The greatest common factor for 4x³+16x² +8x is 4x(x2- 4x - 2).
This solution focuses on simplification:
4x(x2-4x-2)
(4(x3)-24x2)-8x
(22x3-24x2) -8x
Take similar factors aside:
4x3-16x2-8= 4x(x2-4x-2)
Factoring x2 - 4x - 2
x2 is the initial term, and it has a coefficient of 1.
The coefficient of the intermediate term, which would be -4x, is 4.
"The constant," the final term, is -2.
Multiply the constant by the coefficient of the first term. 1 -2 = -2
The second step is to find two -2 factors whose sum is equal to the -4 coefficient of the middle word.
-2 + 1 = -1
-1 + 2 = 1
No two of these factors can be discovered!!
Trinomial cannot be factored.
Hence, The greatest common factor is 4x(x2- 4x - 2).
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In a class of 99 students, one student is 1% of the class (when rounded to the nearest whole percent) and, 99 of the students represent 100%. What positive integer between 1 and 100 cannot be represented as a whole percent?
The positive integer between 1 and 100 that cannot be represented as a whole percent are 8, 15, 36 and many more.
How to find the positive integer that cannot be represented as a whole percent?The class has 99 students.
One student of the class is 1% of the class when rounded to the nearest whole percent. The actual percentage of one student is 1 / 99 × 100 = 100 / 99 = 1.0101010101%
99 of the students represents 100% of the students.
99 / 99 × 100 = 9900 / 99 = 100%
Therefore, the positive integer between 1 and 100 that cannot be represented as a whole percent is as follows:
36, 15, 8 and many more.
8 / 99 ×100 = 800 / 99 = 8.08080808081%
15 / 99 × 100 = 1500 / 99 = 15.1515151515 %
36 / 99 × 100 = 3600 / 99 = 36.3636363636 %
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4. Philips is given an interest free loan to buy a LCD television. He needs to repay the loan by monthly instalments. He repays RM35 for the first month, RM38 for the second month and the repayment increase by RM3 each month until the loan is fully settled.
(a) Show that the monthly instalment earned form an arithmetic series and state its common difference. [2 marks]
(b) If the final monthly instalment if RM212, calculate the number of months it takes Philips to settle the loan. [4 marks]
(c) Determine the sum of the loan taken. [4 marks]
The monthly instalment amounts forms an (a) Arithmetic Progression with common difference 3. (b) Phillips takes 60 months to settle the loan. (c) The sum of the loan is $7410 .
A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
The n-th term of an arithmetic progression is given by:
aₙ = a + ( n - 1 ) d
Where a is the first term and d is the common difference .
(a) Amount of money repaid in the first month = $35
Amount of money repaid in the second month = $38
Amount of money repaid in the third month = $ (38+3) = $ 41
Therefore 41 -38 = 3 and 38 - 35 = 3 . So we see that each monthly instalment is increasing by 3 and the difference between each installment is 3
Therefore the numbers are in an arithmetic progression whose common difference is 3 .
(b) Given the final monthly installment is $ 212
Let us consider that after this is the installment for the n-th month.
∴ aₙ =212 , a= 35 and d=3
Putting the values in the equation of the n-th term of an AP we get:
aₙ = a + ( n - 1 ) d
or, 212 = 35 +(n-1)3
or, 212 - 35 + 3 = 3n
or, n = 60 months
Therefore Phillips takes 60 months to settle the loan.
(c) The formula for the sum of all terms of an AP is given by:
S = (n / 2 ) ( a + aₙ )
or, S = (60/2) × (35+212)
or, S = 30 × 247
or, S = 7410
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What is the decimal equivalent of each rational number? a. ___9/11 b. __4/5 c. ___-17/5 d. __5/9
20 10 12 13 4 1 5 0 19
Place for min , med, mode etc
-x = 7x -56
pls i need anwer
Round to the nearest one-hundred dollars: $3,245.31
A $3,245.30
B $3,300.00
C $3,200.00
D $3,000
Answer:
C
Step-by-step explanation:
Our choices would be 3,300 for 3,200. Those would be the answer rounded to the nearest 100 up and down. 3245.31 is between those numbers. Which number would it be closer to? 3200.
how to increase the accuracy of simpson rule and maclaurin series expansion respectively?
