I assume you're asking to solve for the n-th term in the sequence, [tex]a_n[/tex].
From the given recursive rule,
[tex]a_n = a_{n-1} + 2 \implies a_{n-1} = a_{n-2} + 2[/tex]
and by substitution,
[tex]\implies a_n = a_{n-2} + 2\times2[/tex]
Similarly,
[tex]a_n = a_{n-1} + 2 \implies a_{n-2} = a_{n-3} + 2[/tex]
[tex]\implies a_n = a_{n-3} + 3\times2[/tex]
The pattern continues, so that we can write the n-th term in terms of the 1st one:
[tex]a_n = a_1 + (n-1)\times2 \implies a_n = 10 + 2(n-1) = \boxed{2n+8}[/tex]
So the first few terms of the sequence are
{10, 12, 14, 16, 18, 20, …}
Please help, thanks!!
A cylinder has a height of 4 inches and a
base with a surface area of 113 square
inches. What is its volume?
Answer:
The volume is 452 square inches.
Step-by-step explanation:
Volume=area of base*height
just plug in the values
Find the volume of the trapezoidal prism
Answer:
228 in³
Step-by-step explanation:
Volume of a trapezoidal prism
V = Area x heightFinding Base Area (on the side here)
A = 1/2 x (a + b) x hA = 1/2 x (12 + 7) x 6A = 3 x 19A = 57 in²Volume
V = A x hV = 57 x 4V = 228 in³Drag the tiles to the correct boxes to complete the pairs.
Match each division expression to its quotient.
16 divided by (-8). -2 2/5 divided by 4/5. 33/7 divided by 1 1/7. -12.2 divided by (-6.1)
Answer:
check explanation for answer
Step-by-step explanation:
16 ÷ -8 = -2
- 2 \frac{2}{5} ÷ \frac{4}{5} = -3
3 \frac{3}{7} ÷ \frac{1}{7} = 3
-12.2 ÷ -6.1 = 2
help me please, will mark brainliest!
Step-by-step explanation:
remember (always remember) : a probability is desired cases divided by total possible cases.
what is our total here ?
1388 students at this school
what are our desired cases here ?
every student, who bikes to the school : 207
so, the probability that a randomly picked student is biking to the school is
207/1388 = 0.149135447...
so, b. is the right answer.
please let me know what is not clear to you.
we solved now many probability questions together, but this is very, VERY basic, and you could not do it.
so, what is not "clicking" with you ? what do you need explained ?
Am thinking of a number,l take away 3 the results is 14.what number is it
Expand the binomial using the Binomial Theorem.
(3c − d)^3
Answer:
[tex]27c^3-27c^2d+9cd^2-d^3[/tex]
Step-by-step explanation:
Binomial Theorem
[tex](a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n[/tex]
[tex]\textsf{If }(a+b)^n=(3c-d)^3 \: \textsf{ then}:[/tex]
a = 3cb = -dn = 3Substitute the given values into the formula:
[tex]\begin{aligned}(3c-d)^3 & =(3c)^3+\dfrac{3!}{1!(3-1)!}(3c)^{3-1}(-d)+\dfrac{3!}{2!(3-2)!}(3c)^{3-2}(-d)^2+(-d)^3\\\\& =(3c)^3+3(3c)^2(-d)+3(3c)^1(-d)^2+(-d)^3\\\\& =27c^3-27c^2d+9cd^2-d^3\end{aligned}[/tex]
Drag each expression to its equivalent.
Answer:
x-3+2x+3+2x = 5x
x+8+4x-3x-4 = 2x+4
4x+x-11-5X+25+4x = 4x+14
3x+5-2x-5x+9+8x = 4x+14
5+9x-7-4X-3x+6 = 2x+4
6x-9-5x+4-x+5x+5 = 5x
Step-by-step explanation:
Simplified by adding like terms
help please
What is e in math?
e is the Exponential Constant or Euler's Number.
It has a value of 2.718281828...
[tex]\huge\mathfrak\colorbox{white}{}[/tex]
e to the n is given by:
[tex]\huge{e}^{n}= [\sum_{k=0}^{∞} (\frac{{n}^{k}}{k!})][/tex]
A paint mixes green and white paint in the ratio 13:50. 4 litres of white paint are used. How much green is used? please help me
Answer:
1.04 liters
Step-by-step explanation:
If 50 is 4liters
Then 13 is x
Use this below equation
Value t is for value y then how much for value z
[tex]x = \frac{t}{y} \times z[/tex]
X = 4/50 *13
X = 1.04liters
Or
13/50 = x/4 (cross multiply)
50X = 52
X = 52/50
X = 1.04 liters
Two points of a parallelogram are (1,2) and (2,5). The base of the parallelogram is parallel to the x axis and is 4 units long. Find the coordinates of the other two points of this parallelogram and also find the length of the other pair of parallel sides of the parallelogrma. What would the area of this parallelogram be?
