Answer:
Quotient is [tex]5(x^2+x+1)[/tex] and remainder is 0.
Step-by-step explanation:
Given: [tex]\frac{5x^4+5x^2+5}{x^2-x+1}[/tex]
To find: quotient and remainder
Solution:
In the given question,
Dividend = [tex]5x^4+5x^2+5[/tex]
Divisor = [tex]x^2-x+1[/tex]
[tex]\frac{5x^4+5x^2+5}{x^2-x+1}\\=\frac{5(x^4+x^2+1)}{x^2-x+1}\\=\frac{5[x^2(x^2+1)+1]}{x^2-x+1}\\=\frac{5[x^2(x^2-x+x+1)+1]}{x^2-x+1}\\=\frac{5[x^2(x^2-x+1)+x^3+1]}{x^2-x+1}\\=\frac{5[x^2(x^2-x+1)+x(x^2)+1]}{x^2-x+1}\\=\frac{5[x^2(x^2-x+1)+x(x^2-x+1+x-1)+1]}{x^2-x+1}\\=\frac{5[x^2(x^2-x+1)+x(x^2-x+1)+(x^2-x+1)]}{x^2-x+1}\\=\frac{5[(x^2-x+1)(x^2+x+1)}{x^2-x+1} \\=5(x^2+x+1)[/tex]
So, quotient is [tex]5(x^2+x+1)[/tex] and remainder is 0.
If you are given a paper which has lines which are the length of a needle apart, and then you repeated drop that needle onto the paper, the probability that the needle with cut the line is:
Answer:
The correct option is;
[tex]\frac{1}{\pi }[/tex]
Step-by-step explanation:
Here we have that
[tex]Probability = \frac{Number \, of \, required\, outcomes}{Number \, of \, possible\ outcomes} = \frac{Dimension \, of \, the \, line}{Size \, of \, the \ needle} = \frac{l \times D}{\pi \times D \times l } = \frac{1}{\pi }[/tex]
Therefore, the probability that the needle will cut the line = 1/π.
You start a chain email and send it to 3 friends. The process continues and each of your friends forward the email to 3 other people. What is an expression for the nth term an?
Answer:
[tex]a_{n}=3^{n}[/tex]
Step-by-step explanation:
We can start solving this problem by making a list of the number of chain emails that are sent on each round:
Round one:
[tex]a_{1}=3[/tex]
which represents the three friends you send the mail to.
Round two:
[tex]a_{2}=3*3=9[/tex]
since each of your friends sends the mail to another three friends, then we multiply the original 3 friends by 3 to get a total of 9.
Round three:
[tex]a_{3}=3*3*3=9*3=27[/tex]
on the next round we multiply the previous 9 persons by 3 mails each giving us a total of 27 persons receiving the mail. A patter starts showing here. Notice that for each round we need to take the previous round number an multiply it by 3. When we have a number being multiplied by itself n times, we rewrite it as a power, so the expression for the nth term will be:
[tex]a_{n}=3^{n}[/tex]
which is our final answer.
What is the slope of the line ?
Answer:
-3
Step-by-step explanation:
-2 x (-7) =
24 divided by (-3) =
Answer:
1) 14
2) -8
Step-by-step explanation:
-2 × (-7) = 14
24 ÷ (-3) = -8
What is the distance between points A(13, 2) and B(7, 10)
Answer:
distance = sqrt((x2-x1)^2 + (y2-y1))
distance = sqrt((7-13)^2 + (10-2)^2)
distance = sqrt( -6^2 + 8^2)
distance = sqrt(36+64)
distance = 10
Step-by-step explanation:
Answer:
10 units
Step-by-step explanation:
d = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]
d = [tex]\sqrt{(13 - 7)^2 + (2 - 10)^2}[/tex]
d = [tex]\sqrt{(6)^2 + (-8)^2}[/tex]
d = [tex]\sqrt{36 + 64}[/tex]
d = [tex]\sqrt{100}[/tex]
d = 10 units
Kelly is going to shop with the $200.00 that she earned from doing chores. She wants to save 30% of her money to put into a savings account. She buys a sweater for $60.00 and a new coat for $75.00, with 6% sales tax on both items. Does Kelly still have the amount of money she planned to put into her savings account?
Answer:
No she won't
Step-by-step explanation:
200(0.30)=60
60(0.06)=3.6
60+3.6=63.6
75(0.06)=4.5
75+4.5=79.5
79.5+63.6=143.1
200-143.1=56.9
56.9<60
What is the correct answer?
