do i add up the exponents or subtract? i don't quite understand my homework. if you are going to respond, please send a step by step too please.
(n^2-3n+1)(2n+3)
Multiplying binomials by polynomials btw
Answers
Answer:
2n³ - 3n² - 7n + 3
Step-by-step explanation:
Hi there! Don't worry, polynomials seem hard but you will get them with practice.
I am going to show you 2 methods of multiplying polynomials. These methods are universal, or they work with any polynomial multiplication problem:
Method 1: Distributive PropertyThis is perhaps the most common method. You distribute 1 value to another or multiply each and every single term.
Let's solve it!
(n² - 3n + 1)(2n + 3)n²(2n + 3) - 3n(2n + 3) + 1(2n + 3) n²(2n) + n²(3) - 3n(2n) - 3n(3) + 2n + 3 See how I distributed the values?2n³ + 3n² - 6n² - 9n + 2n + 3Now, we add up like terms. Like terms should have the same coefficient and should be raised to the same power.
2n³ + 3n² - 6n² - 9n + 2n + 3 2n³ - 3n² - 7n + 3There you have it! This is how you solve with The distributive Property Method.
Method 2: Area ModelThis is the next universal method, Area modeling.
Area models can be set up by the number of terms we have. In the first polynomial we have three terms:
n²-3n+1Just for this method, keeping the positive signs helps.
For the binomial, we have two terms (hence, binomial)
2n+3We set up our are model like this, with the terms laid out as side lengths of a rectangle. (Attachment "A")
Next, we find the area of each individual tile. (Attachment "B")
Now, we add like terms. Something nice about area models is that most of the time, the like terms are matched up in a diagonal. (Attachment "C")
2n³ + 3n² - 6n² - 9n + 2n + 3 2n³ - 3n² - 7n + 3We end up with the same answer as before.
-Chetan K
Related Questions
Please help asap
I cant figure out the answer
Answers
Answer:
B
Step-by-step explanation:
using the formula 0.75 time the 160 is 120. so s squared divided by 30.25 should equal approximately 120
going through the answers and dividing them by 30.25 is the easiest way to do so. 60 squared is 3600 divided by 30.25 is 119.008
Write the equation in standard form. Identity the center and radius.
x² + y2 + 8x-4y-7=0
Answers
Answer:
equation;
[tex](x + 4) {}^{2} + (y - 2) {}^{2} = 27[/tex]
Center (-4,2)
Radius is
[tex]3 \sqrt{3} [/tex]
Step-by-step explanation:
Since the x^2 and y^2 have the same coeffiecent this will be a circle in a form of
[tex](x - h) {}^{2} + (y - k) {}^{2} = {r}^{2} [/tex]
Where (h,k) is center
r is the radius
So first we group like Terms together
[tex] {x}^{2} + 8x + {y}^{2} - 4y - 7 = 0[/tex]
Add 7 to both sides
[tex] {x}^{2} + 8x + {y}^{2} - 4y = 7[/tex]
[tex]( {x}^{2} + 8x) +( {y}^{2} - 4y) = 7[/tex]
Since the orginal form of the equation of the circle has a perfect square we need to complete the square for each problem
[tex] (\frac{8}{2} ) {}^{2} = 16[/tex]
and
[tex]( - \frac{4}{2} ) {}^{2} = 4[/tex]
so we have
[tex] {x}^{2} + 8x + 16 + {y}^{2} - 4y + 4y = 7 + 16 + 4[/tex]
[tex] {x}^{2} + 8x + 16 + {y}^{2} - 4y + 4y = 27[/tex]
[tex](x + 4) {}^{2} + (y - 2) {}^{2} = 27[/tex]
To find our center, h is -4 and k is 2
so the center is (-4,2)
The radius is
[tex] \sqrt{27} = 3 \sqrt{3} [/tex]
So the radius is 3 times sqr root of 3.
Ethan's monthly salary is $1850. In a particular month, he spent 20.5% of his salary on room rental, $690 on food and $940 on other expenses. Express the amount that he overspent as a percentage of his monthly salary, giving your answer correct to 2 decimal places.