Answer:
(5,2) and (6,5)
length of side = sqrt10 ~= 3.16 units
Area = 12 sq units
Step-by-step explanation:
It really helps to graph the given information. See image. The sides have the same slope bc they are parallel. If you go UP3 & OVER1 to get from the first point to the second point, then do that again on the right side. See image. Use distance formula or pythagorean thm to find the length:
c^2 = 3^2 + 1^2
c^2 = 9+1
c^2 = 10
c = root10 ~= 3.16
Area of a parallelogram is b•h
A = 4•3
= 12
see image.
Vectors u, v, and w are shown in the graph. What are the magnitude and direction of u + v + w?
Magnitude and direction of u + v + w is equals to 57.871 and 19°.
What is vectors?"Vectors are those quantity of which represents both direction as well magnitude."
According to the question,
As shown in diagram we have,
u + v + w
= (wcos30°)[tex]\^{i}[/tex] + (wsin30°)[tex]\^{j}[/tex] +(vcos20°)[tex]\^{j}[/tex] - (vsin40°)[tex]\^{i}[/tex] -(ucos40°)[tex]\^{i}[/tex] -(usin40°)[tex]\^{j}[/tex]
= ( wcos30° - vsin40° - ucos40°)[tex]\^{i}[/tex] + (wsin30°+ vcos20° - usin40°)[tex]\^{j}[/tex]
Substitute the value of ║w║ = 40 ,║v║=60,and ║u║= 90 we get,
u + v +w
= ( 40cos30° - 60sin40° - 90cos40°)[tex]\^{i}[/tex] + (40sin30°+ 60cos20° - 90sin40°)[tex]\^{j}[/tex]
= (20√3 - 20.5212 - 68.9440)[tex]\^{i}[/tex] + ( 20 +56.3816 - 57.8509)[tex]\^{j}[/tex]
= ( -54.8242)[tex]\^{i}[/tex] + (18.5307)[tex]\^{j}[/tex]
Therefore,
Magnitude = √(-54.8242)² +(18.5307)²
=√3349.0798
= 57.8712
tanθ = ( 0.3380)
⇒θ = tan⁻¹ (0.3380)
= 18.67
≈ 19°
Hence, magnitude and direction of u + v + w is equals to 57.871 and 19°.
Learn more about vectors here
https://brainly.com/question/17108011
#SPJ2
The annual profits for a company are given in the following table, where x represents the number of years since 2002, and y represents the profit in thousands of dollars. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the projected profit (in thousands of dollars) for 2010, rounded to the nearest thousand dollars.
The equation of the best fit is y = 16.89x + 134.95 and projected profit is $2700.07
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}[/tex]
[tex]\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
The line of best fit;
y = mx + c
m = 16.89
c = 134.95
y = 16.89x + 134.95
Plug x = 2010 - 2002 = 8
y = 16.89(8) + 134.95
y = $2700.07
Thus, the equation of the best fit is y = 16.89x + 134.95 and projected profit is $2700.07
Learn more about the line of best fit here:
brainly.com/question/14279419
#SPJ1
What is the y-intercept of the line 15 - 3y = x?
The y-intercept of the line 15 - 3y = x is ( 0 , 5 )
Sure hope this helps you
You start at (3, -2). You move up 5 units. Where do you end?
Answer:
You would end at (3, 3).
Explanation:
You would plot your first mark at 3 on a typical xy graph because the first number in ()'s is always x (horizontal line).
Second, because your second mark is y (vertical line), you would plot -2 on the vertical axis.
Your y plot would be 5 more than -2 because you're traveling up five units, giving you (3, 3).
i need help please on PART B Thanks
Answer:
(a) 1 and 8
(d) 64 and 125
Step-by-step explanation:
In addition to the cubes of 2 through 11 that you found in question 1, it is convenient to add 1³ = 1 to the list for the purpose of answering this question. The cubes of the first 11 integers are ...
1, 8, 27, 64, 125, 216, 343. 512, 729, 1000, 1331
__
This question is asking you to find the numbers on either side of any that are not on the list:
(a) 2 is between 1 and 8
(d) 100 is between 64 and 125
Two cheeseburgers and one small order of fries contain a total of 1320 calories. Three cheeseburgers and two small orders of fries contain a total of 2170 calories. Find the caloric
content of each item.
Answer:
cheeseburger: 470 caloriesfries: 380 caloriesStep-by-step explanation:
The given relations let you formulate two equations in the two unknown values. These can be solved by any of the usual methods.
