Find an explicit formula for the arithmetic sequence 10,-10,-30,-50,...10,−10,−30,−50,...10, comma, minus, 10, comma, minus, 30, comma, minus, 50, comma, point, point, point. Note: the first term should be \textit{c(1)}c(1)start text, c, left parenthesis, 1, right parenthesis, end text. c(n)=c(n)=c, left parenthesis, n, right parenthesis, equals
An explicit formula for the arithmetic sequence is aₙ = 10 - 20(n - 1).
How to write an explicit formula for the arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this mathematical expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.From the information provided, we have the following parameters:
First term, a₁ = 10
Second term, a₂ = -10
Next, we would determine the common difference as follows:
Common difference, d = a₂ - a₁
Common difference, d = -10 - 10
Common difference, d = -20
Substituting the parameters into the mathematical expression, we have;
aₙ = 10 + (n - 1)(-20)
aₙ = 10 - 20(n - 1).
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Martina is taxed at a rate of 25% for her federal taxes. Last year, she reduced her taxable income by contributing to a flexible savings plan in the amount of $2,700. If her
wages before the deduction were $68,000, how much did she save in federal taxes by using the FSA?
▸
Answer:
14300
Step-by-step explanation:
this is the answer that I got I hope it works
Saving of Martina in taxes = $675
What is FSA?A flexible spending account (FSA) is a type of savings account, usually for healthcare expenses, that sets aside funds for later use. It is also known as a flexible spending arrangement, is one of a number of tax-advantaged financial accounts, resulting in payroll tax savings.
Given,
Wages of Martina = $68000
Tax rate = 25%
Amount to flexible savings = $2700
Then saving in taxes = $2700 × 25/100
= $675
Hence, Martina saved $675 in taxes using FSA.
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what do they mean, (Grade 10 real numbers)
X is a positive rational number greater than 1. If the two integers that make up the ratio are both positive, then the numerator must be greater than the denominator for the value of the ratio to be greater than 1.
So now let's look at subtracting the numerator and the denominator. We know that p > q and they are both positive integers.
So, p - q must be a positive integer greater than 1 because it is a positive integer subtracted by a smaller positive integer.
find the difference in centimetres between 5m and 465cm
Answer:
35 cm
Step-by-step explanation:
What is the true solution to 2 In en 5x = 2 In 15?
x= 0
x= 3
x= 9
x= 15
The true solution for 2 ln e^ ln (5x) = 2 ln (15) is x = 3.
Given,
2 ln e^ ln (5x) = 2 ln (15)
Apply log rule;
logₐ (aᵇ) = b
ln (e^ln (5x)) = ln (5x)
2 ln (5x) = 2 ln (15)
Divide both sides by 2;
2 ln (5x) / 2 = 2 ln (15)/ 2
ln (5x) = ln (15)
For ln (5x) = ln (15), solve for 5x = 15;
That is,
5x = 15
Then,
x = 15/5
So,
x = 3
Check this by substituting it to 2 ln (5x) = 2 ln (15);
x = 3
2 ln (5 × 3) = 2 ln (15)
x = 3 makes this true.
Therefore,
The true solution for 2 ln e^ ln (5x) = 2 ln (15) is x = 3.
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+83--95 x + 7+72÷-9 what is the answer
Answer:
7.4
Step-by-step explanation:
Not completely sure because that equation is really hard to read. You might have put it in wrong.
Answer:
-95x + 91
Step-by-step explanation:
72/9 = 8
83 - 95x + 8
91 - 95x or -95x + 91
Help. I'll mark as brainlist. I am always giving brainlist points.
Answer: 18 square unit
Step-by-step explanation:
We can divide the shape into two pieces.
a triangle and a square.
