In the given sequence, the next term is obtained by multiplying the next term by (-1), hence it is a geometric sequence with r = 1. The next two terms are 3, -3.
Arithmetic sequence.
In a arithmetic sequence, the next term = the previous term + common difference. Or mathematically:
a(n) = a(n-1) + d
or d = a(n) - a(n-1) for all n
Where d = common difference.
Geometric sequence.
In a geometric sequence, the next term = the previous term x common ratio. Or mathematically:
a(n) = a(n-1) . r
or r = a(n)/a(n-1) for all n
Where r = common ratio
The sequence given:
3,-3,3,-3, . . . . .
In this sequence:
a(1) = 3
a(2) = -3
a(3) = 3
a(4) = -3
Check whether it has a common differenceThe next two terms means a(5) and a(6). We already have a(4) = -3. Hence,
a(5) = a(4) . r = -3. (-1) = 3
a(6) = a(5) . r = 3. (-1) = -3
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show that the value of cos30 degrees x tan60 degrees + sin30 degrees is an integer
Answer:
Step-by-step explanation:
cos(30) x tan (60) + sin (30) = (√3)/2 x √3 + 1/2 = 3/2 + 1/2 = 4/2 = 2
HELP PLS ASAPPP OR WHATEVA
Answer:
6²
Step-by-step explanation:
6² is 6×6 which is 36
if you write it as 6² then:
6²=6^x
since the bases are equal you can cancel out the bases and it becomes:
x=2
Answer:
a. 6^2
Step-by-step explanation:
A because six times itself is equal to 36.
2+2 i know the answer is four
Answer:
5 50bw syfnauw dux fyq euw eywvr6b
need answers quickly pls!!!! :(
Answer:
17
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}9-6\\\end{array}\right]+\left[\begin{array}{ccc}-5-(9)\\\end{array}\right][/tex]
=3+14
=17
The records at a particular two-year college classify a student as a freshman, a sopho- more, a student that has transferred out, or a student that has graduated. Each year 25% of students transfer, 15% have to repeat the year, and 60% complete the year. Once a student has transferred or graduated they have a 100% chance of staying clas- sified that way. Currently there are 2,000 freshmen, 1,500 sophomores, 500 students that have transferred, and 3,000 graduates. Determine the number of students in each category one year from now. You may use a calculator for any computations in this problem only.
One year from now, there are 300 freshmen, 1425 sophomores, 1375 students that transferred out, and 3900 students graduated.
Each category is based on the percentages given, 25% of students transfer, 15% have to repeat the year, and 60% complete the year and the fact that once a student has transferred or graduated they have a 100% chance of staying classified that way.
Percentage, which was adapted from the Latin word "per centum", which means "by the hundred", is a fraction or a ratio in which the value of whole is always 100. It is represented by the symbol "%".
If currently there are 2,000 freshmen, 1,500 sophomores, 500 students that have transferred, and 3,000 graduates,
Among the 2000 freshmen, 25% of students transfer, 15% have to repeat the year, and 60% complete the year.
students who transfer = 25% of 2000 = 500
freshmen(repeater) = 15% of 2000 = 300
sophomore = 60% of 2000 = 1200
Among the 1,500 sophomores, 25% of students transfer, 15% have to repeat the year, and 60% complete the year.
students who transfer = 25% of 1500 = 375
sophomore(repeater) = 15% of 1500 = 225
students who graduated = 60% of 1500 = 900
Adding the total number of sophomores(freshmen who completed the year and sophomores that have to repeat the year)
sophomores = 1200 + 225 = 1425
Adding the total number of students who transfer,
500 + 500 + 375 = 1375
Adding the total number of student that graduated,
3000 + 900 = 3900
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Note: enter your answer and show all the steps that you use to solve this problem in the space provided. how you would convert the repeating, nonterminating decimal to a fraction? explain the process as you solve the problem. 0 . 1515 . . .
The fraction for 0.1515... is 5/33
It is possible to convert non terminating decimals to fraction. Because decimals are originally obtained from fractions itself.
If we have a terminating decimal number, by multiplying and dividing with powers of 10 gives a fraction.
For example, for the decimal 0.25, multiply and divide it with 100 which gives, 25/100 = 1/4.
