Answer:
D. 2(x - 1)(x – 3)
Step-by-step explanation:
4(x2 – 2x) – 2(x2 – 3)
We would first of all expand the expression given
This becomes
= 4x2 - 8x - 2x2 + 6
Rearrange to enable us simplify
4x2 - 2x2 - 8x + 6
= 2x2 - 8x + 6
Factorize
2 (x2 - 4x + 3)
factorizing further using the factors of 3 that add up to -4
2(x2 - x - 3x + 3)
pick out the common factors
2(x(x-1) -3(x-1)
2(x-1)(x-3)
Option D. 2(x - 1)(x – 3) is right
Using the Factor Theorem, the factored form equivalent to this expression is:
[tex]2(x - 1)(x - 3)[/tex], given by option D.
The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.In this problem, the expression is:
[tex]4(x^2 - 2x) - 2(x^2 - 3) = 0[/tex]
[tex]4x^2 - 8x - 2x^2 + 6 = 0[/tex]
[tex]2x^2 - 8x + 6 = 0[/tex]
Which is a quadratic equation with coefficients [tex]a = 2, b = -8, c = 6[/tex].
Hence:
[tex]\Delta = b^2 - 4ac = (-8)^2 - 4(2)(6) = 16[/tex]
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{8 + 4}{4} = 3[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{8 - 4}{4} = 1[/tex]
Hence, the expression is:
[tex]2(x - 1)(x - 3)[/tex], given by option D.
You can learn more about the Factor Theorem at https://brainly.com/question/24380382
IMAX Movie Prices. There were 322 people at a recent showing of the IMAX 3D movie "300". Admission was $8.75 each for adults and $6.00 each for children. Receipts totaled $2531.50. How many adults and how many children attended?
Answer:
218 adults and 104 children attended.
Step-by-step explanation:
From the information given, you can write the following equations:
x+y=322 (1)
8.75x+6y=2531.50 (2), where:
x is the number of adults
y is the number of children
First, you can solve for x in (1):
x=322-y (3)
Then, you can replace (3) in (2) and solve for y:
8.75(322-y)+6y=2531.50
2817.5-8.75y+6y=2531.50
2817.5-2531.50=8.75y-6y
286=2.75y
y=286/2.75
y=104
Finally, you can replace the value of y in (3) to find x:
x=322-104
x=218
According to this, the answer is that 218 adults and 104 children attended.
Xavier's age is 3 less than Paula's age. Xavier is 11 years old. Which Labtraction equation represents Paula's age?
Answer:
11 + 3
Step-by-step explanation:
Paula = 11-3
Please help! I will mark brainliest if your correct!
The roof top would be 0. At 12 seconds the ball is at -225.6, which would be the ground so the building would be 225.6 meters tall.
The highest positive value is 81.6, so this is the highest the ball goes up.
The value changes from a positive to a negative between 8 and 10, which means that would be around the time it is the same height as the building.
The answers would be:
The first and third choices
A rectangular window has a width of 3.5 yards and a length of 4.5 yards what is the perimeter of the window in yards
Answer:
16 yards
Step-by-step explanation:
Perimeter = 3.5 + 3.5 + 4.5 + 4.5
Perimeter = 16 yards
8. You have 51 coins made up of dimes
and nickels. The coins total $4.55.
How many coins are dimes? How
many are nickels?
Answer:
Solve value problems by setting up a system of equations. ... Once the table is filled in we can easily make equations by adding each column, setting it ... Dime d. 10. 10d. Total. 11. 185. We have 11 coins total.This is the number total. ... twice as many dimes, than we multiply the other variable (nickels) by two.
Step-by-step explanation:
62.837 expanded for decimal
Answer:
60 + 2 + 0.8 +0.03 +0.007
Step-by-step explanation:
Add these up and yo get the same number: 62.837.
Shana wants to use all 62 feet of the fencing she has to make a rectangular run for her dog. She decides to make the length of the run 20 feet. She writes and solves the equation 2 l plus 2 w equals 62 to find the width of the run.
Which statements are true of the solution? Check all that apply.
The value of w is 10 feet.
The value of w can be zero.
The value of w cannot be a negative number.
Substitution is used to replace the variable l with a value of 20.
The subtraction property of equality is used to isolate the term with the variable w.
Answer:
The answers you guys are looking for are C, D, and E
Step-by-step explanation:
I dont have one. :)
The true statements include
(c) The value of w cannot be a negative number.(d) Substitution is used to replace the variable l with a value of 20.(e) The subtraction property of equality is used to isolate the term with the variable w.How to determine the true statements?The equation is given as:
2l + 2w = 62
Where:
l = 20
Substitute l = 20
2 * 20 + 2w = 62
Evaluate
40 + 2w = 62
Subtract 40 from both sides
2w = 22
Divide both sides by 2
w = 11
The above computation means that the true statements include (c), (d) and (e)
Read more about perimeter at:
https://brainly.com/question/24571594
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A woman has a total of 14000 to invest. She invests part of the money in an account that pays 5% per year and the rest in an account that pays 9% per year. If the interest earned in the first year is 940 how much did she invest in each account
Please help me I’m not good with graphs
Answer:
I'm pretty sure it's 2 and 3
A certain triathlon consists of a 3.1-mile swim, a 120-mile bicycle ride, and a 26.6-mile run. At one point, a participant had completed four times as many miles as the
number of miles left to complete. How many miles had he completed at that mark?
