The sequence -5,15,-45,135,-405,. . . . is a geometric sequence and its 10th term is a(10) = 98,415
To determine whether a sequence is an arithmetic or geometric one, we need to check the relation between two consecutive terms.
In an arithmetic sequence, the nth term is obtained by adding the (n-1)th term with a constant, called a common difference (d).The given sequence is:
-5,15,-45,135,-405,....
In this sequence:
a(1) = -5
a(2) = 15
a(3) = -45
and so on.
Notice that:
15 = -5 . (-3) ⇒ a(2) = a(1) . (-3)
-45 = 15 . (-3) ⇒ a(3) = a(2) . (-3)
Since the n-th term is obtained by multiplying the (n-1)-th term by a constant, r = -3, hence, the given sequence is a geometric sequence.
The formula for the nth term in a geometric sequence is given by:
a(n) = a(1) . rⁿ⁻¹
Substitute n = 10, r = -3, and a(1) = -5
a(10) = (-5) . (-3)¹⁰⁻¹
a(10) = (-5) . (-3)⁹
= 98,415
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Guadalupe spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -5.4°F. Between 9am and noon, the temperature rose 9.4°F. Between noon and 3pm, the temperature went down 13.6°F. Between 3pm and 6pm, the temperature went down 16.9°F. What was the temperature at 6pm?
The final temperature of a winter day at 6 pm will be negative 26.5°Ferenhiet.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
For science class, Guadalupe works on a winter day taking the temperature once every three hours. The temperature was -5.4°F at 9 a.m. The temperature increased by 9.4°F from nine till noon. The temperature dropped 13.6°F between noon and three o'clock. The temperature dropped 16.9°F between 3 and 6 o'clock.
Then the temperature at 6 pm will be
⇒ - 5.4°F + 9.4°F - 13.6°F - 16.9°F
⇒ - 35.9°F + 9.4°F
⇒ - 26.5°F
The temperature at 6 pm will be negative 26.5°F.
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Evaluate each expression for x=-2,0,1 , and 4.
(2/3)x+7
The value of the expression for x = -2,0,1 , and 4 is 17/3, 7, 23/2, 29/3.
Given,
The equation is (2/3)x+7
For x = -2,
the value will be -
(2/3)(-2) + 7
= 17/3
For x = 0
the value will be -
(2/3)(0) + 7
= 7
For x = 1
the value will be -
(2/3)(1) + 7
= 23 / 2
For x = 4
the value will be -
(2/3)(4) + 7
= 29 / 3
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Simplify this algebraic expression completely
5y - 3(y + 2)
A.2y - 2
B.2y + 2
C.2y - 1
D.2y - 6
5y - 3(y + 2)
First distribute:
5y - 3(y + 2)
5y - 3y + 6
Add like terms:
5y - 3y + 6
2y + 6 :)
What is the definition of absolute value?
Lesson 2 TTW
The definition of absolute value is
the magnitude of a real number
without regard to its sign.
Find the absolute value of the following numbers:
|-10
Answer: The absolute value of |-10| is 10
Step-by-step explanation: The absolute value of something is the distance from the point to the 0 unit so from -10 to 0 its 10 units.
use the order of operations to simplify. -2+3 x(17-2)-29
Answer:
45x−31
Step-by-step explanation:
Essay writers stink
It's fox season! - Ash the Fox
(Will have new phrase every month!)
what would 85° F be in Celsius degrees? (Round your answer to the nearest degree.)
Answer:
The answer is 29.44 degree Celsius.
Determine the distance between each pair of points. Then determine the coordinates of the midpoint M of the segment joining the pair of points.
G(1,-1,6) and H(1/5,-2/5, 2)
The midpoint is at (6/10 , -7/10 , 4)
In the given statement is
To find the midpoint of the line segment joining the pair of points
G(1,-1,6) and H(1/5,-2/5, 2)
Midpoint:
The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.
m = (A +B)/2
If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =([tex]\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} , \frac{z_{1}+z_{2} }{2}[/tex] )
where:
(x1 , y1 ,z1) are the coordinates of the first point:
(x2 , y2 , z2) are the coordinates of the second point:
Now, We are given the three points G(1,-1,6) and H(1/5,-2/5, 2)
Solving for the midpoint , we have,
m = ([tex]\frac{1+\frac{1}{5} }{2} , \frac{-1+(\frac{-2}{5} )}{2} , \frac{6+2}{2}[/tex])
m =(6/10 , -7/10 , 4)
Therefore, the midpoint is at (6/10 , -7/10 , 4)
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Solve the formula for the height of the figure.
