[tex]\underline{\underline{\large\bf{Given:-}}}[/tex]
[tex]\red{\leadsto}\:[/tex][tex]\textsf{} [/tex][tex]\sf Number \: of \:terms \: in \: A.P,n = 30[/tex]
[tex]\red{\leadsto}\:[/tex][tex]\textsf{} [/tex][tex]\sf Fourth \: term ,a_4 = 11 [/tex]
[tex]\red{\leadsto}\:[/tex][tex]\textsf{} [/tex][tex]\sf last\:term, a_{30} = 89 [/tex]
[tex]\underline{\underline{\large\bf{To Find:-}}}[/tex]
[tex]\orange{\leadsto}\:[/tex][tex]\textsf{ } [/tex][tex]\sf The \: A.P. [/tex]
[tex]\orange{\leadsto}\:[/tex][tex]\textsf{ } [/tex][tex]\sf 23rd\: term, a_{23} [/tex]
[tex]\\[/tex]
[tex]\underline{\underline{\large\bf{Solution:-}}}\\[/tex]
The nth term of A.P is determined by the formula-
[tex]\green{ \underline { \boxed{ \sf{a_n = a+(n-1)d}}}}[/tex]
where
[tex]\sf a = first \:term[/tex][tex]\sf a_n = nth \: term[/tex][tex]\sf n = number \:of \:terms [/tex][tex]\sf d = common \: difference [/tex]Since ,
[tex]\sf a_4 = 11 [/tex]
[tex]\longrightarrow[/tex] [tex]\sf a+(4-1) d= 11 [/tex]
[tex]\longrightarrow[/tex] [tex]\sf a+3d= 11\_\_\_(1) [/tex]
[tex]\sf a_{30}= 89 [/tex]
[tex]\longrightarrow[/tex] [tex]\sf a+(30-1)d=89[/tex]
[tex]\longrightarrow[/tex][tex]\sf a+29d= 89\_\_\_(2)[/tex]
Subtracting equation (1) from equation(2)
[tex]\begin{gathered}\\\implies\quad \sf a+29d-(a+3d) = 89-11 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf a+29d-a-3d = 78 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf a-a+29d-3d = 78 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 26d = 78 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf d = \frac{78}{26} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf d = 3 \\\end{gathered} [/tex]
Putting the value of d in equation (1) -
[tex]\begin{gathered}\\\implies\quad \sf a+3(3) = 11 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf a = 11-9 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf a = 2 \\\end{gathered} [/tex]
First term of A.P, a = 2Second term of A.P.,[tex]\sf a_2= 2+(2-1)\times 3[/tex][tex]\quad\quad\quad\sf =2+3[/tex]
[tex]\quad\quad\quad\sf =5 [/tex]
Third term of A.P.,[tex]\sf a_3= 2+(3-1)\times 3[/tex][tex]\quad\quad\quad\sf =2+6[/tex]
[tex]\quad\quad\quad\sf =8 [/tex]
[tex]\longrightarrow[/tex]Thus , The A.P is 2,5,8,. . . . . .
Now,
[tex]\begin{gathered}\\\implies\quad \sf a_n = a+(n-1)d \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf a_{23 }= 2+(23-1)\times 3 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf a_{23} = 2+22 \times 3 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf a_{23} = 2+66 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf a_{23} = 68 \\\end{gathered} [/tex]
[tex]\longrightarrow[/tex]Thus , 23rd term is 68.
what is the value of the 2 in 0.812
Answer:
the two is in the thousandths place
Step-by-step explanation:
the eight is in the tenths, and the one is in the hundredths
Answer:
.8 tenths
.01 hundredths
.002 thousandths
so the value of 2 would be 2 thousandths or .002 thousandths
Pleaseee helppp meee question 2 !!!
alex is working to simplify 5·(-8)·2
A. what is the product?
B. suppose Alex found the opposite of the correct product. describe an error he could have made that resulted in that product.
please answer quickly!!!!!!!!!!!!