Answers
Answer:
He overspent 8.61% as a percentage of his monthly salary.
Step-by-step explanation:
Answer:
8.61% (2 dp)
Step-by-step explanation:
Salary = 1850
Food = 690
Other = 940
Rent = 20.5% = 20.5/100 = 0.205
Therefore, 20.5% of the salary = 0.205 x 1850 = 379.25
Total spent = 690 + 940 + 379.25 = 2009.25
Percent change = [ (difference between initial and final value) ÷ initial value] x 100
=[(2009.25 - 1850) ÷ 1850] x 100 = 8.61% (2 dp)
In a study of 500 children from a city, 238 were randomly selected to receive a new vaccine. The other 262 children were randomly selected to receive a placebo. The children and the physicians did not know to which group they had been assigned. After five years, 22 of the 238 children who received the vaccine had been infected with malaria; while 28 out of the 262 children who received the placebo had been infected with malaria.
A) Is this an experiment or an observational study?
B) What are the variables? Which are categorical/quantitative?
C) Using the information above, fill in the two-way table to determine whether the vaccine is effective.
Please hellppp (Statistics Math) worth 100 points
Answers
Answer:
A: Experiment
B: The variables are the vaccine and placebo. The kids are categorical.
C: I can't fill out the table if I dont see one... sorry!! Good luck!
Step-by-step explanation:
how many spaces are there total? 5) Jerry had 153 songs on his MP3 player. If he deleted 63 songs, what is the ratio of songs he kept to songs he deleted?
Answers
The table shows the membership cost for two CD clubs. How many CDs would you need to buy in a year in order for the total cost of both memberships to be the same?
CD Club Membership
Club #1: Annual Fee = 50$ and Cost Per CD = 7.50$
Club #2: Annual Fee = 35$ and Cost Per CD = 8.00$
Answers
Answer:
Club 1: 16 would be 120
Club 2: 15 would be 120
=
17
6
× 12 in
WHATS THE ANSWER
Answers
Answer:
34 = 34/1
Step-by-step explanation:
17/6 x 12/1 = 34
I am not entirely sure but if I am understanding what your trying to ask the answer is 34.
Miles is buying a chair that regularly costs $250. Today the chair is on sale for 30% off. The sales tax of 6% is taken on the sales price. What will be the total cost, including tax, if Miles buys the chair today. (I ALREADY KNOW THE ANSWER. BUT I NEED THE WORK FOR THE ANSWER TO SHOW MY TEACHER) (the answer is $185.50)
Answers
Step-by-step Explanation:
First find out what is the price after 30% off.
250 · 0.3 = 75
250 - 75 = 175
Then find the tax and add it on. Remember to calculate the tax AFTER the discount.
175 · 0.06 = 10.50
175 + 10.50 = 185.50
in the given figure ABCD is a piece of land find the length of side BD and BC and the area of the land
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Answer:
use Pythagoras theorem by dividing the plane into two triangles one is triangel ABD and triangle DBC.
According to the graph, what is the value of the constant in the equation below?
Answers
well, let's take a look at the graph hmmmm as "x" is moving further towards the right, the line is going down, or namely "y" is lessening and lessening, which is another way to say that "y" is inversely proportional to "x".
well, we know a few points on the line hmmm let's use say hmm (10 , 8) to get the constant of proportionality. Any point will do btw, we're just using this one.
[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\stackrel{\textit{"H" varies inversely with "w"}}{H=\cfrac{k}{w}}\qquad \textit{we know that} \begin{cases} H=8\\ w=10 \end{cases} \\\\\\ 8=\cfrac{k}{10}\implies \boxed{80=k}[/tex]
5) −r − 10r 6) −2x + 11 +6x 7) 11r − 12r 8) −v + 12v 9) −8x −11x 10) 4p + 2p
pls help me simplify this
Answers
Use the diagram below of similar triangles to find the value of y.
