A geometric sequence with first term 16 and common ratio 0.5, with 10 terms, satisfies the requirements for this problem, and the first four terms are:
16, 8, 4, 2.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
For this problem, we have that:
Sequence begins with a positive integer, hence the first term is 16. (chosen value, any positive integer suffices).The sequence is decreasing by multiplication, hence q > 0 and q < 1, q = 0.5 is a possible value and the sequence is geometric.A finite number of terms, we chose 10.Each term is the previous term multiplied by 0.5, hence the first four terms are:
16, 8, 4, 2.
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Solve the formula for the variable h v=lwh
Answer:
[tex] \sf \: h = \frac{v}{lw} [/tex]
Step-by-step explanation:
Let's solve for h.
v=lwh
Step 1: Flip the equation.
hlw=v
Step 2: Divide both sides by lw.
hlw/lw = v/lw
h=v/lw
Solving Advanced Linear Equations: Mastery Test
Select the correct answer from each drop-down menu.
Consider the equation below.
The equation was solved using the following steps.
Step 1:
Step 2:
Step 3:
Step 4:
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Complete the statements below with the process used to achieve steps 1-4.
-2 to 5x and 8.
6.x
✓16.
-2(5z + 8) = 14 + 6z
-16.
-10z <- 16
-16z
Reset
-
16 = 14
-16z =
30
= 14 + 6z
H
=
H =
Next
30656
-18
Submit T
The solution to the equation where the equation is given as -2(5z + 8) = 14 + 6z is z = -15/8
How to complete the steps to solve the equation?The equation is given as
-2(5z + 8) = 14 + 6z
Open the bracket
So, we have
-10z - 16 = 14 + 6z
Collect the like terms
So, we have
-10z - 6z = 14 + 16
Evaluate the like terms
So, we have
-16z = 30
Divide both sides of the equation by 16
So, we have
z = -15/8
Hence, the solution to the equation where the equation is given as -2(5z + 8) = 14 + 6z is z = -15/8
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Which of the following equations are equivalent to -2m - 5m - 8 = 3 + (-7) + m?
select all that apply
m - 4 = -7m - 8
-8 - 3m = 4 - m
-3m - 8 = 4 - m
-15m = -4m
-7m - 8 = m - 4
-8 - 7m = -4 + m
The equations that are equivalent to the given equation are m - 4 = -7m - 8, -7m - 8 = m - 4 and -8 - 7m = m - 4
How to determine the equations that are equivalent to the given equation?The equation is given as
-2m - 5m - 8 = 3 + (-7) + m
Remove the bracket
So, we have
-2m - 5m - 8 = 3 - 7 + m
Evaluate the like terms
So, we have
-7m - 8 = - 4 + m
The above expression can be written as follows
m - 4 = -7m - 8
-7m - 8 = m - 4
-8 - 7m = m - 4
Hence, the equations that are equivalent to the given equation are m - 4 = -7m - 8, -7m - 8 = m - 4 and -8 - 7m = m - 4
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Is x = -14 a solution to 9x - 7 = -7?
Answer:
since x=-14
9(-14)-7
-126-7=-133.
-7(5x-70=-19-x i neeeeeeeeeeeeeeeeeeeeeeddddddd helppp
Answer:
hope this will help you
Step-by-step explanation:
-7(5x-70)=-19-x
-35x+490=-19-x
490+19=-x+35x
509=34x
x=509/34
x=14.97
Can someone help me I will mark u brilliant
Answer: R'=(-4, -3)
S'=(-4, -10)
T'=(-8, -10)
U'=(-8, -3)
Step-by-step explanation:
When rotated around the origin by 180 degrees, the rectangle will have all its coordinates' x and y values negated.
R=(4,3) ==> R'=(-4, -3)
S=(4,10) ==> S'=(-4, -10)
T=(8,10) ==> T'=(-8, -10)
U=(8,3) ==> U'=(-8, -3)
What is the range of the function on the graph?
all the real numbers
all the real numbers greater than or equal to 0
all the real numbers greater than or equal to 2
all the real numbers greater than or equal to -3
The range of the function on the graph containing all the real numbers greater than or equal to –3 . So the correct option is (d)
What is the range of a function?The collection of all a function's outputs constitutes its range.
