The first second third fourth and fifth term of the sequence
[tex]a_{n}[/tex] = 3n + 2 are 5, 8, 11, 14, 17 and 20 respectively.
According to the given question.
We have formula for finding the terms of the sequence, [tex]a_{n}[/tex] = 3n + 2 .
Therefore, the first term of the sequence [tex]a_{n}[/tex] = 3n + 2 is given by
[tex]a_{1}[/tex] = 3(1) + 2 = 5
The second term of the sequence [tex]a_{n}[/tex] = 3n + 2 is given by
[tex]a_{2}[/tex] = 3(2) + 2 = 8
The third term of the sequence [tex]a_{n}[/tex] = 3n + 2 is given by
[tex]a_{3}[/tex] = 3(3) + 2 = 11
The fourth term of the sequence [tex]a_{n}[/tex] = 3n + 2 is given by
[tex]a_{4}[/tex] = 3(4) + 2 = 12 + 2 = 14
The fifth term of the sequence [tex]a_{5}[/tex] = 3n + 2 is given by
[tex]a_{5}[/tex] = 3(5) + 2 = 15 + 2 = 17
The sixth term of the sequence [tex]a_{5}[/tex] = 3n + 2 is given by
[tex]a_{6}[/tex] = 3(6) + 2 = 18 + 2 = 20
Hence, the first second third fourth and fifth term of the sequence
[tex]a_{n}[/tex] = 3n + 2 are 5, 8, 11, 14, 17 and 20 respectively.
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7b-3(b+1)=2(b − 3)+(2b-6)
Answer: b=8
Step-by-step explanation:
At the end of December, the Cookie Shop had a profit of $15,000. At the end of January, their profit had decreased by 20%. Type the answer in the box to represent the Cookie Shop's profit at the end of January.
The Cookie Shop's profit at the end of January will be $12000.
The profit earned by the shop at the end of December = $15000
The profit decreased by 20% at the end of January
Therefore decrease percentage, which is used to determine the percentage decrease of two values (final value and initial value)
[tex]Decrease percentage = \frac{Final value - Initial Value}{Final Value} * 100[/tex]
According to the formula, the initial value is subtracted from the final value. The resulting value is divided by the initial value and multiplied by 100 to obtain the decreased percentage
Decrease Percentage 20%
Final value = $15000
[tex]20 = \frac{15000 - Initial Value}{15000} * 100[/tex]
[tex]\frac{20}{100} = \frac{15000 - Initial Value}{15000}[/tex]
[tex]\frac{20}{100} * 15000 ={15000 - Initial Value}[/tex]
20 * 150 = 15000 - Initial Value
3000 = 15000 - Initial Value
Initial value = 15000 - 3000
Initial value = $12000
The profit earned by the Cookie Shop at the end of January will be $12000.
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Write the equation of the line that passes through the points (6,-3) and (1,7) in the form y = mx + b.
m=
b=
Please help me asap !
Answer:
a = 71°
Step-by-step explanation:
This looks like a supplementary angle
109 + a = 180
-109 -109
a = 71°
I hope this helps!
Answer:
a = 71°
Step-by-step explanation:
Hello!
The sum of angles on a line is 180°. That means, 109° and a have to add up to 180°.
Angles that add up to 180° are called supplementary angles.
Solve for a180° - 109° = a71° = aa is 71°.
How do I find (rs)(4)=?
How do i also find (r/s)(3)=?
The functions are express as follows:
(rs)(4) = 8(r / s)(3) = 2How to solve composite functions?A composite functions is gotten from the combination of two or more functions.
Therefore,
(rs)(4) = r(4) × s(4)
r(x) = 2√x
s(x) = √x
Hence,
r(4) = 2√4 = 2 × 2 = 4
s(4) = √4 = 2
Therefore,
(rs)(4) = r(4) × s(4) = 4 × 2 = 8
(r / s) (3) = r(3) / s(3)
r(3) = 2√3
s(3) = √3
Hence,
(r / s) (3) = r(3) / s(3) = 2√3 / √3 = 2
Therefore, the functions are express as follows:
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PLEASE!!!!If DEF =110 then what are FEG and HEG?
Answer:
FEG: 70 degrees
HEG: 110 degrees
Step-by-step explanation:
vertical angles are the same, and for supplementary angles you subtract 180, so likes for FEG you subtract 110 from 180, and for HEG its just the same thing
Answer each question to solve the equation. **Remember to state the units in your answer** Jennifer saved some money from her birthday. During the summer, she worked part time at McDonalds. She was paid $15 an hour. The equation 50+15h=1250 represents the amount of money she has. 1. What could the 1250 represent in this situation? A. The amount of money she had saved before B. The amount of money she had at the end of the summer C. The amount of money she earned per hour D. The amount of money she earned per week 2. George said that 10 could not be the solution to the equation. Explain why he is correct (Hint: put 10 in the place of h). 3. Find the solution to the equation. Show your work.