A=1/2bh
h=_
Use the formula to find the height.
h=_mm
Find the H.C.F:
a^3+b^3, a^4+a^2.b^2+b^4, a^4-a^2b+ab^2
Answer:
54 sqrt Mr multiple question is whether you are a man or a boy are you ok
Determine the slope of the line that contains the given points.
E(5,4), F(8,1)
The slope of the line that contains the given points E(5,4), F(8,1) is -1.
It is given in the question that the line contains the points E(5,4) and F(8,1).
We know that:-
The formula to find the slope of a line that contains points (a,b) and (c,d) is given by:-
m = (d-b)/(c-a)
Here, we have
m = slope of the line
(a,b) = (5,4)
(c,d) = (8,1)
Hence, putting the values of (a,b) and (c,d) , we get
Slope of the line that contains the given points E(5,4), F(8,1) is given by:-
(1-4)/(8-5) = -3/3 = -1
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I need this answered please
Answer:
2g+12 = Goran's height
helpp pleasee this is so hard
Step-by-step explanation:
10) [tex]24000(\frac{1}{32} )=\frac{24000}{32} =750[/tex]
Commission = $750
11) Constant of proportionality (k)
k = (Cups of blackberry) / (cups of juice)
[tex]k=\frac{4}{1\frac{1}{3} } =\frac{4}{\frac{4}{3} } =\frac{(4)(3)}{4} =\frac{12}{4} =3[/tex]
3 cups of blackberry for each cup of juice
On the table:
12 cups of black berry required: 12/3 = 4 cups of juice
8 cups of juice required: (8)(3) = 24 cups of blackberries
12) The equation
assign: cups of blackberry: b, cups of juice: j
[tex]b=3j[/tex]
Hope this helps
determine whether the following graph represent a function.
1. one to one function
2. function, but not one to one
3. Not a function
Answer:
Choice 1
It is a one to one function.
Appears to be a cubic function
Step-by-step explanation:
At this rate how long would it take for you heart to beat 700,000 times? express your answer in days . now express your answer in days , hours, minutes, & seconds. (example:2 days , 4 hours 21 minutes, 15seconds)
Based on the rate illustrated, the time that it would take for you heart to beat 700,000 times is 8.10 days.
How to calculate the value?It should be noted that the heart beats 86400 tines on a day.
Therefore, when the heart beats 700,000 times, the number of days will be:
Number of times / Number of times the heart beats in a day
= 700000 / 86400
= 8.10 days
Therefore, the time that it would take for your heart to beat 700,000 times is 8.10 days.
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Please help will give brainliest
A news reporter in a city with several carbon-emitting power plants wanted to see whether local temperatures matched trends in global climate change. She
focused on the four coldest months of the year.
The table shows local temperature data from November through February for the two consecutive cold seasons checked by the reporter.
Average Monthly Temperatures (°F)
2011-2012:
November 61 1
December 51 9
January 53.6
February 56.5
2012-2013:
Nov: 64.2
Dec:56 8
Jan;48.3
Feb: 55.1
How did the mean temperature change between the two cold seasons?
You may use the calculator.
OA.
went down by 1.40
OB.
went up by 0.3°
OC.
went up by 0.9°
OD.
went up by 3.70
The mean temperature change between the two cold seasons is (b) went up by 0.3°
How to compare the mean values of both seasons?The given parameters are:
2011-2012:
November 61 1December 51 9January 53.6February 56.52012-2013:
Nov: 64.2Dec:56 8Jan;48.3Feb: 55.1The mean is calculated as
Mean = Sum/Count
So, we have
2011 - 2012 mean = (61.1 + 51.9 + 53.6 + 56.5)/4
Evaluate
2011 - 2012 mean = 55.8
Also, we have
2012 - 2013 mean = (64.2 + 56.8 + 48.3 + 55.1)/4
Evaluate
2012 - 2013 mean = 56.1
The difference in these mean values are
Difference = 56.1 - 55.8
Evaluate
Difference = 0.3
Hence, the mean temperature change between the two cold seasons is (b) went up by 0.3°
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Paula is scuba diving. Her elevation changes by -374 m in 4.5 min. What rational number represents the average change in Paula's elevation each minute? Show your work.