Answers
Answer:
y = 10.5
Step-by-step explanation:
Δ MOP and Δ MNQ are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{OP}{NQ}[/tex] = [tex]\frac{MO}{MN}[/tex] ( substitute values )
[tex]\frac{y}{7}[/tex] = [tex]\frac{8+4}{8}[/tex] = [tex]\frac{12}{8}[/tex] ( cross- multiply )
8y = 84 ( divide both sides by 8 )
y = 10.5
In a blueprint, each square has a side length of 1/4 inch. Ceramic tile costs $5 per square foot. How much would it cost to tile the bathroom? Carpet costs $18 per square yard. How much would it cost to carpet the bedroom and living room?
(as you can see, I already got the answer for a. I just need the answer for b.)
Answers
b.
Bedroom area
Lenght = 5 squares
= 5 × 1/4 inchi
= 5/4 inchi
Width = 4 squares
= 4 × 1/4 inchi
= 1 inchi
Large area = 5/4 × 1 inchi
= 5/4 inchi
Living room
Lenght = 7 squares
= 7 × 1/4 inchi
= 7/4 inchi
Width = 4 squares
= 4 × 1/4 inchi
= 1 inchi
Large area = 7/4 × 1 inchi
= 7/4 inchi
Total Area
Bedroom area + Living room area
= 5/4 + 7/4
= (5+7)/4 inchi
= 12/4 inchi
= 3 inchi
1 square yard = 1296 square inches
so 1 square inches = 1/1296 square yard
3 inchi = 3×1/1296
= 3/1296
= 1/432
Cost = 1/432 × $18
= $1/24
It would cost $1/24 to carpet the bedroom and living room.
Lisa pours 1/4 a 1 liter bottle of coke for each of her 4 family members. What is the decimal of coke they each receive?
Answers
Answer:
.25
Step-by-step explanation:
Answer:
if there are 4 people and she pours 1/4 of a 1-liter coke bottle equally, it means that she gave each member 25% or 0.25 of a liter or bottle of coke
. The selling price of 15 articles is Rs 1,500 at a gain of 8%. Find C.P of each article
Answers
Rs. 92.59 is each article's CP
Step-by-step Explanation:-
As per conditions given,
[tex]1500 \div 15 \div (1 + 8[/tex]%)
[tex] = > 100 \div 1.08[/tex]
[tex] = > approx. \: 92.59[/tex]
Hence, the CP of each article is Rs. 92.59
Which situation would require determining volume? Nick wants to know how much tile it takes to cover the floor of a room. Min wants to know how much fence is needed to go around the edge of his yard. Sarah wants to know how much water her fish tank can hold. I don't know.
Answers
Answer:
Sarah's fish tank
Step-by-step explanation:
Nick needs area - the space covering a flat surface
Min needs perimeter - the distance around something
Sarah needs volume - the space inside something
2. Find the area of the shaded region. Express your answer in terms of
3 in
6 in
9 in
12 in
18 in
Answers
Answer:
Step-by-step explanation:
Find the area of the rectangle. A = length * width
Find the area of each circle. A = π*radius*radius
Subtract the area of each circle from the area of the rectangle.
A = length * width
A = (3+6+9+12) * 18
A = 30 * 18
A = 540 square inches
Bottom circle
A = π * radius * radius. (radius is 1/2 of the diameter)
A = 3.14 * 6 * 6
A = 133.04 square inches
Middle circle
A = π * radius * radius
A = 3.14 * 4.5 * 4.5
A = 63.59 square inches
Top circle
A = π * radius * radius
A = 3.14 * 3 * 3
A = 28.26 square inches
Subtract the circles from the rectangle.
540 - 133.04 - 63.59 - 28.26 = 315.11 square inches is the area of the shaded part.
is it true or false is this a function (pls help)
Answers
Answer: True
Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
Answer:
True
Step-by-step explanation:
Using the vertical line test since it only passes through the graph once it is a function
Isaac planted 64 fewer trees than Leon. Leon planted t trees. Write an expression that
shows how many trees Isaac planted.
Answers
t - 64
(which is read as 64 trees less than 5)
2) What percent of 87 is 55 ?
Answers
Answer:
If you don't add decimals a 63.