The 1250 represents option B in the situation, George is correct, the solution to the linear equation is h = 80$.
What is a linear equation?
A linear equation has only one or two variables. No variable in a linear equation is raised to a power greater than one or used as the denominator of a fraction. When two values satisfying a linear equation are found and shown, all of the points on a coordinate grid fall on the same line.
Given that,
Jennifer was paid $15 per hour.
Given equation is 50+15h=1250
1)Here 1250 represent B.
Her financial situation towards the end of the summer.
Because as mentioned in the equation 50+15h=1250
Here, 50 is the money already there with her, and 15h was the amount paid to her,
So, by adding those both the amount 1250 will be the amount with Jennifer at the end of the summer.
2)Given equation is 50+15h=1250
By putting 10 in place of h (h=10)
50+15(10)=1250,
50+150=1250,
200=1250$.
Since, LHS is not equal to RHS.
Therefore, George is correct, 10 could not be the solution to the linear equation.
3) Given equation 50+15h=1250
15h=1250-50,
15h=1200,
h=1200/15,
h=80$.
Therefore, the solution for the equation h is 80$.
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the price of a scooter and a cycle are in the ratio 5:2 if the scooter costs ruppes 4,200 more than the cycle ,whats the price of the cycle
The price of the cycle is 2800 and the price of the scooter is 2800+ 4200=7000
Let the price of the cycle be x
Then the price of the scooter will become X + 4200
As the price of a scooter and the price of a cycle are in the ratio of 5:2
So, it can be written as
x+4200: x:: 5:2
which implies
x= 2a and x+4200= 5a
a= x/2 and x+4200/5
equating both the equations, we get
x/2=(x+4200)/5
in order to solve this linear equation, we need to move 2 from the left-hand side to the right-hand side which would result in the change of sign from division to multiplication and we need to move 5 from the right-hand side to the left-hand side which would result in the change of sign from division to multiplication
5x=2x+8400
3x= 8400
X= 8400/3
X= 2800
So, the price of the cycle is 2800 and the price of the scooter is 2800+ 4200=7000
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Help!!
The number of yards Kyle travels on in-line skates, y, varies directly with the amount of time spent skating, t. When Kyle skates for 1.5 min, he can travel 351 yd.
Which equation shows this direct linear variation?
y = 526.5t
Y = 234t
y = 175.5t
y = 352.5t
Answer:
y = 234t
Step-by-step explanation:
Divide the equation by t on both sides. See image.
I REALLY NEED HELP! Given the function defined by f(x)=8x-8, find f(6). Simplify.
Answer:
f(6) = 40
Step-by-step explanation:
f(x)=8x-8
f(6) means to evaluate the function at x = 6.
Substitute 6 for x, and evaluate the right side.
f(6) = 8(6) - 8
f(6) = 48 - 8
f(6) = 40
(-4)² = -(4)² True Or False
Help Quick Please!
Answer: True
Step-by-step explanation: Because Im A Top G
a. Write 64√2 in the form 2^n
We get the expression 64√2 in the form 2ⁿ as 2⁶°⁵.
An expression is a way in which numbers are written.
It can be variables, constants or a combination of both.
We are given an expression:
64 √2
We know that:
64 = 2 × 2 × 2 × 2 × 2 × 2
64 = 2⁶
Also, we can write √2 as
√2 = 2⁰°⁵
We get that:
2⁶ × 2⁰°⁵
simplifying the expression, we get that:
= 2⁶⁺⁰°⁵
= 2⁶°⁵
Therefore, we get the expression 64√2 in the form 2ⁿ as 2⁶°⁵.
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Use the number line below to show 10 + (–6). What is the sum of 10 + (–6)?
Answer:
4
Step-by-step explanation:
when you add a positive number to a negative number you subtract the two instead!
so, rephrase your math problem to
10-6=?
well 4
using the image you go back 6 places and you get 4
f (x) = - |x + 9| find x
Answer:
source?
Step-by-step explanation:
wiyhout one I cannot help you, best of luck!
