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Which recursive formula can be used to represent the sequence 2,5,8,11,14
Answers
I'm in middle school, so I'm not totally sure...
The recursive formula for the given AP series 2,5,8,11,14 is a₁ = 2 and [tex]a_{n} =a_{n-1} + 3[/tex] so option (D) will be correct.
What is Arithmetic progression?The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).
The arithmetic progression has wider use in mathematics for example sum of natural numbers.
Natural number = 1,2,3,4,5,6,7,8...
Now it has the same difference between any two consecutive terms d =2-1 = 3-2
Given an ap series,
2,5,8,11,14
The first term (a₁) = 2
The nth term of AP can be given as
[tex]a_{n} =a_{n-1} + d[/tex] where d is a common difference.
d = 5 - 2 = 3
So,
[tex]a_{n} =a_{n-1} + 3[/tex]
Hence "The recursive formula for the given AP series 2,5,8,11,14 is a₁ = 2 and [tex]a_{n} =a_{n-1} + 3[/tex] ".
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Related Questions
How many comparisons are required to merge these pairs of lists using algorithm 10?
a.1, 3, 5, 7, 9; 2, 4, 6, 8, 10
b.1, 2, 3, 4, 5; 6, 7, 8, 9, 10
c.1, 5, 6, 7, 8; 2, 3, 4, 9, 10?
Answers
How to find the factor for the expression
4x-6y
Answers
To factor the expression, you must try to find the greatest common factor of 4 and 6 since you x and y have no common factors. The greatest common factor is 2 for 4 and 6, since when you divide out the 2, you are left with 2 and 3 which cannot be factored anymore.
5m-1=4m+5 what is m.
Answers
to get this we do
5m+4m = 5 - 1
9m = 4
m = 4/9
The correct answer is 6. In other words, the value of m that satisfies the solving linear equation is m = 6.
In the given equation, we are asked to find the value of m. The equation states that the quantity 5m minus 1 is equal to the quantity 4m plus 5.
To solve this equation, we can use algebraic methods. The goal is to isolate the variable m on one side of the equation.
First, we combine like terms. By subtracting 4m from both sides of the equation, we eliminate the term with m on the right side. This results in the equation m - 1 = 5.
Next, we isolate the variable m by adding 1 to both sides of the equation. This cancels out the -1 term on the left side and gives us m = 6.
Therefore, the correct answer is 6. In other words, the value of m that satisfies the solving linear equation is m = 6.
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if a ball is thrown directly upward with a velocity of 40 ft/s, its height (in feet) after t seconds is represented by 40t-16t^2. what is the maximum height attained by the ball?
Answers
[tex]\bf h(t)=40t-16t^2\implies h(t)=-16t^2+40t+0 \\\\\\ \begin{array}{llll} \qquad \textit{in feet}\\\\ h(t) = -16t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\textit{initial velocity of the object}\\ \qquad 40\\ h_o=\textit{initial height of the object}\\ \qquad 0\\ h=\textit{height of the object at "t" seconds} \end{cases}[/tex]
[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{llll} y = &{{ -16}}x^2&{{ +40}}x&{{ +0}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \left( \stackrel{\textit{it took this long}}{-\cfrac{40}{2(-16)}}~~,~~\stackrel{\textit{to get this high}}{0-\cfrac{40^2}{4(-16)}} \right)\qquad \stackrel{\textit{maximum height}}{0-\cfrac{40^2}{4(-16)}}[/tex]
The maximum height attained by the ball is 25 feet.
Explanation:The maximum height attained by the ball can be found by determining the vertex of the quadratic equation representing the height of the ball. In the given equation 40t - 16t^2, the coefficient of t^2 is negative, indicating a parabolic shape with a maximum point. The formula for the x-coordinate of the vertex is -b/2a, which in this case is -40/(2*(-16)) = 1.25 seconds. Substituting this value into the equation gives the maximum height: 40(1.25) - 16(1.25^2) = 25 feet.
what is the absolute value of the complex number -4-sr2i
Answers
The absolute value of a complex number a + bi is defined as
|a + bi| = √ [(a^2) + (b^2)].
