All integers where n ≥ 1.
We have given that the sequence,
[tex]a_{n} =4-3(n-1)[/tex]
We have to find the domain for n.
What is the meaning of arithmetic sequence?Arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. Difference here means the second minus the first.
That is, [tex]a_{n} =a+(n-1)d[/tex]
where a = first term of sequence.
d =common difference.
n =number of terms which belongs to natural numbers
By the definition of arithmetic sequence n starts with 1
Remember that,the natural number starts with 1
Now, in given sequence for nth term
[tex]a_{n} =4-3(n-1)[/tex]
The domain for n is All integers where n ≥ 1.
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4. A deposit of $1000 is made into a savings account that pays 4% annual interest compounded monthly
a. How much money will be in the account after 6 years?
b. How long will it take for the $1000 to double?
Using compound interest, it is found that:
a) $1,270.70 will be in the account after 6 years.
b) It will take 17.53 years for the $1000 to double.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.In this problem, the parameters are given as follows:
[tex]A(0) = 1000, r = 0.04, n = 12[/tex]
Item a:
Over 6 years, that is t = 6, thus:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(t) = 1000\left(1 + \frac{0.04}{12}\right)^{12 \times 6}[/tex]
[tex]A(t) = 1270.7[/tex]
$1,270.70 will be in the account after 6 years.
Item b:
This is t for which A(t) = 2P = 2000, hence:
[tex]2000 = 1000\left(1 + \frac{0.04}{12}\right)^{12t}[/tex]
[tex](1.0033)^{12t} = 2[/tex]
[tex]\log{(1.0033)^{12t}} = \log{2}[/tex]
[tex]12\log{(1.0033)} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{12\log{1.0033}}[/tex]
[tex]t = 17.53[/tex]
It will take 17.53 years for the $1000 to double.
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Evaluate the expression (9 + 14i) + (7 – 11i) and write the result in the form a + bi.
Answer:
16+3i
Step-by-step explanation:
(9+ 14¡) + (7 - 11¡)
9+ 14¡ + 7 - 11¡
16 + 3i
What is 80% of 150? Please help
Answer:
the answer is x=120
Step-by-step explanation:
look at the photo for the mathematical explanation
simplify (6x^2-7x-5)/(3-x)
Answer:
Simplify —
3
Equation at the end of step
1
:
5
(((6 • (x2)) - 7x) - —) - x
3
STEP
2
:
Equation at the end of step
2
:
5
(((2•3x2) - 7x) - —) - x
3
STEP
3
:
Rewriting the whole as an Equivalent Fraction
3.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 3 as the denominator :
6x2 - 7x (6x2 - 7x) • 3
6x2 - 7x = ———————— = ——————————————
1 3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
6x2 - 7x = x • (6x - 7)
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
x • (6x-7) • 3 - (5) 18x2 - 21x - 5
———————————————————— = ——————————————
3 3
Equation at the end of step
4
:
(18x2 - 21x - 5)
———————————————— - x
3
STEP
5
:
Rewriting the whole as an Equivalent Fraction :
5.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 3 as the denominator :
x x • 3
x = — = —————
1 3
Trying to factor by splitting the middle term
5.2 Factoring 18x2 - 21x - 5
The first term is, 18x2 its coefficient is 18 .
The middle term is, -21x its coefficient is -21 .
The last term, "the constant", is -5
Step-1 : Multiply the coefficient of the first term by the constant 18 • -5 = -90
Step-2 : Find two factors of -90 whose sum equals the coefficient of the middle term, which is -21 .
-90 + 1 = -89
-45 + 2 = -43
-30 + 3 = -27
-18 + 5 = -13
-15 + 6 = -9
-10 + 9 = -1
-9 + 10 = 1
-6 + 15 = 9
-5 + 18 = 13
-3 + 30 = 27
-2 + 45 = 43
-1 + 90 = 89
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Adding fractions that have a common denominator :
5.3 Adding up the two equivalent fractions
(18x2-21x-5) - (x • 3) 18x2 - 24x - 5
—————————————————————— = ——————————————
3 3
Trying to factor by splitting the middle term
5.4 Factoring 18x2 - 24x - 5
The first term is, 18x2 its coefficient is 18 .
The middle term is, -24x its coefficient is -24 .
