Sum of 5th & 8th terms of an AP = 37
11th term = 32
Find:A.P
Solution:We know that,
nth term of an AP – an = a + (n - 1)d
Hence,
⟹ a₅ + a₈ = 37
⟹ a + (5 - 1)d + a + (8 - 1)d = 37
⟹ 2a + 4d + 7d = 37
⟹ 2a + 11d = 37 -- equation (1)
Similarly,
⟹ a₁₁ = 32
⟹ a + (11 - 1)d = 32
⟹ a + 10d = 32
⟹ a = 32 - 10d
Substitute the value of a in equation (1).
⟹ 2(32 - 10d) + 11d = 37
⟹ 64 - 20d + 11d = 37
⟹ 64 - 37 = 20d - 11d
⟹ 27 = 9d
⟹ 27/9 = d
⟹ 3 = d
Substitute the value of d in equation (1).
⟹ 2a + 11(3) = 37
⟹ 2a + 33 = 37
⟹ 2a = 37 - 33
⟹ 2a = 4
⟹ a = 4/2
⟹ a = 2
Now,
General form of an ap = a , a + d , a + 2d...
⟶ Required AP = 2 , 2 + 3 , 2 + 2(3)...
⟶ Required AP = 2 , 5 , 2 + 6...
⟶ Required AP = 2 , 5 , 8...
I hope it will help you.
Regards.
Answer:
→ md - 2nd + 3md = 2 * [ a + (n - 1)d ]
→ 4md - 2nd = 2 * [ a + (n - 1)d ]
→ 2(2md - nd) = 2 * (a + nd - d)
→ 2md - nd - a + d = nd
→ 2md - nd - (md - 2nd) + d = nd
[ From equation (1) ]
→ 2md - nd - md + 2nd + d = nd
→ md + nd + d = nd
→ (m + n + 1)d = n * d
→ (m + n + 1) = n
Step-by-step explanation:
3x-4y=-7 and 4x+3y=24 solve for x
Planets are constantly moving. In fact, the name planet means wanderer. What force(s) is responsible for the constant movement of the planets in our solar system?
A) inertia and gravity
B) gravity only
C) inertia only
D) friction
I know its not math
Open-Ended Which of these situations can be represented by the opposite of 53? Use pencil and
paper. Describe two more situations that can be represented by the opposite of 53.
A book was 53 pages shorter than you expected.
Andrew spent $53.
The temperature was 53°F.
Jennifer sold 53 apples.
Select each situation that can be represented by the opposite of 53.
O A. Andrew spent $53.
OB. Jennifer sold 53 apples.
OC. A book was 53 pages shorter than you expected.
D. The temperature was 53°F.
Answer:
A book was 53 pages shorter than you expected
Jennifer sold 53 apples.
Andrew spent $53.
Step-by-step explanation:
The question proposed that we should determine which situation can be said to be the opposite of 53. From the listed option, we will realize that the following:
A book was 53 pages shorter than you expected
Jennifer sold 53 apples.
Andrew spent $53.
The above options are the opposite of 53. This is because a book that was shorter than expected will need to be refilled.
Suppose Jennifer has x apples, and She sold 53 apples out of it. It means x = -53, which is the opposite of 53.
Andrew spent $53; let say Andrew had y+$53. After spending $53, he has y = - $53, which is the opposite of 53.
But the temperature, which was 53°F, will still be at that position on the thermometer provided it is not being affected by external conditions.
+54- -75 what the answer
Answer:
-21
Step-by-step explanation:
positive 54 decreased negative 75. The answer is -21. why? Because the negative variables is higher than the positive variable in the given.
Answer:
129
Step-by-step explanation:
+54- -75
54+75=129
When you are subtracting 54- -75, the symbols will automatically change to postives.
You could also use the method:
Keep, change, change
54 + +75
I can’t find answers to this question. Please help.
Answer:
Did you try looking it up
Step-by-step explanation:
sorry If I am wrong and don't forget to make me brainliest
please please help me!!
Answer:
g(x) = f(x+1) + 1
Step-by-step explanation:
Since the graph is only moved you don't have to worry about the slope.
To move the graph to the left you add to the x and in this case, it only moved 1 over.
to move the graph up you add to the whole function and in this case, it only moved up 1.
Jacob spent $10 of the $25 in his wallet write a decimal that represents the fraction of the $25 Jacob spent
How do you solve 26 = 18v Equation
Answer:
v = 1.444
Step-by-step explanation:
v = 26/18
v = 1.444
Answer:
26 = 18v
=> 26 / 18 = v (By the law of transposition)
=> 13/9 = v
=> 1.44444 repeating = v (After solving)
If my answer helped, kindly mark me as the brainliest!!