Evaluate the expression 8p2−2s3÷m + 58p^2-2s^3\div m\ +\ 58p
2
−2s
3
÷m + 5, when ppp =3, sss =2, and mmm =4
The solution for the expression ((8p² - 2s³) / m ) + ((58p² - 2s³) / m) + ((58p² - 2s³) / ( m + 5)) is 196.72
Given,
The expression: ((8p² - 2s³) / m ) + ((58p² - 2s³) / m) + ((58p² - 2s³) / ( m + 5))
Where,
Value of p is given as 3
Value of s is given as 2
Value of m is given as 4
Then,
((8p² - 2s³) / m ) + ((58p² - 2s³) / m) + ((58p² - 2s³) / ( m + 5))
= (8 x 3² - 2 x 2³) / 4 + (58 x 3² - 2 x 2³) / 4 + (58 x 3² - 2 x 2³) / 4 + 5
= (8 x 9 - 2 x 8) / 4 + (58 x 9 - 2 x 8) / 4 + (58 x 9 - 2 x 8) / 9
= (72 - 16) / 4 + (522 - 16) / 4 + (522 - 16) / 9
= 56 / 4 + 506 / 4 + 506 / 9
= 14 + 126.5 + 56.22
= 196.22
Therefore, the solution for the expression ((8p² - 2s³) / m ) + ((58p² - 2s³) / m) + ((58p² - 2s³) / ( m + 5)) is 196.72
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HELP ASP SHOW WORK YOULL GET BRAINILEST
Answer:Ill try my best.
The answer is
3rd one
Step-by-step explanation:
subtract 70 from both sides of the equation
10% of a water tank fills every 5 minutes. If you are filling a 40 gallon tank, how many gallons will there be in 30 minutes
explain step by step
By using cross mutliplication, there are 24 gallons in the water tank after 30 minutes.
How to estimate the filling time of a water tank by cross multiplicationAccording to the statement the water tank is full at constant rate, 10 % tank capacity per each 5 minutes. The tank has a capacity of 40 gallons. The gained capacity is determined by the following cross multiplication, where the water capacity is directly proportional to filling time:
x ∝ t
x = (n / 100) · V × (T / t) (1)
Where:
n - Initial capacity percentage of the water tank, in percentage.V - Full capacity of the water tank, in gallons.T - Final time, in minutes.t - Initial time, in minutes.x = [0.1 · (40 gal)] × (30 min / 5 min)
x = 24 gal
There are 24 gallons in the water tank after 30 minutes.
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Match each equation with the correct solution.
PLEASE HELP!! 30 POINTS!!
Answer:
Step-by-step explanation:
You just have to distribute all the equations. Start with the parenthesis. I'll do one for you. 2(x-5) +7 = x+8. Distribute 2(x-5) and you gest 2x-10+7=x+8. subtract x from the right and you get x-10+7=8. Combine like terms so you get x-3=8. Then add 3 on both sides and you get x=11.
What is the pitch when the wavelength is 5 feet? hertz
A) The type of variation between pitch and wavelength is an inverse variation. b) the pitch when the wavelength is 5 feet would be 132 hertz.
What is Inverse Variation?we know that the Inverse Variation is a relationship between two variables in which the product is a constant.
Let x be a pitch of a musical instrument
y be the wavelength
x*y=k
We need to find the value of k for x=220 hertz and y=3 ft
Then x*y=k
220*3=k
k=660
And for x=165 hertz , y=4 ft
x*y=k
165*4=660
k=660
A) Therefore, the type of variation between pitch and wavelength is an inverse variation.
B) the pitch when the wavelength is 5 feet;
x=?
y=5 ft
k=660
x*y=k
Then solve for x
x=k/y
x=660/5
x=132 hertz
Part b) the pitch when the wavelength is 5 feet would be 132 hertz
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The complete question is;
"A musical instrument has a pitch of 220 hertz when the wavelength is 3 feet. When the wavelength is 4 feet, the pitch is 165 hertz. What is the type of variation between pitch and wavelength? What is the pitch when the wavelength is 5 feet? hertz"
what is the value of the 5 in 3,152,308.
HELP ASP SHOW UR WORK WILL GET BRAINILEST AND 10 points
Answer:
7 baskets
Step-by-step explanation:
in the first game, he shot 6 baskets so
34 - 6 = 28
she shot the same number for each of the 4 games,
so divide 28 and 4.
the answer is 7
hope this helps
In a recent year the populations of china was 1.3x10^9According to the census data the population of the us was about 308,745,538 about how many times greater was the population of china than the population of the us step by step pleas
According to the census data, the population of China is more than the population of US by a factor 4.2
How to find how many times greater was the population of China over US populationGiven data
population of China = 1.3x10^9
population of US = 308,745,538
population of china = 1.3x10^9. can be rewritten as = 1,300,000,000
comparing the both figures representing population. we divide the population of China by the population of US
let the number of times the population of china is greater than population of US be x, such that
308,745,538 * x = 1,300,000,000
308,745,538x = 1,300,000,000
x = 1,300,000,000 / 308,745,538
x = 4.2106
x ≅ 4.2
We therefore say that the population of china is more than the population of US by a factor 4.2
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50 pts if you can solve this correctly
Answer:
C.
Step-by-step explanation:
c^2-a^2
will give you b
Answer:
The Answer is C
Step-by-step explanation:
Hope this helps!!!