The last term, "the constant", is -5
Step-1 : Multiply the coefficient of the first term by the constant 18 • -5 = -90
Step-2 : Find two factors of -90 whose sum equals the coefficient of the middle term, which is -24 .
-90 + 1 = -89
-45 + 2 = -43
-30 + 3 = -27
-18 + 5 = -13
-15 + 6 = -9
-10 + 9 = -1
-9 + 10 = 1
-6 + 15 = 9
-5 + 18 = 13
-3 + 30 = 27
-2 + 45 = 43
-1 + 90 = 89
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
18x2 - 24x - 5
——————————————
3
Step-by-step explanation:
The rectangle below has an area of x2 – 25 square meters and a length of x + 5 meters.
What expression represents the width of the rectangle?
Answer:
Width: x - 5
Step-by-step explanation:
x² - 25
x² - 5²
(x - 5)(x + 5)
Step-by-step explanation:
how many other faces are congruent to this one
Answer:
I believe the answer is 1
Step-by-step explanation:
Hope that helps!
Someone pls help??????????????????????????????
I'm about to finish 6th grade and I found out that most of the topics we studied and we are still studying are a bit difficult in math, so what topics I must need to know so I get prepared for 7th grade, would you help me please?
I will appreciate it so much.
Answer:
How to succeed in 7th grade
Strive for a deeper understanding of science. Instead of just memorizing facts, students learn to collect data, use the scientific method, and apply this information to compose reports and ask questions.
Express complex meanings through writing. ...
Stay ahead of the curve in math classes.
Step-by-step explanation:
A function is a relation where each input value is assigned to_____one output value
A. exactly
B. less than
C. at least
Can you show that this quadrilateral is a parallelogram
Answer:
This is a parallelogram.
Step-by-step explanation:
This figure has two pairs of paralel sides with completely different angles.
An angle measureless 60 degrees the measure of it complementary angle. What is the measure of each angle
Step-by-step explanation:
Finally complement of the supplement of twice the angle 60°=90°-60°=30
60 degrees angle is an acute angle because it is less than 90 degrees. 60° in radians is π/3 and the measure of each angle of an equilateral triangle is 60°. Therefore, it is also called a 60-degree angle triangle.
please mark me as brainlist pleaseGiven :
An angle which measures less 60° the measure of its complementary angle.⠀
To Find :
The measure of its complementary angle.⠀
Solution :
Let's assume the one of the complementary angle as "x" and the other angle as (x - 60)° .
Now,
According to the Question :
[tex]\: \qquad \dashrightarrow \sf{{x {}^{ \circ} + (x - 60) {}^{ \circ} = {90}^{ \circ} }}
[/tex]
[tex]\: \qquad \dashrightarrow \sf{{x {}^{ \circ} + (x - 60) {}^{ \circ} = {90}^{ \circ} }}
[/tex]
[tex]\: \qquad \dashrightarrow \sf{{x {}^{ \circ} + x {}^{ \circ} - 60 {}^{ \circ} = {90}^{ \circ} }}
[/tex]
[tex]\: \qquad \dashrightarrow \sf{{{2x}^{ \circ} = {90}^{ \circ} + 60 {}^{ \circ} }}
[/tex]
[tex]\: \qquad \dashrightarrow \sf{{{2x}^{ \circ} = 150 {}^{ \circ} }}
[/tex]
[tex]\: \qquad \dashrightarrow \sf{{x = \dfrac{150 {}^{ \circ}}{2 {}^{ \circ}} }}
[/tex]
[tex]\: \qquad \dashrightarrow \bf{{{x}^{ \circ} = 75 {}^{ \circ} }}
[/tex]
Therefore,
One angle = 75°Other angle = 75° – 60° = 15°⠀
Henceforth ,
The measure of the two angles are 75° and 15° .
Which equation can be used to find the perimeter of a regular octagon with sides of length 12 m?
Question 1 options:
P = 8 + 12
P = 8(12)
P = 12 ÷ 8
P = 2(8) + 2(12)
Answer: P=8(12)
Step-by-step explanation:
A regular polygon has all sides of equal length, meaning a regular octagon has 8 sides of equal length.
A driver can deliver his newspapers in 80 minutes. His friend can take care of the same route in 2 hours. How long would it take them to do the job together?
Using the together rate, it is found that it would take them 48 minutes to do the job together.
What is the together rate?The together rate is the sum of each separate rate.
