Answers
a) The first term of the sequence is; ³¹/₆
b) The term to term rule is; aₙ = ³¹/₆ + (n - 1)²/₆
c) The next three terms are; ³⁷/₆, ³⁹/₆, ⁴¹/₆
d) The 10th term in the sequence is; a₁₀ = ⁴⁹/₆
How to find the nth term of a sequence?The first term of the sequence is given by the expression;
2 ÷ ¹²/₃₁ = ³¹/₆
The second term of the sequence is given by the expression;
3 ÷ ⁶/₁₁ = ³³/₆
The third term of the sequence is given by the expression;
5 ÷ ⁶/₇ = ³⁵/₆
These are the first three terms of a sequence and so the sequence is;
³¹/₆, ³³/₆, ³⁵/₆,....
d = ³³/₆ - ³¹/₆ = ²/₆
Thus, term to term rule is given by the nth term of an arithmetic progression;
aₙ = ³¹/₆ + (n - 1)²/₆
The next three terms are; ³⁷/₆, ³⁹/₆, ⁴¹/₆
The 10th term in the sequence is;
a₁₀ = ³¹/₆ + (10 - 1)²/₆
a₁₀ = ³¹/₆ + ¹⁸/₆
a₁₀ = ⁴⁹/₆
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Related Questions
The following coordinate plane shows three of the vertices of a rectangle. On an 8 by 8 coordinate grid, T is plotted 1 unit right and 4 units up from the origin. P is plotted 6 units right and 2 units up from the origin. Z is plotted 3 units right and 5 units up from the origin. What are the coordinates of Point Z? ( Choose... ) What are the coordinates of Point P? ( Choose... ) Which point has coordinates ( 1 , 4 ) ? Choose... In order to create a rectangle using these points as three of the vertices, what coordinates should be used for the fourth vertex? ( Choose... )
Answers
The coordinates of the points are given as follows:
Point Z: (3,5).Point P: (6,2).Point T has coordinates (1,4).The coordinates of the fourth vertex are of:
(4,1).
What are the ordered pairs?The notation of an ordered pair is given as follows:
(x-coordinate,y-coordinate).
The x-coordinate is the horizontal movement, defined as follows:
Right: positive x-coordinate.Left: negative x-coordinate.The y-coordinate is the vertical movement, defined as follows:
Up: positive y-coordinate.Down: negative y-coordinate.The equivalent sides on a rectangle are congruent, hence the equivalent sides are:
TZ and PM.
Hence the missing coordinate M is:
1 unit down from P, hence y = 2 - 1 = 1.2 units left from P, 6 - 2 = 4.More can be learned about ordered pairs at brainly.com/question/1528681
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The midpoint of AB is M (3, -1). If the coordinates of A are (8, 4), what are the coordinates of B?
Answers
PLEASE HELP ME.!! I WILL GIVE BRAIN LIST
Which graph shows the image of ΔABC after a rotation about the origin?
Answers
Answer: Choice B
Answer:
B
Step-by-step explanation:
A is a reflection across the y-axis.
B is the result of a rotation around the origin either by 90° counterclockwise, or by 270° clockwise.
C is a reflection across the x-axis.
D is a translation (shift) by -5 to the left.
Question 43 of 50
The graph of an exponential function that is increasing is ƒ(x) = (1/5)x.
False
True
Answers
Answer:
Option: A is the correct answer.
Step-by-step explanation:
Clearly from the graph we could observe that the graph is a decay exponential function as the graph of the function is decreasing with the increasing value of x.
Hence, the rate has to be less than 1.
So, option: B and D are ruled out as they represent a growth exponential function.
Also from the graph given in the question we could observe that when x=0 the value of y is:
y=4
So, the exponential function that is represented by the graph is:
Answer: true
Step-by-step explanation:
A random sample of 40 college professors is selected from all professors at a university. The following list gives their ages.
64, 40, 45, 43, 33, 50, 47, 49, 42, 28, 55, 64, 55, 41, 65.
64, 50, 45, 51, 23, 35, 64, 43, 45, 37, 37, 47, 34, 27, 49,
62, 39, 35, 44, 23, 36, 42, 34, 32, 52.
D
Answers
The required leaves values for the given stems are calculated below.
What is Stem-and-Leaf plot?A plot where every information esteem is parted into a "leaf" (typically the last digit) and a "stem" (different digits). For instance "32" is parted into "3" (stem) and "2" (leaf). The "stem" values are recorded down, and the "leaf" values are recorded close to them.
For example , 42, 34, 48, and so on.
Here 42 and 48 qualities will be written in stem 4 as their most memorable digit is 4, while 2 and 8 will be placed in the leaf side.