Because it matches a parabola to the curve rather than a straight line, Simpson's rule is more precise.
The other approaches are only accurate for functions whose graphs are linear, whereas Simpson's rule yields the exact area beneath the graphs of functions of degree two or less (parabolas and straight lines).Why is trapezoidal less accurate than Simpson's rule?
When the underlying function is smooth, Simpson's Rule is more accurate than the trapezoidal rule because it employs quadratic approximations rather than linear ones. In cases where there are an odd number of evenly spaced points, the formula is typically provided.What are Simpson's rule's restrictions?
It is obviously incorrect because the actual integral will always differ from it (except in some cases, such as the area under straight lines). Integrals, unlike Simpson's technique, allow you to obtain precise results in terms of basic constants.Learn more about Simpson's Rule
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Give the rate in miles per hour round to the nearest tenth Rachel jogs 20 feet in three seconds
Answer: The Rate of jogging is 4.6 miles per hour.
Step-by-step explanation: i really hope this helps (:
25 pts - 37.5 if brainliest
Find the equation of the trend line (line of best fit)
Based on the given points on the graph, the equation for the line of best fit or the trend line is y = 1.874x + 3.656
What is the trend line?Due to the fact that the points on the graph are not on a straight line, the least squares method can be used to find the line of best fit equation.
Using a linear regression calculator, you can find the equation of the trend line by inputting the values of y and x in the graph.
When run through a linear regression calculator, the result will be:
y = 1.874x + 3.656
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A 61 in. wood plank is cut into 3 pieces. The longest piece is 5 times the length of the smallest piece. The medium piece
less than 2 times the length of the smallest.
1. If z represents the length of the smallest piece, write the expression that represents the medium size piece.
2. Write an equation to show that length of all the pieces together equal to the total length of 61 inches.
3. What is the length of each piece of wood? Explain how you know you are correct.
The length of the smallest, medium and the longest piece of wood are 7.625, 15.25 and 38.125 inches.
How to represent expressions?The wood is 61 inches and it is divide into 3 pieces.
The longest piece is 5 times the length of the smallest piece.
The medium piece less than 2 times the length of the smallest.
let
z = length of the smallest piece of wood
longest piece = 5z
medium piece = 2z
The equation to represent the total piece together is equal to 61 inches.
z + 5z + 2z = 61
Therefore, the length of each wood piece can be calculated as follows:
z + 5z + 2z = 61
8z = 61
z = 61 / 8
z = 7.625 inches
longest piece = 5(7.625) = 38.125 inches
medium piece = 2(7.625) = 15.25 inches
Therefore, the length of the smallest, medium and the longest piece of wood are 7.625, 15.25 and 38.125 inches.
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How is it similar and how is it different?
Using the intersection operation between two data-sets, it is found that the graph of x > a and x < b is similar to the graph of x > a for a < x < b and different for x > b.
What is the result of the intersection operation between two data-set?The result of the intersection operation between two data-set is the set that contains elements that belong to both sets.
For this problem, we have that a is to the left of b, as a < b, hence:
a is plotted before b on the number line.The intersection between the operations x > a and x < b is the following interval: a < x < b.Hence:
The graph of x > a and x < b is similar to the graph of x > a for a < x < b and different for x > b.
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write a problem based on the information given c = regular cost of one airline ticket 0.2c = amount of 20% promotional discount 3(c - 0.2c) = 330
The question for this information:
The cost of buying 3 airline tickets at a promotional discount of 20% is 330 dollars. Find the regular cost of 1 ticket.