In this problem, consdering the measures in minutes:
The driver's ratio is of [tex]\frac{1}{80}[/tex].His friend's ratio is of [tex]\frac{1}{120}[/tex].The together ratio is of [tex]\frac{1}{x}[/tex].Hence:
[tex]\frac{1}{x} = \frac{1}{80} + \frac{1}{120}[/tex]
[tex]\frac{1}{x} = \frac{3 + 2}{240}[/tex]
[tex]x = \frac{240}{5}[/tex]
[tex]x = 48[/tex]
It would take them 48 minutes to do the job together.
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y-8=-x solve for y
please show work I'm trying to find the y intercept
Graph the points (
–
1.5,4.5) and (
–
3.5,3.5) on the coordinate plane.
Answer:
(Please see attachment)
Step-by-step explanation:
Points on the graph:
(-1.5, 4.5), (3.5, 3.5)
Graph of points (-1.5, 4.5) and (-3.5,3.5) is given in attachment.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The given points are minus one point five comma four point five and minus three point five comma three point five.
(-1.5, 4.5) and (-3.5,3.5)
A coordinate plane is a tool used for graphing points, lines, and other objects
To point these points first we have to consider two lines, horizontal line and vertical line.
The horizontal line is called as X axis and vertical line is called as Y axis.
Then we have to pair (-1.5, 4.5) and (-3.5,3.5) with (x, y) coordinates.
Hence the given graph is the required answer.
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12.
Sandra and Emil are both house painters,
and each charges an hourly rate for a
painting job. The equation y = 13r shows
the total charge, y, in dollars, for hiring
Sandra to paint a house for *hours. The
table below shows the same information
for Emil.
Emil's Charges
2 4 6 8
26 52 78 104
help me pleaseeeeeeeeee
Answer:
10 and 11, The square root of 109 is approximately 10.4 and the two consecutive numbers are 10 and 11.
Questions in the picture
Answer:
18
Step-by-step explanation:
Solve the question in steps
(8+36)/11
44/11=4
Now you have 4+7x2
You do multiplication first
4+14=18
Select the expression that has a sum of seventy-four hundredths.
A seventy hundredths plus four tenths
B sixty eight-hundredths plus six tenths
C six tenths plus twelve hundredths
D four-tenths plus thirty-four hundredths
Write [tex]\sqrt{8}[/tex] in the form [tex]4^n[/tex] - I'm doing GCSE maths and have no clue how to do this without a calculator.
V8 ENGINE
Step-by-step explanation:
Remi buys a fish tank for $70. The sales tax is 8%. What is the total cost of the fish tank, including sales tax?
Answer:
$75.60
Step-by-step explanation:
Given:
Remi buys a fish tank for $70. The sales tax is 8%To Find:
What is the total cost of the fish tank, including sales tax?
Note:
Sales Tax ⇒ Increase ⇒ Add
8% = 0.08
Solve:
$70 × 0.08 = 5.60
$70 + 5.60 = 75.60
Hence, total cost of the fish tank including sales tax is $75.60
~Learn with Lenvy~
In ABC, C = 1.2 inches, a = 7.7 inches and ZB=143°. Find A, to the nearest 10th of
an degree.
Answer: 32.2
Step-by-step explanation:
HELP ASAP PLEASE!!!! :(
Answer:
x = 1 and y = -8/3
step-by-step explanation:
In order to solve this, insert equation 1 into 2solve for x
[tex]\sf 6x+3\left(\frac{4}{3}x-4\right)=-2[/tex]
[tex]\sf 6x+4x-12=-2[/tex]
[tex]\sf \rightarrow 10x = -2 +12[/tex]
[tex]\sf \rightarrow 10x = 10[/tex]
[tex]\sf \rightarrow x = 1[/tex]
solve for y
[tex]\hookrightarrow \sf y = \frac{4}{3} x-4[/tex]
[tex]\hookrightarrow \sf y = \frac{4}{3} (1)-4[/tex]
[tex]\hookrightarrow \sf y=-\frac{8}{3}[/tex]
Answer:
x=1 and y=-8/3
Step-by-step explanation:
The easiest way to solve this is by substitution because the first equation is already in slope-intercept form.
First, take y= 4/3x -4 and substitute it into the second equation as follows: 6x + 3(4/3x -4) = -2
Next, simplify that equation to get 6x + 12/3x -12 = -2.
After that, combine all like values: 10x - 12 = -2.
Finally, add 12 to each side and divide by 10 to get x=1.
To find the y-value, substitute x=1 into either equation and solve for x (I'm choosing the first equation). y= 4/3(1) -4
In order to make simplifying this easier, I find that -4 = -12/3.
Finally, simplify: y= 4/3 - 12/3 = -8/3.
The solution to the system of equations is (1, -8/3), or x=1 and y=-8/3.
i need help with this
Answer:
So you can either buy all roses or all carnations, or spend $30 on each kind:
12 roses
10 carnations
6 roses & 5 carnations
Step-by-step explanation:
If you buy a combination of roses and carnations, the amount of money you spend on each has to be a multiple of both 5 and 6. Since these are relatively prime, their least common is 5(6) = 30.
note: the reason it has to be a common multiple of 5 and 6 is because the total amount - 60 - is a common multiple.
(-1)[-3-(-5)(7)]+(-3+7)(-2)
[tex](-1)[-3-(-5)(7)]+(-3+7)(-2)\\\\=(-1)[-3-(-35)]+(4)(-2)\\\\=(-1)(32)-8=-40[/tex]
Hope it helps!
Mr. Campbell has a square garden with an area of 256 square feet. He wants to put a fence along 3 sides of the garden. How many feet of fencing will he need?
Answer:
Step-by-step explanation:
It should be noted:
Area of square garden = L² = 256
Square root both sides of the equation to find the length of the square garden. Then, use the length of the square garden to calculate the length of fence required for 3 sides of the garden.
Square root both sides.
√L² = √256
=> L = 16
Multiply the length by 3.
3L = 16 x 3 = 48 feet
Thus, Mr. Campbell will need 48 feet of fencing.
This data set represents the widths in yards of pieces of fabric used by a sewing group.
What is the mean of this data set?
{113, 14, 23, 12, 114}
Enter your answer as a fraction in simplest form in the box.
help
The mean of the data set in simplest form is: 4/5 yard.
What is the Mean of a Data Set?Mean = sum of all values in the data set divided by the number of values in the data set.
Mean of the data set = (1 1/3 + 1/4 + 2/3 + 1/2 + 1 1/4)/5
Convert the mixed fractions to improper fractions
(4/3 + 1/4 + 2/3 + 1/2 + 5/4)/5
[(16 + 3 + 8 + 6 + 15)/12]/5
(48/12)/5
= 4/5
Therefore, the mean of the data set in simplest form is: 4/5 yard.
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Answer:
The answer is 4/5 yds hope this helps :DD
Step-by-step explanation:
Answer for: k12 5.02 Quiz: Mean
A wizard walks into a wand shop to
purchase a magic wand. He chooses
a wand that is 22 cm long. Will the
wand fit into the box shown? Explain.
No. You can see this because the length of the box is 21, whilst the length of the wand is 22.
Answer:
Yes, it can fit in.
Using Pythagoras theorem:
Find bottom side, hypotenuse
a² + b² = c²
6² + 21² = (bottom side)²
bottom side = √477
bottom side = 3√53 cm
Then find upper diagonal, hypotenuse
(3√53)² + 5² = diagonal²
diagonal = √502
diagonal = 22.4 cm
Thus the wand can fit in the box diagonally.
Students in Mr. Jacob's class used a number
cube with sides numbered 1 through 6 and a spinner with 4 even-numbered and 4 odd-numbered sections. For each trial, they recorded whether the outcomes for the cube and the spinner were even or odd.
Based on the data in the table, which is closest to the number of times the next 50 trials should result in both the cube and the spinner being even?
A 12
B 25
C 48
D 50
Please explain how you got the answer if you can.. or like a small summary
Answer:
25.
Step-by-step explanation:
the ratio from even to odd is equal. a half chance of getting even 3:6 & 4:8 [ theres 3 even #s on the cube, 3 odds #s on the cube] vice VERSA!! for either even or odd roll. so out of 50, half of 50 is 25. there's a 1:2 chance of even(or in whatever case) 1:2 = 25:50
Find the perimeter of the parallelogram with these vertice
(3,5), (-4, 2), (3, 1), (-4,-2)
Answer:
24 is your answer
Step-by-step explanation:
I first brought one side up as the other went down.
Then found the base and the side and added them all to get
8 as base and 4 multiply both by two then add to get 24
hope this helped.
A brainliest is always appreciated.