Answer:
26.6a
Step-by-step explanation:
possible derivation:
[tex]\frac{d}{da\\}[/tex] (a 26.6)
Factor out constants:
= 26.6 [ [tex]\frac{d}{da}[/tex] (a) ]
the derivative of a is 1 :
= 1 26.6
The Technology Club is trying to raise $1000 raffling cornhole boards. They have already made $100. If they sell raffle tickets for $5 each, how many more must they sell to make at least $1000?
Answer:
180
Step-by-step explanation:
$1000-$100=$900
$900/$5=180
Caan someone help me answer this!!!
Answer:
it took 4 minutes for the tub to drain,
the max amount of water in the tub was 35 gallons
at 10:06 the tub was nither filling nor draining
Step-by-step explanation:
hope this helped! be sure to pay attention to the X and Y lables, this is just reading a graph! :)
Find the point-slope equation of the line using the point (3, 5) and slope 3/2
Answer:
y=3/2x+5
Step-by-step explanation:
so the points are 3,5 and y=mx+b is point slope form.
y = m which is slope and b is y int. so it turns out to be y=3/2x+5.
pleaseee helpppppp helpppppp
Given:
The given table represents the ingredient need to make 4 muffins.
To find:
The amount of flour needed to make 12 muffins.
Solution:
We have, the data for 4 muffins.
From the given table it is clear that,
Flour need for 4 muffins = 250 g
Flour need for 1 muffins = [tex]\dfrac{250}{4}[/tex] g
Flour need for 12 muffins = [tex]\dfrac{250}{4}\times 12[/tex] g
= [tex]250\times 3[/tex] g
= [tex]750[/tex] g
So, 750 g flour is need to make 12 muffins.
Therefore, the correct option is D.
Answer: 750
Step-by-step explanation: If The recipe for four muffins calls for 250g of flour if you multiply 250 by 3 get the answer wich is 750
--
Hope this helps
Mitzy earned $3,156 last year at her weekend job, but realized after the year was over that her employer did not deduct any FICA from her paychecks. How much should she have paid in FICA taxes for her earnings last year? How much should she have paid in Social Security tax? How much should she have paid in Medicare tax? Together, they make up FICA. How much should she have paid in FICA?
which sequence is generated by the rule 3n-1, where n represents the position of a term in the sequence?
Answer:
2,5,8,11 ..........
Step-by-step explanation:
A bakery did a survey among 100 customers to find their food preference . The customers were asked about their preferences for cupcakes or brownies. Out of the total 72 people who liked cupcakes, 37 also liked brownies. There were 59 people who liked brownies.
Part A. Summarize the data by writing the values that the letters A to I in the table below represents
PART B. What percentage of the survey respondents did not like cupcakes or brownies ?
PART C . Do the survey results reveal a greater dislike for brownies or cupcakes? Justify your answer.
PLZZZ HELP
Have you found the answer yet?
Answer:
put 37, 22,59,35,6,41,72,28,100 in chart < That is for the ppl who cant click on the brainly site but it still shows alitttle
For the ppl who can click on brainly:
Part A:
Like Cupcakes
Do Not Like Cupcakes
Total
Like Brownies
37
22
59
Do Not Like Brownies
35
6
41
Total
72
28
100
Part b: 6
Part c: You really have to figure out how to word this 37- 72=35 35-41=6
hope it helps
HELLPPPPPPPPP PLEASE! I WILL MARK AS BRAINLIST
Answer:
It equals 140 because angle 5 is 140
What is the quotient?
-4/5➗2
Machine A and machine B both make car parts.
Machine A makes 7 parts every 10 minutes.
Machine B makes 16 parts every 15 minutes.
On Monday
machine A makes parts for 12 hours
machine B makes parts for 10 hours
Work out the total number of parts made by the two machines on Monday.
I
Total marh
A study of the career paths of hotel general managers sent questionnaires to an SRS of 160 hotels belonging to major U.S. hotel chains. There were 114 responses. The average time these 114 general managers had spent with their current company was 11.78 years. Give a 99%; confidence interval for the mean number of years general managers of major-chain hotels have spent with their current company. (Take it as known that the standard deviation of time with the company for all general managers is 3.2 years.)