Answer:
A. 5*(-8)*2=-80
B. Forgot about the signs
Step-by-step explanation:
Product of Signed Integers
The product of two integers with like (same) signs is positive. The product of two integers with different signs is negative.
A.
Alex is simplifying the product 5*(-8)*2. It can be done in any order, for example, let's multiply 5*(-8) first.
The numbers have different signs, so the product is negative and 8*5 =40, thus: 5*(-8)=-40.
Now we finish the operation multiplying (-40)*2. They have different signs, thus the result is negative and (-40)*2=-80, thus:
5*(-8)*2=-80
B.
If Alex found the opposite of the correct product, that is, 80 is more likely to have been the result of forgetting about the signs. He probably just multiplied the numbers regardless of their signs.
What is 1.2 simplified
Answer:
it is 1 2/10 but simplified to 1 1/5
Step-by-step explanation:
In one month, the median home price in the west fell from $203,400 to $192,300. Find the percent decrease
It takes Jamil 40 minutes to drive to work, plus or minus 8 minutes depending on traffic. Which of the following equations could be solved to find the shortest or longest times she might drive?
Answer:
addition
Step-by-step explanation:
add 40+8 and you get 48 :P
someone answer this??
Answer:
corresponding angle
Step-by-step explanation:
Find the value of xxx in the triangle shown below.
Answer:
Can I get image of it?
Step-by-step explanation:
Answer:
Image?
Step-by-step explanation:
What is the Value of
3.1 + (-4) - (-0.7)
i mostly want to just check my answer
Mr. Townsend bought five hot dogs for his family from the concession stand. Each hot dog cost
$
1.75
. How much change will he get back if he gives the cashier
$
10
? Show your work, including labeling your answer with the appropriate units of measure.
Answer:
1.25
Step-by-step explanation:
so you multiply 1.75 by 5 which is 8.25. You subract 10 by 8.25
A rectangular lawn is 8 meters wide and 18 meters long. What is the perimeter?
Answer:
8x2=16 18x2=36 16+36=52
Step-by-step explanation:
a rectangle has four sides so two sides have to be 8 and the other two have to be 18
Answer:
52
Step-by-step explanation:
1. 8*2=16
2) 18*2=36
3)36+16=52
Triangle XYZ has vertices X(1, 3), Y(0, 0), and Z(–1, 2). The image of triangle XYZ after a rotation has vertices
X'(–3, 1), Y'(0, 0), and Z'(–2, –1). Which rule describes the transformation?
R0, 90°
R0, 180°
R0, 270°
R0, 360°
Answer:
ur answer is.. 90 degree
Step-by-step explanation:
Triangle ABC was transformed using the rule (x, y) -> (-y, x). The vertices of the triangle are shown.
Which best describes the transformation?
would be a R0, 90 degree
i jst took the quiz....
Answer:
90 degrees
Step-by-step explanation:
You ride the train to an after-school job every weekday. The ticket for the trip from school to work costs $3. The ticket for the trip from work back home costs d dollars. How much do you spend on train tickets each day? How much do you spend in a 5-day week?
Answer:
each day= 3+d
each 5-day week= 15+5d
Step-by-step explanation:
Please help! Select the graph of the solution. 2x - 1 > 5
Answer:
See photo below
Step-by-step explanation:
First, start solving it. Add 1 to each side, so it now looks like this: 2x > 6Divide each side by 2 to cancel out the 2 next to x. It should now look like this: x > 3Now, look at your options and pick the graph that fits the solved equation. The last option matches the solved equation exactly, so that's the answer.I hope this helps!
15. Find the value of x.
(7x-1)
(6x - 1)
X =
Answer:
the answer is -1
Step-by-step explanation:
Answer: x = 0
Step-by-step explanation: Firstly, set them equal to each other.