The elements of the co-domain that are mapped are known as the images, while the elements of the domain are known as pre-images.
The set of all images of the domain's elements in this case serves as the function's range, as does the set of all of its outputs.
We have to find the function on the graph.
From the given graph, we can see from the graph that the function's maximum y value is -3 and that the graph keeps going up.
Therefore, the range includes all real values that are greater than or equal to -3.
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Find the remainder when 2x^10 - 3ix^8 + (1 + i)x^2 - (3 + 2i)x + 1 is divided by (x - i)
Be sure to show your work.
Use the polynomial remainder theorem. The remainder upon dividing a polynomial [tex]p(x)[/tex] by a linear factor [tex]x-c[/tex] is exactly [tex]p(c)[/tex].
In this case,
[tex]p(x) = 2x^{10} - 3ix^8 + (1+i)x^2 - (3+2i)x + 1[/tex]
and [tex]c=i[/tex]. Then the remainder is
[tex]p(i) = 2i^{10} - 3i^9 + (1+i)i^2 - (3+2i)i + 1[/tex]
Since [tex]i^2=-1[/tex] and [tex]i^4=1[/tex],
[tex]p(i) = -2 - 3i - 1 - i - 3i + 2 + 1 = \boxed{-7i}[/tex]
PLEASE HELP QUICK WILL GIVE BRAINLIST !!!
How many times larger is 9 x 10^5 than 5 x 10^3?
1.8
18
180
1,800
Answer:
180.
Step-by-step explanation:
9/5 = 1.8 and 10^5/10^3 = 10^2
so tis 1.8 x 10^2 which is 180
pls give branliest
Answer: 180
Step-by-step explanation:
(9 x 10^5) / (5 x 10^3)=
(9 x 10^(2+3)) / (5 x 10^3)=
(9 x 10^2 x 10^3) / (5 x 10^3)=
(9 x 10^2)/5= ==> Divide each side by 10^3
900/5=180
The common difference for the geometric sequence given by 1, -1, -3, -5, -7… is 2.
Answer:
No, the difference is -2.
Step-by-step explanation:
As the sequence progresses, the numbers get smaller(1, -1, -3, ...), and they get smaller by 2. Hence, the change in every number in the sequence as it progresses is -2.
What value of x makes this proportion true?
25/20 = x/4
A. 6
B. 9
C. 20
D. 5
3 1/5 ÷ 3 4/5 answer plsss
Answer: oh ofc! here is the answer it is 0.84210526315
but im not 100% sure it is the right answer
Step-by-step explanation: i really hope this helps have a good day/night (: <3
Can you please help me
A school is organizing a weekend trip to a nature preserve. For each student, there is a $60 charge, which covers food and lodging. There is also a $40 charge per student for the bus. The school must also pay a $30 cleaning fee for the bus. If the total cost of the weekend is $4,030, how many students will be going on the trip?
31 students
40 students
41 students
66 students
Answer:
40 students
Step-by-step explanation:
I think it is 40 students because 60 + 40= 100 then 100 x 40 = 4,000
then the SCHOOL has to pay a $30 cleaning fee so that will add up to $4,030! I hope this helps everybody!
40 students will be going on the trip
How to calculate the number of students that will be going on the trip ?Each student will pay $60 for food and lodging
Each student will also pay $40 for the bus
Total amount of fee that will be paid by each student is
= 60 +40
= 100
The school will pay $30 cleaning fee for the bus, it's only the school that will be paying this fee, the students are not included. This will will be subtracted from the total cost which is $4,030 leaving us with $4,000
Therefore the number of students going on the trip can be calculated as follows
= 4,000/100
= 40
Hence 40 students will be going on the trip
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Frind the sale price if 15% discount is allowed off market price of 25.00. fly
Jack is building a wall.
He uses 300 bricks to build part of the wall.
