Answers
1) Since the degree of the denominator is lower than the numerator's we can divide these expressions through long division that way:
As we can see in each step the aim is to cancel the leading coefficient.
2) Note that a Long Division, has a way to write its answer so we can tell that this is the answer:
[tex]\frac{3x^3-4x^2+5x-2}{3x+2}=\quad x^2-2x+3-\frac{8}{3x+2}[/tex]Note that the remainder is written above the divisor on the final answer.
Related Questions
Calculate Jayden's simple interest on a 5-year car loan for $33,486 at 2.38%.
Answers
Answer:
$3984.83.
Explanation:
[tex]Simple\: Interest=\frac{Principal\times Rate\times Time}{100}[/tex]In this particular case:
• The principal/loan amount = $33,486.
,• Rate = 2.38%.
,• Time = 5 years.
Substituting these into the formula above:
[tex]\begin{gathered} Simple\: Interest=\frac{33,486\times2.38\times5}{100} \\ =\$3984.83 \end{gathered}[/tex]Jayden's simple interest is $3984.83.
Solve the quadratic equation by factoring.2x^2+24x+22=0
Answers
Solution
[tex]\begin{gathered} 2x^2+24x+22=0 \\ Divide\text{ through by 2} \\ x^2+12x+11=0 \\ x^2+11x+x+11=0 \\ x(x+11)+1(x_+11)=0 \\ (x+11)(x+1)=0 \\ x+11=0\text{ or x+1=0} \\ x=-11\text{ or x = -1} \end{gathered}[/tex]Which additional piece of information would you need to prove these two triangles are congruent using the side-side-side or SSS triangle congruence postulate?
Answers
By using congruency of triangles, the result obtained is
The additional information needed to make [tex]\Delta STU \cong \Delta SHU[/tex] by SSS axiom is
TU = SH
Side SH is congruent to side TU
Third option is correct
What is Congruency of triangles?
Two triangles are said to be congruent if the corrosponding sides and corrosponding angles are same.
The different axioms of congruency are SSS axiom, SAS axiom, ASA axiom, AAS axiom, RHS axiom
In [tex]\Delta STU[/tex] and [tex]\Delta SHU[/tex]
ST = HU [Given]
SU is common
The additional information needed to make [tex]\Delta STU \cong \Delta SHU[/tex] by SSS axiom is
TU = SH
Side SH is congruent to side TU
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Complete Question
The diagram has been attached here
The point P. = (x,1/3) lies on the unit circle shown below. What is the value of x insimplest form?
Answers
When a point (x,y) lies on a unit circle, the following equation holds true:
[tex]x^2+y^2=1[/tex]We are given
[tex]y=\frac{1}{3}[/tex]and need to find x.
Let's put it into the equation and figure out x. Shown below:
[tex]\begin{gathered} x^2+y^2=1 \\ x^2+(\frac{1}{3})^2=1 \\ x^2+\frac{1}{9}=1 \\ x^2=1-\frac{1}{9} \\ x^2=\frac{8}{9} \\ x=\sqrt[]{\frac{8}{9}} \\ x=\frac{\sqrt[]{8}}{\sqrt[]{9}} \\ x=\frac{\sqrt[]{8}}{3} \end{gathered}[/tex]We can simplify the square root of 8 by using the radical property:
[tex]\sqrt[]{a\cdot b}=\sqrt[]{a}\sqrt[]{b}[/tex]Thus, square root of 8 becomes:
[tex]\sqrt[]{8}=\sqrt[]{4\cdot2}=\sqrt[]{4}\sqrt[]{2}=2\sqrt[]{2}[/tex]Thus, the simplest form of x is:
[tex]x=\frac{2\sqrt[]{2}}{3}[/tex]What is the domain and range of y=-1/2x+3
Answers
For the function
[tex]y=-\frac{1}{2}x+3,[/tex]the range is all the values y can have and the domain is all the possible values that x can take.
