Download Test Name: MAT 101 Final Exam ONLINE 1. Solve the linear

Test Name: MAT 101 Final Exam ONLINE
1.
Solve the linear equation and simplify your answer.
7𝑦 + 30 = 4𝑦
2.
Solve the linear equation and simplify your answer.
−15𝑤 + 15 = 5(−3𝑤 + 3)
3.
Solve the following linear equation. Write your answer as an integer, a simplified fraction, or a decimal rounded to two
decimal places.
3(2𝑥 − 3) = 4(𝑥 + 6) − 19
4.
Consider the following equation:
4|𝑥 − 1| − 16 = 0
Step 1. Rewrite the equation above in standard form and determine if there is a solution.
Step 2. Using the definition of absolute values, convert the equation above into two equations without absolute value signs.
Step 3. Using the two equations found in Part 2, enter the solution set using set notation.
Step 4. Graph the solution set on the number line below.
5.
Set up the equation for the following word problem and solve the equation. Let 𝑥 be the unknown number.
77 times a number minus 44 is equal to 31 less than the number. What is the number?
Step 1. Write out the equation.
Step 2. Solve the equation for 𝑥. Please enter your answer as an integer, a reduced fraction, or a decimal number rounded to
two places.
6.
Consider the following consecutive integer problem.
The sum of three consecutive integers is 105. Find the three integers.
Step 1. Set up an equation using the variable 𝑛 as the first integer. Enter your answer below. Do not solve the problem.
Step 2. Solve the equation from the previous step.
7.
Edith buys last year's best-selling novel, in hardcover, for $16.80. This is with a 20% discount from the original price. What
was the original price of the novel?
Step 1. Use the variable 𝑥 to set up an equation to solve the given problem. Set up the equation, but do not take steps to
solve it.
Step 2. Solve the equation found in Step 1.
8.
Solve the linear inequality for the given variable. Simplify your solution and use algebraic notation.
−9 < 2𝑧 − 3 < −1
9.
Consider the following inequality:
−2𝑧 + 5 £ 19
Step 1. Solve the linear inequality above for the given variable. Simplify your solution and use interval notation.
Step 2. Graph the solution to the given inequality.
10.
After 4 years, Amanda's account earned $1200 in interest. If the interest rate (in decimal form) is 0.08, how much did
Amanda initially invest?
Step 1. First, choose the correct formula:
E) 𝐶 = 2 ä 𝑟
A) 𝑃 = 4𝑠
B) 𝐴 =
1
ℎ( 𝑏 + 𝑐 )
2
F) 𝑃 = 2𝐿 + 2𝑊
C) 𝐼 = 𝑃𝑟𝑡
G) 𝐶 = 5 ( 𝐹 − 32 )
D) 𝐴 = 𝑏ℎ
H) 𝑃 = 𝑎 + 𝑏 + 𝑐
9
Step 2. Without substitution, solve the formula for the unknown variable in terms of the known variables.
Step 3. Finally, solve the problem for the unknown value of the variable by substituting appropriate values of the known
variables in the formula. (Round your answer to 2 decimal places.)
11.
Determine if the given ordered pair satisfies the equation 𝑥 − 2𝑦 = 15.
Step 1. (−4, 4)
Answer:
A) YES
B) NO
A) YES
B) NO
Step 2. (1, 0)
Answer:
12.
Step 1. Plot the points on the graph.
A (−4, −3), B (5, −6)
[Continued on next page ....]
Step 2. Identify the coordinates of the points A and B on the graph.
13.
A:
(
,
)
B:
(
,
)
Find the 𝑦-intercept and 𝑥-intercept for the given equation.
9𝑥 + 3𝑦 = −9
𝒚 -intercept: (A)
(
,
)
𝒙 -intercept: (B)
(
,
)
14.
Consider the linear equation:
−6𝑥 + 2𝑦 = 6
Step 1. Determine the slope and 𝑦-intercept of the equation above.
slope =
y-intercept = ( 0,
A) Undefined
)
Step 2. Graph the 𝑦-intercept on the axes provided.
Step 3. In step 1, you found the slope. In step 2, you graphed the 𝑦-intercept . Use the slope to find a second point on the
line other than the 𝑦-intercept and then graph the line connecting these two points.
15.
Consider the following linear equation:
2𝑦 − 10 = 0
Step 1. Find two points on the line, and then use your answer to graph the line.
(
,
) and (
,
)
Step 2. Determine the slope for the equation given above. If applicable, write "Undefined" for the slope.
16.
Find the equation of the line shown. Enter your answer in slope-intercept form.
17.
Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given
coordinates.
slope: −4, ordered pair: (3, 1)
18.
Find the equation (in slope-intercept form) of the line passing through the points with the given coordinates.
(2, −4) , (−2, 0)
19.
A textbook salesperson's annual income depends on the amount of her sales. Her annual income is a salary of $14000 plus
17% of her annual sales. Write a linear equation for her annual income for sales of 𝑥 dollars. ( 𝐼 = 𝑚𝑥 + 𝑏 ).
20.
Find the slope of a line that is a) parallel and b) perpendicular to the given line.
5𝑥 + 2𝑦 = −3
21.
Step 1. Does the graph represent a function?
A) Yes
B) No
Step 2. State the domain and range of the graph. If the domain or range is all real numbers indicate "all real numbers":
22.
Consider the function:
𝑓 ( 𝑥 ) = 5𝑥 + 9
Step 1. Find the value of 𝑓 ( 5 ).
Step 2. Find the value of 𝑓 ( 𝑎 + 2 ).
23.
Solve the following system of linear equations by substitution. Please determine whether the given system of linear
equations has one solution, no solution, or an infinite number of solutions. If the system has one solution, please indicate the
solution.
3𝑦
= −6𝑥 + 24
{
3𝑦 =
3𝑥 − 21
24.
Solve the following system of linear equations by addition. Please determine whether the given system of linear equations
has one solution, has no solution or has an infinite number of solutions. If the system has one solution, please indicate the
solution.
3𝑥 + 3𝑦
=
15
{
4𝑥 + 4𝑦 = −20
25.
Admission to a baseball game is $3.00 for general admission and $5.50 for reserved seats. The receipts were $3277.50 for
845 paid admissions. How many of each ticket were sold?
26.
Consider the following word problem:
Steve travels 4 times faster than Bill. Traveling in opposite directions, they are 135 miles apart after 4.5 hours. Find their
rates of travel.
Step 1. Use the variables 𝑥 and 𝑦 to set up two equations to solve the given problem.
Step 2. Use the two equations found in Step 1 to solve for each variable.
27.
A dairy needs 287 gallons of milk containing 6% butterfat. How many gallons each of milk containing 8% butterfat and milk
containing 1% butterfat must be used to obtain the desired 287 gallons?
28.
Simplify the expression using the properties of exponents. (Note that the answer should contain only positive exponents and
please be sure to expand any numerical portion of the answer.)
2
2𝑥3 𝑦−2
(
)
𝑦2
29.
Simplify the expression using the properties of exponents. (Note that the answer should contain only positive exponents, and
please be sure to expand any numerical portion of the answer.)
(−8𝑥 2 𝑦 −3 )(−7𝑥 2 𝑦 3 )
30.
Perform the indicated operation by removing the parentheses and combining like terms.
(−4𝑥 + 7) − (−7𝑥 − 3)
31.
Multiply the polynomials using the distributive property and combine like terms.
(𝑥 + 2𝑦)(2𝑥 − 8𝑦)
32.
Multiply the polynomials using the distributive property and combine like terms.
(𝑥 2 − 𝑥 − 2)(𝑥 − 3)
33.
Find the product of the polynomial factors using the appropriate special product (difference of two squares, square of a
binomial sum, square of a binomial difference, difference of two cubes, or sum of two cubes).
(3𝑥 + 8𝑦)(3𝑥 − 8𝑦)
34.
Find the product of the polynomial factors using the appropriate special product (difference of two squares, square of a
binomial sum, square of a binomial difference, difference of two cubes, or sum of two cubes).
(𝑥 − 2)2
35.
Divide the polynomial in the numerator by the monomial in the denominator.
8𝑥3 − 4𝑥2 − 1
𝑥2
36.
Divide the polynomial in the numerator by the binomial in the denominator.
𝑎3 + 𝑎 − 2
𝑎−1
37.
Factor the given polynomial by finding the greatest common monomial factor and rewrite the expression.
3𝑥 3 𝑦 2 + 21𝑥 3 + 6𝑥 4
38.
Completely factor the expression by grouping. If the polynomial cannot be factored, write "Not factorable by grouping".
𝑝2 − 𝑝𝑢 − 8𝑝 + 8𝑢
39.
Factor the trinomial given using the trial and error method. If the trinomial cannot be factored, write not factorable.
𝑥 2 + 2𝑥 − 35
40.
Factor the trinomial given using the trial and error method. If the trinomial cannot be factored, write not factorable.
2𝑥 2 − 12𝑥 + 16
41.
Factor the trinomial given using the trial and error method. If the trinomial cannot be factored, write not factorable.
𝑑 2 + 8𝑑 − 21