Discounts and allowances are price reductions from a product's or service's base price.
Discount is calculated by subtracting the sell price of an article from its Marked price.
The given conditions in the question are
C=regular cost of a ticketamount of promotional discount=20%=0.2cAnd the expression 3(c - 0.2c) = 330So from the above information we can see that if the price of a ticket is c dollars then the discounted price of 1 ticket will be (c - 0.2c).
Total price of 3 tickets =3(c - 0.2c)
but the total price is 330 dollars
Therefore:
3(c - 0.2c) =330
or, 2.4c=330
or, c=330÷2.4
or, c=137.5 dollars
Hence the regular price of each ticket is 137.50 dollars.
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What is the range of function represented by this graph?
Can anybody help me with this
Answer: is C y=-2x-2
jwndnknwdkwnkw
1,402 x 71 is 71 less than 1,402x 71) -40 yes or no
No , 1,402 x 71 is 71 is not less than (1,402x 71) -40 .
An arithmetic} expression in mathematics is AN expression that is formed from variables and constants, in conjunction with pure mathematics operations (addition, subtraction, etc.). Expressions area unit created from terms.We have given two numbers 1,402 x 71 and (1,402x 71) -40.
As we can see that in second expression we have subtracted 40 from 1,402 x 71 .So , It is obvious that value of second expression will differ by first expression by 40 .
Hence , 1,402 x 71 is 40 more than (1,402x 71) -40 .
So , it is not possible to have 1,402 x 71 is 71 less than (1,402x 71) -40
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A zoologist needs to dive into the shark exhibit to supervise its cleaning. The depth of the water in the exhibit is 40 feet, and the divers can safely descend at a rate of 2 feet per minute. Which number expresses how deep below the water the divers are after 15 minutes? − 30 feet − 15 feet − 40 feet − 2 feet
Answer:
30 feet
Step-by-step explanation:
1 minute = 2 feet
15 minute = ? Feet
15 x 2 = 30
? = 30 feet
What is a solution to this equation?
(1 − 3x)¾ − 1 = x
Answer:
x= -1/3
Step-by-step explanation:
3/4-9/4x-1=x
-1/4-9/4x=x
-1-9x=4x
-9x=4x+1
-9x-4x=1
-13x=1
x= -1/13
hope this helps
certain grocery store charges a fee of 3% of the total bill to have groceries delivered. What is the total price the store charges to deliver $140 worth of groceries?
The total price the store charges to deliver $140 worth of groceries will be $4.20.
How to calculate the percentage?It should be noted that the certain grocery store charges a fee of 3% of the total bill to have groceries delivered.
Therefore, the total price the store charges to deliver $140 worth of groceries will be:
= Percentage charged × Cost
= 3% × $140
= 0.03 × $140
= $4.20
The amount charged is $4.20.
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find the area of the circle
Answer:
113.04 square feet
Step-by-step explanation:
A = π[tex]r^{2}[/tex]
A = π [tex](6[/tex][tex])^{2}[/tex]
A = 3.14 (36)
A = 113.04
Write 0.0000629 in scientific notation
Answer:
6.29 × 10^-5
Step-by-step explanation:
0.0000629
The number part of the answer is 6.29
To go from 0.0000629 to 6.29, the decimal point needs to move 5 places to the right, so the exponent on the 10 must be -5.
0.0000629 = 6.29 × 10^-5
Answer: 6.29*10^(-5)
Step-by-step explanation:
0.0000629=
0.629*10^(-4)= ==> there are 4 zeros before the decimal point.
6.29*10^(-(4+1))=6.29*10^(-5)
Which of the sets can be placed in a one-to-one correspondence?
a. {1,2,3,4,5) and {m,n,o,a,r}
b. {a,b,c,...,f} and {4,8,12,...,20}
c. {t It is a letter in the word jar) and {1,2,3,4}
PERFORMANS
O No
OYes
a. Can the sets {1,2,3,4,5) and (m,n,o,a,r} be placed in a one-to-one correspondence?
MUSICIA
FILOLETN
TRIOTO PRESE
INNOINS FORE
The set which can be placed in a one to one correspondence is:
a. {1,2,3,4,5) and {m,n,o,a,r}
b. Yes.
A rule or method that matches every element of set A with exactly one element of set B and every element of set B with exactly one element of A is known as a one-to-one correspondence.
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the perimeter of a rectangle is 92. the length is (2x+3) and the width is (x+7) . find x
Answer:
x= 12
Step-by-step explanation:
The perimeter of a rectangle is the sum of the lengths of all its sides.
Formula
Perimeter of rectangle= 2(width) +2(length)
Substitute the given information into the formula:
92= 2(2x +3) +2(x +7)
Expand:
92= 4x +6 +2x +14
92= 6x +20
Subtract 20 from both sides:
6x= 92 -20
6x= 72
Divide both sides by 2:
x= 72 ÷6
x= 12
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The coordinates of the endpoints of GH are G(2,7) and H(11,16). Point I is on GH and divides it such that GI:HI is 4:5. What are the coordinates of I?
The coordinates of I ( x, y) = ( 6, 11 )
What is coordinate in math?
A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).
The coordinates of the G = (2,7)
The coordinates of the H = (11,16)
Point I is on GH and divides it such that GI:HI is 4:5.
the coordinates of I ( x, y)
[tex]x = \frac{m_{1}x_{2} + m_{2} x_{1} }{m_{1} + m_{2} }[/tex]
[tex]x = \frac{4 * 11 + 5 * 2}{ 4 + 5}[/tex]
x = 6
[tex]y = \frac{m_{1}y_{2}+ m_{2}y_{1} }{m_{1} + m_{2} }[/tex]
[tex]y = \frac{4 * 16 + 5 * 7}{9}[/tex]
y = 11
the coordinates of I ( x, y) = ( 6, 11 )
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Please, I will mark brainliest.
Answer: RS=2.4
Step-by-step explanation:
QR=RS ==> R is the midpoint of QS, so the distance from point R and point Q is equal to the distance from point R and point S.
7x-6=2x
7x=2x+6
5x=6
x=6/5
x=1.2
RS=2x
RS=2(1.2)
RS=2.4
Public school per-student expenditures increased approximately linearly from $4.6 thousand in 1990 to $10.8 thousand in 2013. Predict the per-student expenditure in 2024.
In 2024 public school per-student expenditures will be about $thousand.
(Round the final answer to two decimal places as needed. Round all intermediate values to two decimal places as needed.
per-student expenditures will be about $ 9.16.
Public school per-student expenditures in 1990 is $4.60
per-student expenditures in 2013 is $10.8
in 23 years per student expenditure has increase of 10.8-4.60 = $6.2
in 1 years per student expenditure has increase of $6.2/23.
in 34 years per student expenditure has increase of ($6.2/23)34 =$9.16
per-student expenditures will be about $ 9.16.
the act of spending (as money, time, or power) 2 : something this is spent hold a file of your costs. expenditure.
What are examples of costs?
Expenditure – this is the whole purchase fee of a great or service. for instance, a agency buys a $10 million piece of device that it estimates to have a useful life of five years. this will be labeled as a $10 million capital expenditure.
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Han ran 1/4 the length of his road,which is 7 miles long how far did han run?
Han ran 1.75 miles
because 25% of 7 is 1.75
I need help with 19 please. I will give Brainly and bunch of extra points. Thank you .
