The first two numbers in a sequence h are h(1) = 2 and h(2) = 6.
1. If h is an arithmetic sequence, write a definition for the nth term of h. Explain
or show your reasoning.
2. If h is a geometric sequence, write down a definition for the nth term of h. Show reasoning
Answer:
Step-by-step explanation:
Given the first two numbers of a sequence as 2, 6...
If it is an arithmetic difference, the common difference will be d = 6-2 = 4
Formula for calculating nth term of an ARITHMETIC sequence Tn = a+(n-1)d
a is the first term = 2
d is the common difference = 4
n is the number if terms
Substituting the given values in the formula.
Nth term Tn = 2+(n-1)4
Tn = 2+4n-4
Tn = 4n-4+2
Tn = 4n-2
2) If the sequence us a geometric sequence
Nth term of the sequence Tn = ar^(n-1)
r is the common ratio
r is gotten by the ratio of the terms I.e
r = T2/T1
r = 6/2
r = 3
Since a = 2
Tn = 2(3)^(n-1)
Hence the nth term of the geometric sequence is Tn = 2(3)^(n-1)
Is the following number rational or irrational?
6 1/2
Answer:
yes it is a rational number
Step-by-step explanation:
if we convert the mixed fraction into an improper fraction, we will get:
6 1/2 = 13/2
Recall that the definition of an Rational number is that it can be expressed as a division of two integers.
in our case, the numerator is 13 (which is an integer) and the denominator is 2 (which is also an integer)
hence according to our definition it is a rational number
The mixed fraction number 6 1/2 is a terminating number. Then the number is a rational number.
What is a rational number?If the value of a numerical expression is terminating then they are the rational number then they are called the rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.
The mixed fraction number is given below.
⇒ 6 1/2
Convert the mixed fraction number into the fraction number. Then we have
⇒ 6 1/2
⇒ 6 + 1/2
⇒ (12 + 1)/2
⇒ 13/2
Convert the fraction number into a decimal number. Then we have
⇒ 13/2
⇒ 6.5
The mixed fraction number 6 1/2 is a terminating number. Then the number is a rational number.
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Maya is comparing ride-sharing company prices. Company M charges $1.75 per mile driven and one-time trip fee of $5. Company N charges $2.50 per mile driven and a one-time trip fee of $3. Which inequality can be used to find x, the minimum number of miles driven so that the total cost at Company M is less than the total cost at Company N? 1.75x+5 2.5x+3 1.75+5x 2.5+3x
Answer:
1.75x+5<2.5x+3
Step-by-step explanation:
-8 and 8 are ___; they are both 8 away from zero.
Two numbers that are the same distance from zero are called opposites.
-8 and 8 are Opposites.
Kennedy invested $5,000 in an account paying an interest rate of 6.4% compounded
daily. Assuming no deposits or withdrawals are made, how much money, to the
nearest cent, would be in the account after 15 years?
The Answer is
A~13057.38
The money, to the nearest cent, would be in the account after 15 years is $13060.
What is Daily Compound Interest ?Due to the high frequency of compounding, daily compounded interest is larger than monthly/quarterly compounded interest since interest is accumulated on a daily basis and is determined by charging interest on principal plus interest gained on a daily basis
It is given in the question that Kennedy invested $5000
Interest rate = 6.4% compounded daily
Assuming no deposits and withdrawals
T = 15 years
The formula for amount obtained after 15 years when interest is compounded daily
[tex]\rm A = (P(1 + \dfrac{r}{n})^{nt})[/tex]
[tex]\rm A = (5000(1 + \dfrac{6.4}{365*100})^{365*15})[/tex]
A = 5000 * 2.612
A = $13060
Therefore , money, to the nearest cent, would be in the account after 15 years is $ 13060.
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The students at Woodward Elementary voted for a school mascot. The falcon won with 5/8 of the votes and the eagle came second with 1/3 of the remaining votes. If 536 students voted for a mascot, how many students voted for the eagle?
Answer:
178.67
Step-by-step explanation:
One third written as a fraction is 1/3. You can also write it as a decimal by simply dividing 1 by 3 which is 0.33.
If you multiply 0.33 with 536 you will see that you will end up with the same answer as above.
