Common difference is 6
Possible values of n is n > 8
Step-by-step explanation:(i) The nth term (Uₙ) of an arithmetic series is given by
Uₙ = a + (n-1)d --------------------(i)
and the sum of the series is given by;
Sₙ = [tex]\frac{n}{2}[/tex](2a + (n-1)d) ---------------------(ii)
Where;
a = first term of the series
d = common difference of the series
n = the term or number of terms to be added.
Interpret the first statement
The third term of the series is 70. i.e
n = 3
Uₙ = U₃ = 30
Substitute these values into equation (i) as follows;
=> 30 = a + (3 - 1)d
=> 30 = a + 2d
=> a = 30 - 2d --------------------(iii)
Interpret the next statement
the sum of the first 10 terms of the series is 450. i.e
n = 10
Sₙ = S₁₀ = 450
Substitute these values into equation (ii) as follows:
=> 450 = [tex]\frac{10}{2}[/tex](2a + (10-1)d)
=> 450 = 5(2a + 9d)
Divide both sides by 5
=> 90 = 2a + 9d ---------------------------(iv)
Solve equations (iii) and (iv) simultaneously
Substitute the value of a in equation(iii) into equation (iv) and solve as follows
=> 90 = 2(30 - 2d) + 9d
=> 90 = 60 - 4d + 9d
=> 90 = 60 + 5d
=> 5d = 90 - 60
=> 5d = 30
Divide both sides by 5
=> d = 6
Therefore, the common difference, d is 6
(ii) Given
Sₙ > 350
From equation (ii), this implies that,
[tex]\frac{n}{2}[/tex](2a + (n-1)d) > 350 -------------------(v)
Let's get the value of the first term 'a'
Substitute the value of d = 6 into equation (iii) and solve as follows
=> a = 30 - 2(6)
=> a = 30 - 12
=> a = 18
Substitute the values of a and d into inequality (v) and solve
[tex]\frac{n}{2}[/tex](2(18) + (n-1)6) > 350
[tex]\frac{n}{2}[/tex](36 + 6n - 6) > 350
[tex]\frac{n}{2}[/tex](36 - 6 + 6n) > 350
[tex]\frac{n}{2}[/tex](30 + 6n) > 350
Multiply both sides by 2
n(30 + 6n) > 700
30n + 6n² > 700
6n² + 30n > 700
Divide through by 2
3n² + 15n > 350
3n(n+5) > 350
Solve the quadratic inequality
Since n specifies the number of terms to be added, it will always be a whole number. Therefore, using trial and error method, the values of n that will satisfy the above inequality will be values greater than 8. i.e
n > 8
In other words, for all values of n greater than 8, the above inequality will be satisfied.
In the diagram below, what is the measure of angle 1?
Answer: 82 degrees
Step-by-step explanation:
I wanna know if any of you guys could possibly help me with my foods work? It’s not hard it’s just a lot of once and I really have to get it done. plz don’t comment to be a moron.
Evaluate -33.
-27
-9
9
27
Answer:
- 27
Step-by-step explanation:
(- 3)³
= - 3 * - 3 * - 3
= - 27
Hope it will help :)❤
Answer:
[tex] - {3}^{3} \\ = - 27[/tex]
a rectangular prism has a base 3 cm by 4 cm and is 5 cm in height
1. It refers to the size of a surface. What is it?
A. Area
B. Height
C. Length
D. Volume
the perimeter of a rectangle parking lot is 322 m. if the length of the parking lot is 86 m, what is the width
"The product of four and a
number is more than ten."
Answer:
x>5/2
Step-by-step explanation:
4x>10
x>10/4
x>5/2
Find the volume of a pyramid with a square base, where the perimeter of the base is 10.1\text{ ft}10.1 ft and the height of the pyramid is 13.4\text{ ft}13.4 ft. Round your answer to the nearest tenth of a cubic foot. Find the volume of a pyramid with a square base, where the side length of the base is 6.1\text{ m}6.1 m and the height of the pyramid is 4.7\text{ m}4.7 m. Round your answer to the nearest tenth of a cubic meter.
Answer:
28.5 ft^3
58.3 m^3
Step-by-step explanation:
volume of a pyramid = 1/3 x length x width x height
Perimeter of a pyramid = 4 x length
10.1 = 4 x length
length = 10.1 / 4 = 2.525
1/3 x (2.525 x 2.525 x 13.4) = 28.5 ft^3
1/3 x (6.1 x 6.1 x 4.7) = 58.3 m^3
the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero
What is the product of 4 cos
14 (cos(37) + i sin (34) and 2 (cos(5) + sin(5)}?
