Answers
Answer:
See Below.
Step-by-step explanation:
The sum of an A.P. is given by:
[tex]\displaystyle S_n=\frac{n}{2}(a+x_n)[/tex]
Where n is the number of terms, a is the initial term, and xₙ is the last term.
Therefore:
[tex]\displaystyle S_{30}=\frac{30}{2}\Big(a+x_{30}\Big)=15(a+x_{30})[/tex]
And likewise:
[tex]\displaystyle S_{20}=\frac{20}{2}\Big(a+x_{20}\Big)=10(a+x_{20})\\\\ S_{10}=\frac{10}{2}\Big(a+x_{10}\Big)=5(a+x_{10})[/tex]
Substitute:
[tex]15(a + x_{30}) = 3(10 (a + x_{20}) - 5(a + x_{10} ))[/tex]
Distribute:
[tex]15a+15x_{30}=30a+30x_{20}-15a-15x_{10}[/tex]
Simplify:
[tex]15x_{30}=30x_{20}-15x_{10}[/tex]
Simplify:
[tex]x_{30}=2x_{20}-x_{10}[/tex]
The nth term for an A.P. is:
[tex]x_n=a+d(n-1)[/tex]
Where a is the initial term and d is the common difference.
So, it follows that:
[tex]x_{30}=a+d(30-1)=29d+a\\ x_{20}=a+d(20-1)=19d+a\\ x_{10}=a+d(10-1)=9d+a[/tex]
Therefore:
[tex]29d+a=2(19d+a)-9d-a[/tex]
Which follows that:
[tex]29d+a=38d+2a-9d-a\\ \\ 29d=29d \\\\ d\stackrel{\checkmark}{=}d[/tex]
QED.
Related Questions
In your own words, how would you define slope?
Answers
Answer:
Slope
Step-by-step explanation:
Slope is the 'steepness' of the line, also commonly known as rise over run. We can calculate slope by dividing the change in the y-value between two points over the change in the x-value.
Answer:
and Mathematics this soap or gradient of a line is a number that describes both the direction and the steepness of the line assault with a greater absolute vinyl indicates a steeper line the direction of a line is either increasing decreasing or horizontal or vertical
Find the perimeter of a triangle with Side A = 2 cm, Side B = 3 cm, and Side C = 5 cm.
Answers
Answer:
gusto Kita Alam muba
Step-by-step explanation:
gusto Kita ok lang ba I don't know what is the answer
Increase 400 litres by 20%
Answers
Answer:
400 Liters increased by 20 percent is 480 Liters.
Store A cost $6 for 3 boxes. Store B costs $5 for 2 boxes. Which store has the better deal? How do you know? please hurry
Answers
Hi there! Your answer to the problem would be Store A..
Step By Step Explainaction:
So we know that store A’s boxes cost $6 for each 3 boxes, and store be cost 5$ for 2 boxes.
Divide 6 with 3 since you want to know how much one would cost. 6 divide 3=6. Let check again by doing multiplication. 3x2 is also 6. This means that the cost for each box for Store A would be 2$.
Store B is the same but dividing 5$ with 2. 2x2=4 but we need to know 5. But 1 is actually .5 or 50% of 2. So it would be 2.5 or 2 and a remainder of 1. Same things...
So it would be Store A that gives cheaper cost. $2>$2.5
Given:
Store A costs $6 for 3 boxes. Store B costs $5 for 2 boxes.To find: Which store has the better deal.
Answer:
In order to do so, we'll need to divide the cost by the number of boxes to retrieve the cost of 1 box. The store with the lowest price for 1 box will have the better deal.
Let's first see what a box costs in Store A.
[tex]\sf \dfrac{Cost}{Number\ of\ boxes}\ =\ Cost\ of\ one\ box\\\\\\\dfrac{6}{3}\ =\ 2[/tex]
At Store A, the cost of a box is $2.
Now let's see what a box costs in Store B.
[tex]\sf \dfrac{Cost}{Number\ of\ boxes}\ =\ Cost\ of\ one\ box\\\\\\\dfrac{5}{2}\ =\ 2.5[/tex]
At Store B, the cost of a box is $2.5.
Since the cost at Store B seems to be a slightly higher price, Store A has the better deal.