__
setupLet x represent the caloric content of a cheeseburger, and y the caloric content of a small order of fries. The problem statement tells us ...
2x +y = 1320
3x +2y = 2170
__
solutionSubtracting the second equation from twice the first gives ...
2(2x +y) -(3x +2y) = 2(1320) -(2170)
x = 470
Using the first equation, we can find y:
y = 1320 -2x = 1320 -2(470) = 380
__
A cheeseburger has 470 calories; a small order of fries, 380 calories.
_____
Attached is a graphing calculator solution.
Find the gradients of lines A and B
Consider the function f(x) = log x. Which two transformations can be used to move
the graph of f(x) to the graph of -f(x+4)?
Select all that apply
The parent function will translate 4 units to the left and reflect over the x-axis option (C) and (E) are correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = log x
First transformation:
Replace x → (x+4)
The parent function will shift left side by 4 units.
Second transformation:
Multiply the function with -1
The function will reflect over x-axis
The function becomes:
g(x) = -log(x+4)
Thus, the parent function will translate 4 units to the left and reflect over the x-axis option (C) and (E) are correct.
Learn more about the function here:
brainly.com/question/5245372
#SPJ1
5x - 8y = - 17
y + 5 = 3x
To answer please type altogether with no spaces. For example if your answer is negative three positive four, type (-3,4)
Answer:
5x - 8y =17
y+5 =3x
Answer | (3,4)
Step-by-step explanation:
I used a calculator
Part 1. Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that f(x) and g(x) are inverses. f(x)= x+a b g(x)=cx−d Part 2. Show your work to prove that the inverse of f(x) is g(x). Part 3. Show your work to evaluate g(f(x)). Part 4. Graph your two functions on a coordinate plane. Include a table of values for each function. Include five values for each function. Graph the line y = x on the same graph. Task 2 Part 1. Create two radical equations: one that has an extraneous solution, and one that does not have an extraneous solution. Use the equation below as a model: a√x+b+c=d Use a constant in place of each variable a, b, c, and d. You can use positive and negative constants in your equation. Part 2. Show your work in solving the equation. Include the work to check your solution and show that your solution is extraneous. Part 3. Explain why the first equation has an extraneous solution and the second does not.A newspaper started an online version of its paper 14 years ago. In a recent presentation to stockholders, the lead marketing executive stated, “The revenues for online ads are more than double that of the revenues for printed ads.” Use the graph below to justify the lead executive’s statement. Determine the approximate year that the two ad revenues were equal. See Text Version Two ocean beaches are being affected by erosion. The table shows the width, in feet, of each beach measured at high tide where 1995 is represented by year 0: Year number Western Beach width (in feet) Dunes Beach width (in feet) 0 100 20 5 90 45 10 80 70 11 78 75 12 76 80 15 70 95 Describe the patterns shown by the erosion data measurements shown for each of the beaches in the table. Between which years will the beaches have approximately the same width? Assuming these rates remain constant, what can you do to get a better approximation of when the two beaches will have the same width?
Answer: 5+10-15=30
5=35
=7
х=49
5√49+10-15=30
30=30
+1+7=4
=-4
it is no solution
Step-by-step explanation:
Kate is the captain of a large cruise ship. As she
drives the ship, she sits 50 meters above the sea.
Paul is the captain of a boat. He sits 15 meters
above the sea. If the radius of the earth is
6,371,000 meters, how much further can Kate see
across the horizon than Paul?
Kate can see across the horizon by 3.33 times further than Paul.
What is the shape of the horizon?The volume of the cone can be used to determine how far they can see across the horizon from the cone shape.
Using the volume of the cone
[tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]
For Kate:
Height (h) = 50 mRadius (r) = 6,371,000 m[tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]
[tex]\mathbf{ V=\pi \times (6371000)^2 \times \dfrac{50 }{3}}[/tex]
V = 2.12526863 × 10¹⁵ m³
For Paul
Height (h) = 15 mRadius (r) = 6,371,000 m[tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]
[tex]\mathbf{ V=\pi \times (6371000)^2 \times \dfrac{15 }{3}}[/tex]
V = 6.3758059 × 10¹⁴ m³
To determine how much further can kate see across the horizon than Paul, we have:
= 2.12526863 × 10¹⁵ m³/6.3758059 × 10¹⁴ m³
= 3.33 times further.
Learn more about Plane shapes here:
https://brainly.com/question/4504103
#SPJ1
Define bisect and midpoint. Using constructions, draw and label an angle bisector and a perpendicular bisector. Show segment addition postulate and angle addition postulate with examples of solving for a variables
Bisect is a word that means to divide a thing, line or a circle into two parts. While midpoint is known as the middle point that exist in a line segment.
