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MATH 116 > Final Review > Flashcards

Final Review Flashcards

1
Q

When simplyifing always remember to

A

simplify the numbers e.q 9/36 to 1/4

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2
Q

<= or full circle

A

[x,y]

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3
Q

< or emty circle

A

(x,y)

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4
Q

Infinite sign

A

(x,y)

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5
Q

When you simplify a negative exponent e.q (y^-6/ 3x^5)^-4 What should you do?

A

As we can see the 3 is on the denominator, so before you start multiply 3 with -4 you convet the exponent 4 to positive by moving 3 to the numerator and then you start multypling. BUTTT, for the y sinci it has -6 we can multiply it with the exponent -4 and it will give us a positive answer withought needing to move it (unless the answer is negative we move it).

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6
Q

How to solve for y in the following problem 4/5=y+5/ 15

Solving a proportion of the form (x+a)/b = c/d

A

We multiply 4 by 15 and 5 by y+5 (the opposites) and we continue to solve for y

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7
Q

How to solve the following word problem?
Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $25 monthly fee and charges an additional $0.12 for each minute of calls. The second plan has a $12 monthly fee and charges an additional $0.16 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?

A

To slove the following problem we will need to write the first plan as follows 25 + 0.12x (we add the x because we do not know the number of calls. It was stated on the problem as for each minute of calls) and the second as 12 + 0.16x and then we combine them 25 + 0.12x = 12 + 0.16x and we start to solve for x

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8
Q

Solve for y, where y is a real number y^1/4 = -2

Solving an equation with exponent 1/a: Problem type 1

A

We put the two sides in parantheses by the exponent 4 (y^1/4)^4 = (-2)^4 and then we start to solve. We will get y = 16. So we will need to check: 2= -2 they are not like each other so it is not true and answer is NO SOLUTION

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9
Q

Solve w^3=-9 where w is a real number.

Solving an equation using the odd-root property: Problem type 1

A

The answer will be -3 square root of 9. The negative is outside the square root because - means -1 and if we multiply it inside the squar root it will give us -1 so we move it to be outside the square root

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10
Q

How to solve a radical quation solving for v such as the following *square root of v = -3 *

A

We raise both sides of the equation to an exponent of 2 (since a square root means 2) and then we will get v=9 as the answer. BUT because it is negative we have to check by replacing v with 9 on the first form of the equation e.q square root of 9 = -3 this will give us 3 = -3 which is not true. The answer is NO SOULTION

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11
Q

TO solve any equation with a square root you have to

A

multily it with 2 so you free the equation from the square root and you start solving

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12
Q

How to solve the radiacal x= square root of x + 6

A

We do the same as always which is raising both sides of the equation to an exponent of 2. This time x is on both sides and we have to solve for x so we will get x^2 = x + 6 we will need to move the x + 6 to the other side and start factoring. We will get (x-3)(x +2) or x= 3,-2 but before we write them asthe answer we should check by replacing x with the 3 and -2 in the first form of the equation. We will see that 3 is true while -2 is not true so we will only write 3 as the answer

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13
Q

How to simplify a square root of w^7

A

= square root of w^6 and square root of w
= w^3 and square root of w
Why w^3? Well because multiplying 2 by 3 will give us 6

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14
Q

How to simplify a radical expression such as square root of 5y^2u and square root of 10yu^6

Simplifying a product of radical expression: Multivariate

A

We combine all the nubers and vaiables inside one quare root and multiply them with each other. We will get square root of 50y^3u^7. We silplify it to be 5yu^3 square root of 2yu

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15
Q

How to simplify a radical expression such as square root of 12x^4w^9 and square root of 3x^6w^4

Simplifying a product of radical expression: Multivariate

A

We will do the same as the others which is multiplying and combining them to one suare root. We will get square root 36x^10w^13. This one is a boit diffrent to simplify it we will do the following: square root 36x^10w^12w
(6)^2(w^5)^2(w^6)^2 square root of w.
Answer: 6w^5w^6 square root of w

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16
Q

In a radical expression like this 8u square root of 48uy - y and square root of 27u YOU

A

MULTIPLY when movig a number inside the root to outside it you multiply it with the number that was outside

17
Q

In a radical expression like this u square root of 2u - 4u square root of 18uy YOU

A

SUBTRACT based on the order that was given. For example you got uy - 12 the answer will be -11

18
Q

When simplyfing a higher radical expression do not forget to

A

Put the expression on the upper left of the square root

19
Q

Write the following as an exponential expression: 4 on the upper left of the square root and a square root of y^3

A

y^3/4
Numerator = exponent
Denominator = upper left of the square root

Do the opposite if youu were asked write it as a radical expression.

20
Q

How to write a radical on its simplified form

A

To simplify it we write the radical using exponents e.q upper left of the square 6 with square root of y^2 will be y^6/2
SECOUND: if it was multilpy it meanse addition and if it was division it means subtraction.

