Week- 16

What I thought:

We are given x= to get rid of the root sign, to do that we will square both sides. Now we have = 10- 3x, since it’s a quadratic equation we can move it all to one side +3x -10 =0 and then factor it. Since there are 3 terms we will be using the method of product and sum, the factors of 10 are 1,2,5, and 10. We will be using 2 and 5 to get our second term which is 3. So after factoring we get (x+5)(x-2)=0, so our answers will be x= -5 and x= 2.

After correcting:

After checking the answer I was reminded to always check the answers for extraneous roots. So to check we just need to plug each answer into x, one at a time. Let’s do -5 first since it’s a negative, we plug -5 into x and get: -5= . First we’ll do what’s in the square root -3 times -5 is 15, then 10+ 15= 25 so now it’s -5= . After we square root 25 we have -5 = 5, and since the two numbers are not the same it means -5 is an extraneous root. Now let’s check 2, again we plug it into the equation, 2= we’ll do what’s in the square root first, -3 times 2 is -6 so then 10- 6= 4. Now we have 2= and after the square root 4 we get 2, both sides are equal which means 2 is not an extraneous root. So in the end there is only one answer x=2.

Week-15

What I thought:

We are given ,     . To find the reference angle, we’ll start with since cos is negative there are two possible quadrants it could be in, quadrant 2 an 3. Now, to find the reference angle we’ll draw our right triangle on the graph, the ratio for cosine is adjacent over hypotenuse which is also equals to x over r. So the 2 is our hypotenuse and -1 is adjacent to the reference angle, so then the last side would be . But I was not sure how to tell if  the angle would be 30 or 60 degrees so I just guessed 30 degrees.

After correcting:

After correcting, I found out how to tell the two angles apart, the beginning is still the same so it’s going to be in quadrant 2 and 3, and the hypotenuse is still 2 and -1 is adjacent to the reference angle, so would be the opposite. We have all the information we need to find the angle, I learned that the 30 degrees angle will always be next to the , making the last angle 60 degrees. So if we look at our graph we see that is opposite of the reference angle. So that means the angle is going to be 60 degrees, we can also confirm by making sure cosine of 60 degrees is .

Week-14

What I thought:

Since it’s an equation with 3 terms, I decided to use the method of finding the common denominator. At first I thought the common denominator was 10x, because I got the 5 mixed up as a denominator. So then I multiplied the first term by 10, then  the second one by 2x and then the last term by 5x. After I got 80-10x= I can tell this is a quadratic equation because of the , so I moved the 80 and negative 10x to the other side. Now we have 0= +10x -80, to get rid of the coefficient on the first term, we need to divide everything by 5. After dividing we have this: 0=5( +2x -16), I tried factoring but it didn’t work so I thought it was already prime and just left it as 0=5( +2x -16).

After Correcting:

After checking the answer and going through it again, I figured out what went wrong, it was when I was looking for the common denominator, it is not 10x, it was 2x. So now that we have the right common denominator we will times the first term by 2, then the second one by 2x and then the last term by x. It looks like this now: 16-10x= and since it’s a quadratic equation we’ll have to move everything to one side to solve it. After moving, we have 0= +10x-16. When I was checking the answers I found out that instead of using factoring we would have had to use complete the square or the quadratic formula. So I chose to complete  the square and I got 0= -41. To isolate ‘x’ we will move negative 41 to the other side of the equal sign, then square root both terms on each side. Now it looks like this: = square root of , after square rooting we get +- = x+5 and lastly we move the 5 to the other side. Our final answer would be +- -5 =x.

Week-13

What I thought:

At first I thought that x-7 and 7-x were different, because they are subtractions and in different order. So then I tried to get the same denominator by multiplying the top and bottom to it’s opposite. So for the first fraction, I multiplied the top and bottom by (7-x) and got . Then for the second one I times the top and bottom by (x-7), so after that we have and we can just put both fractions together now since they both share the same denominator. Then lastly we add the like terms together and our answer is , but clearly that is not one of the options in the question.

After correcting:

After checking my work I realized that it was much simpler than that, I just needed to factor out the negative for the second fractions denominator, to make them the same then that negative is moved to the top. When it moves it gets canceled out by the minus sign, making it . So our final answer would be .

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Week-10

What I thought:

Since all the rest of the questions were quadratic equations, I did not notice that this was different. So I thought that this one was a inverted quadratic function because of the negative sign at the front. Then with the 3 as the coefficient I thought it had a stretch of 3 and that it started at (0,5) since it’s up 5. So my final shape had a really tall and skinny triangle. But then I checked it was really different.

After checking:

The graph showed a linear function instead, so I checked the equation again and found that there were no . So since we know it’s a linear equation, we are told it has a negative slope of 3/1 and that the y-intercept is 5. So the line would be very steep, starting from the top to bottom (left to right).