Now we need to find the fraction corresponding to the decimal 0.1515..
Let x = 0.1515...
First we take 100x = 15.1515...
Now we can subtract the decimal part completely from 15.1515... since it is non terminating.
Now, 100x - x = 15.1515..- 0.1515.. = 15
Therefore, 99x = 15
and x = 15/99 = 5/33
So 5/33 is the fraction for the decimal 0.1515...
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Identify the number as prime, composite or neither. If the number is composite, write it as the product of prime factors. 540
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The number is prime.
B. The number is composite. Its prime factors written as a product are ( )
C. The number is neither prime nor composite.
Answer:B. The number is composite. Its prime factors written as a product are (5*3^3*2^2)
Step-by-step explanation:
Since 540 is an even number, that means it can be divided by 2. This means that the number is composite.
You can keep dividing it by 2 until you can't anymore.
Once you divide 540 by 2 twice, then you get 135.
You can divide it by 5 because the ones digit is 5.
Then you get 27, which is 3 times itself 3 times.
You finally multiply the numbers you divided by, and you get 2*2*5*3*3*3, which is 5*3^3*2^2.
Ximena has procrastinated all her homework until the very last minute. She has 2 hours to spare until midnight, which is when all her homework is due. Her English homework will take 30 more minutes than her Biology homework, and her Math homework will take three times as long as her Biology homework. How long will each subject take?
Answer:
English: 48 minutes
Math: 54 minutes
Biology: 18 minutes
Step-by-step explanation:
Set up each subject with the variable x as the biology homework.:
English: (x+30)
Math: (3x)
Biology: (x)
Now add them together and set it equal to 120 (2 hours into minutes):
x + 30 + 3x + x = 120
Move 120 over to the left and simplify:
5x - 90 = 0
Solve:
5(x - 18) = 0
x - 18 = 0
x = 18
So biology is 18 minutes, and then plug 18 in for all the other subjects:
English: 18+30=48 minutes
Math: 3*18=54 minutes
Biology: 18 minutes
Is -2 greater then or equal to k an inequality
Question 5 (2 points)
Natalie wants to make sure she has enough in her account to go out to dinner with her friends. When she views her online bank statement, her
current available balance is not showing. This is what she can see:
Current posted balance: $87.73
Pending withdrawals/debits: $97.68
Pending deposits/credits: $126.02
Available balance:
What is Natalie's current available balance?
Answer: $
Blank 1:
Natalie’s current available balance is $116.07.
To find current available balance, we need to subtract pending deposits/ credits with pending withdrawals/ debits.
Account Balance = Pending deposits / credits – Pending Withdrawals /debits
= $126.02- $97.68 = $28.34
Available Balance = Account Balance + Current Posted Balance
= $28.34 +$87.73 = $116.07
Current Available Balance = $116.07
The balance in checking or demand accounts that is available for use by the client or account holder is known as the available balance. The accessible balance of an account holder may not match the current balance. Any unfinished transactions are often included in the current balance.
Pending Deposit Credits: Pending check deposits that haven't been processed, haven't been credited to your account, or didn't have availability when we got them.
Pending Deposit Debits: Your account is put on hold for the transaction's amount until it is processed.
Hence Natalie’s current available balance is $116.07.
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m∠3=82.find m ∠4. i need help for my iready question
Write the equation for each line. Use slope-intercept form. m = 1/2 and the y -intercept is (0,0) .
The equation of the line in slope-intercept form with a slope of 1/2 and y-intercept of (0 , 0) is y = 1/2 x.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The slope-intercept form of the equation of a line is given by the formula:
y = mx + b
where m is the slope of the line
b is the y- intercept
Given that the slope of the line is 1/2 and the y-intercept is (0 , 0), write the equation of the line by simply plugging in its values.
y = mx + b
y = (1/2)x + 0
y = 1/2 x
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The Great Pyramid measures 756 feet on each side of the base and the height is 481 feet. Find the volume of the pyramid.
The volume of pyramid is 9.16×10⁷ feet³.