Use the spinner to find the probability.
b. P(pointer not landing on green)
The probability of spinner pointer not landing on green is equal to 2/3 .
As given in the question,
Total colors in the spinner is equal to 6
Each color is 2 times
Total number of colored region =6
Number of green region = 2
Probability of pointer landing on green color region denoted by P(G)
Probability is
=(Total number of favourable outcomes) / (Total number of outcomes )
⇒P(G)=2/6
⇒P(G) =1/3
Probability of pointer not landing on green P(G') =1-P(G)
=1-(1/3)
=2/3
Therefore, the probability of spinner pointer not landing on green is equal to 2/3.
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22. The mass of Mercury is about
3.3 x 1023 kg. The mass of Jupiter is
about 1.9 x 10²7 kg. About how many
times the mass of Mercury is the mass
of Jupiter?
The mass of the planet Mercury is 1.74 × 10⁻⁴ kg time the mass of the planet Jupiter.
Mass of Mercury = 3.3 × 10²³ kg
Mass of Jupiter = 1.9 × 10²⁷ kg
We need to find that how many times the mass of Mercury is the mass
of Jupiter.
For this, we will divide the mass of mercury with the mass of Jupiter.
So, we get that:
= ( 3.3 × 10²³ kg ) ÷ ( 1.9 × 10²⁷ kg )
Solving the expression by using the properties of exponents, we get that:
= 1.74 × 10⁻⁴ kg.
Therefore, we get that, the mass of the planet Mercury is 1.74 × 10⁻⁴ kg time the mass of the planet Jupiter.
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Select the correct answer.
CAMERY
Which expression is equivalent to the given expression?
2x214x + 24
OA. 2(x-8)(x + 3)
OB.
(2x12)(x - 2)
OC. 2(x - 3)(x - 4)
OD. 2(x - 5)(x - 2)
A student claims that the next term of the arithmetic sequence 0,2,4, ....... is 8 . Explain and correct the student's error.
an=a1+d(n−1) by applying this formula next term of the arithmetic sequence is 8.
What is arithmetic sequence?See the pattern
2-0 = 2
4-2 = 2
By this we conclude that next term is not 8.
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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The following function represents the production cost f(x), in dollars, for x number of units produced by company 1:
f(x) = 0.25x2 − 8x + 600
The following table represents the production cost g(x), in dollars, for x number of units produced by company 2:
x g(x)
6 862.2
8 856.8
10 855
12 856.8
14 862.2
Based on the given information, determine which company has a lower minimum and find the minimum value.
g(x) at (10, 855)
f(x) at (16, 536)
g(x) at (16, 536)
f(x) at (10, 855)
A function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable, By the given information, the minimum production cost of company 2 is greater than the minimum production cost of company 1.
What is function?an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
company 1: f(x) = 0.25x² - 8x + 600
f(6) = 0.25(6²) - 8(6) + 600 = 9 - 48 + 600 = 561
f(8) = 0.25(8²) - 8(8) + 600 = 16 - 64 + 600 = 552
f(10) = 0.25(10²) - 8(10) + 600 = 25 - 80 + 600 = 545
f(12) = 0.25(12²) - 8(12) + 600 = 36 - 96 + 600 = 540
f(14) = 0.25(14²) - 8(14) + 600 = 49 - 112 + 600 = 537
company 2:
x g(x)
6 862.2
8 856.8
10 855
12 856.8
14 862.2
Now compare f(x) and g(X)
x g(x) f(x)
6 862.2 561
8 856.8 552
10 855 545
12 856.8 540
14 862.2 537
Therefore based on the given information, the minimum production cost of company 2 is greater than the minimum production cost of company 1.