So, the absolute value of - 4 - (√2)i is
| -4 - (√2)i | = √ [ (4)^2 + (√2)^2 ] = √ [ 16 + 2 ] = √18 = √(9*2) = √9 * √2 = 3√2
Answer: 3√2
Why would a bank charge a fee to noncustomers who use it’s ATM?
ANSWER: Charging a noncustomer helps pay for the cost of keeping the ATM running and supplied with cash. Customers of the bank already cover the ATM costs with regular fees or by allowing the bank to loan out their money.
Answers
Answer:
Bank charges fee to non customers while using ATM. ATM's frequently charge fees to users who are not account holders from that same bank whose ATM you are operating.
This fee goes towards the compensation for the costs associated with owning and operating the machine.
Same bank persons pay many types of fee yearly to their banks, so same bank ATM do not charge any fee.
When using other banks, your bank has to pay some interchange amount to that bank, this is also the reason why banks charge fee, basically they recoup the money that they will have to pay to other banks for interchange.
Find all points on the circle x 2 + y 2 = 100 where the slope is 3 4
Answers
The points on the circle x² + y² = 100 where the slope of the tangent is ¾ are (6, -8) and (-6, 8). This is found by taking the derivative of the circle equation, setting it equal to the slope, solving for y, substituting this into the original circle equation, and solving for x.
Explanation:The equation of the circle is x² + y² = 100. To find the points on this circle where the slope of the tangent is ¾, we need to find the derivative of this equation. The derivative of y with respect to x is dy/dx = -x/y. Set this equal to ¾ and solve for y, which gives y = -4x/3. Substitute this into the original circle equation to solve for x, which yields x = ± 6. Then substitute these x-values back into the equation y = -4x/3 to get y = ± 8. Therefore, the points on the circle where the slope of the tangent is ¾ are (6, -8) and (-6, 8).
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Final answer:
To find points on the circle x² + y² = 100 where the slope is 3/4, differentiate the circle's equation and set the derivative equal to 3/4. Solve the system of equations involving the circle's equation and the line's equation derived from the slope criteria. This process typically yields two points of intersection due to the geometrical properties of circles and lines.
Explanation:
To find all points on the circle x2 + y2 = 100 where the slope is 3/4, we first acknowledge that the given circle is centered at the origin (0,0) with a radius of 10 units. Since the slope of a tangent to the circle at any point can be found using implicit differentiation, let's differentiate the given equation with respect to x. Doing so, we get 2x + 2yy' = 0 where y' denotes the slope of the tangent to the circle at (x,y). Solving for y', we get y' = -x/y. Setting this equal to the given slope of 3/4, we have -x/y = 3/4.
By cross-multiplying and rearranging, we get 4x + 3y = 0. To find the points of intersection between the line and the circle, we substitute x2 + y2 = 100 into this equation. Solving the system of equations will yield the points on the circle where the slope of the tangent is 3/4.
Note: The exact points of intersection would require solving a resulting quadratic equation, which can give two possible points since a line with a given slope (except vertical) will typically intersect a circle at two points.
How much pure acid should be mixed with 6 gallons of a 20% acid solution in order to get a 90% acid solution?
Answers
now, if we want a 90% solution, and say we add "y" gallons, how much acid is in it? well (90/100) * y, or 0.9y.
now let's add "x" gallons of pure acid, now, pure acid is just pure acid, so is 100% acid, how much acid is there in it? (100/100) * x, or 1x or just x.
we know whatever "x" and "y" amounts are, they -> x + 6 = y
and we also know that x + 1.2 = 0.9y
[tex]\bf \begin{array}{lccclll} &\stackrel{gallons}{acid}&\stackrel{acid~\%}{quantity}&\stackrel{acid~gallons}{quantity}\\ &------&------&------\\ \textit{pure acid}&x&1.00&x\\ \textit{20\% sol'n}&6&0.20&1.2\\ ------&------&------&------\\\ mixture&y&0.90&0.9y \end{array} \\\\\\ \begin{cases} x+6=\boxed{y}\\ x+1.2=0.9y\\ ----------\\ x+1.2=0.9\left( \boxed{x+6} \right) \end{cases} \\\\\\ x+1.2=0.9x+5.4\implies x-0.9x=5.4-1.2\implies 0.1x=4.2 \\\\\\ x=\cfrac{4.2}{0.1}\implies x=\stackrel{gallons}{42}[/tex]
To get a 90% acid solution, you should mix 54 gallons of pure acid with the 6 gallons of the 20% acid solution.