Answer:45
Step-by-step explanation:
Sin^-1= 5÷7
Orla and Eduardo each looked at a strand of their hair under a microscope and measured the diameter. Orla's strand was 0.005\,\text{cm}0.005cm0, point, 005, start text, c, m, end text in diameter, and Eduardo's strand was 0.012\,\text{cm}0.012cm0, point, 012, start text, c, m, end text in diameter. How much greater was the diameter of Eduardo's hair?
Answer:
30x2010x943
Step-by-step explanation:
219x29192
Answer:
0.007
Step-by-step explanation:
There are 20 marbles in a jar. There are 6 red marbles, 3 green marbles, and the rest are purple. What is the probability of getting a purple marble if you take a marble out of the bag
Answer:
55% probability of getting a purple marble if you take a marble out of the bag
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, we have that:
20 marbles.
6 are red.
3 are green
The rest(x) are purple.
So
6 + 3 + x = 20
x = 11
20 marbles, of which 11 are purple.
11/20 = 0.55
55% probability of getting a purple marble if you take a marble out of the bag
EMERGENCY!!!! EXTRA POINTS! I HAVE POSTED THIS QUESTION 5 TIMES AND HAD TO REPORT ALL RESPONSES! I ACTUALLY NEED HELP!
The amusement park in Riverdale charges a $10 entrance fee plus $1 per ride. The amusement park in Esterdamb charges a $5 entrance fee and $2 per ride. For how many rides will the cost be the same for both amusement parks? x= # of rides
Number of rides_____?
Cost_____?
Answer:
the price will be the same for either amusement park
Step-by-step explanation:
10+1(x)=?
5+2(x)=?
ex; x=5
10+1(5)= 5+2(5)=
10+5= 5+10=
15 15
Answer:
5 rides, cost of $15
Step-by-step explanation:
With the information given we have two expressions:
10 + 1x and 5 + 2x
Using these expressions we can create this equation:
10 + 1x = 5 + 2x
Knowing some information we can can simply analyze some information:
The closest number each of these equations could equal is 15,
1(5) is 5 + 10 = 15, and 2(5) is 10 + 5 = 15
15 = 15 this is a true statement, so we know this is answer
Hope this helps! Have a good day!
Please help me now I will mark you brainliest
Answer:
Out side the circle
Step-by-step explanation:
This is because the center is 0 and if the point 6, square root seven is on the circle that mean that as far as the circle goes on each side.
when nathan was 2 1/2 years old, he was 34 inches tall. the doctor told his mother that he will be two times and 4 inches taller than that when he is an adult. which of the following equation will give h, nathans height, as an adult
Answer 5 ft 4 in
Step-by-step explanation:
2 1/2 + 2 1/2=5 + 4 inches
Mr. Stewart used a gallon of vinegar to make 15 different color egg dipping containers. He used the same amount of vinegar in each container. How much vinegar in gallons was used in each egg dye container?
Answer:
0.067 gallons ( to 2 decimal places)
Step-by-step explanation:
First, note that since the same amount of vinegar was used in each container, it means that the 1 gallon of vinegar was divided equally to the 15 containers, hence the amount of vinegar used in each dye container is calculated as follows:
total volume of vinegar = 1
number of egg dye containers = 15
if equal volume of vinegar was used in each container:
volume of vinegar in each egg dye container = 1 ÷ 15 = 0.067 gallons ( to 2 decimal places)
Since the area of the circle is StartFraction pi Over 4 EndFraction the area of the square, the volume of the cylinder equals
StartFraction pi Over 2 EndFraction the volume of the prism or StartFraction pi Over 2 EndFraction(2r)(h) or πrh.
StartFraction pi Over 2 EndFraction the volume of the prism or StartFraction pi Over 2 EndFraction(4r2)(h) or 2πrh.
StartFraction pi Over 4 EndFraction the volume of the prism or StartFraction pi Over 4 EndFraction(2r)(h) or StartFraction pi Over 4 EndFractionr2h.
StartFraction pi Over 4 EndFraction the volume of the prism or StartFraction pi Over 4 EndFraction(4r2)(h) or Pir2h.
Answer:
StartFraction 2 Over h EndFraction = StartFraction 3 Over m EndFraction
StartFraction 2 Over n EndFraction = StartFraction 3 Over h EndFraction
StartFraction 2 Over h EndFraction = StartFraction h Over n EndFraction
Startfraction 2 Over h EndFraction = StartFraction h Over 3 EndFraction
Step-by-step explanation:
Answer:
It's D
Step-by-step explanation:
Secant TQ and tangent TR intersect at point T. Chord SR and chord PQ intersect at point V. Find the values of x and y. If necessary, round to the nearest tenth.