Hope it helps. :)
Answer right to get points
Answers
Answer:
C) -1 7/12
Step-by-step explanation:
-6 1/3 divided by 4=-19/12
reduce:
-1 7/12
Jada and Priya are trying to solve the equation 2/3+x=4
Jada says, “I think we should multiply each side by 3/2 because that is the reciprocal of 2/3."
Priya says, “I think we should add -2/3 to each side because that is the opposite of 2/3."
1. Which person's strategy should they use?
2. Explain your reasoning.
Answers
Answer:
Priya is correct. Because 2/3 is being added to x and not multiplied, then subtracting 2/3 from both sides is the correct action.
Step-by-step explanation:
Let's run through solving it that way:
2/3 + x = 4
2/3 - 2/3 + x = 4 - 2/3
0 + x = 4 - 2/3
x = 4 - 2/3
x = 10/3
Three more than a number is
sixty.
(Write the equation
Answers
Answer:
x + 3 = 60
Step-by-step explanation:
Let the number be x
x + 3 = 60
Hope it helps :)
Please mark my answer as the brainliest
Find three ways that you can make the sum of 7/4
Answers
Answer:
1. use fractions
3/4+4/4= 7/4
2. use decimals
0.75+1.00= 7/4
3. find equivalent fractions
3/4= 75/100
4/4= 100/100
75/100+100/100= 175/100
The three ways that in which the sum 7/4 is found are -
1/4 + 6/4 = 7/45/4 + 2/4 = 7/43/4 + 4/4 = 7/4What is the definition of the fraction?Fractions are categorized as a mathematical value that represents a portion of a whole. A fraction is a portion or segment of any quantity taken from the whole, which can be such a number, a fixed number, or a thing.Proper fractions are those whose numerator is less than the denominator. Proper fractions include 5/7, 3/8, and so on.An improper fraction is one where the numerator is greater than or equal to the denominator. It is always equal to or greater than that of the total. For instance, 4/3, 5/2, and so on.For the given question, the given number is 7/4.
This number can be formed in ways as;
1/4 + 6/4 = 7/45/4 + 2/4 = 7/43/4 + 4/4 = 7/4Thus, three ways that in which the sum 7/4 is found are made.
To know more about the fraction, here
https://brainly.com/question/17220365
#SPJ2
1. What is the last step in constructing an angle?
Help please
For 30 points!!!
Answers
Answer:
The second choice. Connect the endpoint and the mark at the angle measure.
Step-by-step explanation:
Answer:
Connect the endpoint and the mark at the angle measure.
Step-by-step explanation:
what is the circumference of a circle with a radius of 4 inches use 3.14 as Pi
Answers
Answer:
C= 25.12
Step-by-step explanation:
c=2pir
so you plug n chug by putting in c=2 times 3.14 times 4
which gives you the answer of 25.12
Match each of the equations with their corresponding graph
Answers
Answer:
equation a and graph E
equation b and graph a
equation c and graph b
equation d and graph D
Step-by-step explanation:
Deborah spent $70 on food and clothes. She spent $26 more on clothes than on food. On your worksheet, solve the question and write your answer below. How much did she spend on food? How much did she spend on clothes?
Answers
Answer:
food : 22
clothes : 48
Step-by-step explanation:
70 - 26 = 44
44 divided by 2 = 22
22 + 26 = 48
70 - 48 = 22
100 POINTS AND BRAINLIEST PLEASE HURRY!
Which of the following sentences uses the word "embolden" correctly?
Jimmy was scared and emboldened by the ghost.
Jenny’s stressful day at school emboldened her to go to bed early.
Jenny’s initial success off the high-dive emboldened her to try again.
Jimmy emboldened the text in order to make it stand out on the page.
Answers
Answer:
Jenny’s initial success off the high-dive emboldened her to try again.
Step-by-step explanation:
embolden means to give (someone) the courage or confidence to do something or to behave in a certain way.
Answer:
I believe the correct answer is C, ‘Jenny’s initial successs off the high-dive emboldened her to try again.’
This is because the word ’bold’ basically means to be without fear.
I hope this helps you some! Have a good rest of your day/night!
Solve: 2(3x-4)(x+5)=0
Answers
Answer:
x= 4/3 or x=−5
Step-by-step explanation:
A triangle has sides with lengths of 6 meters, 8 meters, and 10 meters. Is it a right triangle?
Answers
Answer:
No
Step-by-step explanation:
becuase no
Solve the equations: √y^6=-y^3
Answers
Answer:
√y^6=-y^3
y^6/2=-y^3
y^3+y^3=1
2y^3=1
y^3=1/2
y=
[tex] \sqrt[3]{1 \div 2 } [/tex]
use the gcf and distributive property to express 21+24
Answers
Answer:
3
hope it's helpful ❤❤❤
THANK YOU❤
Answer:
3(7 + 8) is a factored form
Nijah has 45 stickers
she gives 2/5 to her sister and
the remaining 1/3 to brett
how many dose she have left ?
Answers
Answer: 6
Step-by-step explanation:
how many significant figures are in 2856.110
Answers
♀️♀️♀️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Can someone pls answer this
Answers
Answer:
a) 148°
b) 35.35 cm squared
Step-by-step explanation:
a)
[tex]\alpha =2tan(\frac{14}{4} )^{-1} =148[/tex]
b)
[tex]A=4*14-\frac{\pi 4^{2}*148 }{360} =35.35cm^{2}[/tex]
The traffic lights at three different road crossings change after every 48 seconds, 72
seconds and 108 seconds respectively. If they change simultaneously at
7 a.m., at what time will they change simultaneously again?
please tell step by step
Answers
Answer:
7 : 7 : 12 am
Step-by-step explanation:
This question pretty much requires us to obtain the lowest number that is common to all three times. The qay to obtain this is by finding the LCM of all three numbers.
This is given as;
48 = 2 × 2 × 2 × 2 × 3
72 = 2 × 2 × 2 × 3 × 3
108 = 2 × 2 × 3 × 3 × 3
The LCM is = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432 seconds.
Converting to minutes by dividing by 60, the time is = 432 ÷ 60 min = 7 min 12 sec
The next time they would change simultaneously is; 7am + 7 min 12 sec = 7 : 7 : 12 am
7W + 5 + 6 + 3w
Just help me pleAsee
Answers
Answer:
the answer is 10w + 11
Kinda confused on this one so it would be helpful to answer this for 30 points! And marked!
Answers
Answer:
acute
Step-by-step explanation:
straight is just a straight line, 180 degrees perhaps
right is exactly 90 degrees
obtuse is over 90 degrees
I will give Brainliest !
Answers
Answer:i believe it’s A
Step-by-step explanation:
4,5,3 are almost the same and almost the same rotation just letters are different
Part
The point (-3, 6) is on a line with a slope of 4. What are all the points you would also find on the line.
Answers
Step-by-step explanation:
THANK YOU AND PLZ MARK AS BRAINLY AND GIVE RATING ALSO
Help!!Suppose f (x) = x-4. Find the graph of
3/4 f(x)
Answers
Answer:
Jcjdhdydifcjxjdfvb graph1
if An atom has 10 protons, 11 neutrons, and 9 electrons. What is the atomic number of this atom?
A) 9
B) 10
C) 11
D) 21
Answers
Answer:
B
Step-by-step explanation:
Atomic number is equal to the number of protons in an atom.
Please answer quick!
Which segment is the image of Line segment A B reflected across the line y = negative 2?
On a coordinate plane, segment A B goes from (2, negative 7) to (8, negative 3), segment J K goes from (2, 7) to (8, 3), segment G H goes from (2, 3) to (8, negative 1), segment F A goes from (negative 4, negative 3) to (2, negative 7), and C D goes from (negative 8, negative 3) to (negative 2, negative 7).
A.)Line segment A F
B.)Line segment D C
C.)Line segment G H
D.)Line segment J K
Answers
Answer:
C on edge 2021
Step-by-step explanation:
Answer: GH
Step-by-step explanation:
Is y=2x - 5 proportional?
Answers
Answer:
yes
Step-by-step explanation:
Because it is the answr
I WILL GIVE BRAINLIEST TO WHO WRITES THE STEP(WORK) DOWN! NOT JUST AN ANSWER!!!
x/4 < −1.5
Answers
Answer:
x < -6
Step-by-step explanation:
[tex]\frac{x}{4} < -1.5[/tex]
to isolate x, multiply both sides by 4
[tex](4) \frac{x}{4} < -1.5 (4)[/tex]
which gives you:
x < -6