1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
fomenos
3 years ago
10

The sum of the first 5 terms of an AP is 30 and the sum of the four term from T6 to T9 (inclusive) is 69. Find the AP​

Mathematics
1 answer:
Ainat [17]3 years ago
7 0

Answer: The AP = 1, ⁷/₂, 6, ¹⁷/₂, 11 ..............

Step-by-step explanation:

From the first statement,

S₅ = ⁵/₂(2a + ( n - 1 )d }    = 30

       5(2a  + 4d )d           = 60

       10a    + 20d             = 60

reduce to lowest term to easy calculation by dividing through by 10

                      a + 2d       = 6 -----------------------------------1

second statement

sum of the next 4 terms inclusive

T₉  = ⁹/₂(2a + 8d )   = 69

        9(2a  + 8d )    = 30 + 69

            18a + 72d   = 99 x 2

            18a + 72d   = 198

divide through by 18 to reduce to lowest time

                a  + 4d    = 11 ------------------------------------------2

Now solve the two equation simultaneously to find a and d

                 a + 2d = 6

                 a + 4d = 11

                     -2d  = -5

                          d = ⁵/₂.

Now substitute  for d to get a

               a  + 2(⁵/₂) = 6

                a + 5       = 6

                           a   = 6 - 5

                            a = 1.

Therefore the AP = 1 , ⁷/₂ , 6 , ¹⁷/₂ , 11 , ..............

You might be interested in
Students in an introductory statistics course were asked the following questions as part of a class survey:(1) What is your gend
11Alexandr11 [23.1K]

Answers:

Gender = categorical, nominal variable

Sleep length = numerical, continuous

Bedtime = categorical, ordinal

Number of countries visited = numerical, discrete

Scale of dreading semester = categorical, ordinal

=========================

Explanation:

Gender is categorical because there are two categories or labels, male or female. It is nominal because we simply attach names to each label and we can't sort them or order them from highest to lowest. There is no ranking for gender.

Sleep length is numerical as it deals with numbers. I put continuous because someone could write 2.5 hours or 3.75 hours. If whole numbers are only allowed, then the variable would be discrete.

The bedtime portion is categorical as each time slot is a category. Like with the first part, they are simply labels. We can order them however from earliest to later on, which is why this variable is ordinal.

The number of countries visited is numeric as expected, and it's also discrete because we can't visit 0.1 of a country. By "visit", I mean step foot in any part of the country for any length of time. It does not mean you have to explore every square inch of the territory.

The last part is categorical and ordinal. The scale ranking is ordered for us from 1 to 5. Despite the fact we have numbers here, the data is not numerical as the numbers 1 through 5 represent labels of "very little" through "a lot".

5 0
3 years ago
Hank estimate the width of the door to his classroom in feet. what is the reasonable estimate
lubasha [3.4K]
A reasonable estimate would be an estimate of 2.5 feet.
 
7 0
3 years ago
HELP PLEASE<br> I WILL GIVE BRAINLIEST
Olegator [25]

Answer:

<h2>B</h2>

I hoped this helped :))

6 0
3 years ago
Read 2 more answers
Lily has walked 2 miles. Her goal is to 6 miles. Lily plans to reach her goal by walking 3 miles each hour h for the rest of her
suter [353]

Step-by-step explanation:

if she did that she would have walked 36 miles multipy all of the numbers and theres ur answer i think i am so tired so if its wrong i am sooo sorry i havent slept in two days.... hope u have a better day than mine

4 0
3 years ago
I dont understand what the question is asking me​
kipiarov [429]

Answer:

\huge\boxed{\sf

Step-by-step explanation:

∠E = 1/2 (mCD - mAB)

<u>Where mCD = 110° and mAB = 30°</u>

∠E = 1/2 (110° - 30°)

∠E = 1/2 (80°)

∠E = 40°

\rule[225]{225}{2}

Hope this helped!

<h3>~AH1807</h3>
6 0
3 years ago
Other questions:
  • A recipe calls for 2 tablespoons of seasoning for every 7 pieces of chicken. For the family picnic, Joel is making 84 pieces of
    15·2 answers
  • What is the solution to the equation 3/5(x+4)=1.04
    12·1 answer
  • What is the greatest common factor of 24,60 and 36
    8·2 answers
  • Owen measured a line to be 17.9 inches long. If the actual length of the line is 17.8 inches, then what was the percent error of
    11·2 answers
  • In this graph, the y-intercept of the line is( )
    8·1 answer
  • 80 has how many significant digits?
    5·2 answers
  • What is the quotient of −42 and −6?
    6·2 answers
  • What percent of 50 is 36?
    12·2 answers
  • 2 in.<br> 2 in.<br> 2 in.<br> Fine the area
    8·1 answer
  • What is 6x+12+18=180 what is x
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!