Select the correct answer. What is the sum of the first 17 terms of this arithmetic series? Use Sn=n(a1+an/2) .
-28 + (-13) + 2 + 17 + ⋯
A. 1,692 B. 1,564 C. 227 D. 212
Answer:
1564.
Step-by-step explanation:
First term = -28 and common difference = 15.
Sum = (17/2)(2*-28 + (17-1)15)
= 8.5 * 184
= 1564.
Which is the sum of the first 6 terms of the geometric series?
7+21 +63
Answer:
2,548
Step-by-step explanation:
First, we have to find out the rule. The rule is multiply the previous number by 3 to get the next number.
7x3=21
21x3=63
So, we would continue this pattern until we have the first 6 numbers which are 189, 567, and 1701.
The questions is asking for the SUM of the 6 numbers so you would add the those numbers and do this equation:
7+21+63+189+567+1701= 2548
Hope this helps! :)
PLEASEE HELP THIS IS DUE TODAY
Answer:
The first one is 360 degrees. The second one is 1080.
Step-by-step explanation:
The sum of the interior angles of a quadrilateral are always 360. If you subtract 90 from 360 to get 270. Multiply 270 by 4 to get 1080.
Linda bought a new rug that cost r dollars. She use a coupon for 20% discount and sales tax of 10%. If there was a shipping fee of $50 that was applied after the discount and tax , Which of the following expressions show the total amount of money that linda paid for the rug
A city has 18 radio stations, including 9 oldies stations.
What is the probability that a randomly chosen radio station in this city is an oldies station?
Write your answer as a fraction or whole number.
How do i solve for this?
9514 1404 393
Answer:
97.42 square units
Step-by-step explanation:
The area of a sector is given by ...
A = (1/2)r²θ
where r is the radius (12.2) and θ is the central angle in radians. Here, you're given the central angle as 75°, so you need to convert that to radians.
75° = (75°)×(π/180°) radians = (5/12)π radians
Then the area is ...
A = (1/2)(12.2²)(5π/12) = 744.2π/24 ≈ 97.42 . . . square units
__
Equivalently, you can find the area of the circle in the usual way:
A = πr² = π(12.2²) ≈ 467.59465
Then, multiply by the fraction of the circle that is shaded (75°/360°)
sector area = (467.59465)(75/360) = 94.42 . . . square units
The first three terms of a sequence are 7, 13, 19..., find the 64th term.
Answer:
385 is your answer.
Step-by-step explanation:
7 - 1
13 - 2
19 - 3
25 - 4
31 - 5
37 - 6
43 - 7
49 - 8
55 - 9
61 - 10
67 - 11
73 - 12
79 - 13
85 - 14
91 - 15
97 - 16
103 - 17
109 - 18
115 - 19
121 - 20
127 - 21
133 - 22
139 - 23
145 - 24
151 - 25
157 - 26
163 - 27
169 - 28
175 - 29
181 - 30
187 - 31
193 - 32
199 - 33
205 - 34
211 - 35
217 - 36
223 - 37
229 - 38
235 - 39
241 - 40
247 - 41
253 - 42
259 - 43
265 - 44
271 - 45
277 - 46
283 - 47
289 - 48
295 - 49
301 - 50
307 - 51
313 - 52
319 - 53
325 - 54
331 - 55
337 - 56
343 - 57
349 - 58
355 - 59
361 - 60
367 - 61
373 - 62
379 - 63
385 - 64
Find the perimeter of the triangle whose vertices are the following specified points in the plane.