The scores on the statistics test was normally distributed with a mean of 86 and a standard deviation of 5. Jose scored a 93 on his test. What percentage of the class scored less than he did?
The scores on the statistics test was normally distributed with a mean of 86 and a standard deviation of 5. Jose scored a 93 on his test then 1.4% of the class scored less than he did.
What is Normal Distribution?A probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
The scores on the statistics test was normally distributed with a mean of 86, a standard deviation of 5, and Jose scored a 93 on his test.
We need to find the percentage of the class scored less than he did
z=(x-mean)/ S.D
=93-86/5
=7/5
=1.4
Therefore 1.4 percentage of the class scored less than Jose did.
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The number of cakes baked at a restaurant each day for 12 days is shown below. What is the
percentile of 7 cakes?
2, 4, 4, 5, 5, 6, 6, 7, 8, 10, 12, 15
Using it's concept, it is found that the percentile of 7 cakes is the 67th percentile.
What is the percentile of a measure?When a measure is in the xth percentile of a data-set, it is greater than(or equal) x% of the measures and lesser than (100 - x)%.
In this problem, we have that:
There are 12 measures in the data-set.7 is at the position 8, that is, it is the 8th largest element of the data-set.Hence, the percentile of the measure 8 is found as follows:
8/12 = 67th (rounded).
The percentile of 7 cakes is the 67th percentile.
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find the perimeter of the new similar triangle to the triangle below with a ratio of 3:5, old to new triangle
A. 24.17
B. 8.7
C. 14.5
D. 24
E. 9
Answer:
A. 24.17.
Step-by-step explanation:
Perimeter of given triangle
= 4 + 4.5 + 6
= 14.5.
3:5 = 14.5 : P where P is perimeter of new triangle
3/5 = 14.5/P
3P = 5*14.5
P = 14.5 * 5 / 3
= 24,166667
= 24.17.
Determine whether each list is a sequence or a series and finite or infinite. 1,2,4,8,16,32, . . . . . .
From the list of numbers presented:
12481632we can determine that this is a infinite serie.
What are sequences?A sequence is an order of elements that are governed by a pattern, that is, it has variations between each element that remain constant and allow us to determine values before or after the known elements.
A sequence maintains an order, and this numerical order can be finite or infinite, in the given case we have the following list:
1, 2, 4, 8, 16, 32
2ⁿ⁻¹2⁰ = 12¹ = 22² = 42³ = 82⁴ = 162⁵ = 322ⁿ⁻¹
In this series we have the initial value of the same, but we do not know the final value, although we know its behavior, we can say that this series has no end, it is an infinite serie.
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394.82−55.75 helppppppppppp
Answer: 339.07
Step-by-step explanation:
Answer:
339.07.
Step-by-step explanation:
I've attached an image to help break down this problem. (credit to cymath.com)
Hope this helps! :)
Ty plays football at his neighborhood park with his friends. He can make field goals and touchdowns. Field goals are worth 1 point each and touchdowns are worth 6 points each. Ty can no more than 18 points before his neighborhood buddies kick him out of the game for dominating too much.
Write an inequality to describe the constraints.
Use "f" for field goal and "t" for touchdown.
***THE PICTURE IS PART 2***
The inequality that describes the constraints is f + 6t ≤ 18
If Ty has 4 field goals and 3 touchdowns, he cannot remain on the team.
What is the inequality that describes the constraints?Here are inequality signs and what they mean:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
The inequality sign that would be used is ≤ because Ty's score has to be at most 18 points.
The from of the inequality that describes the constraints is:
(point of a touchdown x number of touchdowns) + (point of field goals x number of field goals) ≤ maximum points
(1 x f) + (6 x t) ≤ 18
f + 6t ≤ 18
Ty's total score when he has 3 touch downs and 4 field goals
(1 x 4) + (6 x 3) ≤ 18
4 + 18 ≤ 18
22 ≤ 18
Ty cannot remain on the team because his score exceeds 18. (i.e. 22 > 18).
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Write an equation for each vertical translation of y=f(x) .
2/3 unit down.
The equation for the vertical translation of y=f(x).2/3 unit down is y=f(x)-2/3.
Using equations of the form y=f(x), you may be able to modify the graph in various ways. For example, you can move the chart up, down, left, or right, flip it around the x or y-axis, or stretch or shrink it vertically or horizontally. Understanding these transformations makes it easy to graph different functions. Start with a "basic model" and apply a series of modifications to change it to the desired function.
A point on the graph of y=f(x) has the shape (x,f(x)).
The points on the graph of y=f(x)-2/3 are of the form (x,f(x)-2/3).
So, the graph for y=f(x) -2/3 is the same as the graph for y=f(x) shifted down by 2/3 units.
The new equation is:
y=f(x)-2/3
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