Let a (n) denote the n-th term of the sequence. Since the terms form an arithmetic sequence, you have
a (n) = a (n - 1) + d
for some fixed constant d. You can write any term in the sequence as a function of the first term:
a (n) = [a (n - 2) + d] + d = a (n - 2) + 2d
a (n) = [a (n - 3) + d] + 2d = a (n - 3) + 3d
and so on, down to
a (n) = a (1) + (n - 1) d
so given that a (11) = 57 (so that n = 11), you have
a (1) + 10d = 57 … … … [1]
The sum of the first and fourth terms is 29:
a (1) + a (4) = 29
but we can write a (4) in terms of a (1) :
a (1) + [a (1) + 3d] = 29
which gives us another equation in a (1) and d :
2 a (1) + 3d = 29 … … … [2]
Now solve [1] and [2] :
-2 (a (1) + 10d) + (2 a (1) + 3d) = -2 (57) + 29
-17d = -85
d = 5
a (1) + 10d = a (1) + 50 = 57
a (1) = 7
Then the n-th term of the sequence is given by
a (n) = 7 + 5 (n - 1) = 5n + 2
Describe and correct the error in finding the distance between the points (−3 −2) and (7 4)
Answer:
[tex]2\sqrt{34}[/tex] ≈ 11.6619
Step-by-step explanation:
Answer: 6 units Step-by-step explanation: Use the distance formula, [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]. Plug the x and y values from the given points into the distance formula:
[tex]\sqrt{(7-[-3])^{2}+(4-[-2])^{2}}[/tex]
Simplify:
[tex]2\sqrt{34}[/tex] ≈ 11.6619
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The distance between two coordinate points is 11.66 units.
What is distance formula?The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On 2D plane the distance between two points (x₁, y₁) and (x₂, y₂) is Distance = √[(x₂-x₁)²+(y₂-y₁)²].
The given coordinate points are (-3, -2) and (7, 4)
Substitute (x₁, y₁) =(-3, -2) and (x₂, y₂)=(7, 4) in distance formula, we get
Distance = √[(7+3)²+(4+2)²]
= √(100+36)
= √136
= 11.66 units
Therefore, the distance between two coordinate points is 11.66 units.
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Follow the steps for dividing decimals. Then, round to two decimal places (hundredths).
1.476)6.380
Answer:
4.32
Step-by-step explanation:
The steps required are:
4.322
1.476 )6.380
5.904
____
0.476
0.4763
0.4428
_____
0.0335
0.03358
0.02952
_____
0.00406
0.004060
0.002952
_____
0.0011080
Therefore, the answer is 4.32.
At Gabrielle's Restaurant, 2/5 of the dishes on the menu are vegetarian, or the vegetarian
dishes, 3/4 are pasta dishes. What fraction of the dishes on the menu are vegetarian pasta
dishes?
Plz help!!!
Which equation represents the graph?
Answer:
Option C : y=|x|-6
Step-by-step explanation:
If x plus 3/4 = 1, then which point on the number line could be x?
Answer:
[tex]x = \frac{1}{4}[/tex]
Step-by-step explanation:
Step 1: Subtract [tex]\frac{3}{4}[/tex] from 1
[tex]1 - \frac{3}{4}\\\\= \frac{1}{4}[/tex]
Therefore, the point could be [tex]\frac{1}{4}[/tex]
Ratio of the ages of three children is 2:5:1. The sum of their ages is 32 years. Find the ages of the youngest and the eldest
child.
Answer:the ages of the youngest and the eldest is 4 years and 20 Years respectively
Step-by-step explanation:
Ratio of the ages of three children is 2:5:1.
Total ratio =2+5+1=8
So that
the 1st Child's age =2/8 x 32=8 years
2nd Child's age =5/8 x 32= 20 years
3rd Child's age =1/8 x 32= 4 years
Therefore the ages of the youngest and the eldest is 4 years and 20 Years respectively.
Please answer the question and provide a solid definition of what an expression is, thank you :)
Answer:
Answers are: 2x - 7, and 2x -7 = 14
Step-by-step explanation:
An expression must have variables must have a coefficient, a number that is multiplied divided added or subtracted by our variable. The variable is a place holder.
So our answers would be 2x - 7, and 2x -7 = 14
In the box below, enter the value that is missing from the table.
