pth term of an AP = q
qth term = p
Prove:nth term of A.P. is (p+q-n).
Proof:We know that,
nth term of an AP (an) = a + (n - 1)d
Hence,
⟹ a + (p - 1)d = q
⟹ a + pd - d = q
⟹ a = q - pd + d -- equation (1)
Similarly,
⟹ a + (q - 1)d = p
Substitute the value of a from equation (1).
⟹ q - pd + d + qd - d = p
⟹ qd - pd = p - q
⟹ - d(p - q) = p - q
⟹ - d = 1
⟹ d = - 1
Substitute the value of d in equation (1).
⟹ a = q - p( - 1) + ( - 1)
⟹ a = q + p - 1
Now,
an = q + p - 1 + (n - 1)( - 1)
⟹ an = q + p - 1 - n + 1
⟹ an = p + q - n
Hence, Proved.
I hope it will help you.
Regards.
Step-by-step explanation:
ANSWER
pth term = q
a+(p−1)d=q
qth term = p
a+(q−1)d=p
Solving these equations, we get,
d=−1
a=(p+q−1)
Thus,
nth term = a+(n−1)d=(p+q−1)+(n−1)×(−1)=(p+q−n)
Maggie‘s brother is 11 years younger than four times her age. The sum of their ages is 54. How old is Maggie?
Answer:
Maggie is 13
Step-by-step explanation:
Honestly, I just kept trying ages starting from 10 because I knew it wasn't going to be less than that. Then I did whatever age, in this case 13, and multiply it by 4. Then minus 11 from that number. Then take that end number and add it to the beginning number(maggies age) and you should get 54.
Math Equation Explanation:
13*4 = 52 (Maggies Age) x 4
52-11= 41 The question stated that Maggie's brother was 11 -------------------------------------years younger than her age times 4.
41 + 13 =54 The sum of both their ages.
What is the value of f(-3) if f(x) = -5x - 1
Answer:
F(-3)= -14
Step-by-step explanation:
f(x)= -5x-1
f(x)=-5(-3)-1
f(x)= -15-1
f(x)=-14
Given f(x)=70+11x, find f(x)=158
Answer:
x=8
Step-by-step explanation:
I am assuming you need to find which x value fits this.
So set the two equations equal to each other
158=70+11x, subtract 70 from both sides
88=11x, now, divide by 11 to get x by itself,
8=x, to find these answers, use a calculator or any other method you want.
*MAKE SURE YOU ANSWER CORRECTLY , I NEED HELP ASAP ON THIS EQUATION*
*I WILL GIVE BRAINLIEST*
the first option is the correct answer
Answer:
2 ≤y+3 <6
Step-by-step explanation:
y+3 ≥2 and y+3 <6
Let y+3 = x
x ≥2 and x <6
2 ≤x and x<6
2 ≤x <6
Replace x with y+3
2 ≤y+3 <6
What’s is the answer to 9^11 divided by 9
Answer: 3,486,784,401
Step-by-step explanation:
9 raised to the 11th power is 31,381,059,609
Then divide that by 9 to get 3,486,784,401
what equation would make it a vertical line
An object that is projected straight downward with initial
velocity v feet per second travels a distance s = vt + 16t2,
where t = time in seconds. If Ramón is standing on a
balcony 84 feet above the ground and throws a penny
straight down with an initial velocity of 10 feet per second,
in how many seconds will it reach the ground?
A. 2 seconds
B. 3 seconds
C. 6 seconds
D. 8 seconds
Answer: 2 seconds
Step-by-step explanation:
An object take 2 seconds to reach to the ground. option A is correct.
An object that is projected straight downward with initial velocity v feet pee second.
s = vt + 16t2
s = 84 feet and v = 10
Velocity is ratio of displacement to the time.
We have equation.
s = vt + 16t2
Now, put s = 84 and v = 10
84 = 10t+16t2
8t2+10t-42=0
Taking roots of equation.
We get t = 2 and -21/8
Since time couldn't be negative.
So,
t = 2
Thus, An object take 2 seconds to reach to the ground.
Learn more about Velocity here:
https://brainly.com/question/18084516
#SPJ2
I need help with step 3
[tex]f(x) = ( \frac{1}{4} ) {}^{x} [/tex]
[tex]f(0) = ( \frac{1}{4} ) {}^{0} [/tex]
[tex]f(0) = 1[/tex]
[tex]f(1) = ( \frac{1}{4} ) {}^{1} [/tex]
[tex]f(1) = \frac{1}{4} [/tex]
[tex]f(2) = ( \frac{1}{4} ) {}^{2} [/tex]
[tex]f(2) = \frac{1}{16} [/tex]
#IfWrongPleaseReport
56 men can do a work in 42 days then how many men will do the same work in 14 days
Given : 56 men can do a work in 42 days .
To Find : In how many men will do the same work in 14 days .
Solution : We will use Unitary method here to solve the above problem . This is a case of inversely proportional that is when one will increase the other will decreases . Here if the number of men will increase then the number of days will decrease and vice - versa .
If in 42 days 56 men can do the work ,
Then in 1 day 42 × 56 men can do the work .
Then in 14 days , [tex]\sf \dfrac{42\times\cancel{56}}{\cancel{14}}[/tex] will do the work = 168 .
Hence 168 men will do the work in 14 days .
[tex]\Large\boxed{\red{\bf Answer = 168 \:men}}[/tex]
Graph a line that contains the point -6,1 and has a slope of 5
Answer:
y=5x+31
Step-by-step explanation:
y=mx+b
1=(-6*5)+b
1=-30+b
31=b
y=5x+31
(5*-6)+31
-30+31
1
you can also graph a line on desmos
BRAILIEST, 5 STARS, A THANKS, AND 35 POINTS!!!
Noah’s scores for four Spanish quizzes are 70, 75, 83, and 80. What score must he get on the next quiz to achieve an average of at least 80?
Answer: 92
Step-by-step explanation:
Here's our set-up:
(70 + 75 + 80 + 83 + x) / 5 = 80
Simplify:
(308 + x) / 5 = 80
Multiply both sides by 5:
308 + x = 400
Subtract 308 from both sides:
x = 92
Answer:
92
Step-by-step explanation:
In order to get an 80 in 5 tests, he needs to accumulate 400 points.
If he accumulated 80+70+75+83 points, 308, he would need a 92 on the next test to get an 80 average.
Can someone help me please
Answer:
its c
Step-by-step explanation:
took the testisk...........
When Lucy left her house in the morning, her cell phone battery was partially charged. Lucy's phone lost battery life at a rate of 8% each hour and 3 hours after leaving her house, the battery had 16% remaining battery life. Write an equation for B , B, in terms of t , t, representing the charge remaining in Lucy's battery, as a percentage, t t hours after Lucy left her house.
Answer:
B = 40 - 8t
Step-by-step explanation:
Given that:
Rate at which battery life discharges = 8% per hour ;
Battery life left after 3 hours = 16%
t = hours after Lucy left hiuse
Equation B will be ;
Amount of charge before leaving home - (Discharge rate * number hours)
Amount of charge before leaving home :
Charge left after 3 hours + discharge rate * 3
16% + 8*3
16% + 24% = 40%
Hence,
B = 40 - 8t
Answer:
probably B = 40 - 8t
Step-by-step explanation:
the product of a number and 13 increased by 5 is -12
Answer:
13x + 5= -12
hope this helps :)
how do you convert fractions to decimals?
Answer: division :3
Step-by-step explanation:
The line in a fraction that separates the numerator and the denominator represents division.
To convert a fraction to a decimal, divide the numerator by the denominator.
Pls pls Pls pls pls helpppp meee asappppp i will give BRAINLIEST!!!!!!
Answer:
27ft
Step-by-step explanation:
Answer:
its simple you will need 5ft of carpet
Step-by-step explanation:
Marcia has a monthly income of $3,500. She budgets 8% for her cell phone. What amount does she budget for her cell phone, in dollars and cents?
Answer:
[tex]280 \: dollars[/tex]
Step-by-step explanation:
[tex]3500 \times .08 = 280[/tex]
Simple as that ^^^ Just find 8% of 3500
280,00$
8% of 3500$ equals to
(8/100)*3500=
280,00$=
6 of 12
Sam had a bank account balance of $32. He deposited $28 into his account
Which statement is true about his balance after making the deposit?
A
His balance will be less than $32
B
His balance will be greater than $28.
С
His balance will be between S0 and $28
His balance will be between $32 and $0
Answer:his balance will be between 0 and 28
Step-by-step explanation:
y = 4x2 - 5X-10
vertex
An equilateral triangle with side length 4cm is shown in the diagram, work out the area of the triangle.
Give your answer rounded to 1 DP.
Answer:
4√3cm^2
Step-by-step explanation:
we know that the area of equilateral triangle is √3/4a^2
solve each equation using the quadratic formula. 4x^2-13x+3
Answer:
( 4 x − 1 ) ( x − 3 )
Step-by-step explanation:
Factor by grouping.
Answer:
Your answer is: x = 3 , 1/4
Solve the equation for x by finding a , b , and c of the quadratic then applying the quadratic formula.
Step-by-step explanation:
Hope this helped : )
At noon the temperature was 0°C. If the temperature then rose 3°C per hour, what was
the temperature after 7 hours?
Answer:
21 degrees
Step-by-step explanation:
is this a function or not
Answer:
No
Step-by-step explanation:
x=5 produces y=3 and y=5 so the relation is not a function.
Yes that is function by looking that this
y
A women has 6 dogs, 4 cats, and 8 canaries. In how many ways can she select one of each species?
What is another fraction besides 2/5 that is equivalent to the decimal 0.4?
Answer:
4/9
Step-by-step explanation:
find the value of x.
Answer:
x=11
Step-by-step explanation:
take 90+35 = 125
then take 180-125=55
then take 55 divided by 5 to get the answer of 11
The measure of the sides of a
triangle are in the extended
ratio of 3:5:7. The perimeter
of the triangle is 45 in. What
are the measures of the three
sides?
a) 6, 16, 23
b) 8, 15, 22
c) 6,9,15
d) 3, 5, 7
e) 9, 15, 21
Answer:
e) 9, 15, 21
Step-by-step explanation:
First you multiply each number in the ratio by x and set it equal to the perimeter or 45 in this case.
3x + 5x + 7x = 45
Then you add the like terms and get
15x = 45
Solve for x
x = 3
Now multiply 3 by each number
3•3= 9
3•5= 15
3•7= 21
Answer: 9, 15, 21
PLS TELL ME WHICH ONE IS TRUE PLS DONT LIE
7
Pls answer I’m to tired for this
What is the midpoint
between (-2, -3) and
(1, 2)?
a) (-1,-)
b) (-:-)
c) (-1,-)
d) (-3,-)
Answer:
I think it's B
...........
Answer:
d
Step-by-step explanation:
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
Here (x₁, y₁ ) = (- 2, - 3) and (x₂, y₂ ) = (1, [tex]\frac{1}{2}[/tex] ), thus
midpoint = ( [tex]\frac{-2+1}{2}[/tex], [tex]\frac{-3+\frac{1}{2} }{2}[/tex] ) = ( [tex]\frac{-1}{2}[/tex], [tex]\frac{-3+\frac{1}{2} }{2}[/tex] ) = ( - [tex]\frac{1}{2}[/tex], [tex]\frac{-\frac{5}{2} }{2}[/tex] ) = ( - [tex]\frac{1}{2}[/tex], - [tex]\frac{5}{4}[/tex] ) → d
CAN SOMEONE HELP ME ?
Answer:
sure ill help
Step-by-step explanation:
Answer:
a+b=f
Step-by-step explanation:
180-f= c
180-(a+b)= c
SO
a+b= f