The square is 2*6=12 square unit
and the triangle is 1/2*6*2=6 square unit
So if we sum this up we get the answer
answer = 6+12 = 18 square unit
Tough question help asap
The function values;
f(-2) = 9 x 4⁻² = 9 x 0.0625 = 0.5625f(1/2) = 9 x 4^(1/2) = 9 x 2 = 18f(0) = 9 x 4⁰ = 9 x 1 = 9Given,
The function; f(x) = 9 × 4ˣ
The value of the function is f(x). The slope of the line is m. b is either the function's value at x=0 or the position at which the line in the coordinate plane crosses the y-axis. x is the x-value. coordinate's
Four main categories can be used to classify different sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.
We have to find the following function values;
f(-2) = 9 x 4⁻² = 9 x 0.0625 = 0.5625f(1/2) = 9 x 4^(1/2) = 9 x 2 = 18f(0) = 9 x 4⁰ = 9 x 1 = 9Learn more about functions here;
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Katrina buys a 66-ft roll of fencing to make a rectangular play area for her dogs. Use 2(l+w) = 66 to write a function. for the length, given the width. Graph the function. What is a reasonable domain for the situation? Explain. The function f(w) = gives the length as a function of the width. (Simplify your answer.)
The function for the length when the width is given is l = 33 - w. The domain of the function is 0 < w < 33 and the graph of the function has been plotted
The total length of the roll = 66 feet
The perimeter of the rectangular paly area = 66
The perimeter of the rectangle = 2(l + w)
Then the equation will be
2(l + w) = 66
l + w = 66/2
l + w = 33
The function for length when the width is given
l = 33 - w
Therefore the domain of the function is 0 < w < 33
When w = 1
l = 33 - 1
l = 32
The first point is (1, 32)
When w = 32
l = 33 - 32
l = 1
The second point is (32, 1)
Draw the graph of the function
Hence, the function for the length when the width is given is l = 33 - w. The domain of the function is 0 < w < 33 and the graph of the function has been plotted
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Determine the vertex of the graph of the following parabola. f(x)=−(x+1)2−6
The vertex of the graph of the parabola is at the point (-1, -6)
How to find the vertex of the parabola?We know that for any parabola with a vertex at the point (h, k) and a leading coefficient a, can be written in vertex form as:
y = a*(x - h)^2 + k
In this case the parabola is:
f(x) = (-1)*(x + 1)^2 - 6
Comparing this with the general form, we can see that:
h = -1
k = -6
Then the vertex of the parabola is (-1, -6)
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Which is bigger 21.17 or 2.117
Answer:
21.17
Step-by-step explanation:
If you were to round each number to the nearest whole number you would get :
21.17 ⇒ 21
2.117 ⇒ 2
Now the question is , which is bigger 21 or 2?
Now that is a very straightforward answer (21 in case your still lost)
Hope this helped and have a good day
3) Bill is a freshman attending a 4-year college. He has been approved for a $5,000 with an APR of 6.75%.
He is not required to make any payment for 10 years since his payment will be deferred while his enroll
in school. How much interest will he pay in 10 years?
Interest will he pay in 10 years is $3375.
Given:
Bill is a freshman attending a 4-year college. He has been approved for a $5,000 with an APR of 6.75%.
He is not required to make any payment for 10 years since his payment will be deferred while his enroll in school.
1 year interest = 5000*6.75%
= 5000*6.75/100
= 50*6.75
= 50*675/100
= 1*675/2
= 337.5
10 years interest = 10 * 337.5
= 10 * 3375/10
= $3375.
Therefore Interest will he pay in 10 years is $3375.
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5.2: Bowling for Triangles (Part 2)
Here is a visual pattern of dots. The number of dots D(n) is a function of the step number n.
1. What values make sense for n in this situation? What values don't make sense for n?
Using the pattern, n can represent the the increase of dots according to step.
In the given question we have to find what values make sense for n in this situation.
n is representing the number.
As we can see that there is a pattern given.
In the step 1 have 1 dot, in step 2 have 3 dots, in step 3 have 6 dots and in step 4 have 10 dots.
So if we see the pattern then according to number of step the dots increasing accordingly.
As In step 1 have 1 dot, in step 2, 2 dots increase, in step 3, 3 dots increase and in step 4, 4 dots increase.