7x - 1 = 6x - 1
Now, subtract 6x from both sides:
x - 1 = -1
Add 1 to both sides:
x = 0
And if you need to know what type of function it is, it is an infinite function because if you plug in 0:
7(0) - 1 = 6(0) - 1
You get:
-1 = -1
If both sides are the same, it is an infinite function.
Hope this helps!
Convert to a decimal. 164%
Answer:
1.64
Step-by-step explanation:
Step-by-step explanation:
to remove percentage divide value with 100
164/100
answer in fraction
41/25
answer in decimal
1.64
Jackie is diving 25.65 feet below sea level and then dives down another 16.5 feet. Then he rose 12.45 feet. What is Jackie’s new depth?
Answer:
-29.7
Step-by-step explanation:
Assuming sea level is at 0, you would first subtract 25.65 from 0 to indicate diving 25.65 feet BELOW 0. Then, you subtract 16.5 from that. Then, add 12.45 to that number to get the answer after the diver rose 12.45 feet.
0-25.65= -25.65
-25.65-16.5= -42.15
-42.15+ 12.45= -29.7
OR 29.7 feet below sea level.
HELP!!! NEED RATIO! A TON OF POINTS!
Answer:
yes
Step-by-step explanation:
King Kyle orders the construction of his future mausoleum (a fancy tomb) so that people never forget his awesomeness. His architect draws a floor plan depicting the mausoleum as a rectangle measuring 35\text{ m}35 m35, start text, space, m, end text by 40\text{ m}40 m40, start text, space, m, end text. Move points to redraw the architect's floor plan on the grid below.
Answer:
see attached image
Step-by-step explanation:
The mausoleum's plan measures 35 (width) by 40 (height) meters. Each square represents 2.5 m. When you redraw the tomb on the grid, it should measure 14 (width) by 16 (height) squares.
Answer:
Step-by-step explanation:
27/x = 9/6 fraction on get more math
Answer:
18
Step-by-step explanation:
7.
Meredith spent $367.80 on tulip mand daffodil bulbs for her
flower bed. A bag of tulip bulbs Meredith spent $367.80 on tulip and daffodil bulbs for her flower bed. A bag of tulip bulbs cost $7.95 and daffodil bulbs cost $6.80 per bag. If she bought three times as many tulips as daffodils, how many bags did she buy of each kind?
tulips as daffodils, how many bags did she buy of each kind?
i really do not know the answer
Answer: the answer is D which is really the only answer higher then $36.99
Step-by-step explanation:
Answer: d. 38.47
Step-by-step explanation:
Carlos makes baskets with bags of coffee or boxes of tea. He has 72 bags of coffee and 56 boxes of tea. He wants to put an equal number of bags of coffee and boxes of tea in each basket. Each basket contains only coffee or tea. A. What is the largest number of bags of coffee or boxes of tea that he can put in each basket?
Answer:
1
Step-by-step explanation:
1
solve for x. 36x+2=110. show work
Answer:
Answer to x is 3. so it would be x = 3
Answer:
x=3
Step-by-step explanation:
36x+2-2=110-2
36x=108
36x/36=108/36
x=3
Find the product of-10/5 x (-15/5)
Answer:
6
Step-by-step explanation:use math- way it will help you in future
Answer:
6
Step-by-step explanation:
Equation: [tex]-\frac{10}{5}\cdot -\frac{15}{5}[/tex]
1). Apply [tex]-a(-b)-ab[/tex]: [tex]-\frac{10}{5}(-\frac{15}{5}=\frac{10}{5}\cdot \frac{15}{5}[/tex]
2). [tex]\frac{10}{5}[/tex] simplfies to 2, so [tex]2\cdot \frac{15}{5}[/tex]
3). [tex]2\cdot 3[/tex]
Between which two consecutive whole numbers does \sqrt{3} 3 lie? Fill out the sentence below to justify your answer and use your mouse to drag \sqrt{3} 3 to an approximately correct location on the number line. Between which two consecutive whole numbers does \sqrt{3} 3 lie? Fill out the sentence below to justify your answer and use your mouse to drag \sqrt{3} 3 to an approximately correct location on the number line.
Answer:
It lies between 5 and 6
Step-by-step explanation:
Two consecutive numbers are numbers that come after each other:
x , x + 1 are consecutive numbers.
3 \sqrt{3} = 3√3 = 5.19615242271
Therefore, from the above calculation, we can see that square root of 3 is a number that is between consecutive numbers 5 and 6
Answer:
It lays Between 2 and 3
1+1=?
5
2
4
7
this question is really hard and confusing
Answer:
I think it is 2
Step-by-step explanation:
I hope this is right! Please Rate Brainiest!
Answer:
its obv 478
Step-by-step explanation:
1+1=2 divoided by 400=294-478
Need help, will mark brainliest plus 50 points.
Lia gets paid $450 a week plus a
5% commission on her sales. She
hopes to earn at least $600
dollars each week.
a. Write an inequality to
represent the verbal
description.
b. How much does Lia
need in sales to make
her goal?
Answer:
Step-by-step explanation:
To write the inequality, we need to first caculate the amount of money that Lia would ACTUALLY earn each week and compare that to her goal of $600.
We cannot actually get the amount of money that Lia would get because we don't know her sales so we will represent the sales with a X.
450+ X(5%). -This the amount of money she would egt from her sales. We need to also figure out 5% of 450 to solve the next part of the equation. That is $22.5. 600-450=150/22.5= 6.6666- which is about 7 sales.
In a library 20% of the books are fiction (a) what percentage are non fiction?(b) if there are 6000 books in the library. how many are fiction and how many are non fiction
Answer:
A) 80%
B) Non-Fiction = 4,800 books Fiction = 1,200 books
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
Answers:
a) 80% nonfiction
b) 1200 fiction, 4800 nonfiction
=========================================
Explanation:
part (a)
We only have two choices: fiction or nonfiction
If 20% are fiction, then 100% - 20% = 80% are nonfiction.
The two percentages 20% and 80% add to 100% to represent all the books.
---------------------
part (b)
20% = 20/100 = 0.20
20% of 6000 = 0.20*6000 = 1200
we have 1200 fiction books
6000-1200 = 4800
and we have 4800 nonfiction books
Note how
80% of 6000 = 0.80*6000 = 4800
which helps confirm part (a)
What is the equation of this line?
y= 4/5x-3
y=5/4x-3
y=4/5x+3
y=-4/5x-3
Answer:
the answer is y=4/5x-3
The equation of the line shown in the graph would be, [tex]y = \dfrac{4}{5} x - 3[/tex]
Hence, option 1 is true.
Given that;
Two points on the line are (5, 1) and (0, -3).
Used the concpet of the equation of the line,
The equation of a line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, [tex]m = \dfrac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]
Now,
Since, The equation of line passes through the points (5, 1) and (0, -3)..
So, We need to find the slope of the line.
Hence, the slope of the line is,
[tex]m = \dfrac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]
[tex]m = \dfrac{(- 3 - 1)}{(0 - 5)}[/tex]
[tex]m = \dfrac{(- 4)}{( - 5)}[/tex]
[tex]m = \dfrac{(4)}{( 5)}[/tex]
Thus, The equation of the line with slope 4/5 is,
[tex]y - 1 = \dfrac{4}{5} (x - 5)[/tex]
[tex]y - 1 = \dfrac{4}{5} x - 4[/tex]
[tex]y = \dfrac{4}{5} x - 4 + 1[/tex]
[tex]y = \dfrac{4}{5} x - 3[/tex]
Therefore, The equation of the line will be;
1) [tex]y = \dfrac{4}{5} x - 3[/tex]
So, option 1 is true.
To learn more about the equation of line visit:
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