We are given the measure of each side of Great Pyramid, which will be it's length and width. Also, we are given height. The formula for calculation of volume of pyramid is -
Volume = (length×width×height)÷3
Keep the values in formula to find the volume of Great Pyramid
Volume = (756×756×481)÷3
Performing multiplication on Right Hand Side of the equation to find the volume of Great Pyramid-
Volume = 274908816÷3
Solving the Right Hand Side of the equation, by performing division, we get the volume of Great Pyramid -
Volume = 9.16×10⁷ feet³
The volume of Great Pyramid is 9.16×10⁷ feet³.
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The activation energy of a reaction is 133.5 kj, and frequency factor (a) is 8.23 x 1010 sec -1, at what temperature (in celsius) is the rate constant equal to 0.08857 sec-1?
955°C is temperature (in celsius) is the rate constant equal to 0.08857 sec-1.
What is the short definition of activation energy?
The least amount of energy necessary to bring atoms or molecules into a state where they can undergo chemical transformation or physical transport is known as the activation energy .
K = [tex]A . e^{\frac{-Eq}{RT} }[/tex]
logk = logA = Eq/RT
log0.02629 = log5.57 × [tex]10^{10}[/tex] sec-1 - [tex]\frac{125.6 * 10^{3} }{8.314 * T}[/tex]
= log5.57 + [tex]log 10^{10}[/tex] - [tex]\frac{12.56 * 10^{3 J} }{8.314 * T}[/tex]
= log5.57 + 10log10 - 15.10 * 10³ J/T
-1.5483 = 0.7458 + 10 - 15.10 * 10³/ T
-1.5483 = 10.7458 - 15.10 * 10²/T
- 15.10 * 10³/ T = -1.5483 - 10.7458
15.10 * 10³ /T = 12.2941
T = 15.10 * 10³/ 12.2941
= 1228K
= 955°C
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HELP PLS which one is least
Answer:
Option B
Step-by-step explanation:
→ Find the option with the smallest power
Option B
Aiden leans a 30-foot ladder against a wall so that it forms an angle of 78 ∘ ∘ with the ground. What’s the horizontal distance between the base of the ladder and the wall? Round your answer to the nearest hundredth of a foot if necessary.
Answer:
x=6.24
Step-by-step explanation:
cos 78° =adj/hyp=x/30
cos 78° =x/30
x=cos 78°×30
x=0.2079×30
x=6.237350725
to the nearest hundredth
x=6.24
Dan is saving money to buy a game. So far he has saved $12, which is two-thirds of the total cost of the game. How much does the game cost?
Find the value of x
Step-by-step explanation:
or, x + 65° = 180° [ Being Straight line]
or, x = 180° - 65°
or, x = 115°
Therefore the value of x is 115° .
Now,
or, 4x = 4 × 115° = 460° .
write an equation for the circle
Which equation represents a line which is perpendicular to the line y = 2x - 5?
Step-by-step explanation:
y = 2x + C
we must want to find C
Combine like terms. What is a simpler form of each expression?
(b) -(8 a+3 b)+10(2 a-5 b)
By combining the like terms, the simpler form of expression -(8a+3b)+10(2a-5b) is 12a-53b
Given,
The expression = -(8a+3b)+10(2a-5b)
Expand the terms
-(8a+3b)+10(2a-5b)= -8a-3b+20a-50b
Combining like terms
-8a-3b+20a-50b = 12a-53b
Hence, by combining the like terms, the simpler form of expression is -(8a+3b)+10(2a-5b) 12a-53b
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Suppose a triangle has sides a, b, and c, and let e be the angle opposite the side of length a. If cose < 0, what must be true? O A. a² + b² = ² O B. b² + c²> a² O c. b² + 2² ²
In the given triangle the statement that holds true is [tex]b^2+c^2 < a^2[/tex]. Therefore, the option (c) is the correct option.
What are cosine formulas?In the cosine formulas, the cosine (cos) function is discussed. Consider a right-angled triangle with one acute angle, x. The cosine formula is cosx = (adjacent side) / (hypotenuse), where "adjacent side" refers to the side adjacent to angle x and "hypotenuse" refers to the longest side of the triangle.
As per cosine rule fore given [tex]$\triangle$[/tex]ABC:
[tex]$\cos \theta=\frac{b^2+c^2-a^2}{2 b c}$$$[/tex]
According to the question;
For a given [tex]$\triangle$[/tex]ABC;
cos e < 0.