Likewise, 3 will be the stem, and 4 will be the leaf for esteem 34.
4| 2, 8
3| 4
According to question:65, 40, 47, 47, 33, 55, 44, 49, 46, 22, 58, 65, 56, 41, 63, 65, 54, 42, 58, 29, 39, 66 , 49, 42, 34, 36, 42, 35, 21, 44, 61, 35, 33, 42, 27, 30, 46, 33, 35, 58.
As given in the question that the stem and Leaves are to be separated by a hyphen.
Stem-and-Leaf plot 6 - 5, 5, 3, 5, 6, 1
5 - 5, 8, 6, 4, 8, 8
4 - 0, 7, 7, 4, 9, 6, 1, 2, 9, 2, 2, 4, 2, 6
3 - 3, 9, 4, 6, 5, 5, 3, 0, 3, 5
2 - 2, 9, 1, 7
As we can see above there are 5 stems, where stem 6 has 6 leaves, stem 5 has 6 leaves, stem 4 has 14 leaves, stem 3 has 10 leaves, and stem 2 has 4 leaves.
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I need help with this please help me
Answers
Answer: 18
Step-by-step explanation:
[tex]\triangle HJK \cong \triangle HLK[/tex] by HL. Therefore, [tex]JK=2[/tex] by CPCTC.
Using the segment addition postulate, [tex]GK=9[/tex].
Furthermore, [tex]\triangle HGK \cong \triangle HMK[/tex] by HL. This means that [tex]MK=9[/tex] by CPCTC.
Using the segment addition postulate again, [tex]GM=9+9=18[/tex].
The price of a gallon of unlead gas has risen to $2.88 today. yesterdays price was $2.83. Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answers
Hope this helps!
Leave a 5 star review if your experience was pleasant!
Find the surface area
3yd
3yd
8yd
Answers
Answer: 72
Step-by-step explanation: 3 x 3 x 8 = 72
3 x 3 = 9
9 x 8 = 72
If one of the factors from the product of 3 identical factors of a number is 4, what is that number?
Answers
Answer:
64
Step-by-step explanation:
Since one of the 3 identical factors is 4, then the number is 4×4×4, or 4³
HELP PLEASE this is urgent
Answers
Answer:
10.5 cm
Step-by-step explanation:
YZ corresponds to TU
YZ:TU = 9:3 = 3:1
XY corresponds to ST
ST = 3.5 cm
XY:ST = 3:1
XY/ST = 3/1
XY/3.5 cm = 3
XY = 10.5 cm
Step by step
Line up your known sides
TU and ZY are similar
The dilation rate is small to large x3 ratio
(9/3) therefore
ST to TY is also rate of x3
ST = 3.5 x 3 = 10.5cm
Choose an equation in slope-intercept form for the line that passes through (0,7) and is parallel to the y=4x-19
a. y= (1/4)x - 7
b. y= (1/4)x + 9
c. y = 4x + 3
d. y = 4x + 7
Answers
Answer:
Step-by-step explanation:
You dont even need to look at the slope. For it to pass through (0,7) answer d with the +7 at the end is the only right answer
your welcome
D
mean of 1/3 and - 2/5
Answers
Answer:
-1/30
Step-by-step explanation:
add the two numbers and divide by 2
A line has a slope of 1 and passes through the point (-2, 8). What is its equation in slope-intercept form?
Answers
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{8})\hspace{10em} \stackrel{slope}{m} ~=~ 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{ 1}(x-\stackrel{x_1}{(-2)}) \implies y -8= 1 (x +2) \\\\\\ y-8=x+2\implies {\Large \begin{array}{llll} y=x+10 \end{array}}[/tex]
Answer: The answer is y=x+10
7x - 10y = 28
7x - 3y = 28
Answers
Answer:
(4, 0)
Step-by-step explanation:
7x - 10y = 28
7x - 3y = 28
------------------
(7x - 10y = 28) × -1
-7x + 10y = -28
--------------------------
-7x + 10y = -28
7x - 3y = 28
--------------------------
7y = 0
y = 0
7x - 10y = 28
7x - 10(0) = 28
7x = 28
÷7 ÷7
----------------
x = 4
(x, y)
(4, 0)
I hope this helps!
x-intercepts for 7x - 10y = 28:
(4,0)
y-intercepts:
(0, -14/5)
x-intercepts for 7x - 3y = 28:
(4, 0)
y-intercepts:
(0, -28/3)
Step-by-step explanation:I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Last year, 769 of the 1,307 residents in a small town owned more than one vehicle.