This part of the wall is 5 metres long and 1.5 metres high.
The complete wall will be 8 metres long and 1.5 metres high.
How many more bricks does Jack need to complete the wall?
The amount of bricks that Jack would need to complete the wall is 180.
How many more bricks does he need?The first step is to determine the total amount of bricks he would need to build the wall. In order to determine this value, ratio analysis would be used.
Total bricks needed = (area of wall x number of blocks already used) / (area of wall already built)
Area of wall = 8 x 1.5 = 12
Area of wall already built = 5 x 1.5 = 7.5
Total bricks needed = (12 x 300) / 7.5 = 400 bricks
Number of bricks needed to complete the wall = 400 - 300 = 180 bricks
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Please stop with the trolls
Answer:
6
scale factor b to A = 4
Step-by-step explanation:
scale factor
We multiply the scale factor times the original figure length to get the new figure length
x * scale factor = 1.5
The scale factor is 1/4
x * 1/4 = 1.5
Multiply each side by 4 to get rid of the fraction
x * 1/4 *4 = 1.5 * 4
x = 6
The scale factor from figure B to figure A
1.5 * scale factor = 6
scale factor = 6/ 1.5
scale factor = 4
Pls help me with thisss
Answer:
A
Step-by-step explanation:
Each hash mark between "School" and "Declan's house" is one-eighth of a mile. Starting at "School" count 5 hash marks to the left to get where Harper lives.
Okay what about 124.35$ and the sales tax is 6.75%
Answer:
$132.74
Step-by-step explanation:
First: divide the sales price by 100
6.75 ÷ 100 = 0.0675
Second: multiply the answer from the first step by the original price
0.0675 x 124.35 = 8.393625
round to the hundredths place
8.393625
8.39
Third: add the original price with the answer from the second step
124.35 + 8.39 = 132.74
desperate need in help
Answer: 8x^10
Step-by-step explanation:i guessed but when you multiply exponents you just add them so the exponent is 10 and then 2 cubed is 8
A textile artist is asked
to make a wall-hanging that measures at most
3.75 feet wide by 6.5 feet tall. When finished,
the wall hanging measures 3 3/8 feet wide by
6 3/4 feet tall. Does the wall hanging meet the
specifications?
He wouldn’t be able to meet the specifications as the heigh is greater than the maximum height.
In mathematics, the greater than sign is a basic mathematical notation used to represent an inequality between two values. The symbol used to denote greater inequality is “>”. It is the commonly accepted mathematical notation of two strokes of equal length that meet at an acute right angle. A typical use of the greater than sign is to compare two values, where the first is greater than the second, or one is greater than the other. The greater than sign is an approximation of a closing square bracket.Maximum width of the wall hanging can be 3.75 feet and maximum height can be 6.5 feet.
After completing the work it was found that the width measures 3 3/5 feet and height was 3 3/4 tall.
If the height and width after completing the work is less than or equal to the maximum height and width then he will be able to meet the specifications .
Width
3 3/4
= (12+3)/4
= 15/4
= 3.75
Height
6 3/4
= (24+3)/4
= 27/4
= 6.75
He wouldn’t be able to meet the specifications as the heigh is greater than the maximum height .
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need help with solving this triangle
Answer:90
Step-by-step explanation:
you add 30 + 60 gives you 90 degrees
Randy's swimming coach kept track of his average 50-meter lap times during the first 3 weeks of training.
Week Time (s)
28.8
27.6
27.1
How much greater was the percent of change from Week 1 to Week 2 than from Week 2 to Week 3? Round to the nearest tenth of a percent
Randy's percentage change from Week 1 to Week 2 was 2.37% greater than Week 2 to Week 3.
The percentage change will be calculated by the relation -
Percentage change = change in timing ÷ original time × 100
Calculating percentage change between Week 1 and Week 2
Change = 28.8 - 27.6
Change = 1.2 seconds
Percentage = (1.2 ÷ 28.8) × 100
Percentage = 4.17%
Calculating percentage change between Week 2 and Week 3
Change = 27.6 - 27.1
Change = 0.5 seconds
Percentage = (0.5 ÷ 27.6) × 100
Percentage = 1.8%
So, percent of change from Week 1 to Week 2 than from Week 2 to Week 3 was = 4.17 - 1.8
Percentage change = 2.37%
Therefore, the percentage change from Week 1 to Week 2 was 2.37% greater than Week 2 to Week 3.