(5,6), (4,1) and (-4,2)
Answer:
23 units
Step-by-step explanation:
Let the vertices of the triangle be A(5,6), B(4,1) and C(-4,2)
Perimeter of the triangle = AB + AC + BC
AB = √(5-4)²+(6-1)²
AB = √1²+5²
AB = √1+25
AB = √26
For BC where B(4,1) and C(-4,2)
BC = √(4-+4)²+(1-2)²
BC = √8²+1²
BC = √64+1
BC = √65
For AC where A(5,6) and C(-4,2)
AC = √(5+4)²+(6-2)²
AC = √9²+4²
AC = √81+16
AC = √97
Perimeter = √97 + √26 + √65
Perimeter = 9.85+5.09+8.06
Perimeter = 23
Hence the perimeter of the triangle is approx 23 units
What is the slope of a line that passes through (2, 77) and (98, 5)
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Your answer
Answer:
Step-by-step explanation:
slope = (5-77)/(98-2) = -72/96 = -¾
Write the equation for the line that goes through point (12, 15) with slope = −2.
Enter your answer in slope-intercept form.
Complete the equation below
y = _______________
Use x as your variable.
Enter any non-integer values as fractions.
Answer:
y= -2x +39
Step-by-step explanation:
y= mx+b
m is the slope which is given -2
since we don't know b we can solve the rest using the formula y-y1{ m(x-X1(
y - 15 = -2(x-12)
simplify
y-15= -2x +24
y= -2x + 39
1. h-4w when h =17 and w = 2
2. 2i+3v when i = 3 and v = 2
3. j over 2 + u when j = 30 and u =3
4. 24 over k - 3 when k = 8
5. p+q over 3 when p = 11 and q= 22
The mens taxable is income is rs 14280 the state tex instruction tel him to pay 2%on the first rs3000 of his taxable incom 3% on each of the second and third rs 3000 and 4% o the remainder what is the total amount of income tax that he must pay
Answer:
Rs. 451.2
Step-by-step explanation:
It is given that a men's total taxable income is Rs. 14,280.
He is charged by the state tax for 2% on the first Rs. 3000.
i.e. [tex]$2 \% \times 3000$[/tex]
[tex]$=\frac{2}{100} \times 3000$[/tex]
= Rs. 60
Then he is asked to pay 3% on the second Rs. 3000
i.e. [tex]$3 \% \times 3000$[/tex]
[tex]$=\frac{3}{100} \times 3000$[/tex]
= Rs. 90
Similarly, he pays 3% on the third Rs. 3000
i.e. [tex]$3 \% \times 3000$[/tex]
[tex]$=\frac{3}{100} \times 3000$[/tex]
= Rs. 90
Lastly, he pays 4% on the remaining amount. i.e 14,280 - (3000+3000+3000) = 14,280 - 9000 = Rs. 5280
∴[tex]$4 \% \times 5280 $[/tex]
[tex]$=\frac{4}{100} \times 5280$[/tex]
= Rs. 211.2
Thus the total amount of the income tax the man has to pay is
= 60+90+90+211.2
= Rs. 451.2
At 11:59 PM on December 31 the time square ball in New York city was 735 Feet above the ground one minute later it was 584 feet above ground which of the following gives the rate of change of the ball in feet per second
Answer:
2.52 ft. per second
Step-by-step explanation:
Only the smartest person in their math class can help me with this difficult problem!!!
Step-by-step explanation:
[tex] \tt{(5 {x}^{3} - 3x + 6) - (2 {x}^{2} - 4x + 8)}[/tex]
While subtracting , the sign of each term of second expression changes & remove the parentheses.
⟶ [tex] \tt{5 {x}^{3} - 3x + 6 - 2 {x}^{2} + 4x - 8}[/tex]
Combine like terms. Like terms are those which have the same base. Only coefficients of like terms can be added or subtracted.
⟶ [tex] \tt{5 {x}^{3} - 3x + 4x + 6 - 8 - 2 {x}}^{2} [/tex]
⟶ [tex] \tt{5 {x}^{3} + x - 2 - 2 {x}^{2} }[/tex]
In standard from , the expression should be written in such a way that the power of variables goes from highest to lowest.
[tex] \red{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \tt{5 {x}^{3} - 2 {x}^{2} + x - 2}}}}}}[/tex]
Hope I helped ! ♡
Have a wonderful day / night ! ツ
▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
Answer:
I'm the smartest person in my math class.
Step-by-step explanation:
While subtracting , the sign of each term of second expression changes & remove the parentheses.