Thank You!!
Solve the equation for y: -8x + 4y = 20
A)
y-2x5
B)
y = 2x + 5
y = 2x+5
1/3x + 20
D)
y =
Answer:
y=2x+5
Step-by-step explanation:
1f f(x) = ***, g(x) = x+4, and h(x) - 3x-2, what is (nofog)(x)?
o (hofog)(x) = -2
o (hofog)(x) = 3X-8
o (hºfog)(x) = *=14
(nofog)(x) - 3x-4
Answer:
first option y + 7 = –(x + 6) is correct option
Step-by-step explanation:
Sammi had 19 marbles and bob gave him 1/7 of his marbles now Sammi has 27 how many marbles did bob have originally?
pls help
Answer:
56
Step-by-step explanation:
27 - 19 = 8
8 x 7 = 56
Which negative numbers have an absolute value greater than 3?
Choose all that apply.
-1/2
-4.2
-16/5
-1.8
-5
-12
The double number line shows the approximate number of ounces in a certain number of pounds:
Based on the number line, about how many ounces are there in 10 pounds?
Group of answer choices
144 ounces
160 ounces
176 ounces
192 ounces
Answer:
B- 160
Step-by-Step Explanation:
I did it before and I was rite, so trust me
Answer:
B 160
Step-by-step explanation:
4. What is the slope of the line y = 3? (1 point)
Answer: Undefined or 0
Step-by-step explanation: Y=3 means there would just be a straight line across on (0,3) and when the slope and rise is 0 it means there is no slope or it is undefined
1. How much carpeting is needed in a room that measures 11 feet by 12 feet?
132 feet²
For this question, you have to find area.
Area is length x width
so multiply 11 x 12
You will get 132 feet²
simplify the following
Answer:
D. 64 z^ 2
Step-by-step explanation:
Simplify the expression.
What is 3,050 divided by 75 with a remainder?
The quotient from the given division is 46 and the remainder is 50.
Given that, 3500 divided by 75.
The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Here, 3500/75
75|3500|46
300
_____
500
450
______
50
Thus, quotient = 46 and remainder=50
Therefore, the quotient from the given division is 46 and the remainder is 50.
To learn more about the division visit:
brainly.com/question/1575906.
#SPJ6
help graphs are not my favorite
Answer:
d
Step-by-step explanation:
Last week Karen spent $121.35 on food for her family. She only has $200 to spend every two weeks. How much does hse have left to spend?
Answer:
$78.65
Step-by-step explanation:
take 200-121.35=78.65
$78.65
__________________________________________
Answer:
3.3 x 10⁻⁴
Step-by-step explanation:
Given expression:
[tex]\frac{2.64 x 10^{-3} }{8.0 x 10^{0} }[/tex]
To solve this problem;
10° = 1
So;
[tex]\frac{2.64 x 10^{-3} }{8.0}[/tex]
= [tex]\frac{2.64}{8}[/tex] x 10⁻³
= 0.33 x 10⁻³
= 3.3 x 10⁻¹ x 10⁻³
= 3.3 x 10⁻⁴
-5 -2q = 9
please help me
Answer:
q = -7
Step-by-step explanation:
-5 - 2q = 9
Add 5 to both sides of the equation.
-2q = 14
Divide both sides by -2.
q = -7
Joe plans to book a trip for his family. The base rate for the trip will be 800$ and 75$ for each additional person going, write an equation to represent the linear function in slope intercept form
Answer:
y = 75x + 800
Step-by-step explanation:
1. A tortoise is running on a long, moving sidewalk. Her pedometer doesn't report her speed, but she knows that—since she got on—she's been running for 40 minutes and that she's traveled 3 kilometers. Unfortunately, she realizes she left her suitcase on the ground just before she got on the sidewalk. Since she's too short to climb over the handrails, she decides to turn around and run at the same speed back to her suitcase. If it takes her 2 hours to return to her suitcase, how fast (in kilometers per hour) was the moving sidewalk moving? How fast (in kilometers per hour) was the tortoise running?
Answer:
the sidewalk speed q = 3km/hr
the tortoise speed p is 1.5 km/hr
Step-by-step explanation:
From the given information:
let the speed of the tortoise be p & the speed of the sidewalk be q
she's been running for 40 minutes (40/60 = 2/3) and that she's travelled 3 kilometres
Thus,
p + q = [tex]\dfrac{3}{\dfrac{2}{3}}[/tex]
p + q = 9/2
p + q = 4.5 ----- (1)
when returning, she travelled 3km in 2 hours
i.e. -p + q = 3/2
-p + q = 1.5 ----- (2)
Thus, by using the elimination method for equation (1) and (2)
p + q = 4.5 ----- (1)
-p + q = 1.5 ----- (2)
2q = 6
q = 6/2
q = 3 km/hr
From equation (1)
p + q = 4.5
p + 3 = 4.5
p = 4.5 - 3
p = 1.5 km/hr
Therefore, the sidewalk speed q = 3km/hr and the tortoise speed p is 1.5 km/hr
Rectangle ABCD is shown on the coordinate grid, Rectangle ABCD is
rotated 90° clockwise about the origin to form Rectangle A'B'C'D'. Which
quadrant contains Rectangle A'B'C'D?