Use this historical data to find the probability that a randomly selected resident in this small town owns more than one vehicle.
Answers
Around 58 percent
How many ways can 5 couches snd 7 beds be chosen from a shipment off 11 couches shipme b ts and 10 bed shipments
Answers
The number of ways can 6 couches and 5 beds are chosen from a shipment of 11 couches and 12 beds will be 55440
What are permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
It is given that, the total number of couches and beds will be 11 and 10.
We have to find a number of ways for the 5 couches and 7 beds are chosen from a shipment.
The different methods are there to select 5 couches and 7 beds from a shipment of 11 couches and 10 beds obtained as,
=11C₅× 10C₇
=462×120
=55440
Thus, the number of ways can 6 couches and 5 beds are chosen from a shipment of 11 couches and 12 beds will be 55440
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If angle 1 is 25 degrees in the parallelogram pictured above, what is angle 2
if q is 1x+ 10 and AC is 7x+8 what is the length of AC? Round your answer to the nearest hundredth
Answers
Applying the properties of a parallelogram:
1. Length of AC = 24.8 units
2. x = 1
What are the Properties of a Parallelogram?Some properties of parallelogram we need to recall in order to solve the problem given are:
They have two pair of sides that are parallel to each other and also of the same length.They have two diagonals that bisect each other into equal halves.1. q = 1x + 10
AC = 7x + 8
Therefore:
q = 1/2(AC) [based on the property of a parallelogram]
Substitute
x + 10 = 1/2(7x + 8)
Solve for x
2(x + 10) = 7x + 8
2x + 20 = 7x + 8
2x - 7x = -20 + 8
-5x = -12
x = -12/-5
x = 2.4
Length of AC = 7x + 8 = 7(2.4) + 8
Length of AC = 24.8 units
2. x + 8 = 7x + 2 [based on the property of a parallelogram]
x - 7x = -8 + 2
-6x = -6
-6x/-6 = -6/-6
x = 1
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The value of a brand new car depreciates 10% when leaving the agency and another 5% after the first year of use. After one year of use, the value of a certain automobile is $51,300.00. Which of the following mathematical expressions correctly represent the value (x) of this automobile zero km? x times open parentheses 0 comma 10 plus 0 comma 05 close parentheses equals 51300 double right arrow x equals 342000 x times open parentheses 0 comma 90 plus 0 comma 95 close parentheses equals 51300 double right arrow x equals 26308 x equals 51300 plus 51300 over 10 plus 51300 over 5 double right arrow equals 66690 x equals 51300 minus open parentheses 51300 over 10 plus 51300 over 5 close double right arrow x equals 35910 x times 0 comma 90 times 0 point 95 equals 51300 double right arrow x equals 60000
Answers
The value of the car zero km is given by the expression x = 60000.
LET ME EXPLAIN SOMETHING:
An algebraic expression is one that has several operations between numbers and letters (unknowns): addition, multiplication, subtraction, division, potentiation, rooting, etc.
LET'S GO TO THE SOLUTION:
Let x be the initial value of the car, we know that it depreciates 10% when leaving the agency and another 5% after one year. If the value of this car is $51,300.00 after 1 year, we will have to:
When you leave the agency, your value decreases by 10%:
x·(100% - 10)% = 90% of x = 0.9xAfter a year, its value decreases by 5%:
0.9x·(100% - 5)% = 95% of 0.9x = 0.855x0.855x = 51300
x = 60000
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https://brainly.com/question/953809If a firm sold some inventory on credit as opposed to cash, there is no reason to think that either its current or quick ratio would change. a
Answers
The given statement would be "false".
What is the quick ratio?A quick ratio compares the company's most liquid assets to a short-term commitment. The quick ratio is computed by adding the cash and equivalents of the firm to its short-term investments and account receivable. Divide the figure by the firm's existing liabilities.
As per the question, there is no reason to believe that if a company sold any goods on credit rather than cash, its current or quick ratio would change that would be false.
Thus, the given statement would be "false".
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The question seems to be incomplete the correct question would be:
Find the statement true or false.
If a firm sold some inventory on credit as opposed to cash, there is no reason to think that either its current or quick ratio would change. (T/F)
If a=3 and b=-2i, then find the value of the ab^{2} in fully simplified form.
Answers
[tex]i = \sqrt{-1}[/tex]
Solving the QuestionWe're given:
a = 3b = -2i[tex]ab^2[/tex] = ?[tex]ab^2[/tex]
⇒ Plug in the values for a and b:
[tex]=(3)(-2i)^2[/tex]
⇒ Rewrite i as [tex]\sqrt{-1}[/tex]:
[tex]=(3)(-2\sqrt{-1})^2[/tex]
⇒ Simplify:
[tex]=(3)(-2)^2(\sqrt{-1})^2\\=(3)(4)(-1)\\=-12[/tex]
Answer-12
In a class, the ratio of girls to boys is 2:3. There are 12 boys in the class. How many women are in the class?