170 is the answer
Given ,
520 = 0
.°.
420 = 520-100
320 = 520-200
?= 520-350 = 1700 = 520-520
Mark the relation
f(0)=520f(100)=520-100=420f(200)=520-200=320Similarly
f(350)=520-350=170ratio of 25cm to 40cm
5:8
is the ratio .he she and shd
The ratio of a model building's dimensions to the building's actual dimensions is 1/20. If the height of the model is 18 inches, what is the height of the actual building in feet?
600% of what number is 4,200
Answer: Trust me pleas, 14.29%.
Step-by-step explanation: On my dead moms grave.
Answer:
700
Step-by-step explanation:
600% of 700 is equivalent to multiplying them:
600% × 700 = ?
600% × 700 =
(600 ÷ 100) × 700 =
(600 × 700) ÷ 100 =
420,000 ÷ 100 =
4,200
What is the length of the segment connection the points that have the coordinates (-9, 8) and (2, -5) A √130 B √218 C √290 D √338
Answer:
Step-by-step explanation:
Solve for the missing side of this right triangle.
24 mi
16 mi.
Answer:
384
Step-by-step explanation:
I just went to my calculator and did 24×16 and I got 384
X-2 is a factor of f(x) = x3 – 2x2 + ax +
+18. State the remainder when f(x) divided
by x-9.
Answer:
answer is in the picture above
Answer:
remainder: 504
Step-by-step explanation:
x³ – 2x² + ax +18 = x²(x-2) - 9*(x-2)
a = -9
(x³ – 2x² - 9x +18) / (x-9) = (x² +7x + 54)(x-9) + 504 ... long division
bob bought three more then twice as many apples as Kathy. Together they ought 15 apples. How many did each of them buy?
Answer:
Kathy bought 4 and Bob bought 11.
Step-by-step explanation:
since we already know he bought 3 more than her we can subtract 3 from 15 which is 12, since he bought twice more than her we can divide 12 by 3 which is 4. Multiply by 2 and you get 8, and when you add it to the subtracted 3 you get 11. So she bought 4 and he bought 11
PLEASE HELP ANWSER ASAP PLEASE ILL GIVE BRAINLIEST!!!!
Answer:
3.5944
Step-by-step explanation:
first the fraction is mixed and you need to change the fraction to proper or improper fraction
the denominator 4 is multiply 16
16×4=64
then the numerator 3 is add to 64
64+3=67
the fraction will be
=====67/4
the denominator is not change from the first part
》》do the same thing by the other mixed fraction
the final answer would be 3.5944
first calculate 67÷4=16.75
the second calculate 14÷3=4.66
in the second part i get 14/3 that means i change the mixed fraction to the normal fraction
calculate 16.75÷4.66=3.5944
PLEASE HELP WITH ALGEBRA
Answer:
log 7
Step-by-step explanation:
[tex]log (a)+log6=log(ab)\\\\[/tex]
[tex]log(c)-log(d)=log(c/d)[/tex]
---------------------------------
hope it helps...
have a great day!!
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. Verify your results using the integration capabilities of a graphing utility. y = e^(x-1), y=0, x=1, x=2
Answer:
the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis is;
[tex]\frac{\pi }{2} [e^2 - 1 ][/tex] or 10.036
Step-by-step explanation:
Given the data in the question;
y = [tex]y = e^{(x - 1 )[/tex], y = 0, x = 1, x = 2.
Now, using the integration capabilities of a graphing utility
y = [tex]y = e_2}^{(x - 1 )_[/tex], y = 0
Volume = [tex]\pi \int\limits^2_1 ( e^{x-1)^2} - (0)^2 dx[/tex]
Volume = [tex]\pi \int\limits^2_1 ( e^{x-1)^2 dx[/tex]
Volume = [tex]\pi \int\limits^2_1 e^{2x-2}dx[/tex]
Volume = [tex]\frac{\pi }{e^2} \int\limits^2_1 e^{2x}dx[/tex]
Volume = [tex]\frac{\pi }{e^2} [\frac{e^{2x}}{2}]^2_1[/tex]
Volume = [tex]\frac{\pi }{2e^2} [e^4 - e^2 ][/tex]
Volume = [tex]\frac{\pi }{2} [e^2 - 1 ][/tex] or 10.036
Therefore, the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis is;
[tex]\frac{\pi }{2} [e^2 - 1 ][/tex] or 10.036
Solve –9.4 Greater-than-or-equal-to 1.7x + 4.2.
Answer:
x≤-8
Step-by-step explanation:
Answer:
x ≤ -8
Step-by-step explanation:
Good Luck!
I need help on Section 5- Topic 10 Algebra Nation, Algebra 1 Practice book. If anyone could give me answers to the questions, I will be extremely thankful!
Step-by-step explanation:
Just post a pic of the page
Which rules define the function graphed below?
eOf
y
4
0.3)
3
(3,2)
1
2
3
4
В
7
x
2
3
Answer: y= 2x+3; y=-1/3x+3
Step-by-step explanation:
First option on edge
y = 2x + 3 and y = -(1/3)x + 3 define the function graphed below.
The correct option is 1.
What is a graph?Graph, a visual depiction of statistical information or a relationship between variables that serves a purpose. Graphs serve a predictive purpose because they have the advantage of displaying broad trends in the quantitative behavior of data. But, as just approximations, they may be imprecise and occasionally deceptive. The majority of graphs include two axes: a horizontal axis that represents a set of independent variables and a vertical axis that represents a set of dependent variables. A broken-line graph, in which time is typically the independent variable, is the most typical type of graph.
The graph of the functions and the points on the line is given.
The points for 1st function = (0, 3)
The points for 2nd function = (3, 2)
The given function:
y = 2x + 3
Substituting (0, 3)
3 = 2(0) + 3
3 = 3
Similarly, for y = -(1/3)x + 3
Substituting (3, 2)
2 = -(3/3) + 3
2 = -1 + 3
2 = 2
Hence, y = 2x + 3 and y = -(1/3)x + 3 define the function graphed below.
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Which situation can be represented by -85+85 choose all that apply
There are 58 students in a classroom with 7
tables. If 8 students can sit at a table, how
many students cannot sit down at tables?
8x7=56, so 56 students can sit at a table, 58-56=2 students without a table.
Your answer would be 2.
Answer:
2 students cannot sit down at tables.
Step-by-step explanation:
Since there are a total of 58 students and only 7 tables and each table can only fit 8 students, you'll need to calculate how many students can sit at 7 tables first:
7(8) = 56 So, with 8 students sitting at all 7 tables, there are 56 students that can sit at a table.
To find how many students can't sit at a table you'll have to subtract 56 from 58,
58-56 = 2 So, 2 students will not be able to sit down at tables.
A truck has a trailer that has a length of 20 feet, a width of 8 feet, and a height of 12 feet. What is the volume of the trailer?
Answer:
1920
Step-by-step explanation:
20*8*12=1920
If anyone could help I would be so happy!
Answer: well i cant help... so dont be happy! :)
Mrs. Garcia wants to paint her patio floor. She needs to determine the area so she will know how much paint to buy. What is the area of the patio floor shown?
Answer: 375 ft
Step-by-step explanation:
break the shape into three parts in order to find the area of each of them look at the picture. I broke the parts into numbers 1 ,2 ,and 3. You can take the area for number one bye using the length given which is 20 and the width which is 5. Multiply the length times width and you'll receive the area. Box 2 : subtract 5 - 15 in order to get the width which is 10 and use the lengths given at the top which is 20. multiply them in order to get the area. box 3 : in order to get the width you can subtract 30 by 20 + 5 which leaves you with 5, which is the width. The length is already given to you on the side which is 15. Multiply 5 by 15 in order to get the area.once you get all of the areas for the boxes which should be 100, 200, 75. add them all up to obtain the area of the shape which should equal 375 ft.
Simplify : -sqrt(9+y)^2 if y<-10
Answer:
−y−9
Step-by-step explanation:
Answer:
9+y is the correct answer
Step-by-step explanation:
Plz help this if you want points
Answer:
First Question:
A) -15+20x B) 36x+28
Second Question:
-10/5, 1/25, 1/2, 3/5, 5/8
The net of a triangular prism is shown
below.
8.5 cm
10 cm
10 cm
10 cm
What is the total surface area of the prism?
A 470 cm?
C 390.5 cm?
B 385 cm
D 342.5 cm
Answer:
i think a.... sorry if im wrong
Step-by-step explanation:
HELP PLEASE EDCITE !!!!
Answer:
between 30 and 60
Step-by-step explanation: