Is it possible to have more than one arithmetic series with four terms whose sum is 44? Explain.
Answers
Answer:
Yes it is.
Step-by-step explanation:
Let the AP be a, a+d, a+2d, a+3d and so on, then
4a + 6d = 44 which gives
a = (22–3d)/2 = 11 -1.5d
Assume that the AP has n terms, then nth term is given as :
a + (n-1)d = 11 - 1.5d + (n-1)d = 11 - (n-2.5)d
The second equation then becomes:
(11 - 1.5d)(n-2.5d) = 140
which simplifies to
42n -110d - 6nd + 15d^2 = 560 or put simply
6n = 15d -5 - (5 * 7 * 17)/(d-7)
As n is an integer, so must be 6n and therefore so must be (5*7*17)/(d-7) which means d = 12, 14 or 24
which gives 6n = 56, 120 and 320 respectively.
Again as n is an integer, the only possible answer is n = 20, which occurs when d = 14 and a is -10 which gives us the series -10, 4, 18, 32 .. 256
The terms be a-3d,a-d, a+d,a+3d
Sum = 4*a = 44.
a = 11;
Product
( a-3d)(a+3d) = 140
11*11- 9*d*d = 140
d*d = - 19/9.
Negative. No real common difference.
The meaning of ‘ extreme' is important.
The AP has more than four terms.
a,a+d,a+2d,a+3d,….,a+(n-1)d.
Sum condition
4a + 6d = 44
2a + 3d = 11 eqn-1
Answer:
Yes, look at the picture I attached for explanation
Step-by-step explanation:
Related Questions
Need help on this Its almost summer need to pass :D
Answers
Answer:
3
Step-by-step explanation:
8*3 + 8*3
(24) + (24) = 48
8*6 = 48
Five-sixths of Paco's stamps have pictures of animals.
How many stamps with pictures of animals does Paco have? Use the table to answer the question.
Paco has____ stamps with pictures of animals.
Answers
Answer:
20
Step-by-step explanation:
fraction of stamps that has animals on it x total number of stamps paco has = pictures with animals on it
(5/6) x 24 = 20
During a marathon, Jane ran 6 miles. Jessica ran 5.068 miles. How many more miles did Jane run than
Jessica?
Answers
Answer:
0.932 miles
Step-by-step explanation:
To find out the difference we subtract
6 - 5.068 = 0.932
Add the units (miles)
0.932 miles
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
0.9 miles
Step-by-step explanation:
Solve
Given:
Jane = 6 miles
Jessica = 5.068
To find: How many more miles did Jane run than Jessica
Which is simply the difference between both miles.
So,
6 - 5.068 = 0.932
In the nearest tenths, Jane ran 0.9 miles more than Jessica.
ILL GIVE BRAINLEST, Find the value of x.
Answers
Answer:
x=6, y=128
set 5x+16 = 7x+4
-2x=-12
x=6
plug x into equation= 46
180-46=134
y+6=134
y=128
Answer:
x= 45 Degrees
Step-by-step explanation:
Total Triangle= 180 Degrees
Subtract Right Angle: 180-90= 90 Degrees
Divide by 2 because it is an isosceles triangle: 90/2= 45 Degrees
Find the length of the third side right triangle
Answers
12^2 + 9^2 is 225
15^2 is 225
therefore 12^2+9^2=15^2
Find the value of x, y, and z
Answers
Answer:
x=180-43-59=78
y=180-78=102
z=78-49=29
Step-by-step explanation:
water tank is being filled with water. Before water is pumped in, the water level in the tank is 12 inches high. After 20 minutes, the water level is 54 inches high.
If t represents the time in minutes and h represents the water level, which of the following equations can be used to model this situation?
A. H = 42 + 12t
B. H = 2.1t - 12
C. H = 12t + 2.1
D. H = 2.1t + 12
Answers
Answer:
D. H = 2.1t + 12
Step-by-step explanation:
Let us assume the t be the time in minutes
And h be the water level
Now before reaching to the equation that need to be used
before this, determine the inches per minute i.e.
= 54 inches - 12 inches
= 42 inches in 20 minutes.
Now for per minute, it would be
= 42 inches ÷ 20 minutes
= 2.1 inches per minute
After this, multiply the inches per minute with the minutes t and add the sale to the beginning value i.e. 12
So the equation is
H = 2.1t + 12
hence, the last option is correct
Hey Everyone! How are y’all?! Well, my teacher wants me to type a presentation about Dubai. Some friends gave me some ideas. So far I have Animals, Famous Attractions, The Burj Khalifa and Favorite Foods. Anyone got more ideas for me?
Answers
Answer:
Hm. Seems like you have it covered... how about culture?
Step-by-step explanation:
Hope I helped a lil :)
Best of luck <3
Answer:
History
Dubai’s golden era began in 1966. Oil was found at the offshore Fateh field, which is also known as the Fath of Oil. At that time, even the brightest brains could not begin to imagine Dubai relishing in the opportunities that are present in Dubai today. Oil became the gateway to a brand new world. Although it wasn’t a gateway for the locals to connect outside of Dubai, it was a gateway for foreigners to come into Dubai.
Merely a half a century ago, all of these big edifices, businesses, and residential developments were not even thought to exist. It may be hard to believe, but the village was indeed replaced by a thriving city. In 1883, Dubai’s current leaders took control, and ruled the village. Back then, the most critical financial source was limited to pearl-fishing.
Step by step, the whole city was replenished by new buildings, modern edifices and high-end apartments. The number of residents and which is of more importance, tourists is still increasing, and thus the hotels, townhouses, penthouses and apartments for rent are of high demand. Today, when you look at the exceptional oasis created by Sheik Mohammed bin al-Maktoum, along with the crown prince, it is hard to believe that this was once a village with a limited source of finances.
Does it help?
Please someone help!5m^2 - 26m -24 =0
Answers
Answer:
roots are at -4/5 and 6
Step-by-step explanation:
(5m + 4)(m - 6) = 0
5m + 4 = 0
5m = -4
m = -4/5
m - 6 = 0
m = 6
Marven has a coupon that discounts the rental of a full-size car by $25. They decide to buy insurance for each day. If the cost is $465, how many days, d, will they rent the car? Write and solve an equation. If they still use the coupon, how many days could they rent the small car with insurance if they have $465 to spend?
Answers
Answer
it would take them 18.7 days. sorry if i get this wrong im learning this too
Step-by-step explanation:
Ms. Sandoval walked 2 miles a
day for 5 days. If she did this for
8 weeks, what was the total
amount of miles she walked?
Answers
Answer:
Step-by-step explanation:
since 5 has nothing to do with this question lets put the 5 aside and focus with the 2 miles and the 8 weeks.. if there is 7 days in a week and there is 8 weeks that is 56 days in total.. multiply by 2 miles per day would equal...
i believe (112)
A picture frame is 9 inches by 12 inches, what is the area of the picture frame?
Answers
Answer:
108 inches
Step-by-step explanation:
What is the solution for the system of equations? y=2x+7y=−4x−5 Question 1 options: (−2, 1) (1, −2) (3, −2) (−2, 3)
Answers
Answer:
Answer Below \/
Step-by-step explanation:
Answer:
(-2,3)
Step-by-step explanation:
Pls answer this ASAP giving brainliest to first person
Answers
Answer:
2 cm^3
Step-by-step explanation:
4/5 x 3/2 x 5/3 = 2
Hope this helps!
Answer:
4/5 x 5/3 x 3/2 = 2cm3
Step-by-step explanation:
The 3 is the unit
Lisa makes 35 dollars per month babysitting . She spends 25% of what she earns on entertainment. How much does she spend on entertainment.
1. 4.50$
2. 8.75$
3. 10.00
4. 25.00$
Answers
Brandon observes a marble travel along a horizontal path at a constant rate. The
marble travels z of the length of the path in 30 seconds. At that rate, how many
seconds does it take the object to travel the full length?
First, reason down from ſ to 3. Enter all values as fractions
(proper or improper) or whole numbers. You will need to
convert mixed numbers to improper fractions.
seconds
0
O
2/3
full lengths
Answers
Answer:
you really shouldn't put your name on the internet like that
Step-by-step explanation:
Pls help me, i need the answer rn. Please, ty. (dont scam ;-;)
Answers
The point P = (2/5, y) lies on the unit circle shown below. What is the value of y in
simplest form?
Answers
Using the unit circle, it is found that the value of y is given by:
[tex]y = \pm \frac{\sqrt{21}}{5}[/tex]What is the unit circle?The unit circle is a circle centered at the origin with radius 1, hence, it's equation is given by:[tex]x^2 + y^2 = 1[/tex]
At point P, we have that [tex]x = \frac{2}{5}[/tex], and hence, we have to find the value of y.