--4 cot (--45)
cos (390)
sin (330)
1000 + 874 + 53528 - 1026 =
Answer:
54376
is the answer .......
what is the value of x
Answer:
8
Step-by-step explanation:
Lines have angles that are equal to 180. Therefore, because we already have 140 of the 180 necessary, we can subtract 140 from 180 to get 40. 40 divided by 5 is 8.
Hope that this helps!
Answer:
I. x=8
Step-by-step explanation:
lines form 180° angles so
140 +5x= 180 ; subtract 140 from both sides
5x= 180-140; divide both sides by 5
x= 40/5 = 8
f(x) = x2
g(x) = 3x2
Which option could show the graphs of f and g?
Answer:
2 Transformations
Step-by-step explanation:
A reflection in the x axis accounts for the minus sign and because there's a 3 there, it is a stretch in the y direction scale factor 3. hope this helps :)
-2x + 6 greater than or equal to -4
Answer:
C
Step-by-step explanation:
-2x+6 [tex]\geq[/tex]-4
-6 -6
-2x [tex]\geq[/tex]-10
divide both sides by -2
-2/2=-1
-10/2=-5
-5*-1=5
x[tex]\geq[/tex]5
x is greater than 5 so the number should be larger than 5 or equal to 5.
WILL MARK BRAINLIEST IF GOTTEN RIGHT!!!!
Answer:
C
Step-by-step explanation:
Using Pythagoras' identity in right triangle BPO
with PB = 4 ( half of AB ) and OB = 5 ( radius of circle )
OP² + 4² = 5²
OP² + 16 = 25 ( subtract 16 from both sides )
OP² = 9 ( take the square root of both sides )
OP = [tex]\sqrt{9}[/tex] = 3
156 divided by 3 with remaining
Answer: 52
Step-by-step explanation:
Divide 156 by 3, you get 52 with a remainder of 0.
In long division, you would write it as:
To perform the division, start by dividing 3 into the first digit of 156, which is 1.
3 ) 156 ( 52
- 15
_______
6
-6
_______
0
3 cannot go into 1, so you move to the next digit, 15. 3 can go into 15 five times (3 * 5 = 15). After subtracting 15 from 15, you have 0.
Now, you bring down the last digit, 6, to form 6. Since 3 can go into 6 two times (3 * 2 = 6), the final quotient is 52, and the remainder is 0.
In summary, 156 divided by 3 is equal to 52, with no remaining or fractional parts.
Learn more about Divided here:
brainly.com/question/15381501
#SPJ6
The running back ran a total of 258 yards during the football game last Sunday. That was ten less than three times the amount of yards, y, that he ran two weeks ago. Which equation can be used to find the number of yards that he ran two weeks ago?
Answer:
258 = 3y - 10
3y = 258 + 10
3y = 268
Step-by-step explanation:
A grocer has 2 kinds of tea, one that sells for $8.00 per pound and the other that sells for $6.00 per pound. How many pounds of each kind must he use to make 50 pounds of tea that will sell for $7.40 per pound?
Answer in _____ pounds of $8.00 tea and _____ pounds of $6.00 tea
ASAP-WILL MARK BRANLIEST!
Answer:
35 pounds of $8.00 tea and 15 pounds of $6.00 tea
Step-by-step explanation:
Let x represent the pounds of tea of the $8 kind. 8x would represent the total cost of that type of tea. We can also say 50 - x is the pounds of tea of the $6 kind, so 6(50 - x) is the total cost of that type of tea. 50 * 7.4 represents the total cost of all the tea, and the expression 8x + 6(50 -x) would also represent the same thing. We can write this as an equation,
8x + 6(50 -x) = 50 * 7.4
simplify,
8x + 300 - 6x = 370
2x + 300 = 370
and solve.
2x = 70
x = 35
This means there is 35 pounds of the $8 kind.
We can subtract that from 50 to find,
50 - 35 = 15,
15 pounds is the amount of the $6 kind.
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
Answer:
narr
Step-by-step explanation:
Aşağıda verilen kesirlerin yüzde sembolü kullanılarak verilen gösterimlerden hangisi yanlıştır A 3/4=%75 B 2/4=%50 C 8/25=%32 D 15/75=%12
Cevap:
D
Adım adım açıklama:
Verilen İfadelerin Değerlendirilmesi:
3/4 = 0.75; 0,75 *% 100 =% 75 - doğru
2/4 = 1/2; 1/2 *% 100 =% 50 - Corect
8/25 = 0,32 *% 100 =% 32 - doğru
15/75 = 1/5 = 0,2 * 100 =% 20,% 12 olarak verildiği için yanlıştır
ILL GIVE BRAINLIEST. plsss help asap
Answer:
first one
Step-by-step explanation:
Answer:
It will be the first answer, Both balls will at the same rate
PLEASE HELP ME ASAP
A 30°-60°-90° triangle has a shorter leg with a length of 14 cm. The hypotenuse of the triangle is ___ cm.