You may also find it useful to know that if you multiply 0.33 with 100 you get 33.33. Which means that our answer of 178.67 is 33.33 percent of 536.
What is the equation of the line that is perpendicular to
the given line and passes through the point (3,0)?
A. 3x+5y=-9
B.3x+5y=9
C.5x-3y=-15
D.5x-3y=15
Answer:
answer is D
shown below
The equation of the line that is perpendicular to the given line and passes through the point (3,0) is 3y - 5x = -15.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
We have the points as (-3, 2) and (2, -1).
So, the slope of line
slope = (-1 -2)/ (2 -(-3))
slope = -3/5
So, the slope for the perpendicular line is
slope= 5/3
Now, using the slope intercept form
y= mx+ b
y= 5/3x + b
and, the line passes through (3, 0)
0= 5/3(3)+ b
b= -5
Then, the equation of line is
y= 5/3x -5
3y - 5x = -15
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HELP PLS WILL GIVE BRAINLISTE
Answer:
6%
Step-by-step explanation:
:0
Answer:
25%
Step-by-step explanation:
i did a quiz on this the right answer is 25%
Find the missing values to make the statement true.
90°– 27 ° 38’ 55” = 63°21'4"
DID I DO THIS CORRECTLY ?
Answer:yes
Step-by-step explanation:
Leah is paid semimonthly. How many fewer paychecks does she
receive in 2 years compared to someone who is paid weekly?
Answer:
Leah has 80 less paychecks than the weekly person.
Step-by-step explanation:
Leah is getting 24 paychecks in 2 years, Weekly person gets 104 paychecks in 2 years, 104 - 24 = 80 paychecks.
what is 143x+4=12 please help
HELP ME WITH THIS I NEED TO ANSWER IT ASAP
Answer:
e 125x
f 125 x 12 =150
Step-by-step explanation:
answer please im begging you QwQ
Answer:
A is your answer
Step-by-step explanation:
how do I answer a question in here
Answer:
Just go to a post you feel/know you can solve, tap or click on it and you should see an answer button!
Match question it has 3 answers I’m giving brainly
Answer:
1st 2nd and 4th option are correct
Answer:
B
Step-by-step explanation:
C is wrong because -11 + 4 is -7
E is wrong because you can't change the negative sign just for one value on one equation
If the statement is rewritten as a conditional statement in if-then form, which best describes the conclusion?
A student who earns 85% earns a B.
O If a student earns 85%
O If a student earns a B
O Then a student earns 85%
O Then a student earns a B
Answer:d
Step-by-step explanation:
Each quarter weighs 0.2 ounces. How much money has been stolen from the bank? Report the amount in $. Ex. "$528" *
Answer:
$640
Step-by-step explanation:
512/0.2 = 2560 quarters
2560 quarters = 640 US Dollars
Hope this helps !
The total amount that was stolen is 640 US dollars.
How to determine the total amount that was stolen?The weight of the amount is given by;
Weight = 512 ounces
The weight of each quarter will be;
Unit weight = 0.2 ounces
So, the total amount would be;
Total = 512/0.2
Evaluate;
The Total amount = 2560 quarters
1 quarter = $0.25
So, we have:
The Total amount = $0.25 * 2560
Now Evaluate the product
The Total amount = $640
Hence, the total amount that was stolen is 640 US dollars.
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3x+3y=180 what is the answer to this problem
Answer:
If you are solving the equation for x :
3x + 3y = 180
3x = -3y + 180
x = -y + 60 or x = 60 - y
If you are solving the equation for y:
3x + 3y = 180
3y = -3x + 180
y = -x + 60 or y = 60 - x
find the value of each power 5^-2
Answer:
5⁻² = 1/25
3⁴ = 81
Step-by-step explanation:
5⁻² = 1/5² = 1/25 3⁴ = 3² * 3² = 9*9 = 81Question 9 (4 points)
Given that the two triangles shown below are similar, find the value of x
3
40°
60°
6
8
80°
5
40°
y
Answer:
x = 4.8
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask me in the comments below :)
What is the value of x?
1/4x + 17 = x - 4
Please explain:
Answer:
x=28
Step-by-step explanation:
Solve |x + 3| = 7.
A. x= -4
B. x= 10
C. x= 4
D. x= -10
Answer:
C. x= 4
Step-by-step explanation:
|x + 3| = 7
x + 3 = 7
x = 7 - 3
x = 4
Answer:
x = 4
Step-by-step explanation:
|x + 3| = 7
=> x + 3 = 7
=> x = 7 - 3
=> x = 4
Multiply 15×2.23**
Simplify the expression: 4x+2+12x+17*
Divide: 0.24÷0.012**
Give two numbers that are less than -4.
Answer:
33.45
16x+19
20
I have a few questions so if you can answer all correct I’ll mark brainliest!
A toy car costs $60. It is reduced by 10% in a sale. How much
does it cost in the sale?
I have $78. I spend $45 on some CDs and $12 on a t-shirt. How much money is left
The ratio of lions to tigers in the zoo is 3:5 if there are 9 lions how many tigers are there?
Answer:
1.) $54
2.) $21 left
3.) 15 tigers
Step-by-step explanation:
1.) If the original price of an item was $60, and it was reduced by 10%, that means it is now being sold at 90% of its original value.
To find out the new price, simply take the original value and multiply it by 90% (as a decimal).
60*.90=54
So the new price is $54
2.) This is simple subtraction. If you spend $45 on some CDs and $12 on a t-shirt, you spent a total of $57. Subtract $57 from your total of $78.
78-57=21
You are left with $21
3.) Ratios are all about multiplication. If the ratio of lions to tigers is 3:5, that means that the number of lions is going to be any factor of 3, as long as it corresponds to the same factor of 5 for the tigers.
For example, if there are 9 lions, there must be 15 tigers.
3*3=9
5*3=15
There are 15 tigers
Find the distance between points (-1,-4) and (2,2)
Answer:
5
Step-by-step explanation:
2. Lenny is making pasta for dinner. The recipe calls for 3 cups of sauce to serve 15
people. If Lenny serves 60 people, how many cups of sauce does he need?
Given that f(x) = 2x - 2 and g(x) = 5x. Find the value of f(0) + g(3).
Answer: 13
Step-by-step explanation:
f(0)=2(0)-2
f(0)=-2
g(3)=5(3)
g(3)=15
-2+15=13
Hope this helps!
Answer:
Step-by-step explanation:
f(0) = 2(0) - 2 = 0 - 2 = -2
g(3) = 5(3)= 15
-2 + 15 = 13
To borrow $3,000 from the bank to buy first car the interest rate is 5% how muvh money will you owe the bank at the end of one year
Answer:
I=150
Step-by-step explanation:
I=Prt
I=3000(?)(?)
divide 5% by 100
I=3000(0.05)(?)
1 year= 1
I=3000(0.05)(1)
I=150
According to the question,
Principle,
P = 3000Interest rate,
r = 5% or 0.5Time,
t = 1 yearWe know that,
→ [tex]I = Prt[/tex]
By substituting the values, we get
[tex]= 3000\times 0.5\times 1[/tex]
[tex]= 150[/tex]
Thus the above approach is right.
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Need help asap. Thanks!
Answer:
A- SAS
Step-by-step explanation:
The statements tell you the outer two lines are congruent and the top two angles as well, then through the properties of equality you know the inner line is congruent to itself. That means you have two sides and an included angle making it SAS.
To play indoor soccer at the Sun Oaks Club, you must pay a $100 membership
fee, plus $10 for each hour you use the facilities. a) The function f represents the
cost of playing soccer at Sun Oaks depending on how many hours you play. The
function g represents the cost if the hourly rate were halved. Write each
function. *
Given that:
Membership feet to play indoor soccer at the Sun Oaks Club = $100
Hourly rate = $10
To find:
The function f represents the cost of playing soccer at Sun Oaks.
Here, fixed cost is $100.
Let the number of hours of playing be t. So, total variable cost is $10t.
Total cost = Fixed cost + Variable cost
[tex]f(t)=100+10t[/tex]
So, the required function is [tex]f(t)=100+10t[/tex].
Now, if the hourly rate were halved. Then,
Hourly rate [tex]= \$ \dfrac{10}{2} = \$ 5 [/tex]
So, total variable cost is $5t and total cost function is
[tex]g(t)=100+5t[/tex]
So, the required function is [tex]g(t)=100+5t[/tex].