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Answer: it's A
Step-by-step explanation:
g(x) at (10, 855)
According to a college survey, 22% of all students work full time. If 12 college students are randomly selected, find the probability that exactly three of them work full time.
The probability that exactly three of them work full time is 0.25.
How to calculate the probability?It should be noted that from the information, we want to find P(X = 3).
This will be illustrated as:.
12C3(1 - 22%)^9(0.22)³
= 220(0.78)^9(0.22)³
= 0.250
Therefore, the probability that exactly three of them work full time is 0.25.
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When rocket approaches the moon engineers needed to plan how the lunar
Answer:
G would equal x because she is a guy and needs to poop
Step-by-step explanation:
4 and 1 over 7 divided by 2 over 3
(Ignore messy writing I rush myself)
Answer: If the question is 41/7 divided by 2/3 then the answer is 123/14 or 8 11/14
Step-by-step explanation:
What is 3 5/6×3????????????
Answer: 17.5
Step-by-step explanation: If the question is (35/6) * 3. Then it is 17.5
[tex]\frac{35}{6}*\frac{3}{1} = \frac{105}{6} = \frac{35}{2}[/tex]
which is 17.5 in decimal form
Answer:
11 1/2
Step-by-step explanation:
3 5/6x 3
multiply 3 by the denominator then add 5
so 3x6=18/6+5/6= 23/6 x 3
so 23/6 x 3/1 = 69/6
simplify 69/6 = 11 3/6 or 11 1/2
what is the average rate of change, please simply your answer (PICTURE BELOW)
Answer:
The answer to this question is 0
Step-by-step explanation:
see attached photo for explanation
Kareem has 26 2 3 feet of vinyl siding and 33 3 4 feet of wooden siding. he cuts the vinyl siding into 3 1 3 feet long strips and the wooden siding into 2 1 4 feet long strips. how many more strips of wood siding than vinyl siding does he have
Kareem has 7 more strips of wood siding than vinyl siding.
What is a siding?
A siding is a brief railroad track with one or both ends opening into the main track, used to switch one of two meeting trains until the other has passed. Or a siding is any of a number of different forms of weatherproof face for frame buildings, made up of individual sections fastened together as shingles, plain or shaped boards, various sheet metal components, or other composition materials.
Number of vinyl siding strips = 2623/313 = 8.38 ≈ 8 strips
Number of wooden siding strips = 3334/214 = 15.57 ≈ 15 strips
Therefore, extra strips of wooden siding = 15 - 8 = 7 strips
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100 POINTS + BRAINLEIST PLS ANWER ASAP
C is the correct answer:)
How to simplify arational algebraic expressions
Answer:
To simplify any rational expressions, we apply the following steps:
Factorize both the denominator and numerator of the rational expression. Remember to write each expression in standard form.
Reduce the expression by cancelling out common factors in the numerator and denominator
Rewrite the remaining factors in the numerator and denominator.
Step-by-step explanation:
Example:
Simplify: (x^{2} + 5x + 4) (x + 5)/(x^{2} – 1)
Solution:
Factoring the numerator and denominator to get;
⟹ (x + 1) (x + 4) (x + 5)/(x + 1) (x – 1)
Now cancel the common terms.
⟹ (x + 4) (x + 5)/(x – 1)
64^1/2 x 27000^2/3 all over2^-4 x 3^0 x 5^2
The equation (64^1/2 x 27000^2/3 all over2^-4 x 3^0 x 5^2) is solved to be 9216
How to solve the given equationGiven data
64^1/2 x 27000^2/3 all over2^-4 x 3^0 x 5^2
Rewriting gives:
( 64^1/2 x 27000^2/3 ) / ( 2^-4 x 3^0 x 5^2 )
the solution; we first note that
64^1/2 = √64 = 8
27000^2/3 = ∛27000^2 = 900
3^0 = 1
2^-4 = 1 / 2^4 = 1 / 32
5^2 = 25
substituting gives:
= ( 8 * 900 ) / ( 1/32 * 1 * 25)
= 7200 / 25/32
= 7200/25 * 32
= 288 * 32
= 9216
The equation (64^1/2 x 27000^2/3 all over2^-4 x 3^0 x 5^2) is solved to be 9216
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