So, n can represent the the increase of dots according to step.
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Angles X and Y are supplementary. Angle X measures 127.42°, and angle Y measures (m − 12)°. Find m∠Y. anwsers 115.42° 74.84° 64.58° 52.58°
The measure of angle Y, m ∠Y, is 52.58°. The correct option is the last option 52.58°
Calculating the measure of an angleFrom the question, we are to determine the measure of angle Y.
From the given information,
Angles X and Y are supplementary angles.
NOTE: Supplementary angles are angles that sum up to 180°
Thus,
m ∠X + m ∠Y = 180°
Also,
From the given information,
Angle X measures 127.42°
That is,
m ∠X = 127.42°
Therefore,
127.42° + m ∠Y = 180°
m ∠Y = 180° - 127.42°
m ∠Y = 52.58°
Hence, the measure of the angle is 52.58°
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Apply the properties of operations to multiply the expression
The properties of operations to multiply the expression are commutative property, associative property, and distributive property.
Let us understand the properties of operations to multiplication:
The foundation of arithmetic is the Properties of Operations; we use them when performing computations and recalling basic facts.
There are basically three properties of operations to multiplication which are:
Commutative Property: The commutative property of multiplication states that the order in which values are multiplied does not matter and will result in the same answer. That is to say: a * b = b * aAssociative Property: The associative property of multiplication states that when three or more numbers are multiplied, the order in which the multiplication occurs has no effect on the answer. That is to say: (a * b) * c = a * (b * c)Distributive Property: Students are asked to create two groups of six (2 x 6) using connecting cubes and to locate two hidden facts inside the 2 x 6 such as 2 x 3 and 2 x 3. That is: 2 x 6 = 2 x 3 + 2 x 3.Thus, the properties of operations to multiply the expression are commutative property, associative property, and distributive property.
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Which number is divisible by 5 and 10? I NEED HELP FAST
Answer: Many even numbers are divisible by ten. A simple answer to that is 20. 30 is also, and so is 40. Any number going up by 10 will be divisible by 10 and 5. 10 is also divisible by 10 and 5.
Consider the polynomial function []
p
given by p(x)=5x3+8x2−3x+1
A(x)
. Evaluate the function at x=−2
x
.
Bob invested his savings in two investment funds. The amount he invested in Fund A was 3 times as much as the amount he invested in Fund B. Fund A returned a 5% profit and Fund B returned a 7% profit. How much did he invest in Fund B, if the total profit from the two funds together was $2200?
The amount that he invested in Fund B if the total profit from the two funds together was $2200 is $8,800.
How to find the amount invested?Let x represent the amount invested in Fund B
Let 3x represent the amount invested in Fund A
Hence,
.07x + .05(3x) = 2200
.07x + .15x = 2200
.25x = 2200
Divide both side by .25x
x = 2200/.25
x = $8,800 (invested in Fund B)
Fund A:
3x = 3(8,800)
3x = $26,400 (Invested in Fund A)
Therefore $8800 was invested in Fund B.
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Clayton's mortgage payment was originally $2,460 per month. Now, after refinancing his home loan, Clayton's mortgage payment is $1,968. What is the percent of decrease in Clayton's mortgage payment?
please
Answer:
20%
Step-by-step explanation:
2460-1968=492
492/2460=0.20
Check answer2460 x 0.20 = 492
You have a 64-ounce pitcher of tea.
After you pour as many 7-ounce cups of tea as possible, how much tea will be left
over?
Answer:
You can pour nine 7-ounce cups of tea (63 ounces) and be left with one ounce of tea.
Step-by-step explanation:
Dividing 64 by 7 and finding the remainder.
pls help I don't get the problem
Simplified form is the -(1+sinα).