In our function there seems to be no restriction on what values x and y can take—our function is defined for all real values of x and y — therefore, the domain and the range of our function is all real numbers.
I need help with homework question and please help with plotting the points on the graph please it’s highly important for the equation. I have the answer already I just need help plotting the dots on the line. It’s two lines. One line has two points and the second line has two points as well and I already have the outcome but really I stress on placing the coordinates on the line
Answers
Given the set of inequalities:
-2x - 2y > 1
y ≥ -2
Let's graph the system of linear inequalities and shade the solution set.
For the first inequality, rewrite in slope-intercept form:
y = mx + b
Add 2x to both sides:
-2x + 2x - 2y > 2x + 1
-2y > 2x + 1
Divide through by 2:
[tex]\begin{gathered} \frac{-2y}{-2}>\frac{2x}{-2}+\frac{1}{-2} \\ \\ y<-x-\frac{1}{2} \end{gathered}[/tex]Now, let's get two points from this inequality.
When: x = 1.5:
[tex]\begin{gathered} x=1.5 \\ y<-1.5-\frac{1}{2} \\ y<-2 \\ \\ \\ \text{WHen x = 0} \\ y<-0-\frac{1}{2} \\ y<-0.5 \end{gathered}[/tex]For the first inequality, we have the points:
(x, y) ==> (1.5, -2), (0, -0.5)
Plot the points and connect the points using a dashed line.
Shade the area below the boundary region since y is less than.
• For the second inequality:
[tex]y\ge-2[/tex]
This inequality is a horizontal line at y = -2.
We can get any two points on the line:
(x, y) ==> (4, -2), (1.5, -2)
Draw a dashed line at y = 2.
Find the missing length indicated. Leave your answer in the simplest radical form.92112-1620649
Answers
Apply teh altitude theorem:
9/12 = 12/x
Solve for x:
9x = 12 (12)
9x = 144
x = 144/9
x = 16
Lola has 8 bear figurines. These bear figurines make up 40% of her collection of animal figurines. Find the total number
Answers
Hence, the total number of bear figurines are 20
solve for y in the equation below
2 4y = 9
Answers
Answer:9/24
Step-by-step explanation
What are the first and third quartiles of rainfall of this data? Q1 = 5. Q3 = 8 Q1 = 6, Q3 = 8 Q1 = 4, Q3 = 7 Q1 = 5, Q3 = 7.5
Answers
Answer:
Q1 = 5, Q3 = 8
Explanation:
There are a total of 19 dots on the chart.
[tex]\begin{gathered} Item\; in\; Q_1=\frac{1}{4}\times19 \\ =4.75th\text{ item} \end{gathered}[/tex]The 5th item on the chart =5, therefore:
• Q1 = 5
Similarly:
[tex]\begin{gathered} Item\; in\; Q_3=\frac{3}{4}\times19 \\ =14.25th\text{ item} \end{gathered}[/tex]The 14th and 15th item on the chart =8, therefore:
• Q3 = 8
What 4x 5 + 2?????? ????
Answers
Given:
[tex]4\times5+2[/tex]To find the value:
Using the BODMAS rule,
[tex]\begin{gathered} 4\times5+2=(4\times5)+2 \\ =20+2 \\ =22 \end{gathered}[/tex]Hence, the answer is 22.
IF AN AUTO DRIVING AT 40MPH DRIVES 4 HOURS, ANDSTOPS, AND THEN DRIVE '2 HOURSMORE AT 10 Metly thoutte(MILES) DID IT GO?
Answers
• We assume here that the auto drives at 40 mph for 4 hours.
,• Then, it stops and then drives for 2 hours at 10 mph.
,• We need to find the total miles the auto drove.
,• To answer this question, we need to know that we have a constant rate at each part of the driving of the auto: in the first part, it drove at a constant speed of 40 mph. In the second part, it drove at a constant speed of 10 mph.