Therefore, [tex]\quad \frac{b^2+c^2-a^2}{2 b c} < 0 \\[/tex]
[tex]b^2+c^2 < a^2[/tex]
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Three friends live in houses with backyards adjacent to a neighborhood bike path. They decide to have a round-robin party using their three homes, inviting their friends to start at one house and then move to each of the other two. If one friend's house is centered at the origin, then the location of the other homes are (5,12) and (13,0) . Write a coordinate proof to prove that the triangle formed by these three homes is isosceles.
The distance of AO and BO are the same so the given triangle will be an isosceles triangle.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
The given vertices are making a triangle as shown below in the figure.
Distance between A(5,12) and O(0,0) is
⇒ [tex]\sqrt{(5 - 0)^2 + (12 - 0)^2}[/tex]
⇒ 13
Distance between B(13,0) and O(0,0) is
⇒ [tex]\sqrt{(13 - 0)^2}[/tex]
⇒ 13
Since the two sides are the same so triangle will be isosceles.
Hence "The distance of AO and BO are the same so the given triangle will be an isosceles triangle".
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What is the slope of the function?
pls answer
Answer:
slope = -4
Step-by-step explanation:
slope = [tex]\frac{y2-y1}{x2-x1}[/tex] = [tex]\frac{-10 - (-2)}{-2 - (-4)}[/tex] = [tex]\frac{-10 + 2}{-2 + 4}[/tex] = [tex]\frac{-8}{2}[/tex] = -4
One of the same side angles of two parallel lines is three times the other angle Find the two angles
The two angles are 45° and 135°.
What is angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle and corner whether constituting a projecting part or a partially enclosed space.
Given:
One of the same side angles of two parallel lines is three times the other angle.
According to given question we have
Let the smaller side= x,
The larger side = 3x.
The two angles are supplementary.
x + 3x = 180°
4x = 180°
Divide by 4 on both sides we get,
x = 45°
3x = 135°
Therefore, the two angles are 45° and 135°.
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Find the value of x for the given values of a and b .
b=3 x+4 a , for a=-9 and b=12
The value of X in the equation that allows a solution with the values of "a" and "b" is x = 16
What are the equations?An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.
Equations can be graphed, just like a function.
We write the given equation
b = 3x + 4a
and we have the values of the coefficients a and b, and these are:
a = -9b = 12We substitute these values in the equation:
b = 3x + 4a
(12) = 3x + 4(-9) :::: We solve the equation
12 = 3x -36
3x = 12 + 36
3x = 48
x = 48/3
x = 16
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A home improvement store sells bags of sand, which are labeled as
weighing 35 pounds. The equipment used to package the sand produces bags
with a weight that is within 8 ounces of the labeled weight.
a. Write an absolute value equation to represent the maximum and minimum
weight for the bags of sand.
b. Solve the equation and interpret the result.
The maximum and the minimum weight for the bags of sand are 36 and 35 pounds respectively
Write an absolute value equation to represent the maximum and minimum weight for the bags of sand.Here, we have
Weight = 35 pounds
Labeled weight = within 8 ounces
Convert ounce to pounds
So, we have:
Labeled weight = within 0.5 pound
The equation is then represented as
|x - 35| = 0.5
Where x represents the labeled weight
b. Solve the equation and interpret the result.In (a), we have
|x - 35| = 0.5
Expand
x - 35 = 0.5 and x - 35 = -0.5
Add 35 to both sides
x = 36 and x = 35
Hence, the maximum and the minimum weight for the bags of sand are 36 and 35 pounds respectively
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what is average rate of change???? be willing to help with the next 2 please!
here you go :) explanation up top
What is the square root of 125 in simplest form
Answer:
[tex]5\sqrt{5}[/tex] = ~11.18
Please answer, attachment is the question.
6 points!
please
Answer:
s = 8 cm
Step-by-step explanation:
the area (A) of a square is calculated as
A = s² ( s is the side length )
given A = 64 cm² , then
s² = 64 ( take square root of both sides )
s = [tex]\sqrt{64}[/tex]
s = 8 cm