Answer:
28 cm
Step-by-step explanation:
side opposite of 30° = x = shorter leg / opposite.
side opposite of 60° = x√3 = adjacent.
side opposite of 90° = 2x = hypotenuse.
34
Select the correct answer from each drop-down menu.
4 units
4 units
6 units
6 units
4 unitst
The total area of the three triangles is
square units.
The area of the figure is
square units.
Reset
Nextk
Answer:
The total are of the three triangles is 36 square units.
The area of the figure is 60 square units.
Answer:
first box 36 second box 60
Step-by-step explanation:
Two vehicles are traveling at constant speeds. The distance traveled over a period of
time by the first vehicle is shown in the graph below. The distance traveled over a
period of time by the second vehicle is shown in the table below. Which vehicle is traveling
at a greater speed?
Vehicle 1
Vehicle 2
Distance (miles)
(3,120)
(2,80)
Time Distance
(hours) (miles)
5 150
8 240
Time (hours)
T
Answer:
Step-by-step explanation:
vehicle one is traveling at a greater speed. from the graphs we can see that in one hour the care would travel 40 miles.
the table shows the 2nd vehicle traveling 30 miles in one hour
So car 1 is going faster :)
Answer:
Vehicle 1 is Moving Faster.
Step-by-step explanation:
For vehicle 1.
(2,80) (3,120)
∆Distance= 120-80 = 40miles
∆time = 3-2=1hr
So V=Distance/time = 40miles/1hr
V1 = 40miles per hour.
For car 2.
∆Distance=240-150 =90miles
∆time=8-5 = 3hrs
V=90/3
V=30Miles per hour.
So Car1 is Moving faster and at a velocity of 40Miles per hour.
what basic trigonometry identity would you use to identify that sin x cos x tan x = 1 - cos^2x
Answer:
tanx = sinx/cosx
Step-by-step explanation:
Given the expression
sin x cos x tan x = 1 - cos^2x
According to trigonometry identity
tan x = sinx/cosx
Substitute into the expression. From LHS
sin x cos x tan x
= sin x cos x (sinx/cosx)
= sin²x
Also since sin²x+cos²x = 1
Hence sin²x = 1 - cos²x (RHS)
The correct option is therefore tanx = sinx/cosx
Which expression has a value of 2/3?
A. 8 + 24 divided by 12 x 4
B. 8 + 24 divided by (12 x 4)
C. (8 + 24) divided by (12 x 4)
D. 8 + (24 divided by 12) x 4
Answer:
C)
Step-by-step explanation:
A) 8 + 24 ÷ 12 x 4 = 8 + 2 x 4 = 8 + 8 = 16
B) 8 + 24 ÷ (12 x 4) = 8 + 24 ÷ 48 = 8 + 1/2
C) 32 ÷ 48 = 2/3
D) 8 + 2(4) = 16
FBISD bought 12 new chairs for $28.99 each, and 8 tables for $45.50 each. What is the total price, including 8.25% sales tax.
A)$772.39
B)$711.88
C)$347.88
D)$60.51
Please hurryyyyy please
Answer:
d
Step-by-step explanation:
Carly buys 3 more band concert tickets than choir concert tickets. Band concert tickets cost $3.50 per ticket. What is the cost for the choir concert and band concert tickets?
Answer:
I'm not to sure, but I'll say 10.5
If you multiply 3.50 x 3 you'll get 10.5
If you add you'll get 13.5.
If it's an addition I'll recommend to go with 13.5
If it's a multiplication I'll recommend to go with 10.5
There are 1030 books in the library we bought 67 more books for the library how many books are there in the library now?
Answer:
1097
Step-by-step explanation:
1,030+ 67= 1097
Answer:
1097 Books
Step-by-step explanation:
1030+67=1097
draw the graph of 4x-3y=0
Answer:
[tex] slope = \frac{4}{3} [/tex]
Step-by-step explanation:
Hope it is helpful....
Using the graph, what is one solution to the equation f(x) = g(x)?
x = 3.9
x = 1
x = 0.25
x = −2
Answer:
I THINK ITS 1x
Step-by-step explanation:
1x+2-2=1x