Explanation:To solve this problem, we can use the formula for concentration:
Concentration = (Volume of pure acid) / (Total volume of solution)
Let x represent the volume of pure acid to be added. We know that the total volume of the solution after adding the pure acid is 6 gallons + x gallons. We also know that the concentration of the 20% acid solution is 0.2.
Using the formula, we can set up the equation:
0.9 = x / (6 + x)
Multiplying both sides of the equation by (6 + x), we get:
0.9(6 + x) = x
Simplifying the equation, we have:
5.4 + 0.9x = x
Subtracting 0.9x from both sides of the equation, we get:
5.4 = 0.1x
Dividing both sides of the equation by 0.1, we get:
54 = x
Therefore, you should mix 54 gallons of pure acid with the 6 gallons of the 20% acid solution to get a 90% acid solution.
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What is 65 3/5 - 24 1/3
Answers
If the circular opening of the pipe has a diameter of 21 inches and the oil was estimated to be flowing at 30 inches/second, how many cubic feet of oil were leaving the pipe each second? Each day?
Answers
First, find the area of the circular opening. A = pi (r^2). Here,
A = pi(10.5 inches)^2.
To obtain the volume of water that flows out of the pipe per second, multiply this area by the 30 inches per second rate.
That comes out to a volume per second of Volume rate = pi*(10.5 inches)^2 * 30 inches per second:
Volume rate = 3.14(110.25 in^2)(30 inches/sec)
= 10390.8 cubic inches per second
Convert this result to cubic feet per second. Recall that 1 cubic foot = (12 inches)^3, or 1728 cubic inches / 1 cubic foot.
Thus, 10390.8 cubic inches per second comes out to
10390.8 cubic inches
---------------------------- = Just over 6 cubic feet per sec.
1728 cu. inches
---------------------
1 cu. ft
How many sec in 1 day? 1 day = 24 hours
1 hour = 60 minutes
60 seconds = 1 minute
Figure out how many seconds there are in 1 day, and then multiply your result by 6 cu. ft. / sec.
To find the flow rate of oil, first calculate the cross-sectional area of the pipe using the formula for the area of a circle, A=πr². Then, multiply the area by the given oil speed to find the volume of oil flowing every second. Multiply this by the number of seconds in a day to find the amount of oil leaving the pipe each day, and remember to convert from cubic inches to cubic feet.
Explanation:The question is asking us to find the volume of oil leaving the pipe per second and per day. To calculate the flow rate of oil, we first find the cross-sectional area of the pipe by using the formula for the area of a circle A=πr², where r is the radius of the pipe (half the diameter). Since the diameter given is 21 inches, the radius is 10.5 inches.
Next, use the given flow rate of 30 inches/second to calculate the volume of oil flowing every second. This is done by multiplying the area by the oil speed V = A * oil speed.
To find the amount of oil leaving the pipe each day, we multiply the volume per second by the number of seconds in a day .
Note: To convert cubic inches to cubic feet (since the question asks for cubic feet), remember there are 1728 cubic inches in 1 cubic foot.
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Albert thought of a number, added 5, multiplied the result by 2, took away 6 and then divided by 2 to give an answer of 8
Answers
6+5=11
11*2=22
22-6=16
16/2=8
Starting with 8:
8*2 = 16 + 6 = 22/2 = 11- 5 = 6
Now, lets check it and start from the beginning with this new number (6), and follow everything Albert did and we will get 8.
6+5= 11*2= 22-6 = 16/2 = 8
Solve for x.y = mx+b
Answers
- _ + _
m m
this is the answer
Solve for x means to isolate x.
y - b = mx
We now divide both sides by m to isolate x.
(y - b)/m = x
If m and n are two positive real numbers whose product is 10, what is the minimum value of m + 2n
Answers
2 + 2(4)
The minimum value of (m + 2n) is 8.95 and this can be determined by using the arithmetic operations.
Given :
If m and n are two positive real numbers whose product is 10.
Given that m and n are two positive real numbers whose product is 10 that is:
mn = 10
[tex]\rm m= \dfrac{10}{n}[/tex] ---- (1)
The minimum value of (m + 2n) can be determined by using the following calculation.
Put the value of m in the given expression.
[tex]\rm = \dfrac{10}{n}+2n[/tex] ---- (2)
Now for minimum value differentiate the above expression with respect to n.
[tex]\rm =-\dfrac{10}{n^2}+2[/tex]
Now equate the above equation to zero.
[tex]\rm \dfrac{10}{n^2}=2[/tex]
[tex]\rm n = \sqrt{5}[/tex]
Now, put the value of n in equation (2).
[tex]\rm Minimum \;Value = \dfrac{10}{\sqrt{5} }+2\sqrt{5}[/tex]
= 8.95
The minimum value of (m + 2n) is 8.95.
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Solve for x. 9x = 3x -36
Answers
9x-3x=3x-36-3x
6x=-36
6x/6= -36/6
x=-6
hope this helps!
9x - 3x = 3x - 3x - 36
6x = -36
x = -36 / 6 = -6 answer
a 9 pound bag of sugar is being split into containers that hold 2/3 of a pound. how many containers of sugar will the 9 pound bag create?
Answers
well
[tex]\bf 9 \div \frac{2}{3}\implies \cfrac{9}{\frac{2}{3}}\implies \cfrac{\quad \frac{9}{1}\quad }{\frac{2}{3}}\implies \cfrac{9}{1}\cdot \cfrac{3}{2}\implies \cfrac{27}{2} \\\\\\ \textit{2 goes \underline{13 times} into 27, with a \underline{remainder of 1}}\implies 13\frac{1}{2}[/tex]
Answer:
13 1/2
Step-by-step explanation:
2.8y+6+0.2y=5y-4 what is the solution to the linear equation
Answers
3y + 6 = 5y - 4
6 = 2y -4
10 = 2y
5 = y
I hope this helps love! :)
Find the exact circumference of a circle with the given radius. 5 inches C = 2.5 in. 10 in. 25 in.
Answers
Answer: The exact circumference of the circle is [tex]10\pi[\tex] in.
Step-by-step explanation:
Since, the circumference of a circle is,
[tex]C=2\pi r[/tex]
Where, r is the radius of the circle,
Here, r = 5 inches,
Hence, the circumference of the circle is,
[tex]C = 2\pi(5) = 10\pi\text{ in}[/tex]
Thus, The exact circumference of the circle is [tex]10\pi[\tex] in.
Prove: the sum of four consecutive integers is never divisible by 4 g
Answers
Missing: g
[tex]n+n+1+n+2+n+3=4n+6[/tex]
4n is divisible by 4, but 6 is not, so the sum 4n+6 is not divisble by 4.
A customer pays $3.27 for oranges and $4.76 for pears. How many pounds of fruit does the customer buy?
Answers
3.27/1.09=3lbs. of oranges
then take 4.76 and divide that by 1.19 (for the pears)
4.76/1.19=4lbs. of pears
add 4+3 to get how many lbs. in all
4+3=7
A total of 7 pounds of fruit does the customer buy.
Given that, a customer pays $3.27 for oranges and $4.76 for pears.
The cost of 1 pound orages=$1.09 and the cost of 1 pound pears=$1.19
What is a unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Now, the number of pounds of oranges =3.27/1.09=3 pounds
The number of pounds of pears =4.76/1.19=4 pounds
Total weight=3+4=7 pounds
Therefore, a total of 7 pounds of fruit does the customer buy.
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Find the area of the following circle. Use = 3.14
r = 5 yd.
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write all names that apply to each number 121/121
Answers
1
one
etc
hope this helps
Describe or show two ways to find the following product: 1/4 x 2/3.
Answers
2/3 = 0.666666667
0.25(0.666666667) = 0.166666667 = [tex] \frac{1}{6} [/tex]
______________________________
[tex] \frac{1}{4} ( \frac{2}{3}) = \frac{2}{12} = \frac{1}{6} = 0.166666667[/tex]
A lender estimates the closing costs on a home loan of $50,000 as listed below.
Closing Cost
Charge
Loan origination
$200
Title insurance
$530
Attorney’s fees
$600
Appraisal
$265
Inspection
$575
Recording fees
$130
Escrow
$800
If the lender's good faith estimates are accurate, are they a reasonable amount for closing costs? Why or why not?
a.
Yes, because the lender esitmated 3.08% of the home loan in closing costs which falls between 3 - 5%.
b.
Yes, because the lender estimated 4.6% of the home loan in closing costs which does not fall between 3 - 5%.
c.
No, because the lender estimated 6.2% of the home loan in closing costs which does not fall between 3 - 5%.
d.
No, because the lender estimated 17.7% of the home loan in closing costs which does fall between
Answers
Answer:c.
No, because the lender estimated 6.2% of the home loan in closing costs which does not fall between 3 - 5%
Step-by-step explanation:
Summation of the cost of loan =200+530+600+265+575+130+800
=3100
Now percentage of the estimate=
(3100/50000)*100%
=6.2%
C- The lender should not consider them as reasonable amount of closing costs because the lender estimated 6.2% of the home loan in closing costs which does not fall between 3-5%.
The lender cannot be accepting these costs as this will lead to the lender incurring losses over a longer period after doing all the necessary calculations.
The lender has disbursed a home loan of $50000 on which he has estimated certain closing costs and are considered to be true and accurate. The costs are loan origination, title insurance, attorney's fees, appraisal, inspection, recording fees, escrow, etc.The amounts will add up as a summation of all the fees and charges as titles above are mentioned which will end up totaling to $3100[tex]200+530+600+265+575+130+800=3100[/tex]
The calculation of of costs in to the percentage of total home loan is calculated as dividing the cost with total loan amount which will be totaled as 6.2%.[tex]\frac{3100}{50000} *100= 6.2[/tex]
The costing of this home loan is way above the ideal range of 3-5% and is not worth disbursing and may be called back.Hence, the correct option is C that the amounts of $3100 are not a reasonable amount of closing costs because the lender estimated 6.2% of the home loan in closing costs which does not fall between the range of 3-5%.
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spiders can walk on walls write the statement in if then form
Answers
If then because statements are much like they seem.
(3x-3)° [6{x-10)]° what is the value of x
Answers
Divide both sides by 18 °:(x - 1) (x - 10 ° x) = 0
Split into two equations:x - 1 = 0 or x - 10 ° x = 0
Add 1 to both sides:x = 1 or x - 10 ° x = 0
Collect in terms of x:x = 1 or (1 - 10 °) x = 0
Divide both sides by 1 - 10 °:Answer: x = 1 or x = 0
The actual answer to this equation is x=19 not x=1 or n=0
Carlos has 5/8 pound of pumpkin seeds. He puts the seeds evenly into 20 envelopes. How much pumpkin seed is in each envelope?
Answers
20/1 divided by 5/8:
20 x 8 = 160
1 x 5 = 5 = 160/5
Simplify: 32
Hope this helps you!
I hope this helps.Good Luck!
drag and drop the correct numbers into the boxes to complete the table. amounts may be rounded to the nearest cent
Answers
on a map 1 inch equals 18.4 miles. If two cities are 4.5 inches apart on the map, how far are they actually apart?
Answers
4.5 * 18.4 = 82.8 miles
round to the nearest tenth 10.357
Answers
Min Jee wants to build a small patio using either brick or paver stones. It will be 70 inches long and 49 inches wide. Each brick covers an area of 3 1/2 inches by 7 1/2 inches, and cost $0.59. Each paver covers an areas 8.4 inches by 8.4 inches and costs $1.88. What would be less expensive to use, and by how much?
Answers
1 Paver = 8.4 in by 8.4 in = 70.56 sq. in. and costs $1.88
patio's area 70 * 49 = 3430 sq. in.
number of Bricks to complete the Patio :
3430 / 26.25 = 130.67 round up to 131
total cost of bricks:
131 * $0.59 = $77.29
number of Pavers to complete the Patio:
3430 / 70.56 = 48.6 round up to 49
total cost of pavers:
49 * $1.88 = $92.12
$92.12 - $77.29 = 14.83
the bricks would cost less by $14.83