Step-by-step explanation:
because 55 out of 87 correct on a test would be a 63%
FIRST PART OF MY LAST QUESTION ONLY FOR ONE PERSON TO uSE
Answers
Answer:
C
Step-by-step explanation:
You just need to convert some of the mixed numbers so that they have a denominator (of the fraction part) as 8:
10 4/8 = 10 1/2
10 6/8 = 10 3/4
11 2/8 = 11 1/4
Please I’m confused…
Answers
Answer:
I believe it should be
4 : 1 : 200
Step-by-step explanation:
Just an answer and a simple explanation. Please and Thank you!
Answers
Answer:
x = 15°
Step-by-step explanation:
If you use Vertical Angles, you can move the two algebraic expressions next to each other and totaling 90° (because m and n are perpendicular)
x + 21 + 3x + 9 = 90°
combine like terms.
4x + 30 = 90
subtract 30 from both sides.
4x = 60
divide by 4.
x = 60/4
x = 15
A restaurant owner washed 94 kilograms of vegetables, some spinach and some cucumbers. The spinach came in 10-kilogram bags and the cucumbers came in 9-kilogram bags. The owner washed 10 bags of vegetables in all. How many bags of each kind did he wash?
Answers
Answer:
6 bags of cucumber
4 bags of spinach
Step-by-step explanation:
let s = number of bags of spinach
let c = number of bags of cucumber
If the owner washed 10 bags of vegetables in total, then
s + c = 10
The spinach came in 10kg bags and the cucumbers came in 9kg bags, and the owner washing 94kg of veg in total:
10s + 9c = 94
Rewrite s + c = 10 to make s the subject, substitute it into 10s + 9c = 94, then solve for c:
s + c = 10
⇒ s = 10 - c
⇒ 10(10 - c) + 9c = 94
⇒ 100 - 10c + 9c = 94
⇒ -c = -6
⇒ c = 6
Substitute c=6 into s + c = 10 and solve for s:
s + 6 = 10
⇒ s = 4
Describe the steps you would use to factor the
trinomial 4x2 - 4x - 3.
-
Answers
Answer:
5-4x
Step-by-step explanation:
8 - 4x - 3
5 - 4x
im so confused pleaseeee help
Answers
Answer:
99mm^2
Step-by-step explanation:
Area of a rectangle: A = l*w
Length: 11mm
Width: 9mm
A = 11 * 9
A = 99 mm^2
Hope this helps!
Determine whether the statement makes sense or not (Please help)
Answers
=======================================================
Explanation:
The number [tex]7 \times 10^{10}[/tex] is the number 7 followed by 10 zeros
[tex]7 \times 10^{10} =[/tex] 70,000,000,000 = 70 billion
According to statista.com, there are roughly 229 million drivers in the US (based on a 2019 survey).
Divide the two amounts to get:
(70 billion)/(229 million) = (70*1000 million)/(229 million) = 305.677 approximately
This indicates that each driver uses about 306 gallons of gas per day.
This value is way too high.
Therefore, the initial claim does not make sense.
------------
Upon further research, the site eia.gov states that Americans use about 337 million gallons of gasoline per day (not 70 billion).
Notice how (337 million)/(229 million) = 1.472 approximately which is far more realistic. It makes more sense to have any given driver use somewhere between 1 or 2 gallons of gas per day. Of course, all of this depends on the person's location from home to work, the amount of traffic, etc.
Select the choice that translates the following verbal phrase correctly to algebra:
the product of 12 and y increased by 11
Answers
Step-by-step explanation:
( 12 × y ) + 11
The product of 12 & y = 12 × y
Increasing = adding = (12×y) + 11
12y + 11.
What number is plotted on the number line?
Answers
Answer:
The number 0.7 is plotted on the number line.
Answer:
0.7.Step-by-step explanation:
Count up 0 to 1.
Stop at the point.
If you stop at the point, you should know what the point is.
The point is graphed at 0.7.
3 ratios equivalent to 5 : 2
Answers
Answer:
25/10 ,30/12,10/4
Step-by-step explanation:
1) 5/2*5/5
2)5/2*6/6
3)5/2*2/2