Quadrant
Quadrant II
Quadrant III
Quadrant IV
A train leaves New Delhi at 4:00 p.m. and reaches Lucknow at midnight. Its speed is 55km/h. What is the distance between Delhi and Lucknow?
Answer:
[tex]\boxed{440 km}[/tex]
Step-by-step explanation:
→ Work out time between New Delhi and Lucknow
12:00 - 4:00 = 8:00
→ State the speed formula
Speed = Distance ÷ Time
→ Rearrange to make distance the subject
Distance = Speed × Time
→ Substitute in the values
55 × 8 = 440 km
Can someone answer this for me?
Answer:
D 26
Step-by-step explanation:
154+154=308
308-360=52
52 divided by 2
=26
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
I'm not sure if my way of doing it is the way your teacher wants it solved but I would do...
[tex]150+150+x=360[/tex]
so now we just have to solve the equation...
[tex]308+x=360\\x=52[/tex]
ok and now before you judge me that still isn't the answer we still have to divide the 52 by 2 because 52 is the sum of both the smaller angles, so you'll get...26°
choice D
2x+5/3 = 3x-10
Please can anyone help?
Answer:
first bring x value together
Step-by-step explanation:
like 2x and 3x together and then take 5/3 to RHS and solve
Please please please please help please please help
Answer:
B
Step-by-step explanation:
What is five times seven divided by nine
Answer:
3.9 or 3.88888888889
Step-by-step explanation:
5*7=35
35/9=3.88888888889=3.9
Answer:
5*7 = 35 / 9 =3
Step-by-step explanation:
because it is the closest
Select all polynomials that are divisible by (x-1)(x−1)left parenthesis, x, minus, 1, right parenthesis. Choose all answers that apply: Choose all answers that apply: (Choice A) A A(x)=3x^3+2x^2-xA(x)=3x 3 +2x 2 −xA, left parenthesis, x, right parenthesis, equals, 3, x, cubed, plus, 2, x, squared, minus, x (Choice B) B B(x)=5x^3-4x^2-xB(x)=5x 3 −4x 2 −xB, left parenthesis, x, right parenthesis, equals, 5, x, cubed, minus, 4, x, squared, minus, x (Choice C) C C(x)=2x^3-3x^2+2x-1C(x)=2x 3 −3x 2 +2x−1C, left parenthesis, x, right parenthesis, equals, 2, x, cubed, minus, 3, x, squared, plus, 2, x, minus, 1 (Choice D) D D(x)=x^3+2x^2+3x+2D(x)=x 3 +2x 2 +3x+2
Answer:
Step-by-step explanation:
For us to be able to determine the polynomials that are divisible by (x-1), this means that x-1 must be a factor for the functon to be able to divide any of the polynimial.
Since x-1 is a factor, we can get the value of x
x-1 = 0
x =0+1
x = 1
Next is for to substitute x - 1 into the polynomial and see the ones that will give us zero
For A(x)=3x^3+2x^2-x
A(1) = 3(1)^3+2(1)^2-(1)
A(1) = 3+2-(1)
A(1) = 5-1
A(1) = 4
Since A(1) ≠ 0, then x-1 is not divisible by the polynomial function.
For B(x)=5x^3-4x^2-x
B(1)=5(1)^3-4(1)^2-1
B(1)=5-4-1
B(1)=1-1 = 0
Since B(1) = 0, hence x-1 is divisible by 5x^3-4x^2-x
For the polynomial C(x)= 2x^3-3x^2+2x-1
C(1)=2(1)^3-3(1)^2+2(1)-1
C(1)=2-3+2-1
C(1)= -1+1
C(1)= 0
Since C(1) = 0, hence x-1 is divisible by the
For the polynomial D(x)=x^3+2x^2+3x+2
D(1)=1^3+2(1)^2+3(1)+2
D(1)=1+2+3+2
D(x) = 8
Hence the polynomial D(x) is not divisible by x-1
Hence the correct options are B(x)=5x^3-4x^2-x and 2x^3-3x^2+2x-1
Answer:
B(x) and C(x)
Step-by-step explanation: