Answer:
[tex]d = q(z-1)[/tex]
[tex]S_n = \frac{nq}{2}(2 + (n-1)(z-1))[/tex]
[tex]S_{10} = 5q(9z -7)[/tex]
Step-by-step explanation:
Given
[tex]T_1 = q[/tex]
[tex]T_2 = qz[/tex]
Solving (a1): The common difference (d)
d is calculated as
[tex]d = T_2 - T_1[/tex]
This gives:
[tex]d = qz - q[/tex]
Factorize:
[tex]d = q(z-1)[/tex]
Solving (a2): Sum of n terms
This is calculated using:
[tex]S_n = \frac{n}{2}(2*T_1 + (n-1)d)[/tex]
Substitute values for T1 and d
[tex]S_n = \frac{n}{2}(2*q + (n-1)q(z-1))[/tex]
[tex]S_n = \frac{n}{2}(2q + q(n-1)(z-1))[/tex]
Factorize:
[tex]S_n = \frac{n}{2}(q(2 + (n-1)(z-1)))[/tex]
[tex]S_n = \frac{nq}{2}(2 + (n-1)(z-1))[/tex]
Solving (b): Sum of first 10.
In this case, n = 10
So:
[tex]S_n = \frac{nq}{2}(2 + (n-1)(z-1))[/tex]
becomes
[tex]S_{10} = \frac{10 * q}{2}(2 + (10-1)(z-1))[/tex]
[tex]S_{10} = 5 * q(2 + 9(z-1))[/tex]
[tex]S_{10} = 5q(2 + 9(z-1))[/tex]
[tex]S_{10} = 5q(2 + 9z-9)[/tex]
[tex]S_{10} = 5q(2 -9+ 9z)[/tex]
[tex]S_{10} = 5q(-7+ 9z)[/tex]
[tex]S_{10} = 5q(9z -7)[/tex]
Given that the first term and the second term of an arithmetic sequence is q and qz respectively, therefore:
a. Common difference (d) = [tex]\mathbf{d = q(z - 1)}[/tex]
Sum of the first n terms is: [tex]\mathbf{S_n = \frac{qn}{2}[2 + (n - 1)(z - 1)]}[/tex]
b. [tex]\mathbf{S_{10} = 5q(9z - 7)}[/tex]
Recall:
The common difference (d) of an arithmetic sequence = difference between the next term and the previous termSum of n terms, [tex]S_n[/tex] of arithmetic sequence = [tex]\frac{n}{2}[2a + (n - 1)d][/tex]Given:
First term, [tex]T_1 = q[/tex] (this is also "a")Second term, [tex]\\\\T_2 = qz[/tex]a. Common difference (d) = [tex]T_2 - T_1[/tex]
Substitute[tex]d = qz - q\\\\\mathbf{d = q(z - 1)}[/tex]
Sum of n terms:
[tex]T_n = \frac{n}{2}[2a + (n - 1)d][/tex]
Substitute by plugging in the value of d and a[tex]S_n = \frac{n}{2}[2(q) + (n - 1)q(z - 1)]\\\\S_n = \frac{n}{2}[2q + q(n - 1)(z - 1)]\\\\S_n = \frac{qn}{2}[2 + 1(n - 1)(z - 1)]\\\\\mathbf{S_n = \frac{qn}{2}[2 + (n - 1)(z - 1)]}[/tex]
b. Sum of the first 10 terms:
Substitute n = 10 into [tex]S_n = \frac{qn}{2}[2 + (n - 1)(z - 1)][/tex][tex]S_{10} = \frac{q(10)}{2}[2 + (10 - 1)(z - 1)][/tex]
Simplify[tex]S_{10} = 5q[2 + (9)(z - 1)]\\\\S_{10} = 5q(2 + 9z - 9)\\\\[/tex]
Add like terms[tex]\mathbf{S_{10} = 5q(9z - 7)}[/tex]
In summary, given that the first term and the second term of an arithmetic sequence is q and qz respectively, therefore:
a. Common difference (d) = [tex]\mathbf{d = q(z - 1)}[/tex]
Sum of the first n terms is: [tex]\mathbf{S_n = \frac{qn}{2}[2 + (n - 1)(z - 1)]}[/tex]
b. [tex]\mathbf{S_{10} = 5q(9z - 7)}[/tex]
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Find all x-intercepts of the function. Express your answer as a list of x-values
f(x) = x^3+x^2+x-1
Answer:
(0.54368901,0)
Step-by-step explanation:
Subsititute 0 for y and solve to find the x-intercepts.
