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MATH 116 > Test 3 - Final Exam > Flashcards

Test 3 - Final Exam Flashcards

1
Q

Test 3

Slope =

How to find the slope

Week 9

A

y2-y1/x2-x1

It is Minus NOT addition

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2
Q

Distance or d=

How to calculate the distance between two points

A

Square root of (x2-x1)^2 + (y2-Y1)^2

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3
Q

How to find the y-intercept and x-intercept of the line. (EQUATION)

A

To find the y-intercept, we set x=0 and the same for the x-intercept, we set y=0.

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4
Q

|-19| should be:

A

19

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5
Q

How to find the midpoint M of the line segment

A

Using the formula (x1+x2/2, y1+y2/2)

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6
Q

A vertical line means

A

undefined, while a horizintal line means zero

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7
Q

How to graph a line

A

First, we choose some x-values. Then, we evaluate the equation for each of the x-values.
e.q y=3x we will do the following: y=3(1)= (1,3)

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8
Q

Find an ordered pair (x,y) that is a solution to the equation.

A

There are infinitely many ordered pairs, To find one, we can choose a value for one of the variables and solve for the other variable. E.q x-5y=5 we can give x a value of 0 and be left with 5y=5. Thn, we solve y by diving 5 by 5 and we will get the following answer (0, 1)

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9
Q

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

Week 10

A

We use the same slop of the equation and then change the y and x to the point that was provided

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10
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.

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11
Q

How to list each zero of f according to its multiplicity (multiplicity 1,2, and 3)

A

E.q multiplicity 2 means (x+5)^2 to find it zero means we do the following x+5=0 which equals x= -5
so, its zero is -5

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12
Q

What is the y-intercept

A

y=mx+b
If you were asked to graph, the points will look like this (0,b)

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13
Q

Joe is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Joe has been adding money. Suppose that x and y are related by the equation y=550+20x.
1. What is the change per week in the amount of money in the account?
2. What was the starting amount of money in the account?

A
  1. the answer will be the slope which is 20
  2. the answer will be the y-intercept which is 550
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14
Q

How to find the decond point on the line after finding the y-intercept e.q y=5x+3 will be (0,3)

A

To fnd the second point, we will use the slope e.q 5. The rise (y) is 5 and the run (x) is 1 so we will take the first point we got from the y-intercept (0,3) and add (0+1, 5+3) = (1, 8). The answer or the second point will be (1,8)

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15
Q

How to solve the following: The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 44 minutes of calls is $18.84, and the remaining credit after 73 minutes of calls is $14.78. What is the remaining credit after 93 minutes of calls?

A

We subtract 73 from 44 = 29 m
$18.84 - $14.78 = $4.06
IF we are looking to find the dollars we will divide them with 29. they will look like this 4.06/29 and the opposite if we want to find the minutes e.q 29/4.06
After dividing we get 0.14.
To find the remaining credit after 93 we subtract it from 73 (depend on the number) we get 20.
we multiply 20 by 0.14 = 2.8 then we subtract (or add, depends if it was increase or decrease) 14.78-2.8=11.93
Answer: 11.93

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16
Q

How to draw a graph to help solve the equation. Then find the solution to the equation.

A

First, if the equation was 3x=-3 we will move the -3 to the other side so it can give use the following order: y=mx+b
After, we give x a value and start graphing
Then, we look at the graph to 0 and see where the point will be based on the line and this will be the x sloution

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17
Q

How to find all the zeros of the quadratic function. e.q x^2+9x+20

A

We solve (or simplify) the quation x^2+9x+20
so it will be (x+4)(x+5)
The zeros wil be: -4,-5

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18
Q

How to choose the statement that best describes how (something) and (something) are related based on the graph given, and how to give the requested value.

A

We look at the point if the point on y is 45 and x is 0 and the next point in y is 35 and x is 1then we will subtract 45 from 35 (based on the graph we will know if it was an increase ADD or decrease SUBTRACT) The answer will be 10

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19
Q

What is the ratio for a Direct variation

A

k= y/x

equation will be y=kx

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20
Q

What is the ratio for an Inverse variation

A

k=xy

equation will be y=k/x

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21
Q

How to determine whether the table shows a direct variation, an inverse variation, or neither.

