^2.\)

6) Solve for all x in the equations below

a) (x - 5)² - 3 = 0

My answer: x = 5 ± √3 . . . . . .Yes.

b) (x + 2)² + 50 = 0

My answer: x = -2 ± 5i√2 . . . . . . Yes.

7) Perform the indicated operations on the complex numbers below and simplify (a + bi form)

a) (-5 - 3i) + (5 - 6i)

My answer: -9i . . . . . . . Yes, unless the instructor wants it stipulated as \(\displaystyle \ 0 - 9i.\)

b) (2 - 3i) - (-4 + 3i)

My answer: 6 - 6i . . . . . . Yes.

c) (2 + 7i)(3 - 2i)

My answer: 20 + 17i . . . . . Yes.

d) (2 + 3i)/(5 - i)

My answer: (6 + 17i)/26 . . . . . . Incorrect. There are at least two issues. 1) "6" isn't part of the numerator. 2) Your answer is not in the required a + bi form. Your answer, providing that neither a nor b is an integer, must be expressed as \(\displaystyle \ \dfrac{c}{d} + \dfrac{e}{f}i.\)

8) Solve the quadratic equation, x² - 8x - 2 = 0 by completing the square

My answer: x = 4 ± 3√2 . . . . . . Yes.

9) Solve the following quadratics for all x by using the quadratic formula

a) 2x² + 6x = 3

My answer: x = (-6 ± 2√15)/4 . . . . . . . Incorrect. The fraction has not been reduced.

b) x² + 2x + 8 = 0

My answer: x = -1 ± 2i√7 . . . . . . . Incorrect. It appears that you did incorrect cancelling of factors between the numerator and the denominator.

10) Solve the following 3X3 system of linear equations by finding the ordered triple:

2x + 4y - z = -2
x - 2y + z = -5
-2x + y + 2z = 7

My answer: x = -8.2, y = 5.8, z = 8.8 . . . . . . Incorrect. 1) Those three values only satisfy the first equation. 2) You don't have it in the required form of (x, y, z).
Click to expand...
.
 
Can some one explain how to do 5d, I forgot how to find that. All I did was double the time it took for it to reach its maximum.

and would 7d be: 6 + (17i/26)

or 3/13 + 8.5i/13

would 9c be

x = (-3 ± √15)/2

would 9b be:

x = -1 ± i√7

(i'm confused as how to simplify fractions with square roots)

And I see where I went wrong with #10, I accidently wrote the equation down wrong when I added them

This is a summer semester math class so we're covering a ton of information really fast and I'm also in a another summer semester english class at the same time :(
 
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droptimus said:
Can some one explain how to do 5d, I forgot how to find that. All I did was double the time it took for it to reach its maximum.

Lookagain has already told you how to do this one:

solve for 't' in

-16t2 + 60t + 4 = 0

You need to read the responses carefully (and read your book/classnotes carefully)

and would 7d be: 6 + (17i/26)

or 3/13 + 8.5i/13

would 9c be

x = (-3 ± √15)/2

would 9b be:

x = -1 ± i√7

(i'm confused as how to simplify fractions with square roots)

And I see where I went wrong with #10, I accidently wrote the equation down wrong when I added them

This is a summer semester math class so we're covering a ton of information really fast and I'm also in a another summer semester english class at the same time :(
Click to expand...
.
 
droptimus said:
What method are you supposed to use to solve for t in -16t2 + 60t + 4 = 0
Click to expand...

The above is a quadratic equation - solve it using standard solution techniques (most of the time taught in Algebra II in high schools).
 
droptimus said:
and would 7d be: 6 + (17i/26)

or 3/13 + 8.5i/13


No. \(\displaystyle \ \ \ \ \ \ \) (I'm going to show you more detailed steps here than in a typical post of mine.)



\(\displaystyle \dfrac{2 + 3i}{5 - i} \ = \)

\(\displaystyle \dfrac{2 + 3i}{5 - i} \cdot \dfrac{5 + i}{5 + i} \ = \)

\(\displaystyle \dfrac{(2 + 3i)(5 + i)}{(5 - i)(5 + i)} \ =\)

\(\displaystyle \dfrac{(2)(5) + 2i + 15i + (3i)(i)}{25 - i^2} \ = \ \ \ \ \ \ \ \ \)(You were already okay with the eventual denominator of 26, but I'll proceed with it anyway.)

\(\displaystyle \dfrac{10 + 17i + 3(-1)}{25 - (-1)} = \)

\(\displaystyle \dfrac{10 - 3 + 17i}{25 + 1} \ = \)

\(\displaystyle \dfrac{7 + 17i}{26} \ = \ \ \ \ \ \ \ \ \ \ \)(I already stated to you in a prior post that there is no "6" in the numerator.)


\(\displaystyle \dfrac{7}{26} + \dfrac{17}{26}i \ \ \ \ \ \ \ \ \ \ \ \)(You must split it up to write it in the required a + bi form, as well as make sure each/any fractions are reduced.)



- - - - - - - - - - - - - - - - - - - - - - - - -



would 9c be . . . . . . . There is no "9c." You must have made a typo and meant to type "9a."

x = (-3 ± √15)/2


Yes.\(\displaystyle \ \ \dfrac{-6 \pm \ 2\sqrt{15}}{4} \ = \ \)

\(\displaystyle \dfrac{2(-3 \pm \sqrt{15})}{4} \ = \)

\(\displaystyle \dfrac{-3 \pm \sqrt{15}}{2}\)

- - - - - - - - - - - - - - - - - - - - - - - - - - -

would 9b be:

x = -1 ± i√7

Yes.\(\displaystyle \ \ \dfrac{-2 \pm \ 2i\sqrt{7}}{2} \ = \ \)

\(\displaystyle \dfrac{2(-1 \pm i\sqrt{7})}{2} \ = \)

\(\displaystyle -1 \pm i\sqrt{7}\)



(i'm confused as how to simplify fractions with square roots)
Click to expand...
.
 
Subhotosh Khan said:
The above is a quadratic equation - solve it using standard solution techniques (most of the time taught in Algebra II in high schools).
Click to expand...

I'm just drawin a blank here, its not perfect square its not the -b/2a ... should i just plug this into the quadratic formula to figure it out?
 
droptimus said:
Where did this -4 come from, why do you divide by -4?
Click to expand...
droptimus, 4 is the greatest common factor of all of the coefficients (and that constant term). And so you can divide both sides by 4 (or -4). And, by dividing through (or multiplying through) both sides by a negative number, you make the coefficient on the squared term positive. That new quadratic equation may be easier to work with.


\(\displaystyle \dfrac{-16t^2}{-4} \ +\ \dfrac{ \ 60t \ }{-4} \ + \ \dfrac{ \ 4 \ }{-4} \ = \ \dfrac{ \ 0 \ }{-4}\)



\(\displaystyle 4t^2 - 15t - 1 = 0 \)

Now use the quadratic formula...[/QUOTE]
 
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Okay thank you very much everyone. and lookagain, you were very helpful :)
 
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