21
Q

How to solve a system of equations that have fractions

A

We first find the LCD and then we multiply the LCD by each side. Then, wwe continue to solve the system as the others.

22
Q

What should you do if you were asked to solve a system of eyuation that wants (x,y) or (x,y)?

A

We combine the first equation with the second equation so they become one. Then we factor to get the x(s). Then we take the x(s) or the answe and put them as the first form of the equation to get the y(s)

23
Q

How to solve the following word problem?
A phone company offers two monthly plans. Plan A costs $26 plus an additional $0.11 for each minute of calls. Plan B has no initial fee but costs $0.13 for each minute of calls.
(A) For what amount of calling do the two plans cost the same?
(B) What is the cost when the two plans cost the same?

A

So, we write the quation for the first plan which is 26+0.11x and the second plane which is 0.13x (we write the x because wh do not know how many calls or the problem did not state how much) then we combine them as 26+0.11x = 0.13x and start to solve.
(A) will be the soultion for x which is 1300
(B) we will take the soultion and put it on the place of the x in one of the equation. For example, 0.13(1300). The answer will be 169

24
Q

How to factor the following: 20v^3x^3x^7-12v^9w^5

A

We look at the common multiplication whic is 4 and the smalles exponent on the variables v and w which is 3 so the answer will be 4v^3w^3(5x^7-3v^6w^2)

25
Q

How to simplify 4u^2-6u/ 2u^2-12u

A

We first factor it and then we will get 2u(2u-3)/2u(u-6)
because we have 2u and 2u outside the parantheses we will cancel them and leave the answer withought them

26
Q

i^2 =

A

-1

27
Q

How to solve the following: square root of -7 multiplied by a square root of -11

Simplifying a product and quotient involving square roots of negative numbers

A

A square root of a negative number is NOT true so to covert it to a positive number we use i in the left of the square root or radical and combine the numbers 7 and 11 and multiply them. Since they both are negative and we have the i on a multiplication we add it to be* i^2* and because i^2=-1 the final answe will be negative - square root of 77

28
Q

How to solve the following: square root of - 40 divided by square root of -5

Simplifying a product and quotient involving square roots of negative numbers

A

A square root of a negative number is NOT true so to covert it to a positive number we use i in the left of the square root or radical and combine the numbers to one square root of 40/5. Since they both are negative and we have the i on a division we add subtract the i by the i so the final answe will be 2 and a square root of 2

29
Q

How to find the dicriminant and the number of real solutions?

A

We will use b^2 - 4ac (which is the square root of the quadratic formula)
The diriminant will be the answer we’ve got and the number of real solutions will be based on the following: b^2 - 4ac > 0 means 2 real solutions
b^2 - 4ac = 0 means one real solution
b^2 - 4ac < 0 meanse there are no real solutions

30
Q

How do you rewrite or solve the following equation in order to graph: -4 = -2x

A

We do NOT add 4 to -2x, instead we add it to the other side so it look like this -2x+4

31
Q

If you were asked to solve a system of equation and find the solutions of (x,y) what should you do?

A

Simply after you finish graphing the equation we look at the points of interactions betwen the equations on the graph and take them as the solutions

32
Q

When you are asked to solve for a specific variable in n equation where there are many what should ou do?

A

multiply all the numbers with the denominator(s) and then we have to do this STEP which is the variable that are repeted on two numbers whe have to factor it example would be gf+5df = 3dg if we were asked to dolve for g we will move the df to the side of the 3dg so we can do the following g(3d-f) and then we move the 3d-f to the denominator of the other side which will look like 5df/3d-f and in this way we solved for g

33
Q

How to find the equation of the line that is perpendicular and passes through a point

A

We use a slope that give a result of -1 (e.q 9 will be -1/9).
IMPORTANT TO NOTE: when multiplying the slope with x and the result was a fraction e.q (7/11) you multiply x with 7, and y with 11 as well as giving it the denominator 11.

34
Q

How to solve the following u^3= -28

A

u= - upper left 3 square root of 28

35
Q

How tos olve the following word problem: The area of a rectangle is 44, and the length of the rectangle is 3 less than double the width. Find the dimensions of the rectangle.
Find the Length and Width

A

We write the equation of the length which is L= 2w (since it is doble) - 3
Remeber we will have to gactor so to solve for w we will replace L with w so it look like this w(2w-3)=44 this will give us 2w^-3x-44 we factor it. If we get a negative answer we do not use it and only use the positive one then this answer will be for the width. To find the length we take the answer of the width and rplace it with w on the first form of the equation L= 2(answer)- 3 and we solve.

36
Q

REMEMBER

A

2y+2x=3456

MATH 116 (7 decks)

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