A

We will look at the numbers provided and use the ratio for each variation. For example, we start to use the direct variation ration if all the numbers give the same answer it means that we choose the direct variation option and write the answe as the form of the ratio e.q y=k/x if not then we do the same thing for the inverse variation ratio

22
Q

How to find a polynomial of degree that has the following zeros. 5, 0, -9

A

We use the factor therom whic means the following: 5 will be x-5 and 0 will be x (because x-0 give us a 0) and -9 will be x+9 {because x-(-9) give use +9}
Answe will be: x(x-5)(x+9)

23
Q

What is the ratio for a Joint variation

A

k=y/xz

equation will be y=kxz

24
Q

Write an equation that expresses the following relationship.
w varies directly with the cube (and square) of u and inversely with d

A

w=ku^3/d (if it was square it will be u^2)

25
Q

How to determine whether the equations provided shows a direct variation, an inverse variation, or neither.
8/y=x and y=x/2

A

The first equation we will multiply y for each side this will give us 8=xy. Then we divide x for each side and we will get the answe as inverse variation y=8/x
The second equation numetor is x this means we should relpac it with1 and move the x to look like this: y= 1/2x this shows a direct variation

26
Q

Suppose that y varies inversely with x, and y=8 when x=3. Also, Find y when x=6.

A

This means the equation is y=k/x and we should use the numbers provided to solve for k so 8=k/3 will give us 23=k so the equation is y=24/x
To find y when x is 6 we use the equation and replace x with 6 this will give us y=4

27
Q

How to use synthetic division

A

First, we move the first number to the 3rd row and then start to multiply. We use addition.

28
Q

Interepting direct variation from the graph.
(a) How many revolutions does Pablo make per foot of distance traveled?
(b) What is the slope of the graph?

A

(a) since it is a direct variation equation that means the line start from 0. So, we look at two points and we divide them to get the revolution.
(b) to find the slope we use the slope= rise/run and choose to points, divide them, and we get the answer.

29
Q

How to divide and find the Quotient and Remainder

A

Depending on the numbers provided we will do a long divison. We use subtraction. We will try to eluminate numbers as much as we can to get the reminder. The quotient will be the numbers we use or multiplyed to get to the reminder.

30
Q

Factor Theorem:

A

A polynomial p(x) has a factor x-c if and only if p(c)=0.

31
Q

How to use the Factor Theorem to determine whether x-1 is a factor of P(x)=-2x^4+x^3+5x^2-4.

A

First we get the zero of x-1 whic is x=1 or 1
Then we change all the x to 1 e.q -2(1)^4 and multiply. The, we add if the answer is 0 then it is a factor if not than it is not a factor

32
Q

How to solve a percentage mixture problem?
e.q: A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 8% vinegar, and the second brand contains 13% vinegar. The chef wants to make 270 milliliters of a dressing that is 12% vinegar. How much of each brand should she use?

A

First we give let x represent the first and y the second brand. We convert the percentage to the following 0.08 and 0.13 . The chef wants to make 270 milliliters of a dressing that is 12% vinegar so we multiply 0.12 with 270 and we will get 32.4. Lastly we wrote two equations x+y=270 and 0.08x+0.13y=32.4
We use ALEXS calculate and the Window min number will be -500

33
Q

How to solve a tax rate or interest problem?
e.q: A theater group made appearances in two cities. The hotel charge before tax in the second city was $1000 higher than in the first. The tax in the first city was 7%, and the tax in the second city was %7.5. The total hotel tax paid for the two cities was 800. How much was the hotel charge in each city before tax?