⟶ 5x³-3x +6-2x²+4x-8
Combine like terms. Like terms are those which have the same base. Only coefficients of like terms can be added or subtracted.
⟶ 5x³-3x+4x+6-8-2x²
⟶ 5x³+x-2-2x²
In standard from , the expression should be written in such a way that the power of variables goes from highest to lowest.
3x^2-24x+50=0
help i write a test!!!
Answer:
2.8 i think
Step-by-step explanation:
Mark reduce the size of a photo to a height of 4 inches. What is the new width if it was originally 16 inches tall and 8 inches wide?
Answer:
Step-by-step explanation:
new height is ¼ of original height
new width = ¼×8 = 2 inches
Answer:
2 inches
Step-by-step explanation:
To find the new width, find the scale factor that was used to reduce the photo.
Since 16 divided by 4 is 4, 4 is the scale factor.
To find the new width, divide 8 by 4:
8/4
= 2
So, the new width is 2 inches
The student council at Oxford High School is making T-shirts to sell for a fundraiser, at a price of $12 apiece. The costs, meanwhile, are $10 per shirt, plus a setup fee of $130. Selling a certain number of shirts will allow the student council to cover their costs. How many shirts must be sold? What will the costs be?
Answer:
Number of shirts to breakeven = 65 shirtsCost of breakeven shirts = $650Step-by-step explanation:
First find the profit they will make from each shirt:
= Selling price - Cost price
= 12 - 10
= $2
They need to cover the cost of setting up which is $130. The number of shirts to sell given a profit of $2 from each shirt is:
= 130 / 2
=65 shirts
Cost of selling 65 shirts:
= 65 * 10 per shirt
= $650
275 students brought their lunch. Which was 25% of the students. How many students went on the trip?
Answer:
1,100
Step-by-step explanation:
Wow that's a lot of students. Anyway, 25% is one fourth of the 100%, so we multiply 275 by 4 and we get 275.
fin the value of x inthe figure below
what is the interest on RS. 1000 at 10 p.c.p.a for 1 year.
Answer:
Interest wil be 10% of 100 which is 10
So, interest will be Rs.10
And total amount to be payed will be 100+10 which is Rs.110
Answer:
Interest= Rs. 10
Step-by-step explanation:
Interest of Rs.100 on 10 p.c.p.a is 10% of 100
i.e., 100*10/100 = 10
Thus we have 10 as the interest
The diameter of a circle is 14km. What is the circles circumference?
Answer:
Step-by-step explanation:
c=d[tex]\pi[/tex]
c=14x3.14
c=43.96
angles and triangles
Answer:
x=120
y=60
z=60
Step-by-step explanation:
ill give 18 points!! please help me :))
Answer:
Step-by-step explanation:
3. 10x + 6 = 8x
8x = 10x + 6
-2x = 6
x = -3
4. y = 8(1) - 5= 8 - 5 = 3
y = 8(2) - 5 = 16 - 5 = 11
y = 8(5) - 5 = 40 - 5 = 35
y = 8(0) - 5 = 0 - 5 = -5
y = 8(-1) - 5 = -8 - 5 = -13
[tex]10x + 6 = 8x[/tex]
[tex]6 = 8x - 10x[/tex]
[tex]6 = - 2x[/tex]
[tex]6 \div - 2 = x[/tex]
[tex] - 3 = x[/tex]
Number 4 :[tex]y = 8x - 5[/tex]
When [tex] x = 1, y = \bold{ 3} [/tex]
[tex]y = (8 \times 1)- 5[/tex]
[tex]y = 8 - 5[/tex]
[tex]y = 3[/tex]
When [tex] x = 2, y = \bold{ 11} [/tex]
[tex]y = (8 \times 2)- 5[/tex]
[tex]y = 16 - 5[/tex]
[tex]y = 11[/tex]
When [tex] x = 5, y = \bold{35} [/tex]
[tex]y = (8 \times 5)- 5[/tex]
[tex]y = 40 - 5[/tex]
[tex]y = 35[/tex]
When [tex] x = 0, y = \bold{-5} [/tex]
[tex]y = (8 \times 0)- 5[/tex]
[tex]y = 0 - 5[/tex]
[tex]y = - 5[/tex]
When [tex] x = -1, y = \bold{-13} [/tex]
[tex]y = (8 \times - 1)- 5[/tex]
[tex]y = - 8 - 5[/tex]
[tex]y = - 13[/tex]
Some help ppplllsssss
Answer:
the answer is b
Step-by-step explanation:
Side Angle Side
Given f(x) = -3x + 5, solve for x when f(x) = -4
Answer:
3
Step-by-step explanation:
Given
f(x) = - 3x + 5
f(x) = - 4
-3x + 5 = - 4
- 3x = - 4 - 5
- 3x = - 9
x = 3
Hope it will help :)
Answer:
x=3
Step-by-step explanation:
i believe it's like this, i am not sure
Y= -3x +5
-4= -3x+5
subtract 5 on both sides
-9= -3x
divide -3 on both sides
x=3
Hi! Please without looking it up I am doing my writing and speaking test for Spanish and I'm trying to figure out what is "Then" in Spanish...Mind you they use translator detectors so please don't look it up and just help me with it. This is the sentence "There are more tables in the kitchen then in my room." I literally just need to know what "Then" is in Spanish! Thank you!
Answer:
The sentance you but then would be than which would be Hay más mesas en la cocina que en mi habitación but the word then would be entonces and example sentance is entonces iré allí which is then i will go over there
and than is que, an example sentace en lugar de que yo vaya allí which is rather than me going over there
Step-by-step explanation:
Answer:
Hi Alycia! The answer to your question is Hay más mesas en la cocina que en mi habitación
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☁Brainliest is greatly appreciated!☁
Hope this helps!!
- Brooklynn Deka
xD
PLEASE HELP ME ASAP!!!!!! USE THIS LINK I WILL GIVE BRAINLEAST
https://brainly.com/question/21436005
Answer:
okie
Step-by-step explanation:
Answer:
Ok
Step-by-step expl
The ratio of the length to the width of the rectangle is 10:6. Of the perimeter of the rectangle is 160 meters, find the measure of the width. Show your work
Answer:
60 meters, see explanation.
Step-by-step explanation:
We know that the ratio of length : width is 10 : 6. So for every 10 meters of length, we also have 6 meters of width. This problem is much easier since we are given the P = 160 meters.
You can see that if we multiply the ratio by ten, we get 100 : 60, where 100 + 60 = 160 total meters. From here, it is clear that the width would be 60 meters.
In the diagram of circle M shown, the measure of major arc PRQ=268 . Which of the following
is the measure of angle PRQ ?
Step-by-step explanation:
The Answer is 46
The measure of Arc PRQ is 268. Another part of the arc is PQ. PRQ+PQ forms a full circle In which a circle has 360 degrees. Using that
[tex]268 + x = 360[/tex]
[tex]x = 92[/tex]
Since we are asked to the measure of PRQ and it is inscribed in arc PQ. It is half of PQ so the answer is
[tex]92 \div 2[/tex]
which is 46.
Olivia does chores every Saturday morning. She spends of her time cleaning her room. Of the remaining of her time, she spends of it cleaning the kitchen. How much of Olivia's total time does she spend cleaning the kitchen?
Answer:
4/7 of her total time cleaning the kitchen
Step-by-step explanation:
Olivia does chores every Saturday morning. She spends 1/3 of her time cleaning her room. Of the remaining 2/3 of her time, she spends 6/7 of it cleaning the kitchen. How much of Olivia's total time does she spend cleaning the kitchen?]
Let
x = her total time
Room cleaning = 1/3x
Time remaining = 2/3x
Of the remaining 2/3 of her time, she spends 6/7 of it cleaning the kitchen.
Kitchen cleaning = 6/7 of 2/3x
= 6/7 * 2/3x
= (6*2)x/(7*3)
= 12/21x
= 4/7x
Olivia spent 4/7 of her total time cleaning the kitchen