The explicit equation for the nth term of the geometric sequence 3584, 896, 224 is:
[tex]a_n=3584(0.25)^{n-1}\\\\\text{Where } n\geq 1 \text{ ,n = 1, 2, 3, 4, .........}[/tex]
Solution:
Given that we have to find the explicit equation for nth term of geometric sequence
Given sequence is:
3584, 896, 224
A geometric sequence has a common ratio
Let us find the common ratio. Divide each term by the previous term.
[tex]r=\frac{896}{3584} = 0.25\\\\r = \frac{224}{896} = 0.25[/tex]
Thus the common ratio is 0.25
The formula for nth term of geometric sequence is given as:
[tex]a_n=ar^{n-1}[/tex]
Where,
[tex]a_n[/tex] is the nth term of sequence
a is the first term of sequence
r is the common ratio
Here in given sequence 3584, 896, 224
first term = a = 3584
common ratio = r = 0.25
Therefore,
[tex]a_n=3584(0.25)^{n-1}[/tex]
[tex]\text{Where } n\geq 1 \text{ ,n = 1, 2, 3, 4, .........}[/tex]
"n" is a natural positive number greater than or equal to 1
Thus the explicit equation to find nth term is found
WILL GIVE BRAINIEST AND POINTS :
[tex]m \angle LKN + m \angle \boxed{KLM} = \boxed{180}[/tex] because they are [tex]\text{supplementary angles}[/tex]
This is true of any parallelogram. The adjacent angles of any parallelogram are supplementary, meaning they add to 180 degrees. You can use the same side interior angle theorem here as well.
------------------
Because KA cuts angle K in half, and LA does the same to angle L, this means that we're dividing everything by 2 in that equation at the top of the page. So we have,
[tex]\frac{m \angle LKN + m \angle KLM}{2} = \frac{180}{2}[/tex]
and that turns into
[tex]m \angle LKA + m\angle KLA = 90[/tex]
which tells us that angle KAL must be 90 so that the three angles of triangle KAL add to 180 degrees. For any right triangle, the acute angles are complementary, meaning they add to 90 degrees.
Which expressions are equivalent?
A. 1/5 k - 2/3 j and - 2/3 j + 1/5 k
B. 1/5 k - 2/3 j and - 1/5 k + 2/3 j
C. 1/5 k - 2/3 j and 1/5 j -2/3 k
D. 1/5 k - 2/3 j and 2/3 j - 1/5 k
Answer: A
Step-by-step explanation:
The yearbook club had a meeting. The meeting had 12 people, which is two-thirds of the club. How many people are in the club?
people
Answer:
18 people
Step-by-step explanation:
4x2 - 14 + y - (8 + 13)
What is the value of the expression when x = 4 and y = 7?
OA. 67
OB. 9
Oc. 41
OD. 35
What is the sum of x,three-fourths x, and 90% of z
The sum of x, three-fourths x, and 90% of z is x + (3/4)x + 0.9z.
Explanation:
The sum of x, three-fourths x, and 90% of z is calculated by adding these three terms together. Let's break it down:
x is simply x, no changes or calculations needed.
Three-fourths x can be written as (3/4)x.
90% of z can be written as 0.9z.
Therefore, the sum of x, three-fourths x, and 90% of z is x + (3/4)x + 0.9z.
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olve for x. -3x = -15 x = -45 x = 5 x = -5
Answer:
it 1/4
Step-by-step explanation:
i did the other anwser and it anwsered after i got it wrong
For the given interval, is the function increasing or decreasing?
Answer:
increasing
Step-by-step explanation:
What is the answer to 7=-3c-2
Answer:
c= -3
Step-by-step explanation:
Mr. Phillips is mixing paint for his art
class. How many 6-ounce bottles can
he fill with the quantities of paint shown
at the right? Explain.
Paint
-64 ounces of blue
12 ounces of yellow
-32 ounces of white
Answer:
Mr. Phillips can fill 18 bottles of paint
Step-by-step explanation:
The first thing you should do in this case is to know how many ounces of paint you have:
Painting = 64 + 12 + 32 = 108
Then, to calculate the number of 6-ounce bottles you must divide the total number of ounces by 6:
n = (108) / (6) = 18
A new computer system sells for approximately $2000 and depreciates at the rate of $500 per year.
what are you asking
Step-by-step explanation:
A car rental firm has the following charges for a certain type of car: $25 per day with 100 free miles included, $0.15 per mile for more than 100 miles. Suppose you want to rent a car for one day, and you know you'll use it for more than 100 miles. What is the equation for relating the cost y to the number of miles x that you drive the car?
y = 25 + 0.15x is the equation for relating the cost y to the number of miles x that you drive the car
Solution:
Let "y" be the total cost of car rental
Let "x" be the number of miles you drive the car for more than 100 miles
A car rental firm has the following charges for a certain type of car:
$25 per day with 100 free miles included, $0.15 per mile for more than 100 miles
Suppose you want to rent a car for one day, and you know you'll use it for more than 100 miles
Therefore,
Car is rented for one day
You will use it for more than 100 miles
Therefore, equation is framed as:
Total cost = $ 25 + 0.15(number of hours)
[tex]Total\ Cost = 25 + 0.15x\\\\y = 25 + 0.15x[/tex]
Thus the equation for relating the cost y to the number of miles x that you drive the car
See attached photo!! Please help Asap!!! CORRECT ANSWERS ONLY!! THANKS IN ADVANCE!!
Which construction might this image result from?
A.
construction to copy a line segment
B.
construction of a perpendicular bisector
C.
construction of a perpendicular to a line through a given external point
Answer:
C. construction of a perpendicular to a line through a given external point
Step-by-step explanation:
The crossing arcs below the line are equidistant from the marked points on the line (J and K), and those are equidistant from point A. If we call the point of intersection of those crossing arcs point X, we know that AX is a perpendicular bisector of JK.
However, J and K are not part of the "given" of this construction. Rather, they are the result of the first step of drawing arcs centered at A. So the fact that AX bisects JK is not important. What is important is that AX is perpendicular to the line and goes through the given point A.
This is a partially-completed construction of a perpendicular to a line through the given external point A.
Mason opens a savings account by making a $165.85 deposit. Every week, he deposits another $20.50 in the account. The following expression shows the amount of money that will be in the account x weeks after Mason opens it.
165.85 + 20.5x
How much money will be in the account after 10 weeks?
Answer:
$370.85
Step-by-step explanation:
sub the 10 for the x
370.85
Answer:
First multiply 10 by 20.5 because x represents the number of weeks. You get 205. Next add 165.85 to that and you get 370.85 as your final answer.
expression show the sum of 5 less than y and the product of 3 and g
The expression that shows the sum of 5 less than y and the product of 3 and g is (y - 5) + 3g
Step-by-step explanation:
Let us revise some important words to translate a statement to algebraic expression
The sum ⇒ addThe product ⇒ multiplyThe quotient ⇒ divideLess than ⇒ subtractMore than add∵ 5 less than y
- That means subtract 5 from y
∴ 5 less than y = y - 5
∵ The product of 3 and g
- That means multiply g by 3
∴ The product of 3 and g = 3g
∵ The sum of 5 less than y and the product of 3 and g
- That means add (y - 5) and 3g
∴ the expression = (y - 5) + 3g
The expression that shows the sum of 5 less than y and the product of 3 and g is (y - 5) + 3g
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What is the median of the numbers below?
5,4,5,8,3,5,2
Answer:
5
Step-by-step explanation:
2,3,4,5,5,5,8
you must put them in order, and it will always be in the middle :)
What expression is equal to 5(3x-2)
Answer: 15x-10
Step-by-step explanation:To solve this problem you have to do the distributive property. You must do 5 times 3x and 5 times -2. 5 times 3x is 15x and 5 times -2 is -10. This means the answer is 15x-10.
Answer:
Step-by-step explanation:
5(3x - 2)
Opening bracket
= 5(3x) - 5(2)
= 15x - 10
is searching online for airline tickets. Two weeks ago, the cost to fly from Orlando to Denver was $250. Now the cost is $365. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
Percent increase without baggage = 46%
Percent increase with baggage = 66%
Step-by-step explanation:
Cost of ticket two weeks ago= Old value = $250
Increased cost = New value = $365
Change = New value - Old value
Change = 365 - 250 = $115
Percent increase = [tex]\frac{Change}{Old\ value}*100[/tex]
Percent increase = [tex]\frac{115}{250}*100[/tex]
Percent increase = [tex]\frac{11500}{250}=46\%[/tex]
There is 46% increase in the price.
Change after additional baggage = 115+50 = $165
Percent increase = [tex]\frac{165}{250}*100[/tex]
Percent increase = [tex]\frac{16500}{250}=66\%[/tex]
Percent increase without baggage = 46%
Percent increase with baggage = 66%
Keywords: percentage, division
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The percent increase in the cost of airline tickets from Orlando to Denver is 46%. If an additional $50 baggage fee is charged, the percent increase is 66%.
Explanation:To calculate the percent increase, we can use the formula: Percent Increase = ((New Value - Old Value) / Old Value) x 100. In this case, the old value is $250 and the new value is $365. Therefore, the percent increase is ((365 - 250) / 250) x 100 = 46%.
If the airline charges an additional $50 baggage fee, the new ticket price would be $365 + $50 = $415. To calculate the percent increase from the original price, we can use the same formula. The old value is still $250 and the new value is $415. Therefore, the percent increase with the added baggage fee is ((415 - 250) / 250) x 100 = 66%.
HELP
Joy needs 8 feet of fabric for a project she is working on, but the store only sells the fabric in meters. One meter of fabric costs $1.15. How much will the fabric cost?
[1 ft = 0.305m]
$9.20
$2.12
$2.81
$30.16
The fabric cost is $2.81.
Given that,
Joy needs 8 feet of fabric for a project she is working on, but the store only sells the fabric in meters.
One meter of fabric costs $1.15.
We have to determine,
How much will the fabric cost?
According to the question,
Joy needs 8 feet of fabric for a project she is working on, but the store only sells the fabric in meters.
One meter of fabric costs $1.15.
Then,
The fabric cost = one meter fabric cost × fabric measurement
The fabric cost = 8 × $1.15
The fabric cost = 9.20 feet
The value of [1 ft = 0.305m],
Therefore,
The fabric cost = 9.20 × 0.305 m = $2.81
Hence, The fabric cost is $2.81.
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Final answer:
To determine the cost of 8 feet of fabric when the store sells by the meter, one must convert feet to meters and then multiply by the price per meter, resulting in approximately $2.81.
Explanation:
The student, Joy, needs to convert feet to meters in order to purchase fabric. Since 1 foot is equal to 0.305 meters, she needs to convert 8 feet to meters by multiplying 8 feet by 0.305. This results in approximately 2.44 meters of fabric needed. Given that one meter of fabric costs $1.15, we multiply 2.44 meters by $1.15 per meter to find the total cost. Therefore, the fabric will cost approximately $2.81.
can someone help me with this problem please
Answer:
Option C that is [tex]x=4,DF=EG=15[/tex] the right choice.
Step-by-step explanation:
Given,
A rectangle with the measures of its diagonal DF and EG.
Measure of diagonal DF = [tex]5x-5[/tex]
Measure of diagonal EG = [tex]x+11[/tex]
Note:Diagonal length of the rectangle are same.
So DF = EG
[tex]5x-5=x-11[/tex]
Subtracting [tex]x[/tex] and adding [tex]5[/tex] on both sides.
We have,
[tex]5x-x=11+5[/tex]
[tex]4x=16[/tex]
Dividing 4 both sides.
[tex]x=\frac{16}{4}=4[/tex]
So the value of [tex]x[/tex] is [tex]4[/tex].
Now plugging the value of [tex]x=4[/tex],we will find the numeric value of DF and EG.
DF = [tex]5x-5 =5(4)-5=15[/tex]
EG= [tex]x+11=4+11=15[/tex]
Both are equal DF = EG.
So x=[tex]4[/tex] and the length of diagonals are equal, DF = EG = [tex]15[/tex] unit.
For the function f(x) = 3(x − 1)2 + 2, identify the vertex, domain, and range.
a- The vertex is (1, 2), the domain is all real numbers, and the range is y ≥ 2.
b- The vertex is (1, 2), the domain is all real numbers, and the range is y ≤ 2.
c- The vertex is (−1, 2), the domain is all real numbers, and the range is y ≥ 2.
d- The vertex is (−1, 2), the domain is all real numbers, and the range is y ≤ 2.
See picture reply for solution steps.
Final answer:
The vertex of the function f(x) = 3(x − 1)² + 2 is (1, 2), the domain is all real numbers, and the range is y ≥ 2, Option A is correct in the given options.
Explanation:
The vertex of the function f(x) = 3(x − 1)² + 2 is (1, 2), because the vertex form of a quadratic function is given by f(x) = a(x − h)² + k, where (h, k) is the vertex. In this case, a = 3, h = 1, and k = 2. The domain of the function is all real numbers, because there are no restrictions on x. The range of the function is y ≥ 2, because the minimum value of the function is 2 (occurring at the vertex) and y can be any value greater than or equal to 2.
100 Points! What are the classifications of each system?
Drag the answer into the box to match each system.
Answer:
Part 1) Is a inconsistent system
Part 2) Is a consistent independent system
Part 3) Is a consistent dependent system
see the attached figure
Step-by-step explanation:
we know that
If a system has at least one solution, it is said to be consistent .
If a consistent system has exactly one solution, it is independent .
If a consistent system has an infinite number of solutions, it is dependent
If a system not have solution, it is said to be inconsistent
Part 1) we have
[tex]x+5y=-2\\x+5y=4[/tex]
This system of linear equations has two parallel lines (their slopes are equal) with different y-intercept
so
The lines don't intersect
The system has no solution
therefore
Is a inconsistent system
Part 2) we have
[tex]y=3x+4\\-2x+y=4[/tex]
we know that
If two lines have different slopes, then the lines intersect at one point and the system of equations has one solution
In this problem, the lines have different slopes (m=3 and m=2)
so
The lines intersect at one point
The system has one solution
therefore
Is a consistent independent system
Part 3) we have
[tex]3x+y=4[/tex] ----> equation A
[tex]-6x-2y=-8[/tex] ----> equation B
Multiply equation A by -2 both sides
[tex]-2(3x+y)=-2(4)[/tex]
[tex]-6x-2y=-8[/tex] ----> equation C
Compare equation B and equation C
Are identical lines
so
The system has infinity solutions
therefore
Is a consistent dependent system
Answer:
1) inconsient system
2) consient system
3) consient system
y=x
y=-6x–14
(substitution method)
Answer:
The solution is the point (-2,-2)
Step-by-step explanation:
we have
[tex]y=x[/tex] ----> equation A
[tex]y=-6x-14[/tex] ----> equation B
Solve the system by substitution
substitute equation A in equation B
[tex]x=-6x-14[/tex]
Solve for x
[tex]6x+x=-14\\7x=-14\\x=-2[/tex]
Find the value of y
substitute the value of x in the equation A
[tex]y=x[/tex]
so
[tex]y=-2[/tex]
therefore
The solution is the point (-2,-2)
Which part of the angle is the vertex?
A. Point X
B. YX
C. YZ
D. Point Y
Is there a graph?
If you have more info you will get the best answer.
Answer: POINT Y :))
Explanation in the picture below :) hope i helped!!
Graph the linear equation.
4x+6y=−12
Answer:
Step-by-step explanation:
Answer:
The points are (-3,0) and (0,-2)
Step-by-step explanation:
What is the sum of 1/3 and 1/6
What is the solution set to the inequality (x-3)(x+5) ≤ 0
Answer: x less than or equal to 3, x less than or equal to -5.
Step-by-step explanation:
split into two
x-3<0 // x+5<0
x<3 // x<-5
Answer:
-5 ≤ x ≤ 3
Interval notation : [-5 , 3]
Step-by-step explanation:
Look at the photo below for the details.
:)
can someone help me on 12,13,14 :)
Answer:
m∠XYZ = 166
AB = 2√5
Modpoint (1 , 5)
Step-by-step explanation:
Look at the photo below for the details.
:)
421 divided by 27 with reminders
Answer:
15 remainder 16
Step-by-step explanation:
421 divided by 27 with remainders is equal to 15 remainders 16.
We have,
When dividing 421 by 27, we get a quotient of 15 and a remainder of 16.
The division can be expressed as:
421 ÷ 27 = 15 with a remainder of 16.
This means that 421 can be divided by 27 a total of 15 times, with a remaining value of 16.
Thus,
421 divided by 27 with remainders is equal to 15 remainders 16.
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The Washington's by a studio apartment for 240,000 they pay a down payment of 60000 their down payment is what percent of the purchase price
Answer:
25%
Step-by-step explanation:
Given:
The price of the studio apartment = 240,000
Down payment = 60,000
We need to find the percentage of down payment.
Solution:
Using percentage formula.
[tex]Percentage = (\frac{Value}{Total\ value})\times 100[/tex]
Here value = Down payment
Total value = Price of the apartment
Now we substitute Down payment and Price of the apartment in above formula.
[tex]Percentage = (\frac{60000}{240000})\times 100[/tex]
[tex]Percentage = \frac{6\times 100}{24}[/tex]
[tex]Percentage = \frac{600}{24}[/tex]
[tex]Percentage = 25\%[/tex]
Therefore, Down payment is 25% of the purchase price.
Write the polynomial function, in standard form, that has zeros -3, 4, and 1.
Answer:
OPTION D
Step-by-step explanation:
Given the zeroes (roots) of a polynomial are: - 3, 4 & 1.
An [tex]$ n -degree $[/tex] polynomial has [tex]$ n - roots $[/tex] (zeroes). The converse is also true.
Here, we are given three roots of the polynomial. That means, the polynomial must be of third degree.
Also, (x - a) is a factor of the polynomial if and only if x = a is a root of the polynomial.
Here, -3, 4 & 1 are roots. So, the factors are: (x + 3), (x - 4) and (x - 1) .
Multiplying them will result in the polynomial.
[tex]$ (x + 3)(x - 4)(x - 1) $[/tex]
[tex]$ \implies (x^2 - 4x + 3x - 12)(x - 1) $[/tex]
[tex]$ \implies x^3 -x^2 - 4x^2 + 4x + 3x^2 - 3x - 12x + 12 $[/tex]
Simplifying, we get: [tex]$ \textbf{x}^\textbf{3} \textbf{-} \textbf{2x}^\textbf{2} \textbf{-} \textbf{11x} \textbf{+} \textbf{12}$[/tex]
Hence, OPTION D is the right answer.