Let [tex]\sf a+b,a-b,ab,\dfrac{a}{b}[/tex] form an arithmetic sequence. What is the sixth term of this sequence?
Answer:
171/40 or 4 11/40Step-by-step explanation:
AP givena + b, a - b, ab, a/bTo find6th termSolutionCommon difference
Difference of first two
d = (a -b) - (a + b) = -2bDifference of second two
d= ab - (a - b)Difference of last two
d = a/b - abNow comparing d:
-2b = ab - (a - b)ab - a = - 3ba(1 - b) = 3ba = 3b/(1 - b)and
a/b - ab = -2ba(1/b - b) = -2ba = 2b²/(b² - 1)Eliminating a:
2b²/(b² - 1) = 3b/(1 - b)2b/(b+1) = -32b = -3b - 35b = - 3b = -3/5Finding a:
a = 3b/(1 - b) = 3*(-3/5) *1/(1 - (-3/5)) = -9/5*5/8 =-9/8So the first term is:
a + b = -3/5 - 9/8 = -24/40 - 45/40 = - 69/40Common difference:
d = -2b = -2(-3/5) = 6/5The 6th term:
a₆ = a₁ + 5d =-69/40 + 5*6/5 = -69/40 + 240/40 =171/40 = 4 11/40what is equal to 2/5
Answer:
0.4
Step-by-step explanation:
You buy a house for $230,000. It appreciates at a rate
of 2.8% per year. Find the value after 15 years
Answer:
1,232,142
Step-by-step explanation:
bro just use a calculator
If the area of each of the triangular regions is as shown, what is the area of the polygon?
18
17
16
Answer:
18
Step-by-step explanation:
Katie's baby took 3 naps. Each nap was of an hour long.
6
How long did the baby nap in all? Move numbers to the blanks to answer the question.
Answer:
18 naps
Step-by-step explanation:
We have the keyword each, so we are multiplying, so our equation is:
3 x 6 = 18
So, Katie's baby napped for 18 hours in all
Answer:
18 is the answer
If the simple interest on $6,000 for 10 years is $5,400, then what is the interest rate?
Answer:
9%
Step-by-step explanation:
p*r*t = Interest
$6000*x*10 years = $5400
interest ÷ time ÷ principal = rate
5400 ÷ 10 ÷ 6000 = 0.09
0.09 = 9%
Please help!!!———————-
f(n) = 2000 + 500(n-1)
Step-by-step explanation:
most logical explanation considering the other options make no sense
a. The sum of a number and one is equal to one added to the number.
Need help ASAP... 10 points!!
Answer:
I'm 89.73% sure that the answer is 90 degrees
Step-by-step explanation:
because you are on a right angle
The depth (inches) of water that accumulates in the spring soil from melted snow can be determined by dividing the cumulative winter snowfall (inches) by 12. Determine the amount of winter snow that accumulates 6 inches of water in the soil.
a.
6 inches of snow
b.
84 inches of snow
c.
72 inches of snow
d.
12 inches of snow
Answer:
C
Step-by-step explanation:
its just 12 times 6
Answer:
c
Step-by-step explanation:
I took the test and got it right
A Porsche uses 2.5 litres of fuel every 2 kilometres it travels. How much fuel does it use if it travels 50 kilometres
Answer:
The Porsche uses 62.5 liters in 50 kilometers
Step-by-step explanation:
Amount of fuel Porsche uses = 2.5/2 liters/kilometer
= 1.25 L/Km
Distance to be travelled = 50 kilometer
Amount of fuel used in 50 km = 1.25 * 50
= 62.5 Liters
Therefore the Porsche uses 62.5 liters in 50 kilometers
Happy to help :)
The line passes through (6,3) and (-1,-8)
Answer:
OK AND CAN U TELL ME WHAT TO ANSWER SO I CAN HELP
Step-by-step explanation:
THIS IS THE LINE I DID ON A GRAPH
Answer:
=gitchie ggitchei yayadada
Peter has 36 shirts in his closet, 2/9 of the shirts are striped. If the remaining shirts
are solid, how many shirts is that? What fraction of Peters shirts are solid?
Answer:
28 shirts are sold
7/9 of the shirts are sold
Step-by-step explanation:
hope this helps <3
Find the least common multiple (LCM) of 4 and 5.
9514 1404 393
Answer:
20
Step-by-step explanation:
4 and 5 have no common factors*, so their least common multiple is their product:
4 × 5 = 20
The LCM of 4 and 5 is 20.
_____
* We're concerned with integer factors greater than 1. Of course, 1 is a factor of everything, We could say this as "no common prime factors". For computing the LCM, we really want the GCF (greatest common factor) for use in the formula ...
LCM(m, n) = mn/GCF(m, n)
An item on sale costs 85% of the original price. The original price was $75.
Answer:
$63.75
Step-by-step explanation: I think
Which data sets have outliers? Check all that apply
14,21,24,25,27,32,35
15,30,35,41,44,50,78
16,32,38,39,41,42,58
17,23,28,31,39,45,75
18,30,34,38,43,45,68
Answer:
C.16, 32, 38, 39, 41, 42, 58
and
E.18, 30, 34, 38, 43, 45, 68
its C. & E.
they both have outliers lol
Evalute the root in the question below in the screenshot
(precalc)
Answer:
Graph attached
Step-by-step explanation:
jenkins-traub method for the complicate calculation
it has 1 real root: 1.5164
2 complex roots : neglected
Convert to centimeters: 43 meters
Mrs. Davis and Ms. Moore bought treats for their students. Mrs. Davis bought cookies for $12.56 and Ms. Moore bought popcorn for $11.08. Another teacher, Mrs. Baynes, couldn't go to the store, but wanted to help with the cost of the treats. If the teachers split the cost evenly, how much would each teacher have to pay?
Answer:
4.546
Step-by-step explanation:
total cost=12.56+11.08
=13.64
total no of person=3
cost for each person=13.64/3
=4.5467
Quadrilateral RUST has a vertex at R (1,2). U S What are the coordinates of R'after a dilation by a scale factor of 3, centered at the origin, followed by the translation (x, y) - (x + 2, y)?
A. (5,8)
B. (5,2)
C. (9,6)
D. (5,6)
Answer:
D. [tex](5,6)[/tex]
Step-by-step explanation:
Let [tex]R(x,y) = (1,2)[/tex], we proceed to perform all operations described on statement:
1) Dilation
[tex]R'(x,y) = O(x,y) + k\cdot [R(x,y)-O(x,y)][/tex] (1)
Where:
[tex]O(x,y)[/tex] - Point of reference.
[tex]R(x,y)[/tex] - Original point.
[tex]R'(x,y)[/tex] - Dilated point.
[tex]k[/tex] - Scale factor.
If we know that [tex]O(x,y) = (0,0)[/tex], [tex]R(x,y) = (1,2)[/tex] and [tex]k = 3[/tex], then the dilated point is:
[tex]R'(x,y) = (0,0) +3\cdot [(1,2)-(0,0)][/tex]
[tex]R'(x,y) = (0,0) +3\cdot (1,2)[/tex]
[tex]R'(x,y) = (3,6)[/tex]
2) Translation
[tex]R''(x,y) = R'(x,y) + T(x,y)[/tex] (2)
Where:
[tex]R'(x,y)[/tex] - Original point.
[tex]T(x,y)[/tex] - Translation point.
[tex]R''(x,y)[/tex] - Translated point.
If we know that [tex]R'(x,y) = (3,6)[/tex] and [tex]T(x,y) = (2,0)[/tex], then the translated vector is:
[tex]R''(x,y) = (3,6)+(2,0)[/tex]
[tex]R''(x,y) = (5,6)[/tex]
Therefore, the correct answer is D.
Answer:d
Step-by-step explanation:
Find the product of each pair of complex conjugates.
(3 + 8i)(3 – 8i) =
Step-by-step explanation:
By Difference of Squares,
a² - b² = (a + b)(a - b).
=> (3 + 8i)(3 - 8i) = 3² - (8i)²
= 9 - 64i² = 9 - 64(-1) = 73.
LCM of 189024
please give me answer my question
Answer:
360
Step-by-step explanation:
We need to find the LCM of 18,90 and 24.
The prime factorization of 18 = 2 × 3 × 3
The prime factorization of 90 = 2 × 5×3×3
The prime factorization of 24 = 2 × 3×2×2
LCM is least common multiple.
LCM = 2 x 2 x 2 x 3 x 3 x 5
= 360
Hence, the LCM of 18,90 and 24 is 360.
What is the area, in square units, of the parallelogram shown below?
21
56
63
81
Answer:
63
Step-by-step explanation:
You find the area of a parallelogram the same way you would a rectangle.
A = lw or A = bh so A = (9)(7). A = 63
Answer:
C. 63
Step-by-step explanation:
To find the area of a parallelogram, it is the same formula to find a rectangles area. L x H or Base x Height.
Have a great day!
Help pleaseeeeeee I’m so lost
Answer:
yes no no yes
Step-by-step explanation:
Tanner's employer pays 60% of his medical insurance. If the insurance costs $40
per week. How much Tanner and his employer pay for the entire year?
Answer:
Tanner's employer pays $1251.43 a year and tanner pays $834.29
Step-by-step explanation:
Which is a factor of 72
Answer:
1,2,3,4,6,8,9,12,18,24,36 and72
An individual rides a bike at a rate of 15 miles per hour for h hours. Write an equation that expresses the situation, let x be the independent variable and y be the dependent variable.
Answer:
15y+x
Step-by-step explanation:
Consider the line 2x+8y=8.
What is the slope of a line
parallel to this line?
What is the slope of a line perpendicular to this line?
Answer: parallel = - 1/4
Step-by-step explanation: perpendicular= 4
Answer:
Parallel = -1/4 ; Perpendicular = 4
Step-by-step explanation:
First, I'll put the line into slope-intercept form.
2x + 8y = 8
8y = -2x + 8
y = -1/4x + 1
Now we know that the slope is -1/4.
A parallel line would have the same slope of -1/4.
A perpendicular line would have a slope of 4.
Find the slope intercept equation of the line.
Which graph represents the solution to the system of inequalities?
{y<−4x+1
{y≥−14x
Answer:
1st graph on line 2
Step-by-step explanation: