Answer:
[tex]T_7 = 11[/tex]
[tex]T_n = 2n- 3[/tex]
Step-by-step explanation:
Given
[tex]S_n = n^2 -2n[/tex]
[tex]T_n = S_n - S_{n-1}[/tex]
Solving (a): T7
Substitute 7 for n in [tex]T_n = S_n - S_{n-1}[/tex]
[tex]T_7 = S_7 - S_{7-1}[/tex]
[tex]T_7 = S_7 - S_6[/tex]
Calculate S7 and S6
[tex]S_n = n^2 -2n[/tex]
[tex]S_7 = 7^2 - 2 * 7 = 35[/tex]
[tex]S_6 = 6^2 - 2 * 6 = 24[/tex]
So:
[tex]T_7 = 35 -24[/tex]
[tex]T_7 = 11[/tex]
Solving (b): Tn
[tex]T_n = S_n - S_{n-1}[/tex]
Where [tex]S_n = n^2 -2n[/tex]
Calculate[tex]S_{n-1}[/tex]
We have:
[tex]S_{n-1} =(n-1)^2 - 2(n-1)[/tex]
Open brackets
[tex]S_{n-1} = n^2 -2n + 1 -2n +2[/tex]
[tex]S_{n-1} = n^2 -2n-2n + 1 +2[/tex]
[tex]S_{n-1} = n^2 -4n + 3[/tex]
So:
[tex]T_n = S_n - S_{n-1}[/tex]
[tex]T_n = n^2 - 2n - (n^2 -4n + 3)[/tex]
[tex]T_n = n^2 - 2n - n^2 +4n - 3[/tex]
Collect Like Terms
[tex]T_n = n^2 - n^2- 2n +4n - 3[/tex]
[tex]T_n = 2n- 3[/tex]
how do movement skills in volleyball transfer to tennis?
Answer:
Tennis – It's not difficult to see that tennis and volleyball have their similarity; both involve hitting a ball over the net in the hope that the opponent won't be able to return it. Much like tennis, volleyball requires short and explosive movements and cat-like reflexes, rather than long runs down a pitch.
HELP PLSS- okok so i need the answer to this, please help :(
Answer:
second
Step-by-step explanation
-5/12 because -2/3 + 1/4 = -5/12
Answer:
2nd one
Step-by-step explanation:
Tyler is designing a banner that will welcome people to a festival. The design for the banner has an
area of 1.5 square feet. The actual banner will be a dilation of the design by a factor of 5. What will
the area of the actual banner be?
Answer:
7.5 sq ft
Step-by-step explanation:
1.5*5=7.5
The design is 1/5 of the actual size, so you just multiply by 5 to get the real size.
I need help with these answers?
Q 7 = 6
Q 8= -x + 2
Q 9= 6m + 2
Q 13= 43f × 56
Q 15= 18x
Solve the given proportion.
x/2=8/4
x=
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
i need help on this question for my math homework:))) please help!
The length of a rectangle is twice as long as the width of the rectangle.
The area of the rectangle is ||32|| cm||^2||.
Find the dimensions of the rectangle.
(2 marks)
cm
~ Width =
cm
O Height =
Submit Answer
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Answer: length = 8cm
Width = 4cm
Step-by-step explanation:
Let the width of the rectangle be represented by x.
Since the length of a rectangle is twice as long as the width of the rectangle, then the length will be: = 2 × x = 2x
Note that, Area of a rectangle = Length × Width
Therefore,
2x × x = 32
2x² = 32
Divide both side by 2
2x²/2 = 32/2
x² = 16
x = ✓16
x = 4
Therefore, width = 4cm
Since length = 2x
Length = 2 × 4cm = 8cm
Check: length × width = Area
8cm × 4cm = 32cm²
What is the inverse equation for f(x)=x+6
Answer:
y^-1 = x - 6
Step-by-step explanation:
change f(x) to 'y'
switch 'x' and 'y'
solve for 'y'
Answer:
Step-by-step explanation:
y = x + 6
x = y + 6
y + 6 = x
y = x - 6
f^-1(x) = x - 6
Find value of x
Find value of y
Answer:
Step-by-step explanation:
use SOH CAH TOA
Sin = Opp / Hyp
Cos = Adj / Hyp
Tan = Opp / Adj
then we know the adjacent side and the angle, and want to find the Hyp, so use CAH
Cos(60) = ( 8[tex]\sqrt{3}[/tex] / 3 ) / Hyp ( cos(60) = 1/2 )
Hyp = (8[tex]\sqrt{3}[/tex] / 3) / (1/2)
Hyp = 2 ((8[tex]\sqrt{3}[/tex] / 3)
Hyp = 16[tex]\sqrt{3}[/tex] / 3
x = 16[tex]\sqrt{3}[/tex] / 3
Now use SOH
Sin (60) = Opp / 16[tex]\sqrt{3}[/tex] / 3 ( sin(60) = [tex]\sqrt{3}[/tex]/2 )
(16[tex]\sqrt{3}[/tex] / 3)([tex]\sqrt{3}[/tex]/2) = Opp
16 * 3 / 6 = Opp
8 = Opp
y = 8
:)
Find the median and mean of the data. Which reflects the best measure of the center? 23, 27, 60, 154, 17, 15, 28
Answer:
Mean=16.75
Median=15.5
Mode=13
Range=16
Step-by-step explanation:
bright and Ernest saved money in the ratio 3:5if Ernest saved $10 how much did bright save
Answer:
Bright saved 6 dollars.