Answer:
The 99% confidence interval for the mean number of years general managers of major-chain hotels have spent with their current company is between 11.01 years and 12.55 years.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575*\frac{3.2}{\sqrt{114}} = 0.77[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 11.78 - 0.77 = 11.01 years
The upper end of the interval is the sample mean added to M. So it is 11.78 + 0.77 = 12.55 years
The 99% confidence interval for the mean number of years general managers of major-chain hotels have spent with their current company is between 11.01 years and 12.55 years.
which of the following can be a Pythagorean triplets?:
a) 2cm 2cm ,4cm b) 5cm, 12cm ,13cm c) 3cm ,5cm ,6cm d) 7cm, 4cm 5 cm.
need full solution
or I'll report
As we know that,
Pythagoras triplet
1) a² + b² = c²
Let
[tex]\sf \: {2}^{2} + {2}^{2} = {4}^{2}[/tex]
[tex]\sf \: 4 + 4 = 16[/tex]
8 ≠ 16Hence, A can't be Pythagoras triplet2) a² + b² = c²
[tex]\sf \:5 {}^{2} + {12}^{2} = {13}^{2}[/tex]
[tex]\sf \: 25 + 144 = 169[/tex]
169 = 169Therefore, B can be Pythagoras triplet3)a² + b² = c²
[tex]\sf {3}^{2} + {5}^{2} = {6}^{2}[/tex]
[tex]\sf 9 + 25 = 36[/tex]
34 ≠ 36Hence, C can't be Pythagoras triplet4) a² + b² = c²
[tex]\sf {5}^{2} + {4}^{2} = {7}^{2}[/tex]
[tex]\sf \: 25 + 16 = 49[/tex]
41 ≠ 49Hence, D can't be Pythagoras tripletTherefore :-Only B can be Pythagoras triplet.
What is ?l4 as a mixed number?
Answer:
It's a whole number. It cannot be a mixed number. Anyways I would have to know the denominator.
I’m in break out rooms and it’s so awkward, and no ones talking. Can someone help me?
Answer:
why did you delete my answer??????
Step-by-step explanation:
simplify the fraction completly
60/100
Answer: 3/5
Step-by-step explanation: simplified completely
Answer:
35 is the simple answer for this fraction
inverse equation x-19 = -23
Answer:
Isolate the X by adding 19 on both sides sicne the invers of -19 is 19
-23+19= -4
now you’d get
x= -4 since its a one step equation and X is isolated
Driving would be more pleasant if we didn't have to put up with the bad habits of other drivers. A newspaper reported the results of a Valvoline Oil Company survey of 500 drivers in which the drivers marked their complaints about other drivers. The top complaints turned out to be tailgating, marked by 22% of the respondents; not using turn signals, marked by 19%; being cut off, marked by 14%; other drivers driving too slowly, marked by 9%; and other drivers being inconsiderate marked by 5%.
Required:
Make a Pareto chart showing percentage of drivers listing each stated complaint.
Answer and Explanation:
The Pareto chart is used in descriptive statistics and shows graphically the most frequent occurencies(complaints in this case) using bars and lines.
Please find attached
PLEASE help!!!!
Im timed!
Answer:
it would be B
Step-by-step explanation:
2. The ratio of pretzels to peanuts in a trail mix is 4:9.
At the same rate if there are 80 pretzels how many
peanuts are there?
Answer:
170 peanuts I believe
Step-by-step explanation:
just did mental math, not sure if it's the right way
arrange the given decimals in an sending order ascending means you are going to arrange the decimals in increasing order
1.) 1.7 0.9 1.07 1.9 0.7
2.) 2.0342 2.3042 2.3104 2.4
3) 5.012 5.1 0.502
4.) 0.6 0.6065 0.6059 0.6061
5.) 12.9 12.09 12.9100 12.9150
6.) 3.21 3.021 3.12 3.121
7.)5.5 5.059 5.0090 5.05
8.) 0.09 0.012 0.0089 0.0189
9.)1.3 1.309 1.03 1.39
10.) 4.01 4.0011 4.011 4.101
Step-by-step explanation:
1.) 1.7 0.9 1.07 1.9 0.7
The correct order is; 0.7, 0.9, 1.07, 1.7, 1.9
2.) 2.0342 2.3042 2.3104 2.4
The correct order is; 2.0342, 2.3042, 2.3104, 2.4
3) 5.012 5.1 0.502
The correct order is; 0.502, 5.012, 5.1
4) 0.6 0.6065 0.6059 0.6061
The correct order is; 0.6, 0.6059, 0.6061, 0.6065
5) 12.9 12.09 12.9100 12.9150
The correct order is; 12.09, 12.9, 12.9100, 12.9150
6) 3.21 3.021 3.12 3.121
The correct order is; 3.021, 3.12, 3.121, 3.21
7) 5.5 5.059 5.0090 5.05
The correct order is; 5.0090, 5.05, 5.059, 5.5
8) 0.09 0.012 0.0089 0.0189
The correct order is; 0.0089, 0.012, 0.0189, 0.09
9.)1.3 1.309 1.03 1.39
The correct order is; 1.03, 1.3, 1.309, 1.39
10) 4.01 4.0011 4.011 4.101
The correct order is; 4.0011, 4.011, 4.01, 4.101