A

The first euation will be the hotel charge before tax in the second city whic is y+x=1000
The second equation will contain the perentages and total tax paid which is 0.07y+0.075x=800
We use ALEXS calculate and the Window min number will be -10,000

34
Q

How to solve a time, distance, and rate problem?
e.q A motorboat takes 3 hours to travel 108 miles going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

A

We have to seperate rate, time, and distance. The rate for this equation is x-y (down) and x+y (up) because it goes upstream and downstream. The time is 3 (up) and 2 (down). The distance will be 3(x+y) and 2(x-y). We put each into an equation e.q 3(x+y) =108 nd solve by dividing 3 by each side. We use ALEXS calculator and the Window min -10,000

35
Q

How to solve a system of equation (with fractions)

A

we look at the two equations that was provided and at the denominator. We find the LCD and multiply each side. then if we start to add or subtract to elimanate one of the variables (if we coudn’t we we multiply one of the equations with one number that can give a product that could be elimanitad) If we elimanite x we will get the answer for y. To find x, we will use one of the equations and change y to the answer that we got.

36
Q

Two systems of equations are given below.
For each system, choose the best description of its solution. If you choose the following answer, what should you do? The system has infinitely many solutions.
They must satisfy the following equation: y=

A

If we got the answer 0=0 or any other number and they are the same e.q 3=3 We choose one of the equations that was provided and fix the equation to fit the following order y=mx+b and then we write it into the answer

If we got 0=3 or any number that are not the same this means NO SLOUTION

37
Q

When you use the ALEKS graphing calculator to solve the system of equations. What Window max and min number you use?

A

-300 and 300

38
Q

How to solve a word problem using a system of linera equation?
e.q A party rental company has chairs and tables for rent. The total cost to rent 8 chairs and 3 tables is $36. The total cost to rent 2 chairs and 5 tables is $43. What is the cost to rent each chair and each table?

A

We put the total cost to rent 8 chairs and 3 tables for $36 in an equation of the following form Ax+By=c and do the same for the other total cost. Then, we eluminate one of the variables (if we could not then we multiply it with a number that will could eluminate one of the variables) If we eluminate x and get the answer of y, then we choose one of the equations to solve for x and find it.

39
Q

How to graph the system below and write its solution.
2x+2y=4
y=-x+2

A

For the first equation we find the x-intercept and y-intercept by seeting each value for 0 and solve.
For the second equation we give x a value and solve (value,result)

40
Q

How to solve a word problem involving a sum?
e.q The sum of two numbers is 66. The smaller number is 14 less than the larger number. What are the numbers?

A

First we write the equations: y+x=66 and y=x-14
then we use the first equation and the second equation in one equation which will look like this (x-14)+x=66. Since it is an addition it will give us 2x -14=66
and then we continue to solve. Then we use the answer to find y

41
Q

How to use substitution to solve the system. or two equations

A

we combine the second equation to the first e.q if the first equation eas 3x-2y=16 and the second y=2x-9 it will look like this 3x-2(2x-9)=16 and continue to solve. To find y, we use one of the equation and the answer we got.

42
Q

Still air, water, or whatever MEANS

A

The number is more

43
Q

If you face an equation asks you to find the rental cost for each movie and each video game how you solve it?

A

Using the form Ax +By =C and then try to eluminate one of the variables (if not then we multiply it with a numbe) then, we finish solving. If we found y then we need to find x by choosing one of the equations and the answer we got for y.

44
Q

How to solve a value mixture problem NOT a percentage mixture?
e.q The Turner family and the Taylor family each used their sprinklers last summer. The water output rate for the Turner family’s sprinkler was 20 per hour. The water output rate for the Taylor family’s sprinkler was 35 per hour. The families used their sprinklers for a combined total of 40 hours, resulting in a total water output of 1025. How long was each sprinkler used?

A

The comined hours and total water output will have an equation y+x=40.
The second equation wll be for the rate per hour and the total water output 20y+35x=1025
We use the ALEXS calculator and the Window min is -300

45
Q

Final Test

When graphing an inequality and you was provided with one equation that is bigger and equal in the same time. How would you show the equal in the graph?

A

Equal = straight line
Not qual = dash line

46
Q

At most means

A

Less than or equal to

47
Q

At least means

A

More than or equal to

48
Q

A is less than B

A

A < B

49
Q

A is at most B

A

A <= B

50
Q

A is mor than B
A is greater than B

A

A > B

51
Q

A is at least B

A

A => B

MATH 116 (7 decks)

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