On January 1, Year 1, Jana started a small flower merchandising business that she named Jana’s Flowers. The company experienced the following events during the first year of operation: Started the business by issuing common stock for $43,000 cash. Paid $28,000 cash to purchase inventory. Sold merchandise that cost $20,000 for $42,000 on account. Collected $37,000 cash from accounts receivable. Paid $9,800 for operating expenses. Required a. Organize ledger accounts under an accounting equation and record the events in the accounts. In the last column of the table, provide appropriate account titles for the Retained Earnings amounts. b-1. Prepare an income statement. b-2. Prepare a balance sheet. b-3. Prepare a statement of cash flows. c. Since Jana sold inventory for $42,000, she will be able to recover more than half of the $43,000 she invested in the stock. Do you agree with this statement?
a) The organization of ledger accounts under an accounting equation and journal entries are as follows:
Accounting Equation:Assets = Liabilities + Equity
Cash + Inventory + A/Receivable C.Stock R/Earnings
1. $43,000 $43,000
2. -28,000 $28,000
3. $42,000 42,000 S/Revenue
4. -20,000 -20,000 COGS
5. 37,000 -37,000
6. -9,800 -9,800 Op Exp.
Bal. $42,200 $8,000 $5,000 $43,000 $12,200
Journal Entries:Debit Cash $43,000
Credit Common Stock $43,000
Debit Inventory $28,000
Credit Cash $28,000
Debit Accounts Receivable $42,000
Credit Sales Revenue $42,000
Debit Cost of goods sold $20,000
Credit Inventory $20,000
Debit Cash $37,000
Credit Accounts Receivable $37,000
Debit Operating expenses $9,800
Credit Cash $9,800
b1)
Jana's Flowers
Income StatementFor the year ended December 31, Year 1
Sales Revenue $42,000
Cost of goods sold $20,000
Gross profit $22,000
Operating expenses $9,800
Net income $12,200
b2) Jana's Flowers
Balance SheetDecember 31, Year 1
Cash $42,200
Accounts Receivable $5,000
Inventory $8,000
Total assets $55,200
Common Stock $43,000
Retained Earnings 12,200
Total equity $55,200
b3) Jana's Flowers
Statement of Cash FlowsFor the year ended December 31, Year 1
Net income $12,200
Changes in working capital:
Accounts Receivable (5,000)
Inventory (8,000)
Operating cash flow ($800)
Financing activities:
Common Stock $43,000
Cash flows $42,200
c) I do not agree with this statement. It does not necessarily flow that Jana selling $42,000 in goods will be able to recover more than half of the $43,000 she invested in her business. So far, she has made $12,200 from her investment.
Data Analysis:Cash $43,000 Common Stock $43,000
Inventory $28,000 cash $28,000
Accounts Receivable $42,000 Sales Revenue $42,000
Cost of goods sold $20,000 Inventory $20,000
Cash $37,000 Accounts Receivable $37,000
Operating expenses $9,800 Cash $9,800
Thus, it will take time for Jana to recover her investment in the business.
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PLEASE SHOW YOUR WORK!!!!!!
Craig’s job pays him $18.75 per hour, plus overtime at
the usual rate. Last month, Craig worked the following
hours per week:
• Week 1 = 37 hours
• Week 2 = 47 hours
• Week 3 = 42 hours
• Week 4 = 39 hours
The monthly payment to Craig is $ 3093.75
Given,
The payment got by Craig for his job = $ 18.75 per hour
Weekly working hours of Claig:
Week 1 = 37 hours
Week 2 = 47 hours
Week 3 = 42 hours
Week 4 = 39 hours
We have to find the total monthly payment of Craig:
That is,
Week 1 + Week 2 + Week 3 + Week 4
For getting the weekly salary, we have to multiply hourly payment with hours worked:
So,
Week 1 = 37 × 18.75 = 693.75
Week 2 = 47 × 18.75 = 881.25
Week 3 = 42 × 18.75 = 787.5
Week 4 = 39 × 18.75 = 731.25
Now calculate the total monthly payment:
That is,
693.75 + 881.25 + 787.5 + 731.25 = 3093.75
Therefore,
The monthly payment to Craig is $ 3093.75
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please help..I am.so.confused
Answer:
67
Step-by-step explanation:
Answer:
there asking you what the veritable represent