Answer:
x=4, y=9.6
Step-by-step explanation:
Using Theorem of Intersecting Secant and Tangent
[tex]TP X TQ=TR^2[/tex]
[tex]9(9+12+x)=15^2\\9(21+x)=225\\189+9x=225\\9x=225-189\\9x=36\\x=4[/tex]
Next, we apply Theorem of Intersecting Chords
SV X VR=PV X VQ
5 X y = x X 12
Recall: x=4
5y=4 X 12
5y=48
y=48/5=9.6
Therefore: x=4, y=9.6
Jamal and Cleo mow lawns together, Jamal can mow an average lawn in 60 minutes by
himself. Cleo would take 90 minutes for the same job. How long would it take both of
them together to mow one (1) lawn
how much money does ron have each month
Answer:
after paying all expenses Ron will have $10 leftover each month.
Answer:
10 on edge
Step-by-step explanation:
The leaning Tower of Pisa was completed in 1372 and makes 86 degree angle with the ground. The tower is 50 meters tall, measured vertically from the ground to the highest point. If you were to climb to the top then accidentally drop your keys, where would you start looking for them?
How far from the base of the tower would they land?
I made having no luck in figuring this out.
Answer:
The distance where the keys would drop from the base is 3.5m
Step-by-step explanation:
Height of the tower = 50m
Angle it makes to the ground = 86°
To solve this question, you have to understand that the tower isn't vertically upright and the height of the tower is different from the distance from the top of the tower to the ground.
The tower makes an angle 86° to the ground and that makes it not vertically straight because a vertically straight building is at 90° to the ground.
See attached document for better illustration.
The distance from where the keys drop to the base of the tower can be calculated using SOHCAHTOA
We have to use cosθ = adjacent / hypothenus
θ = 86°
Adjacent = ? = x
Hypothenus = 50m
Cos θ = x / hyp
Cos 86 = x / 50
X = 50 × cos 86
X = 50 × 0.06976
X = 3.488 = 3.5m
The distance where the keys would drop from the base of the tower is approximately 3.5m
At the beginning of the month, Tim has $50. He mows 2 lawns and washes 1 car. Then, he buys two video games that cost $15 each and a sweatshirt that costs $35. How much money does Tim have left? (please put just your answer with the $)
Answer:
Tim has $50. 15+15=30-35=5
Tim has $5 left
Divya’s recipe calls for 3.25 pounds of beef, 0.65 pounds of onions, 0.2
pounds of potatoes, 0.15 pounds of tomatoes, and 0.33 pounds of asparagus.
How much will Divya pay for all the ingredients in the recipe? Show your work.
The beef price is $10.65
Onions price is $2.49
Potatoes are $3.29
Tomatoes are $8.45
Asparagus is $4.99
3.25 pounds of beef is 3.25 * 10.65 = 34.61
0.65 pounds of onions is 0.65 * 2.49 = 1.62
0.2 pounds of potatoes is 0.2 * 3.29 = 0.66
0.15 pounds of tomatoes is 0.15 * 8.45 = 1.27
0.33 pounds of asparagus is 0.33 * 4.99 = 1.65
Adding these up we get 34.61 + 1.62 + 0.66 + 1.27 + 1.65
This is equal to 39.81
A recipe is mixture of ingredients.
Divya will pay $39.81 for all the ingredients in the recipe.
The beef price is $10.65 per pound
So, price of 3.25 pounds of beef is , [tex]3.25 * 10.65 = 34.61[/tex]
Onions price is $2.49 per pound
So, price of 0.65 pounds of onions is, [tex]0.65 * 2.49 = 1.62[/tex]
Potatoes are $3.29 per pound
So, price of 0.2 pounds of potatoes is , [tex]0.2 * 3.29 = 0.66[/tex]
Tomatoes price are $8.45 per pound.
So, price of 0.15 pounds of tomatoes is , [tex]0.15 * 8.45 = 1.27[/tex]
Asparagus price is $4.99 per pound.
So, price 0.33 pounds of asparagus is , [tex]0.33 * 4.99 = 1.65[/tex]
Hence, total amount paid by Divya is,
[tex]=34.61 + 1.62 + 0.66 + 1.27 + 1.65=39.81[/tex]
Thus, Divya will pay $39.81 for all the ingredients in the recipe.
Learn more:
https://brainly.com/question/18994792
Compare the ordered pairs of the pre-image to the
image to answer these questions.
Is the dilation an enlargement or reduction?
The point of dilation is about what coordinate?
What is the scale factor?
