Given:
The first two terms in an arithmetic progression are -2 and 5.
The last term in the progression is the only number in the progression that is greater than 200.
To find:
The sum of all the terms in the progression.
Solution:
We have,
First term : [tex]a=-2[/tex]
Common difference : [tex]d = 5 - (-2)[/tex]
[tex]= 5 + 2[/tex]
[tex]= 7[/tex]
nth term of an A.P. is
[tex]a_n=a+(n-1)d[/tex]
where, a is first term and d is common difference.
[tex]a_n=-2+(n-1)(7)[/tex]
According to the equation, [tex]a_n>200[/tex].
[tex]-2+(n-1)(7)>200[/tex]
[tex](n-1)(7)>200+2[/tex]
[tex](n-1)(7)>202[/tex]
Divide both sides by 7.
[tex](n-1)>28.857[/tex]
Add 1 on both sides.
[tex]n>29.857[/tex]
So, least possible integer value is 30. It means, A.P. has 30 term.
Sum of n terms of an A.P. is
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
Substituting n=30, a=-2 and d=7, we get
[tex]S_{30}=\dfrac{30}{2}[2(-2)+(30-1)7][/tex]
[tex]S_{30}=15[-4+(29)7][/tex]
[tex]S_{30}=15[-4+203][/tex]
[tex]S_{30}=15(199)[/tex]
[tex]S_{30}=2985[/tex]
Therefore, the sum of all the terms in the progression is 2985.
What are the slope and y-intercept of the graph of y =(-1/3)x + 1
Answer:
[tex]slope \: = - \frac{1}{3} x \\ y - interept \: = \: 1[/tex]
Step-by-step explanation:
Hope this helps!
what is the average number of a question
Answer:
Overall, across all grades and subjects, the average test question count is 10, the second favorite number of questions is 5. A major contributor in determining the question count for an assignment is its assessment type.
Hope I helped!! If I did please give brainliest because I cant level up without having 1 more ;(
<3 Enjoy,
Dea
Answer:
that's so ez
Step-by-step explanation:
but idc.......!!!!!!!!
What is Mario's cycling rate?
miles per hour
Answer:
7 miles per hour
21/3=7
14/2=7
7/1=7
Step-by-step explanation:
Answer:
the answer is 7 miles per hour
hey
please solve
it's really easy
Answer:
(2x + 1)×3 = 1×(3x+4)
6x + 3 = 3x + 4
6x-3x = 4 -3
3x = 1
x = 1/3
Find the slope of the line graphed
Answer:
The slope is [tex]\frac{3}{5}[/tex] because if you do the rise over run method, it goes up 3 times and right 5 times, therefor being [tex]\frac{3}{5}[/tex].
Help please!!! This is worth 20 points of my grade
Answer:here’s number one hope I helped
Step-by-step explanation:
PLZZZZZZZ ANSWER ILL GIVE U BRAINLIEST
Mario is playing an online puzzle game. He has 50 points and earns 3 points for each puzzle he solves correctly. He will advance to the intermediate level if his score is over 80 points. Which inequality can Mario use to find how many more puzzles he must solve to advance to the intermediate level?
Answer:
y = 3x + 50
x = # of levels completed
Step-by-step explanation:
Answer:
The inequality 50 + 3x > 80 can be used by Mario to find how many more puzzles he must solve to advance to the intermediate level.
Step-by-step explanation:
Given that:
Points of Mario in online puzzle game = 50 points
Points earned for each puzzle solved correctly = 3 points
Points needed to advance to intermediate level = over 80 points
Let,
x be the number of puzzles needed to be solved by Mario to advance to next level.
Points Mario already have + Points for each puzzle * Number of puzzles > Points needed to advance
50 + 3x > 80
Hence,
The inequality 50 + 3x > 80 can be used by Mario to find how many more puzzles he must solve to advance to the intermediate level.
2. Tomatoes cost $0.70 per pound.
Weight (lb)
2.