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For which value of x is line n parallel to line m?
(Click document to see image.)
Answer: 70
Step-by-step explanation:
Looking at line p, we can form an equation to find the missing angle that would make the line equal to 180* (all straight lines, unless stated otherwise, should be assumed they are a 180* angle). We can use the equation below:
[tex]180 = 80 + 30 + x\\x = 180 - (80 + 30)\\x= 70[/tex]
If lines n and m are parallel, the angles should be equal when looking at an intersecting line.
Hope this helps!
If the difference of a number and eight is tripled, the result is six more than the number. Find the number. Round your answer to the nearest integer, if necessary.
If the difference of a number and eight is tripled and the result is six more than the number, the number is 15
How to find the number using variable?The difference of a number and eight is tripled, then the result is six more than the number.
Therefore, the number will be represented by a variable
let the number = x
Hence,
3(x - 8) = x + 6
Therefore, let's open the bracket
3(x - 8) = x + 6
3x - 24 = x + 6
subtract x from both sides of the equation
3x - 24 = x + 6
3x - x - 24 = x - x + 6
2x - 24 = 6
add 24 to both sides of the equation
2x - 24 + 24 = 6 + 24
2x = 30
divide both sides by 2
x = 30 / 2
x = 15
Therefore, If the difference of a number and eight is tripled and the result is six more than the number, the number is 15
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add it
3+8+6+3+3+3+6
The answer to it would be 32.
Answer:
32
32 is the answer hope this helps
The variables and y vary inversely. Use the given values to write an equation relating and y. Then find y when x = 3.
x = 5, y = -4
An equation is y =
When x = 3, y =
Answer:
x=5$
$y=-4
Step-by-step explanation:
the solution is easy no more you have to put the first numbers and put it in order
Which is the following in an irrational number?
A. -8.264264264...
B. -5/9
C. 17.47
D. 4.28192489...
*
Answer:
D
Step-by-step explanation:
Irrational numbers are those which cannot be expressed by the ratio of two integers.
A is rational because it is a recurring decimal. Recurring decimals can be represented by the ratio of two integers (this one can be represented by the fraction -2752/333, which is a ratio of two integers).
B is a fraction with two integers, therefore it is rational. -5/9 is a ratio of two integers.
C can be represented by 1747/100.
D is an infinite decimal but isn't recurring like A, meaning it cannot be represented by the ratio of two integers, and is therefore it is irrational, unless you are shown further digits of the decimal which prove it to be recurring, which is not the case here.
10x-6-10x-2 simplified please show steps
Answer:
Step-by-step explanation:
1) group any number with an X together and rewrite answer (if there is a negative in front of a number always carry it with it when rearranging.)
10x-10x-6-2
2) lets solve the numbers with Xs together
10x+10x= 20x
3) now lets solve whole numbers
-6-2=-8
4) bring down the 20x and the -8/ rewrite problem with your solved numbers
20x-8
5) we have to have X alone so in order to get rid of the 20 in front of the X you must divide 20 by 20x,
20x/20 ( it cancel's out and now you're left with X)
X=-8
6) but whatever you do to one side of the equal sign you have to do to the other side so now you must divide -8/20 which will leave you with
Answer: X=-0.4 or -2/5
Which expression is the simplest form of 3x³ – x² + 2 (x³ − 4x²)?
Answer: [tex]x^{2} (5x-9)[/tex]
Step-by-step explanation:
[tex]3x^3 - x^2 + 2(x^3 - 4x^2)[/tex]
[tex]= 3x^3 - x^2 +2x^3 - 8x^2[/tex]
[tex]=5x^3 -9x^2[/tex]
[tex]=x^2 (5x-9)[/tex]