Given in question,
[tex]cos^{2}[/tex]α/sinα-1
[tex]sin^{2}[/tex]α + [tex]cos^{2}[/tex]α = 1
[tex]cos^{2}[/tex]α = 1 - [tex]sin^{2}[/tex]α
[tex]cos^{2}[/tex]α/sinα-1 = (1 - [tex]sin^{2}[/tex]α ) / (sinα-1)
= (1-sinα)(1+sinα)/(sinα-1)
= (1-sinα)(1+sinα)/-(1-sinα)
= (1+sinα)/-1
= -(1+sinα)
Hence, in simplified form [tex]cos^{2}[/tex]α/sinα-1 = -(1+sinα)
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The point N lies on the segment MP
Find the coordinates of N so that MN is 3/7
of MP.
M(-4,6)
N (?,?
P (17,-22)
The coordinates of N are (5,-6) so that segment MN is 3/7 of MP.
Given the coordinates of M is (-4,6) and the coordinates of P is (17,-22).
now we have to find the coordinates of N such that the MN : NP is 3:4 .
We will use the section formula:
The section formula states that:
[tex]{\displaystyle N=\left({\frac {mx_{2}+nx_{1}}{m+n}},{\frac {my_{2}+ny_{1}}{m+n}}\right)}[/tex]
Where the coordinates of the points are given and the ratio in which the points are divided is given.
Now we will substitute the values:
[tex]{\displaystyle N=\left({\frac {17\times 3+4\times -4}{3+4}},{\frac {3\times-22+4\times 6}{3+4}}\right)}[/tex]
Solving we get:
N=(5,-6)
The Section formula is used to determine the coordinates of things like the point that separates a line segment (internally or externally) into a particular ratio.
Both physics and mathematics regularly employ this formula. In mathematics, it is used to find the centroid and incenters of a triangle, but in physics, it is used to find the center of mass, equilibrium points, etc. The section formula is often used to find the midpoint of a line segment.
Therefore coordinates of N are (5,-6) so that MN is 3/7 of MP.
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party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 3 tables is $25. The total cost to rent 6 chairs and 5 tables is $49. What is the cost to rent each chair and each table?
The cost to rent each chair and each table is $2.75 and $6.50 respectively.
How to calculate the cost?The total cost to rent 2 chairs and 3 tables is $25. This will be:
2c + 3t = 25
The total cost to rent 6 chairs and 5 tables is $49. This will be:
6c + 5t = 49
2c + 3t = 25
6c + 5t = 49
6 × (2c + 3t = 25)
2 × (6c + 5t = 49)
12c + 18t = 150
12c + 10t = 98
Subtract
8t = 52
Divide
t = 52/8
t = 6.5
Cost to rent table = $6.50
Since 2c + 3t = 25
2c + 3(6.5) = 25
2c + 19.5 = 25
Collect like terms
2c = 25 - 19.5
2c = 5.5
c = 5.5/2
c = 2.75
Cost to rent chair = $2.75.
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See question in screenshot below:
Answer:
1440/17 degrees (approximately 84.7059 degrees)
19π/9 radians ---> or π * 19/9 radians
Step-by-step explanation:
The conversion factor for radians to degrees is 180/π
8π/17 * 180/π = 1440/17 degrees (approximately 84.7059 degrees)
The conversion factor for degrees to radians is π/180
380 * π/180 = 380π/180 = 19π/9 radians
Evaluate for A(12). Round your answer to the nearest hundredth.
The value the function A(12) is 2960.94
How to evaluate the function?From the question, we have the following function definition that can be used in our computation:
A(t) = 710e⁰°¹¹⁹⁺
To calculate the function A(12), we set t to 12
i.e. calculate A(t) when t = 12
This equation becomes
A(12) = 710e⁰°¹¹⁹ˣ¹²
Evaluate the products
A(12) = 710e¹°⁴²⁸
Evaluate the exponents
A(12) = 2960.94
Hence, the solution is 2960.94
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Find the slope of this line.make it a fraction.