What is the value of f(0)?
A. -2
B.-1
C.0
D.1
Answer:
The answer is C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
f(0) means the graph of f(x) in which the value of the variable x in the function f is zero.. So, f(0) represents graph for zero value of x
The sum of the number and three times its reciprocal is 79/10. Find the
number.
hi
so x + 3 (-x) = 79/10
x-3x = 79/10
-2x = 79/10
x = 79/10 / -2
X = 79/ 10 * -1/2
x = - 79/20
x = - 3.95
PLEASE HELP PLEASE i really need help
Answer:
The constant of proportionality is 6 because 6x2=12 6x4=24 6x6=36 and it keep going
Step-by-step explanation:
a nursery sells kentucky bluegrass seed for $5.75 per pound and tall fescue seed for $4.50 per pound. the nursery sells a mixture of the two kinds of seed for $5.25 per pound. let k represent the amount of kentucky blue grass seed the nusery uses in in 5 pounds of the mixture
Answer:
[tex]k=3[/tex]
Step-by-step explanation:
Given that:
Per pound cost of kentucky bluegrass seed = $5.75
Per pound cost of tall fescue seed = $4.50
Per pound cost of mixture of seeds = $5.25
[tex]k[/tex] is the amount of kentucky blue grass.
Total amount of the mixture = 5 pounds
Therefore, amount of tall fescue seed = (5 - [tex]k[/tex]) pounds
To find:
The value of [tex]k[/tex].
Cost of [tex]k[/tex] pounds of kentucky bluegrass seed = [tex]\$5.75k[/tex]
Cost of (5 - [tex]k[/tex]) pounds of tall fescue seed = [tex]\$(5-k)4.50[/tex]
As per question statement:
[tex]5.75k+(5-k)4.50=5.25\times 5\\\Rightarrow 575k+5\times 450 -450k=525\times5\\\Rightarrow 125k=75\times5\\\Rightarrow k =3\ pounds[/tex]
Amount of kentucky blue grass seed used = 3 pounds
Amount of tall fescue seed used = 5-3 = 2 pounds
If ABC=DEC b=48degree and E=x+4
X=
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]x + 4 = 48[/tex]
Subtract sides 4
[tex]x +4 - 4 = 48 - 4[/tex]
[tex]x = 44°[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
4x+c=w make x a subject
plz help me
answer me fast
and i want answer kn step by step
Answer:
x =w-c/4
Step-by-step explanation:
solution
here,
4x+c=w
or, 4x=w-c
:.x=w- c/x
As x subject, the linear equation is x = 1/4(w -c).
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
We have a linear equation,
4x+c=w.
To make x a subject:
4x = w - c
x = 1/4(w -c)
Therefore, the expression is x = 1/4(w -c).
To learn more about the linear equation;
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Determine the expression
trinomial and i believe its a degree of 4
I will give brainliest :)
Write an equation to represent the following situation.
You go to Montgomery's and have $10 to spend.
Drinks cost $2, a bag of chips costs $1, and a pack of
gum costs $0.50. If you buy four bags of chips, how
many drinks can you buy?
•4 + 2x = 10
•2x + 1 = 10
•4 + 2x = 0.50
•1+ 2+ 4 = 10
Answer:
4 + 2x = 10
x = 3
Step-by-step explanation:
For the function below, find ordered pairs for: x = -2 and x = 5 y = 9 - 4x
Answer:
(- 2, 17 ) and (5, - 11 )
Step-by-step explanation:
Given
y = 9 - 4x
Substitute the given values of x into the equation and evaluate for y
x = - 2, then
y = 9 - 4(- 2) = 9 + 8 = 17 ⇒ (- 2, 17 ) ← ordered pair
x = 5, then
y = 9 - 4(5) = 9 - 20 = - 11 ⇒ (5, - 11 ) ← ordered pair
Which equation has the correct sign on the product?