,• We can say that the total distance for the first part is:
,• d1 = 40 miles/hour * 4 hours ---> ,d1 = 160 miles.
,• In the second part:
,• d2 = 10 miles/hour * 2 hours ---> ,d2 = 20 miles.
,• Then, the total miles it went was:
,• ,d1 + d2 = 160 miles + 20 miles = 180 miles.
,• The auto drove for 180 miles.
,•
,•
Find the z-score for a test score of 86% if themean was 75% and the standard deviationwas 6 points.
Answers
ANSWER
[tex]1.833[/tex]EXPLANATION
To find the z-score, we have to apply the formula:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]where x = Score
μ = Mean
σ = Standard deviation
Therefore, the z-score for the test score is:
[tex]\begin{gathered} Z=\frac{86-75}{6} \\ Z=\frac{11}{6} \\ Z=1.833 \end{gathered}[/tex]Lyndie is making reduced copies of a photo 25 centimeters in height. She sets the copy machine to an 80% size reduction.
PART A
Write a percent equation that represents the relationship of the height of the first copy to the height of the original photo. 38 3-3 Represent and Use the Percent Equation
PART B
Lyndie wants to make another copy that will have a height of 17 cm. The copy machine settings increase or decrease in increments of 5%. Which photo should she make her copy from, the original or her first copy? Explain.
Answers
The succession time should be atleast t=9 to get a final copy that is less than 15% of the original size.
Lyndie is making reduced copies of a photo 25 centimeters in height. She sets the copy machine to an 80% size reduction.
Part a
Let the size of the page be q, when it is reduced to 80%, its size becomes
= 80%*q
= 0.80(q)
= 0.80q
When you want to return it into its original size q, you need to multiply the page by x
such that
x(0.80q) = q
[tex]x = \frac{q}{(0.80q)}[/tex]
[tex]x = \frac{1}{0.80}[/tex]
x = 1.25
x = 125%
Hence, the enlargement needed to be done is 25%.
Part b
The size of the page after t number of copying done is given by
[tex]C(t) = C_{0}(0.80)^{t}[/tex]
where [tex]C_{0}[/tex] is the original size of the page.
We want to find a value for t ∈ Ζ such that
[tex]\frac{C(t)}{C_{0} } = (0.80)^{t}[/tex]
[tex]0.15 \leq (0.80)^{t}[/tex]
To solve this equation, we can apply natural logarithm.
≅ [tex]In(0.15) \leq In(0.80)^{t} \\\\In(0.15) \leq tIn(0.80)\\\\\frac{In(0.15)}{In(0.80)} \leq t\\ \\0.80 \leq t[/tex]
Hence the answer is the succession time should be atleast t = 9 to get a final copy that is less than 15% of the original size.
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-4(0.25b-2) - (7 - b) + 3/2 (4b - 2/3)simply please
Answers
-4(0.25b-2) - (7 - b) + 3/2 (4b - 2/3)
We must open the parenthesis first by multiplying the elements in it be the elements outside
Bearing in mind that
- * - = +
- * + = -
-4(0.25b-2) - (7 - b) + 3/2 (4b - 2/3)
= -b - 8 -7 + b + 6b - 1
Now we rearrange so all like terms are together noting the signs before each term
= -b + b + 6b - 8 - 7 - 1
= 6b - 16
You may leave the answer in this form or go further to factorize
= 2 (3b - 8)
Hi there… I need some help help with this question.
Answers
ANSWERS
a. 1/2
b. 1001
c. 20
d. 8
e. 0.16
EXPLANATION
a. There are 4 women and 4 men on the hiring committee, which is a total of 8 people. The probability that a randomly selected person is a woman is,
[tex]P(W)=\frac{4}{8}=\frac{1}{2}[/tex]Hence, the probability that the person drawing the names from the hat is a woman is 1/2.
b. The applicant pool consists of 6 database administrators and 8 network engineers, which is a total of 14 applicants. We want to choose 4 applicants,
[tex]_4C_{14}=\frac{14!}{4!(14-4)!}=\frac{14\cdot13\cdot12\cdot11\cdot10!}{4!\cdot10!}=\frac{14\cdot13\cdot12\cdot11}{4!}=1001[/tex]Hence, there are 1001 ways to choose the group to be hired.
c. There is a total of 6 database administrators, and we want to choose 3,
[tex]_3C_6=\frac{6!}{3!(6-3)!}=\frac{6!}{3!\cdot3!}=20[/tex]Hence, there are 20 ways of choosing 3 database administrators.
d. There is a total of 8 network engineers, and we want to choose 1,
[tex]_1C_8=\frac{8!}{1!\cdot(8-1)!}=\frac{8\cdot7!}{1\cdot7!}=8[/tex]Hence, there are 8 ways of choosing 1 network engineer.
e. In part b, we found that there is a total of 1001 ways of choosing the 4 people to be hired. Also, in parts c and d, we found that there are 20 ways of choosing 3 database administrators and 8 ways of choosing 1 network engineer. The probability that this is the combination of people hired is,
[tex]P(3DA+1NE)=\frac{20\cdot8}{1001}=\frac{160}{1001}\approx0.16[/tex]Hence, the probability that the random selection of four persons to be hired will result in 3 database administrators and 1 network engineer is approximately 0.16.
This question is very complicated which is something we are barely learning. I hope you can help and I appreciate the help.
Answers
There are four walls, one roof and one floor.
Mr. Smith will only paint the walls, but in one of them there is a door not to be painted.
The two walls with no doors have dimensions of 6 feet x 5 feet.
Their individual area is 6 * 5 = 30 square feet.
Their combined area is 2 * 30 = 60 square feet.
The back wall and the front wall have dimensions of 12 feet x 6 feet.
Their individual area is 12 * 6 = 72 square feet.
The front wall has a door of dimensions of 3 feet x 5 feet.
The area of the door is 3 * 5 = 15 square feet.
This area must be subtracted from the area of the fron wall.
Area of the front wall = 72 - 15 = 57 square feet.
The total area to be painted in blue is:
60 + 72 + 57 = 189 square feet
Two occupations predicted to greatly increase in number of jobs are pharmacy technicians and network systems and data communication analysts. The number of pharmacy technician jobs predicted for 2005 through 2014 can be approximated by 7.1x-y=-254. The number of network and data analyst jobs for the same years can be approximated by 12.2x-y=-231. For both equations, x is the number of years since 2005 and y is the number of jobs in thousands.Solution to the ordered pairs:(5, 286)Use your result from part (a) to estimate the year in which the number of both jobs is equal.
Answers
Given the system of equations:
7.1x - y = -254
12.2x - y = -231
Where x is the number of years since 2005
y is the number of Jobs in thousands.
After solving the system, we have the solution:
(x, y) ==> (5, 286)
Let's determine the year in which the number of both jobs is equal.
The graph of both lines will meet at the solution point.
Given that x represents the number of years since 2005, the year which the number of both jobs is equal will be 5 years after 2005.
Hence, we have:
Year in which number of both jobs are equal = 2005 + 5 = 2010
Therefore, in 2010, the number of both jobs will be equal.
ANSWER:
2010
X-31The rational expression +5x X+2is equivalent to
Answers
SOLUTION
Step 1 :
In this question, we are meant to simplify the rational fractions:
[tex]\frac{\text{x - 3 }}{5\text{ x }}\text{ + }\frac{1}{x\text{ + 2}}[/tex][tex]=\frac{(\text{ x - 3 ) ( x + 2 ) + 5 x }}{5\text{ x ( x + 2 )}}[/tex][tex]=\frac{x^2\text{ + 2 x - 3 x -6 + 5 x }}{5\text{ x ( x + 2 )}}[/tex][tex]=\text{ }\frac{x^2\text{ + 4x - 6 }}{5\text{ x ( x + 2 )}}\text{ --OPTION B}[/tex]Jen Butler has been pricing Speed-Pass train fares for a group trip to New York Three adults and tour children must pay $124. Two adults and three children must pay $88. Find the serice of the addit's ticket and the price of a child's ticketThe price of a child's ticket is $The price of an adult's ticket is $
Answers
It is given that two adults and three children pay $88.
Represent it as equation
2x+3y=88
Then three adults and four children pay $124.
It is written is equation form as follows.
3x+4y=124
Here x is adults' price and y is children's price.
Solve the system of equation as follows.
[tex]\begin{gathered} 3x+4y=124 \\ 2x+3y=88 \\ 6x+8y=248 \\ 6x+9y=264 \end{gathered}[/tex]Now subtract each of the last two equations to get -y=-16
Hence y = 16
Substitute in equation 1, we get
[tex]\begin{gathered} 2x+48=88 \\ 2x=40 \\ x=20 \end{gathered}[/tex]Therefore, adult price is $20 and children price is $16
Question 7 of 10Estimate the sum of the decimals below by rounding to the nearest wholenumber. Enter your answer in the space provided.8.9995.496+ 1.199
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given decimals
[tex]8.999+5.496+1.199[/tex]STEP 2: Round the given decimals
[tex]\begin{gathered} 8.999\approx9 \\ 5.496\approx5 \\ 1.199\approx1 \end{gathered}[/tex]STEP 3: Find the sum
[tex]9+5+1=15[/tex]Hence, the sum is estimatedly 15
what relationship between the number of extracurricular activists and gpa do the data suggest ?A)the more extracurricular activists a student participates in, the higher the students gpa.b) students who participate in exactly 2 extracurricular activities have the highest gpac) the fewer extracurricular activities a student participates in the higher the students gpad) there is no relationship between the number of extracurricular activities and gpa
Answers
Solution
For this case we can create the following table sorted by Extracurricular activities:
Name EAGPA
Overdown D03.1
Richards Z01.8
Garrison F12.8
Minton M13.5
House W23.9
Villanueva C23
Chapman V33.7
Solomon P43.3
West H 82.8
Lycan A 92.3
If we plot EA against GPA we have:
Then the best answer is:
d) there is no relationship between the number of extracurricular activities and gpa
Find the area of the given geometric figure. If the figure is a circle, give an exact area and then use 22/7 as an approximation for pie to approximate the area. r=2in
Answers
the area of a circle is given by:
[tex]\text{Area}=\pi\cdot radius^2[/tex]Step 1
replace
[tex]\begin{gathered} \text{Area}=\frac{22}{7}\cdot(2inches)^2 \\ \text{Area}=\frac{22}{7}\cdot4in^2 \\ \text{Area}=\frac{22\cdot4}{7} \\ \text{Area}=12.57 \end{gathered}[/tex]so, the answer is 12.57 square inches
What is the value of x?
Answers
Answer:
The two angles are congruent, so: 2x+2=3x-52
2x-3x=-2-52
-x=-54
x=54
feet by You are preparing to tile the backsplash in a kitchen. The area you are tiling measures 8 1/2 feet. The tiles you plan to use are sold in boxes that have enough tiles to cover 10 square feet. What is the minimum number of boxes of tiles you should order to complete the job?A.1B. 2C. 12D. 13E. 20
Answers
hello
the area of the room is given by
[tex]8\frac{1}{2}by1\frac{1}{2}[/tex]let's convert the mixed fraction to improper fraction
[tex]\begin{gathered} 8\frac{1}{2}=\frac{17}{2} \\ 1\frac{1}{2}=\frac{3}{2} \end{gathered}[/tex]now, let's multiply the two dimensions given to find the area in squared feet.