[tex]x^2 + y^2 = 1[/tex]
[tex]\left(\frac{2}{5}\right)^2 + y^2 = 1[/tex]
[tex]\frac{4}{25} + y^2 = 1[/tex]
[tex]y^2 = 1 - \frac{4}{25}[/tex]
[tex]y^2 = \frac{21}{25}[/tex]
[tex]y = \pm \sqrt{\frac{21}{25}}[/tex]
[tex]y = \pm \frac{\sqrt{21}}{5}[/tex]
To learn more about the unit circle, you can take a look at https://brainly.com/question/16852127
In triangle ABC, AB = 5 inches and BC = 3 inches. Which of the choices represents all possible values for AC, inches?
- 3 < AC < 7
- 3 ≤ AC ≤ 7
- 2 < AC < 8
- 2 ≤ AC ≤ 8
Answers
Answer:
-2 < AC < 8
Step-by-step explanation:
The last side has to be less than the sum of the other 2 sides, or less than 8. The only answer choice with this is the 3rd one.
Find the perimeter and area of each quadrilateral.
Answers
Liza is building a storage container in her basement.
The container will have two sections that are connected.
How many cubic foot boxes can she store in the container?
Enter your answer in the box.
6 ft
2 ft
6 ft
8 ft
2 ft
6 ft
Answers
Answer:
312
Step-by-step explanation:
Box (1). 2*2*6=24
Box(2). 6*8*6=288
24+288= 312
In how many ways can a committee of three men and three woman be formed from a group of ten men and nine woman?
A committee of three men and three woman can be formed from a group of ten men and nine woman in _________ different ways.
Answers
Answer:
multiply ur options, so 9x10= 90
Step-by-step explanation:
5/6 x 2/7
please help me again
Answers
Answer:
[tex] \frac{5}{6} \times \frac{2}{7} \\ = \frac{5 \times 2}{6\times 7} \\ = \frac{10}{42} [/tex]
How many more orders for cheese were
for 3/4 pound or less than for 1 pound or
more?
Answers
Answer:
1 whole pound silly
Step-by-step explanation:
Answer:
Its 8
Step-by-step explanation:
please help me with this
Answers
Answer:
Your answer is 1/10
Step-by-step explanation:
The ratio of strawberries to bananas in a smoothie recipe are shown in the graph below.
Which table shows the same data?
Answers
Answer: The last table is the correct answer.
Step-by-step explanation: The ratio is 6 strawberries to 1 banana.
The ratio of strawberries to bananas in a smoothie recipe is; 6 strawberries to 1 banana. The last table is the correct answer.
How to obtain real measurements from the ratio of two measurements?Suppose the real measurements were "a" and "b"
Then their ratio will be formed as
[tex]\dfrac{a}{b} = \dfrac{p \times x}{q \times x} = \dfrac{p}{q}[/tex]
where is a common factor (not 1)
This shows that to get the real measurements from the given ratio, we need to assume to have some factor possibly cancelled from both the numerator and the denominator.
Thus, a = px, b = qx
Noted that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.
The ratio 6 strawberries to 1 banana.
6 :1
The ratio of strawberries to bananas in a smoothie recipe is; 6 strawberries to 1 banana. The last table is the correct answer.
Learn more about ratio here:
brainly.com/question/186659
#SPJ2
how much it must decrease 65432 to reach 100000
Answers
Answer:
165432
Step-by-step explanation:
165432 - 65432 = 100000
The Cohens found 8 pairs of shorts with the following prices:
$10, $11, $11, $16, $16, $17, $18, $38
Which statements about the prices are true? Select all that apply.
The median is $16.
The range of the prices is $28.
The interquartile range is between $6 and $7.
If the price that is the farthest from the mean is removed, the median will change.
If the price that is farthest from the mean is removed, the mean will become larger.
Answers
Answer:
the range of the prices is $28
Step-by-step explanation:
the range is 38-10 so it’s 28
Oscar Corporation is planning to construct an elliptical gate at its headquarters. The width of the ellipse will be 5 feet across and its maximum height along the center will be 3 feet. The company wants to place two bright spots at the foci of the ellipse. How far from the center of the ellipse will the spots be located?
Answers
Answer:
A: 2 Feet
Step-by-step explanation:
Got it right
The distance from the center of the ellipse to where the spots are located will be B. 2 feet.
How to calculate the distance?From the information given, the The width of the ellipse will be 5 feet across and its maximum height along the center will be 3 feet.
The distance from the center of the ellipse to where the spots are located will be:
= 5 - 3
= 2 feet.
Learn more about distance on:
https://brainly.com/question/2854969
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Question
The estimated fuel economy of a car is 27 miles per gallon (mpg), but your friend
who has this car says she gets only about 24 mpg. Explain how both of these
statements can be correct.