Pre-image
Answer: Reduction
(0,0)
1/3
Step-by-step explanation:
Answer:
1-reduction
2-(0,0)
3-1/3
Step-by-step explanation:
If 3x and 71/x are two prime numbers V x equivalent to R, then number of x so that 3x + 71/x = 10 is/ are
Answer:
x = 5/3Step-by-step explanation:
Guven two prime numbers to be 31/x and 71/x, if their sum is 10 as given;
3x + 71/x = 10 then to find the value of x, the following steps must be taken;
Step 1
Find the LCM of the given equation;
3x + 71/x = 10
[tex]\frac{3x^{2}+71 }{x} =10\\[/tex]
Step 2:
Cross multiplying;
[tex]3x^{2} +71=10x\\3x^{2} -10x+71 =0\\[/tex]
Using the general formula to get the value of x;
x = -b±√b²-4ac/2a
a=3, b=-10, c=71
= 10±√(-10)²-4(3)(71)/2(3)
= 10±√100-852/6
= 10±√-752/6
= 10±27.4i/6
= 10+27.4i/6 or 10-27.4i/6
x = 5/3+27.4i/6 or 5/3-27.4i/6
Since the values of x are real values then, our answer will be the real part of the complex number gotten.
x = 5/3
If the front of a playhouse is shown in a scale drawing and the height of the door is 1.8 inches. The scale that maps the drawing is 1 inch to 2.5 feet . What is the actual height in feet of the play house door?
Answer:
4.5 feet
Step-by-step explanation:
Here, we are concerned with calculating the actual height in feet of the door given the scale used in the maps drawing.
In the scale, scale to actual is 1 inch to 2.5 feet
let 1.8 inch scale = x actual feet
Thus mathematically, by cross multiplying; we have;
x = 2.5 * 1.8 = 4.5 feet
The total time T (in hours) needed to fly from New York to Los Angeles and back can be
modeled by the equation below, where d is the distance (in miles) each way, a is the average
speed (in miles per hour), and j is the average speed (in miles per hour) of the jet stream.
Simplify the equation. Then find the total time to the nearest minute it takes to fly 2468 miles
when a = 512 miles per hour and j = 103 miles per hour.
Answer:
complicated process just think and do the math If I was helpful pls be thnked
Step-by-step explanation:
Four students spoke to the Home and School parents for a total of 2/3 hour. Each student spoke for the same amount of time. How long did each student speak?
creo que la respuesta el 10 minutos, porque dice "horas" pero no dice a cuantas horas equivale :) espero que te aya adudado auque sea un poquito
Georgianna wants to use the linear model associated with the data in the table to make a prediction.
A 2-column table with 5 rows. The first column is labeled time (minutes) with entries 0, 5, 10, 15, 30. The second column is labeled distance (miles) with entries 0, 4, 9, 13, 18.
Which range of time values describes the entire interval over which she would be interpolating?
0 to 5 minutes
0 to 18 minutes
0 to 30 minutes
18 to 30 minutes
Answer:
0 to 30 minutes on edg.
Step-by-step explanation:
Answer:
c on e 2020
Step-by-step explanation:
solve the equation 18=n-18
n=_____
Answer:
36
Step-by-step explanation:
Which of the expressions are equivalent to the one below? Check all that
apply.
6*(2+8)
A. 6•(8+2)
B. 6•2+6•8
C. (8+2) •6
D. (6•2) + 8
Answer:
B
Step-by-step explanation:
When you have a number or numbers by parentheses, you take the number outside them and multiply it to each number that is inside the parentheses. In this case you would do 6*2 + 6*8. If I helped, please mark as brainliest! :)
Answer:
A, B, & C are all correct!
Step-by-step explanation:
Margo can purchase tile at a store for $0.89 per tile and rent a tile saw for $45. At another store she can borrow the tile saw for free if she buys tiles there for $1.39 per tile. How many tiles must she buy for the cost to be the same at both stores?
Margo must buy ____ tiles for the cost to be the same at both stores.
Answer:
She must buy 90 tiles for the cost to be the same at both stores
Step-by-step explanation:
Let x be the no. of tiles bought for the cost to be the same at both stores
Margo can purchase tile at a store for $0.89 per tile at shop 1
Cost of x tiles =0.89x
She rent a tile saw for $45.
So, total cost at Store 1 = 0.89x+45
At another store she can borrow the tile saw for free if she buys tiles there for $1.39 per tile.
So, cost of 1 tile = 1.39
Cost of x tiles = 1.39x
ATQ
0.89x+45=1.39x
45=1.39x-0.89x
45=0.5x
[tex]\frac{45}{0.5}=x[/tex]
90=x
Hence She must buy 90 tiles for the cost to be the same at both stores
maya was asked whether the following equation is an identity (2x+3)(x+1) = 2(x+1)^2 + (x+1)
Answer:
Maya is correct.
Step-by-step explanation:
Khan Academy gave me the answer.