[tex]\frac{17}{2}\times\frac{3}{2}=\frac{51}{4}[/tex]the area of the room is 51/4 ft^2
we can now find how many boxes of tiles will cover the room
1 box covers 10ft^2
let the number of boxes of tiles to cover 51/4ft^2 be represented by x
1 box = 10
x box = 51/4
[tex]\begin{gathered} 1=10 \\ x=\frac{51}{4} \\ \text{cross multiply both sides and solve for x} \\ 1\times\frac{51}{4}=10\times x \\ \frac{51}{4}=10x \\ \text{divide both sides by 10} \\ \frac{\frac{51}{4}}{10}=\frac{10x}{10} \\ x=\frac{51}{4}\times\frac{1}{10}=\frac{51}{40}=1.275 \end{gathered}[/tex]the number of boxes required to cover the room is 1.275 boxes and he'll need a minimum of 2 boxes to do so.
the answer is option B
Sam read 6 books in the time it took his little sister, faith, to read 1/2 of a book
Sam's sister read how many times as many books as sam read?
Answers
Answer:
3
Step-by-step explanation:
6 x 1/2 = 3
An unusual die has the numbers 2,2,3,3, 7 and 7 on its six faces. Two of these dice are rolled, and the numbers on the top faces are added. How many different sums are possible?
Answers
To find the total numbers of sum, we just have to elevate the number of faces by the second power.
[tex]6^2=36[/tex]There are 36 total numbers of sums.
However, there are just 6 different sums.
[tex]\begin{gathered} 2+2=4 \\ 2+3=5 \\ 2+7=9 \\ 3+3=6 \\ 3+7=10 \\ 7+7=14 \end{gathered}[/tex]Therefore, there are 6 different sums.Use to reflect over the x-axis. Identify the transformed vector.
Answers
To reflect the given matrix over the x-axis, you have to multiply both matrices:
[tex]\begin{bmatrix}{1} & {0} \\ {0} & {-1}\end{bmatrix}\cdot\begin{bmatrix}{7} \\ {-12}\end{bmatrix}[/tex]Multiply each term of the first row of the first matrix with the corresponding terms of the column of the second matrix and add the results:
Repeat the process for the second row of the first matrix
The resulting matrix is:
[tex]\begin{bmatrix}{1} & {0} \\ {0} & {-1}\end{bmatrix}\cdot\begin{bmatrix}{7} \\ {-12}\end{bmatrix}=\begin{bmatrix}{(1\cdot7)+(0\cdot-12)} \\ {\square}(0\cdot7)+(-1\cdot-12)\end{bmatrix}=\begin{bmatrix}{7} \\ {12}\end{bmatrix}[/tex]The correct option is option D.
The rectangular floor of a classroom is 28 feet in length and 30 feet in width. A scale drawing of the floor has a length of 14 inches. What is the perimeter, in inches, of the floor in the scale drawing?
Answers
The Solution:
Given:
Required:
To find the perimeter (in inches) of the floor in the scale drawing.
Step 1:
Find the value of x.
By the similarity theorem:
[tex]\frac{14}{x}=\frac{28}{30}[/tex]Cross multiplying, we get:
[tex]\begin{gathered} 28x=14\times30 \\ \\ Dividing\text{ both sides by 28, we get} \\ \\ x=\frac{14\times30}{28}=\frac{30}{2}=15\text{ in.} \end{gathered}[/tex]Step 2:
Find the perimeter, in inches, of the floor in the scale drawing.
By formula, the perimeter is:
[tex]\begin{gathered} P=2(L+W) \\ \text{ Where:} \\ L=14\text{ inches} \\ W=x=15\text{ inches} \\ P=perimeter=? \end{gathered}[/tex]Substituting these values in the formula, we get:
[tex]P=2(14+15)=2\times29=58\text{ inches}[/tex]Therefore, the correct answer is 58 inches.
A school track team member ran for a total of 149.5 miles in practice over 57.5 days. About how many miles did he average per day?
Answers
Data
• Total: 149.5 miles
,• Days: 57.5
,•