Answer:
[tex]\frac{-2}{3}[/tex]
Step-by-step explanation:
to find the slope of linear line, you need two points. It does not matter which pints you use. I am going to use (0,5) and (3,3) The slope is the change in y over the change is x. Our y values are 3 and 5. Our x values are 3 and 0
[tex]\frac{3-5}{3-0}[/tex] = [tex]\frac{-2}{3}[/tex]
$4.25,$6.71,$3.24,$5.06,$4.94 what is the average ?
The average of the number given is $4.84.
The average can be calculated as follows:
Sum up all the numbersGiven X
X =$4.25+$6.71+$3.24+$5.06+$4.94
X =$24.2
To find the average, you need to divide the X by n or the amount of numbers, where n=5= X ÷ n
= $24.2 ÷ 5
= $4.84
Hence, the average is $4.84
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NO LINKS!! State the Domain and Range for each graph
Both end points are represented by closed circles, it means both points are included.
The graph is restricted between the end points from left to right and between the end point and the highest point from bottom to top.
Domain, the set of possible x- coordinates:
x ∈ [- 2, 6]Range, the set of possible y- coordinates:
y ∈ [- 3, 7]The graph on the rightBoth end points are represented by arrows directed to left and right, it means both ends are indefinite but lines are parallel to the x-axis.
It makes x-values infinite but y-values restricted between the two lines.
Domain, the set of possible x- coordinates:
x ∈ (- ∞, + ∞)Range, the set of possible y- coordinates:
y ∈ [1, 5]Answer:
1. Domain: [-2, 6]
Range: [-3, 7]
2. Domain: (-∞, ∞)
Range: [1, 5]
Step-by-step explanation:
Definitions
Domain: The set of all possible input values (x-values).Range: The set of all possible output values (y-values).Open circle: The value is not included in the interval.Closed circle: The value is included in the interval.Arrow: The function continues indefinitely in that direction.Note: Assume that each square on the given graphs is 1 unit.
Question 1The domain of the function is restricted since the curve has two distince endpoints. As each endpoint is marked by a closed circle, the x-value of the endpoints is included in the domain.
Domain: [-2, 6]The function has a maximum point at (-1, 7) and a minimum point at (6, -3).
Therefore, the range of the function is restricted.
Range: [-3, 7]Question 2As there are arrows at both endpoints of the function, and the function is continuous between the arrowheads, the domain is unrestricted.
Domain: (-∞, ∞)The maximum y-value is y = 5. When x < 1, the line continues indefinitely at y = 5.
The minimum value is y = 1. When x > 1, the line continues indefinitely at y = 1.
Therefore, the range of the function is restricted.
Range: [1, 5]Solve the inequality.
Question 1
3y≤−9
The solution is
The solution of the given inequality is y ≤ -3.
The given inequality is -
3y ≤ −9
We have to solve this given inequality.
Now, we have the inequality as -
3y ≤ −9
=> y ≤ -3
Thus, the solution of the given inequality is y ≤ -3.
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Jillian sells handmade t- Shirts and large purses; each tea shirt costs $15. Each Large purse goes for $59 and the cost of small purses is $32 each. In the first week she sold 4 t-shirts and 3 large purses and 9 small. In the second week she sold another 5 t-shirts, 7 large bags and 4 small ones. Last week she sold 8 t-Shirts and also sold 3 large purses and 5 small purses. What was the exact amount she made in 3 weeks?
Jillian made the exact amount was $1598 in 3 weeks.
Each t-shirt costs $15.
Each Large purse goes for $59
And the cost of small purses is $32 each.
In the first week, she sold 4 t-shirts and 3 large purses, and 9 small ones.
Her earning in the first week = 4 × $15 + 3 × $59 + 9 × $32 = $525
In the second week, she sold another 5 t-shirts, 7 large bags, and 4 small ones.
Her earning in the second week = 5 × $15 + 7 × $59 + 4 × $32 = $616
Last week she sold 8 t-Shirts and also sold 3 large purses and 5 small purses.
Her earning in the Last week = 8 × $15 + 3 × $59 + 5 × $32 = $457
The exact amount she made in 3 weeks = $525 + $616 + $457 = $1598
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