Group of answer choices
1. 13
2. 18
3. 8
4. 11
Answers
Answer:
8
Step-by-step explanation:
Because we multiply 4 by both sides
2 times 4 is 8 for girls
4 times 3 is 12 for boys
So it asked for girls and 4 times 2 is 8
So the answer is 8
8 women are in the class.
hi! Can someone please help me out? Thank you so much :) I’ll give brainly. Question is in image
Answers
Answer:
d) 189.3 in²
Step-by-step explanation:
Area of rectangle is,
→ w × l
→ 10 × 15
→ 150 in²
Area of semi circle is,
→ (1/2)πr²
→ (1/2) × 3.14 × (5)²
→ 1.57 × 25
→ 39.3 in²
Now the total area will be,
→ 150 + 39
→ 189.3 in²
Thus, total area is 189.3 in².
solve for U
3u − –2 = 8
U=
Answers
3(2) - -2 =8
3 times 2 equals 6.
And 6 plus 2 equals 8.
When a subtraction symbol is in front of a negative number you add.
+*+=+
+*-= -
-*- = +
-*+= -
So back to the Question
3*2= 6
6+2= 8
U=2
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-14x - 6 + 8 What is the answer???
Answers
Answer:
The answer is 2-14x or
-12x
HELP!! PLS JT WONT TAKE LONG. IS THIS PHOTO CURVE A NORMAL DISTRIBUTION. WHY OR WHY NOT.
Answers
Answer:
no, it isn't symmetrical
Step-by-step explanation:
give me brainliest pls
{ | ∈ and 3 ≤ < 9} ROOSTER MODE
Answers
The rooster form of the given set is {3, 4, 5, 6, 7, 8}
What is the rooster form of set?The contents of a set can be described by listing the elements of the set, separated by commas, inside a set of curly brackets. This way of describing a set is called roster form.
Given a set, {I ∈ ≤3<9}
Converting in rooster form, {3, 4, 5, 6, 7, 8}
Hence, The rooster form of the given set is {3, 4, 5, 6, 7, 8}
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If fx)=1/9x-2, what is f¹(x)?
0 f¹(x)= 9x + 18
0 f¹(x)= 1/9x+ 2
0 f¹(x)= 9x+2
0 f¹(x)= -2x + 1/9
Answers
Answer:
f⁻¹(x)= 9x + 18
Step-by-step explanation:
1. Replace f(x) with x, and x with y: x=1/9y-2
2. Solve for y:
x=1/9y-2
9x=y-18
9x+18=y
3. Replace y in step 2 with f⁻¹(x)
31 MULTIPLE CHOICE which of the following is not possible geometry
Answers
Answer:
? where are the questions i will edit when answer arrive.
Step-by-step explanation:
Find the distance between (−7, 2) and (−6, 3). Round your answer to the nearest tenth.
Answers
Answer:
[tex]\huge\boxed{\sf D=1.4 \ units}[/tex]
Step-by-step explanation:
Points:[tex](x_1,y_1)=(-7,2)[/tex][tex](x_2,y_2)=(-6,3)[/tex]Distance Formula:Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Put the above points in the formula.
[tex]D=\sqrt{(-6-(-7))^2+(3-2)^2} \\\\D=\sqrt{(-6+7)^2+1^2} \\\\D=\sqrt{1^2+1} \\\\D=\sqrt{1+1} \\\\D=\sqrt{2} \\\\D=1.4 \ units\\\\\rule[225]{225}{2}[/tex]
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
From the solution to the given inequality, the correction representations are -6x + 15 < 10 - 5x and a number line from -3 to 7, with an open circle at 5 and an arrow pointing to the right.
Solving Linear InequalitiesFrom the question, we are to determine the correct representations of the given inequality
The given inequality is
-3(2x - 5) < 5(2 - x)
To determine the correct representation, we will solve the inequality
Solving the inequality
-3(2x - 5) < 5(2 - x)
Clear the parentheses by applying the distributive property
-6x + 15 < 10 - 5x
Add 6x to both sides
-6x + 6x + 15 < 10 - 5x + 6x
15 < 10 + x
Subtract 10 from both sides
15 - 10 < 10 - 10 + x
5 < x
Therefore,
x > 5
Hence, the correction representations are -6x + 15 < 10 - 5x and the number for x > 5
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