The value of the 43rd term of the arithmetic sequence will be 482.
What is the sum of an arithmetic sequence?Let a be the first term, L be the last term, n be the number of terms, and d be a common difference.
Then the sum of the arithmetic sequence will be
Sₙ = (n / 2)[a + L]
Sₙ = (n/2) [2a + (n − 1) d]
An A.P.'s eighth term is worth 160 while their twentieth term is worth 880.
160 = (8/2)(2a + 7d)
2a + 7d = 40 ...1
880 = (20/2)(2a + 19d)
2a + 19d = 88 ...2
From equations 1 and 2,
40 - 7d + 19d = 88
12d = 48
d = 4
Then the value of 'a' is given as,
2a + 7(12) = 40
2a = 40 - 84
2a = -44
a = -22
The value of the 43rd term is given as,
aₙ = a + (n - 1)d
a₄₃ = - 22 + (43 - 1)(12)
a₄₃ = - 22 + 42 x 12
a₄₃ = - 22 + 504
a₄₃ = 482
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Given that f ( x ) = 3 x − 7 and g ( x ) = 3 x + 9 , evaluate f ( g ( 2 ) )
Answer:
38
Step-by-step explanation:
f ( x ) = 3 x − 7
g ( x ) = 3 x + 9
f(g(2))
First find g(2)
g(2) = 3(2)+9 = 6+9 = 15
Then find f(15)
f(15) = 3*15 -7 = 45 -7 =38
your friend says that there are 36 feet in 12 yards is your friend correct? explain your reasoning.
PLEASE HURRY!!
Answer:
Yes
Step-by-step explanation:
1 yard is 3 feet. so 12 yards is 36 by 12*3
find the slope with the given numbers
Answer:
[tex]m=-\frac{1}{26}[/tex]
Step-by-step explanation:
Formula:
[tex]Slope:m=\frac{y_2-y_1}{x_2-x_1}\\[/tex]----------------------------------------------------------------------------------------------------------------
Work:
[tex]m=\frac{-15-(-16)}{-7-19}\\\\m=-\frac{1}{26}[/tex]
i realy need it very desparate
Answer: how to stop deppreshon
Step-by-step explanation: The mainstay of treatment is usually medication, talk therapy, or a combination of the two. Increasingly, research suggests these treatments may normalize brain changes associated with depression.
{x: x belongs to N and (x-1)(x-2) = 0}, finite set or infinite set?
Explanation:
We have a set of x values such that (x-1)(x-2) = 0. Breaking that down leads to either x-1 = 0 or x-2 = 0 through the zero product property. Solving each of those equations gets us x = 1 and x = 2 as the two items in this set.
So the original set your teacher gave you turns into the roster form {1,2}. There are two items in this set and we can see it's a finite set since it does not go on forever. Note that everything in this set is a natural number.
Fill in the blanks below in order to justify whether or not the mapping shown
represents a function.
The picture needs to be answered.
Answer:
if 3 children go to the water park, 4 adults can go: TRUE
if 6 children go to the water park 3 adjults can go: FALSE
no adults, 6 children: TRUE (even 9 children can go)
no children, 6 adults: TRUE
10x is indeed the cost of the children
15y is indeed the cost of the adults
Given m|n, find the value of x. (6x-9) → (5x+10)
__________
[tex] \: [/tex]
6x - 9 = 5x + 10
6x - 5x = 10 + 9
x = 19✔
Given m||n, find the value of x.
т
Rt
>m
(2X-22)
(5x-8)°
>
Given angles are supplementary.
[tex]\\ \sf\longmapsto 2x-22+5x-8=180[/tex]
[tex]\\ \sf\longmapsto 7x-30=180[/tex]
[tex]\\ \sf\longmapsto 7x=180+30=210[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{210}{7}[/tex]
[tex]\\ \sf\longmapsto x=30[/tex]
How many 1/4 cup servings are in 5/6 cups of yogurt?
Answer:
3.3
Step-by-step explanation:
1/4*3 = 3/12 (find lcd lowest common factor )
5/6 *2 10/12 figure out how many time 3 goes into 10 about 3.3 repeating
Answer: [tex]\right] \left[\begin{array}{ccc}0.3 cups\\\end{array}\right] \\[/tex]
Step 1: Write the problem as a mathematical expression.
1/4 and 5/6
Step 2: Convert the fraction to a decimal by dividing the numerator by the denominator.
0.3 cups
Definitions:
A. Fraction- A number used to name a part of a group or a whole. The number below the division line is the denominator, and the number above the division line is the numerator.
B. Expression- A mathematical symbol, or combination of symbols, representing a value, or relation.
Have a great day!
Write an equation. A number is doubled, then 9 is added. The result is 23.
Answer:
2n + 9 = 23
Step-by-step explanation:
let the number be n then double the number is 2n and adding 9 gives
2n + 9 ( the result is 23 ) , so
2n + 9 = 23 ← is the equation modelling the statement
Peter brought 8 lemons for 6 dollars each lemon was the same price what was the cost for 1 lemon.
Answer:
75 cents
Step-by-step explanation:
We can use a ratio to solve
8 lemons 1 lemon
------------- = ------------
6 dollars x dollars
Using cross products
8x = 6*1
8x = 6
Divide by 8
8x/8 = 6/8
x = .75
One lemon costs .75
how do i find the sum of (5/4q + 1) + (q - 4) + (-1/4q + 2)
Answer:
2q-1
Step-by-step explanation:
Add:
Look at only the q's inside the parenthesis and see if there are other q's in it, in this case there are none.
Now look outside the parenthesis and add the q's outside of it which is 5/4q, q and -1/4q
5/4q-1/4q is q
q+q is 2q
Now do the same thing with the numbers that doesn't have variables
1-4+2=-1
So the answer is 2q-1
Hope this helps!
Answer:
2q -1
Step-by-step explanation:
(5/4q + 1) + (q - 4) + (-1/4q + 2)
5/4q + 1 + q - 4 - 1/4q + 2
5/4q + q - 1/4q + 1 - 4 + 2
2q -1
Madelyn has two summer jobs. During the week she works in the grocery store, and on the weekend she works at a nursery. She gets paid $22 per hour to work at the grocery store and $21 per hour to work at the nursery. How much does she earn if she works 11 hours at the grocery store and 10 hours at the nursery? How much does she earn if she works gg hours at the grocery store and nn hours at the nursery?
Answer:
242$ in grocery store and 210$ in nursery
Step-by-step explanation:
A special type of door lock has a panel with five buttons labeled with the digits 1 through 5. This lock is opened by a sequence of three actions. Each action consists of either pressing one of the buttons or pressing a pair of them simultaneously.
There are several ways the door can be locked, these ways illustrate combination.
There are 3375 possible combinations
From the question, we have:
[tex]\mathbf{n = 5}[/tex] --- the number of digits
[tex]\mathbf{r = 3}[/tex] ---- the number of actions
Each of the three actions can either be:
Pressing one buttonPressing a pair of buttonsThe number of ways of pressing a button is:
[tex]\mathbf{n_1 = ^5C_1}[/tex]
Apply combination formula
[tex]\mathbf{n_1 = \frac{5!}{(5-1)!1!}}[/tex]
[tex]\mathbf{n_1 = \frac{5!}{4!1!}}[/tex]
[tex]\mathbf{n_1 = \frac{5 \times 4!}{4! \times 1}}[/tex]
[tex]\mathbf{n_1 = 5}[/tex]
The number of ways of pressing a pair is:
[tex]\mathbf{n_2 = ^5C_2}[/tex]
Apply combination formula
[tex]\mathbf{n_2 = \frac{5!}{(5-2)!2!}}[/tex]
[tex]\mathbf{n_2 = \frac{5!}{3!2!}}[/tex]
[tex]\mathbf{n_2 = \frac{5 \times 4 \times 3!}{3! \times 2 \times 1}}[/tex]
[tex]\mathbf{n_2 = 10}[/tex]
So, the number of ways of performing one action is:
[tex]\mathbf{n =n_1 + n_2}[/tex]
[tex]\mathbf{n =5 + 10}[/tex]
[tex]\mathbf{n =15}[/tex]
For the three actions, the number of ways is:
[tex]\mathbf{Action = n^3}[/tex]
[tex]\mathbf{Action = 15^3}[/tex]
[tex]\mathbf{Action = 3375}[/tex]
Hence, there are 3375 possible combinations
Read more about permutation and combination at:
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{(2, 2),(4, 4),(6, 6),(8, 8)}
Is a Function – { ( 2, 2 ),( 4, 4 ),( 6, 6 ),( 8, 8 ) }
Is not a Function – { ( 2, 2 ),( 4, 4 ),( 6, 6 ),( 8, 8 ) }
{(0, 3),(3, 5),(5, 6),(8, 4)}
Is a Function – { ( 0, 3 ),( 3, 5 ),( 5, 6 ),( 8, 4 ) }
Is not a Function – { ( 0, 3 ),( 3, 5 ),( 5, 6 ),( 8, 4 ) }
{(1, 2),(3, 3),(4, 8),(6, 3)}
Is a Function – { ( 1, 2 ),( 3, 3 ),( 4, 8 ),( 6, 3 ) }
Is not a Function – { ( 1, 2 ),( 3, 3 ),( 4, 8 ),( 6, 3 ) }
{(3, 4),(5, 2),(5, 6),(7, 3)}
Is a Function – { ( 3, 4 ),( 5, 2 ),( 5, 6 ),( 7, 3 ) }
Is not a Function – { ( 3, 4 ),( 5, 2 ),( 5, 6 ),( 7, 3 ) }
which is not a function and which is a function?
{(2, 2),(4, 4),(6, 6),(8, 8)} Is a function.
{(0, 3),(3, 5),(5, 6),(8, 4)} Is a function.
{(1, 2),(3, 3),(4, 8),(6, 3)} Is a function.
{(3, 4),(5, 2),(5, 6),(7, 3)} Is not a function.
For a relation to be a function, every x value must have only one y value.
To make rice in a factory, Lois mixes rice and water in the ratio 2 : 3. If she uses 10 cups of rice, how many
cups of water does she need?
Answer:
15 cups
Step-by-step explanation:
2:3
10:?
2x5:3x5
10:15
Ben deposited $500 into a savings account at a local bank that earned 5% interest per
year. How much interest does he earn per year?
Answer:
$25
Step-by-step explanation:
500*0.05=25
Answer:
$25 because 100 is half of 500
how do I do this please help
Answer:
i do not know what it all says
Step-by-step explanation:
Reasoning There were 43 students on the playground. Some more students joined them. Now there are 63 students on the playground. How many students joined? EnVision Lesson 3-5
Answer:
20
Step-by-step explanation:
63 - 43 = 20
Answer:
20 students
Step-by-step explanation:
because 43+s=63
63-43=20
s=20
so it have 20 students on the playground
Work out the size of angle x 126 degrees exterior and 43 degrees interior
Answer:
The answer is 83°
Step-by-step explanation:
by the sum of iner and outer angle=180°
180-126= 54°
x=180-43+54
x=180-97
x=83°
hope that helped.?<3
An engineer is estimating the weight of a steel beam. The actual weight of the beam is 152 pounds. The engineer's estimate is 150 pounds.
Find the absolute error and the percent error of the engineer's estimate. If necessary, round your answers to the nearest tenth.
Answer/Step-by-step explanation:
To find the absolute difference, we simply have to see by how much pounds the estimation was off.
The real measure was 152 pounds, the estimated weight was 150.
D = 152- 150 = 2 pounds.
For the percent of error, we divide the absolute difference (52) by the real value () and we'll get the % of error. So,
%D = 52 / 152 = 0.0034, so 0.34%
1) Jen spends $5.98 on ribbon. Ribbon costs $0.92 per meter. How many
meters of ribbon does Jen buy?
Answer:
6.5
Step-by-step explanation:
5.98÷0.92= 6.5m
Explain why it does not matter which point you choose when writing the
equation of the line in point-slope form, given two points.
Answer:
because, it will completely change the slope
Step-by-step explanation:
It does not matter which point you choose when writing the
equation of the line in point-slope form because the slope of the line remains same.
What is a slope ?A slope can be thought of as rate of change of y axis with respect to x axis.
We have been asked in this statement that why it doesn't matter that which point we choose when writing the equation in point slope form.
Let us understand this with an example,Suppose we have two pair of points. (x₁,y₁) = (2,3) and (x₂,y₂) = (5,9).
We know slope(m) is = (y₂-y₁)/(x₂-x₁).
Slope(m₁) = (9-3)/(5-2)
= 6/3
= 2.
Now if interchange the points (x₁,y₁) = (5,9) and (x₂,y₂) = (2,3).
Slope(m₂) = (3-9)/(2-5)
= -6/-3
= 2.
So, even when interchanging the points the slope m₁ = m₂ this is the reason why it doesn't matter which point we choose.
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Molly is helping her younger sister run a lemonade stand. They earn $2 for each cup of
lemonade they sell.
Write an equation that shows how their total earnings, y, depend on the number of cups sold,
X.
Do not include dollar signs in the equation.
y =
Answer:
y= x • 2
Step-by-step explanation:
The amount of money they make is dependent of how many 2 dollar cups they sell.
(please crown me brainleist I need to level up)
Find the value of 4+n when n=12
Answer:
16
Step-by-step explanation:
N equals 12, so
4 + 12 = 16
Answer:
4 + n = 16
Step-by-step explanation:
n = 12 so 4 + 12 is 16
Please help me this question…
the area of the rectangle is 0.1 square meter
the square root of negative 9 is not negative 3 because..
Answer:
You cant have a negative square root
Explanation:
The answers will always be positive or a perfect square
Hope this Helps
I need the answer for this
Answer:
JK = 12.6
Step-by-step explanation:
Similarity says ratio of any cooresponding sides are equal to the ratio of any other cooresponding sides. SO
25.2/66 = JK/33
33(25.2/66) = JK
12.6 = JK
Given the function f(x)=x^2+2x+1, find each value of the function
Answer:
1 9/16
Step-by-step explanation:
F(1/4) means u plug in 1/4 for x
so the equation would be
f(1/4)=1/4^2+2 1/4 + 1
f(1/4)=1/16+1/2+1
f(1/4)= 9/16 +1
f(1/4)= 1 9/16
its not nine teen its one and 9 over 16 just clarification