6
co
Price ($)
1.40 2.10
Answer:
The answer is 45lb
Step-by-step explanation:
which is bigger 7/10 or 13/16
Answer:13/16
Step-by-step explanation:trust me bro
Answer:
13/16
Step-by-step explanation:
So what we want to do here is find the smallest common denominator. I personally find 160 the easiest to work with.
7x16=112(numerator for 7/10)
10x16=160(denominator)
This gives us the fraction 112/160.
13x10=130
16x10=160
This gives us the fraction
130/160
Therefore 13/16 is bigger.
Please mark brainliest!
What the answer to this
Answer:
it's a trick question, it's still (-9,0)
Step-by-step explanation:
Answer:
-9,0
Step-by-step explanation:
The rule is (x,y) to (x,-y)
Since -0 = 0 it is (-9,0)
Given f (x) = 3x² – 7x + 1, what is f(-3)?
Answer:
49
Step-by-step explanation:
f(-3)= 3(-3)² - 7(-3) + 1
= 3(9) - (-21) + 1
= 27 + 21 + 1
=49
notes: negative × negative = positive
The perimeter of a rectangle is 26 cm. The rectangle has a length of 8 cm. What is the width of the rectangle?
a) right an equation that can be solved using the distributive prop property.
b)Solve the equation
Answer:
A. 2(8)+2(w)=26
B. 16+2w=26
Subtract 16 from both sides of the equation
2w=10
Divide both side by 2
The width is 5
Step-by-step explanation:
NEED ANSWER ASAP-
What is the value of x?
Given:
The figure.
To find:
The value of x.
Solution:
In triangle HIJ, HJ is diameter of the circle.
[tex]\angle HIJ=90^\circ[/tex] [Thales's Theorem]
[tex]HI=IJ[/tex] [Given]
[tex]\angle IHJ=\angle IJH=x-42^\circ[/tex] [Base angles of isosceles triangles are equal]
Now,
[tex]\angle HIJ+\angle IJH+\angle IHJ=180^\circ[/tex] [Angle sum property]
[tex](90^\circ)+(x-42^\circ)+(x-42^\circ)=180^\circ[/tex]
[tex]2x+6^\circ=180^\circ[/tex]
[tex]2x=180^\circ-6^\circ[/tex]
[tex]2x=174^\circ[/tex]
Divide both sides by 2.
[tex]x=\dfrac{174^\circ}{2}[/tex]
[tex]x=87^\circ[/tex]
Therefore, the value of x is [tex]87^\circ[/tex].
Renee spent $15.50 on Amazon today and Alex spent $9.69. How much more did Renee spend than Adam
Answer:
$5.81
Step-by-step explanation:
15.50-9.69=5.81
Answer:
$5.81
Step-by-step explanation:
Subtract. Hope this helped you!! Do you have a calculator
100 POINTS PLEASE HURRY Brianna solved a two-step equation, but she made a mistake along the way.
0.1x + 3 = 1.7
(-3) + 0.1x + 3 = 1.7 + (-3) Line 1
0.1x = -1.3 Line 2
(-0.1) + 0.1x = -1.3 + (-0.1) Line 3
x = -1.4 Line 4
What mistake did Brianna make?
On Line 1, Brianna should have subtracted 3 instead of adding -3.
On Line 1, Brianna violated the addition property of equality.
On Line 3, Brianna should have divided by 0.1 instead of subtracting 0.1.
On Line 3, Brianna violated the addition property of equality.
Answer:
3rd row
Step-by-step explanation:
there were multiple mistakes there ngl but out of the amswers i saw it should be that brianna should habe divided
What should be done first to simplify: 122 – 15 – 5 – 1 + 6
Answer:
122-15-5-1
Step-by-step explanation:
122-15-5-1 is 101 which makes 101+6, in which the answer is 107.
Answer:
122-15-5-1=101+
101+6=107
Step-by-step explanation:
here are four cards 6 2 7 3
how do i solve the second question?
Answer:
276
Step-by-step explanation:
Answer:276
Step-by-step explanation:trust me bro
Robert is a high school basketball player. In a particular game, he made some three point shots and some free throws (worth one point each). Robert made a total of 9 shots altogether and scored a total of 23 points. Write a system of equations that could be used to determine the number of three point shots Robert made and the number of free throws he made. Define the variables that you use to write the system.
Answer:
let t = number of three-point shots
let f = number of free throw shots
Step-by-step explanation:
t + f = 9 (he made a total of 9 shots altogether)
3t + 1f = 23 (number of shots multiplied by their point value)
substitution method: t = 9 - f
3(9 - f) + f = 23
27 - 3f + f = 23
-2f = -4
f = 2
find 't': t + 2 = 9
t = 7
What is the value of x?
a.) 0.4 mi
b.) 6 mi
c.) 0.6 mi
d.) 4 mi
Answer:
0.6 or should be anyway.......
hope this helps you
Find the percent increase or decrease to the nearest percent.
From 14 books to 40 books
A. 65% increase
B. 186% increase
C. 186% decrease
D. 65% decrease
Answer:
A
Step-by-step explanation:
Rewrite the following equation in slope-intercept form
y - 4 = 3(x + 2)
Deanna will cook a turkey for about 15 minutes per pound of turkey.
If she bought an 11-pound turkey, how long should she cook it for, in minutes?
Answer:
165 minutes is how long it would take
Answer:
11×15
lbs× minutes per lbs
Leah and her children went into a restaurant and will buy hotdogs and tacos. She
must buy a maximum of 13 hotdogs and tacos altogether. Write an inequality that
would represent the possible values for the number of hotdogs purchased, h, and the
number of tacos purchased, t.
Answer:
The equation to solve this is: h + t is less than or equal to 13
Step-by-step explanation:
Margie's vegetable garden contains cucumbers, corn, potatoes, and tomatoes. About
of the garden consists of potatoes. What percent of the vegetables in Margie's
garden are NOT potatoes?
Answer:
60%
Step-by-step explanation:
2/5 to 100%
we have to make the bottom number equal 100
5*20=100
what we do to one side we have to do to the other when multiplying and dividing fractions
2*20=40
40/100
we're looking for the OTHER vegetables so subtract that from the total
100/100 - 40/100 =60/100 or 60%
Answer:
60%.....................
(20 PTS) WILL GIVE BRAINLIST
Answer:
-6
4
9
19
29
Step-by-step explanation
Plug the numbers into the x.
5(-2)+4
5(0)+4
5(1)+4
5(3)+4
5(5)+4
PLEASE HELP ME FOR 14 POINTS
Answer:
i got 34:34:112
Step-by-step explanation:
sorry im bad at explaining things but i added a picture
Answer:
34, 34, 112
Step-by-step explanation:
(6x+10)+(x + 17)+(4x-34) = 180
=> 6x+x+4x = 180 -27+34
=> 11x = 187
=> x = 17
6(17) + 10= 112
17+17 = 34
4(17) -34 = 68 - 34 = 34
Please mark Brainliest if this helps!
Charlie is mailing packages each small package costs hin $2.06 to send each large package costs him $4.30 how much will it costs him to send 7 small packages and 5 large packages
(-8)+(-6.9) PLSS HELPP MEEE
Answer:
-14.9
Step-by-step explanation:
just remove the parenthesis and add
Answer:
The answer would be -14.9.
Bob and Cheryl are taking a road trip that is 188.60 miles. Bob drove 1/4 of the total distance
How many miles did Bob drive?
Answer: 47.15 miles.
Bob drove 47.15 miles.
To find how much Bob drove simply divide the total distance 188.60 miles by 4.
188.60/4 = 47.15
150 adults complete a survey 80 are women the ratio of men and women in its simplest form
Answer:
Step-by-step explanation:
150 - 80 equals 70
70:80 = 7:8
please give me brainliest, I'm going to cry if you don't >:(