Answer:
$6
Step-by-step explanation:
10 divide 5 is 2 so
3 multiply 2 is 6 so he saved 6 dollars
PLZ HELP REALLY NEED ANSWER ILL GIVE BRAILIEST FOR CORRECT ONE
What is the surface area of the rectangular prism?
Enter your answer in the box.
in²
Answer:
A=166 in²
Step-by-step explanation:
A=2(wl+hl+hw)
A= 2(5x7+4x7+5x4)
A=2(35+28+20)
A=2(83)
A=166 in²
WILL GIVE BRAINLEST !
hAVE A GOOD DAy :)!
Answer:
1, 2 * 3^3 * 17
2, 8
Step-by-step explanation:
64 is perfect sqr root 8*8 = 64
Find such a coefficient a for the linear equation ax –y=4, so that the graph of the equation would pass through the point M (3, 5).
PLEASE ANNOTATE SOME IMAGE AND SEND ME IM DESPERATE CORRECT ANSWER GETS LE BRAINLY
suppose v varies directly as g, and v= 36 when g = 4. find v when g=11
Answer:
v = 99 when g = 11
Step-by-step explanation:
Set this up as an equation
36/4 = v/11
Cross multiply
36 × 11 = 4 × v
396 = 4v
Divide both sides by 4 to isolate variable v
396 ÷ 4 = 4v ÷ 4
99 = 1v
99 = v
How do I go about solving this?
Answer:
you want to bring down the numbers.. so try 3 for the second one
Step-by-step explanation:
Which of the following is equal to the expression listed below?
(18 × 24) - (18 × 9)
a.(24 - 18) × (18 - 9)
b.24 × (18 - 9)
c.18 × (24 - 9)
d.18 - (24 × 9)
Answer:
C
Step-by-step explanation:
good luck. hope this helps
which of the following can be written as the sum of 2 prime numbers
a)11
b)15
c)17
d)23
e)29
Answer:
b)15
Step-by-step explanation:
13+2=15
Hope that helps
As a student give one reason why we need to know if our client is comfortable in our service
Answer:
you need to know if your client is comfortable in your service so that if he or she is not comfortable you correct you mistake and make he or she comfortable
Step-by-step explanation:
Can you plz help me plz
Which equation represents a line that is perpendicular to the y-axis?
SEE PIC
Answer: c
Step-by-step explanation:
y = -8
Jamal has 30 ounces of a 20% saline solution. This means 20% of the solution is salt. He combines this solution with 25 ounces of a 30% saline solution.
What is the total amount, in ounces, of salt in the combined mixture? Please help and please provide an explanation?
Answer:
12.5 or 12 1/2 (may be wrong)
Step-by-step explanation:
First I set up a formula to solve how many ounces of salt there were out of 30,
x/30=20/100, I crossed multiplied and got 5/30, next, I set up the same formula for how many ounces of salt there were out of 25, x/25=30/100, I got 7.5, the last thing I did was add them both together leading me to the answer 12.5 or 12 1/2. Hope this helps! Please say if I am wrong.
PLEASE HELP THESE ARE MY ONLY POINT ;-; PLEASE
Answer:
a) max 12000 , min 0
b) no solution
c) pricing based on profit
Step-by-step explanation:
a) look at the parabola
b) there is more than one x (0)
c) the y intercepts represent his profit based on how much he priced the items at
The angle are supplementary find the missing angle measure
I give you brainiest if you answer correct
Answer:
12. 50
13.41
Step-by-step explanation:
To find the supplement, subtract the number from 180. For instance for 13. Do 180-139 to find the supplement.
HELP!!!!! What is the length plz help me besties
Answer: 30 inches
Step-by-step explanation:
20/8 = x/12
20(12) = 8x
240 = 8x = 30
(Need help)
If there are 150 people born in the world every minute; how
many are born every Hour? Day? Year?
Step-by-step explanation:
150 x 60 = 9,000 every hour
9000 x 24 = 216,000 every day
216000x 365 = 78,840,000 every year
Answer:
Hour: 9,000 people
Day: 216,000 people
Year: 78,840,000 people
Step-by-step explanation:
In order to solve this, you need to identify how many minutes there are in an hour, a day, and a year:
Hour: 60 minutes
Day: 60 minutes × 24 hours = 1,440 minutes
Year: 60 minutes × 24 hours × 365 days = 525,600 minutes
Now, you need to multiply each of these numbers by 150 to find how many people are born every hour, day, and year:
Hour: 60 minutes × 150 people = 9,000 people
Day: 1,440 minutes × 150 people = 216,000 people
Year: 525,600 minutes × 150 people = 78,840,000 people
Relation between an event and a second event, where the second event is understood as a consequence of the first. which one
Group of answer choices
Exponential Growth
Rate of Change
Causation
Correlation
2. The value the item has changed to. Also known as the finished value (after).
Group of answer choices
Rate of Change
New Value
Skewed Distributions
Original Value
Answer:new value
Step-by-step explanation:
Find the quotient. Express the remainder as a decimal.
Answer:
no rubdvghwcuebhc vn2egchgvsbjhcekdnax dj
Step-by-step explanation:ncvjhdrbecjfv n
A salesman earns 3% commission for everything he sells. Yesterday, he sold a large screen television for $2,400 and a video game system for $500. How much money did the salesperson make on commission?
Write an equation of line that crosses the y- axis at -4 and has a slope 1/2
Answer:
y=1/2x-4
Step-by-step explanation:
the answer is y=1/2x-4