What is Angle addition postulate?This theory states that if two angles are said to be put beside each other, the resulting angle is said to be equal in terms of the sum of the two real angle measures.
Note therefore, that that Bisect is a word that means to divide a thing, line or a circle into two parts. While midpoint is known as the middle point that exist in a line segment.
Learn more about bisector from
https://brainly.com/question/11006922
#SPJ1
#3
the price of a watch was decreased by 35% and
sold for $75.99. what was the original price of the
watch in dollars?
a. $26.60
c. $116.91
b. $49.39
d. $217.11
Step-by-step explanation:
it means
$75.99 = original price × 0.65 ((100-35)/100)
original price = $75.99/0.65 = $116.9076923... ≈
≈ $116.91
Write 0.030 in scientific notation
Please help :)
Help me please help me
Answer:
m = -10.7
Step-by-step explanation:
m + 4.1 = -6.6
Subtract 4.1 from both sides:
m + 4.1 = -6.6
- 4.1 - 4.1
m = -10.7
Final answer: m = -10.7
Hope this helps!
There are 440 fish in a pond. If Dylan has caught 45% of them, how many has he caught?
Answer:
198
Step-by-step explanation:
45% of 440
= [tex]\frac{45}{100}[/tex] × 440
= 0.45 × 440
= 198
What is the eighth term of the sequence below?
5, 9, 13, 17, …
A. 33
B. 30
C. 29
D. 34
Answer:
A. 33
Step-by-step explanation:
Add 4 to each number
1. 5 is your first number
2. 5+4= 9 is your second number
3. 9+4= 13 is your third number
4. 13+4= 17 ...
5. 17+4= 21 ...
6. 21+4= 25 ...
7.25+4= 29 ...
8.29+ 4= 33 is your eight number
Solve for x and show your steps. Is the solution extraneous? Check your work to show how you determined if the solution is extraneous or not.
The square root of the quantity 2 x minus 7 end quantity equals 1.
Answer:
Solve for x , 1x − 2+1x + 2=4(x − 2)(x + 2) .
1x − 2+1x + 2=4(x − 2)(x + 2)
(x − 2)(x + 2)(x − 2)+(x − 2)(x + 2)(x + 2)=4(x − 2)(x + 2)(x − 2)(x + 2)
(x−2)+(x+2)=4
2x=4
x=2
But 2 is excluded from the domain of the original equation because it would make the denominator of one of the fractions zero--and division by zero is not allowed! . Therefore, it cannot be a root of the original equation. So, 2 is an extraneous solution. So, the equation has no solutions.
Step-by-step explanation:
An equal when substitute x = 4, the solution is not extraneous the solution x = 4 is valid for the original equation.
The equation is: √(2x - 7) = 1
Step 1: Square both sides of the equation to remove the square root:
(√(2x - 7))² = 1²
Simplify:
2x - 7 = 1
Step 2: Add 7 to both sides to isolate the term with "x":
2x - 7 + 7 = 1 + 7
Simplify:
2x = 8
Step 3: Divide both sides by 2 to solve for x:
2x / 2 = 8 / 2
Simplify:
x = 4
Now, we have found that the solution for x is 4.
To check if the solution is extraneous, we need to substitute the value of x back into the original equation and see if both sides are still equal:
Original equation: √(2x - 7) = 1
Substitute x = 4:
√(2(4) - 7) = 1
Simplify:
√(8 - 7) = 1
√1 = 1
1 = 1
To know more about equation here
https://brainly.com/question/29657983
#SPJ3
Hey, could someone help me with this? If you could that would be great!
It's a 3 part question, this is the first part.
The quadratic function is f(x) = x^2 - 7.
I would like help on the third question...
Answer:
The correct answer should be C.
Step-by-step explanation:
A. is equal to x² -5.291503x +7
B. is equal to x² +5.291503x +7
C. is equal to x²2 -7
C. is the only one with a negative 7 since (-)(+)= -
If a polynomial function f(x) has roots –9 and 7 – i, what must be a factor of f(x)? (x – (7 i)) (x – (–7 – i)) (x (7 i)) (x (7 – i))
if the roots of the polynomial function are -9 and 7 - i, then the other factor of the polynomial function is x - (7 + i)
How to determine the other factor?The roots of the polynomial function are given as:
-9 and 7 - i
The root is 7 - i is a complex number.
This means that its conjugate must also be a root of the factor.
The conjugate of 7 - i is 7 + i
So, we have:
x = 7 + i
Equate to 0
x - (7 + i) = 0
Hence, the other factor of the function is x - (7 + i)
Read more about polynomial functions at:
https://brainly.com/question/2833285
#SPJ4
Answer:
A on edge 23
Step-by-step explanation:
trust me bro