A 45(-4)=180 B 13•3= -39
C (-8)(-8)= -64 D (-18)4 = -72
answer:
the answer is a
Calculate the mean, the variance, and the standard deviation of the following discrete probability distribution. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your final answers to 2 decimal places.) x −41 −27 −8 −3 P(X = x) 0.29 0.35 0.21 0.15
Answer:
a) Mean is -23.47
b) Variance is 206.59
c) standard deviation is 14.37
Step-by-step explanation:
Given that;
x −41 −27 −8 −3
P(X = x) 0.29 0.35 0.21 0.15
X.P -11.89 -9.45 -1.68 -0.45
a) mean
Mean = ∑X.P = -11.89 + -9.45 + -1.68 + -0.45
Mean = -23.47
b) the variance
E(x²) = ∑x²P(X=x)
= (−41²×0.29) + (−27²×0.35) + (−8²×0.21) + (−3²×0.15)
= 487.49 + 255.15 + 13.44 + 1.35
= 757.43
So
Var(X) = E(x²) - [∑X.P]²
Var(X) = 757.43 - [-23.47]²
= 757.43 - 550.8409
= 206.5891 ≈ 206.59
Therefore Variance is 206.59
c) standard deviation
standard deviation SD(X) = √Var(X)
SD(X) = √206.5891
= 14.3732 ≈ 14.37
Therefore standard deviation is 14.37
The graph of an equation with a negative discriminant always has which characteristic?
OO
no x-intercept
no y-intercept
no maximum
no minimum
Jill and Katie are making bracelets to sell at The Windmill. They determined that each bracelet would have six beads and four charms.How many bracelets can they sell if they have 80 charms? show all work
Answer:
20 bracelets
Step-by-step explanation:
Since they must use 4 charms per bracelet, 80 divided by 4 is 20 so 20 bracelets can be made.
What can be used as a factor to rewrite 16f^2-25g^2?
Answer:
B = 5g
16f2 - 25g2
Step-by-step explanation:
In March it rained 8.23 inches. It rained 5.96 inches less in April than in March.
How much did it rain in April?
There are 24 female performers in a dance recital. The ratio of men to women is 7:8. How many men are in the dance recital?
Choose the definition for the function PLS HELP
Answer:
Which function please explain
Find the measures of Angles A,B, and C
Answer:
A = 102 B = 78 C = 56
Step-by-step explanation:
All three sides of a triangle added up equals 180.
So 41 + 37 + A = 180
A = 102
A straight line = 180 degrees.
One measurement is 102, so the other is 78.
You now know B is 78, and that 3 angles equal 180.
46 + 78 + c = 180
c= 56
It takes andre 4 minutes to swim 5 laps. At this rate heswims how many laps per minute.
Answer: It takes him 1 minute and 25 seconds
Step-by-step explanation:
5 divided 4
4 times 1 = 4
5-4=1
put the decimal and make 1=10 Ans.: 1.25
4 times 2 = 8
10-8=2
put the 0 = 20
4 times 5 =20
20-20=100
The function
The function g(x) has a slope of —5/6. The value of g (x) is 5 when x is 6. Explain how the graph
of g(x) can be used to find the x-intercept. (2 points)
Item
help lol due tonight
Answer:
Can't see your questions clearly
Step-by-step explanation:
which equation is equivalent?
Answer:
C
Step-by-step explanation:
One pound of candies costs $3.50.
How many pound of candies can be bought for $7?
Answer: 2 pounds
Step-by-step explanation: 3.50 + 3.50 = 7$ so the answer is 2
Answer:
2 pounds of candy can be bought for $u
Step-by-step explanation:
We have 2 "$3.50" in "$7" and we know that for every $3.50 we have, we can buy 1 pound of candies. Therefore, for $7, we can buy 2 pounds of candies
I hope this helps! :)
#13 Easton is planning on buying a new pair of cowboy boots. When he
went to Eastern Outfitters last week they costs $60 on the black Friday
sale. This week, they aren't on sale anymore and they cost $85. What is the
percent of change on the boots? *
O 25%
O 45%
O 55%
75%
You start an account with $2,500 and an annual interest rate of 6.5% compounded yearly. How much is in the account after 7 years?
I need an expression and a solution
I'm pretty sure it's this:
Answer:
y=a( 1+ r/n)^ nt
growth is a= 2500 yearly is n= 1
y= 2500( 1+ .065/1)^ 1.7 = $3884.97
72.05-29.69?????????????????
Answer:
42.36
Step-by-step explanation:
Big boi questions just use the caculator
romona has $800 in her bank account
Um not sure what you're asking for bud you didn't finish.
Answer:
Okay?????? I don't think you finished
What is a mutual fund’s
A pool of money where investors buy shares and a fund manager invests them and gives the investor the return; the way that most Americans invest their money because of the ease. hope that helps!
to calculate the perimeter of the parallelogram you need the two side lengths 12 inches and 15 inches
Answer:
the answer would be 54
Step-by-step explanation:
If the shape is a parallelogram then two sides will be equal lengths. same with the other two sides.
if you need the perimeter then you need to add the lengths of all the sides. so that would be 12 12 15 and 15. Add those together and you get 54 inches.
Answer:
i think the answer is 54