An arithmetic sequence is a sequence with a constant
increase or decrease also known as the constant difference
In the sequence 10, 40, 70, 100, ….
The constant difference between the terms is 30
A recursive formula for a sequence would be:
a1= first term in the sequence
an = term you are trying to find
an-1 = previous term in the sequence
d = constant difference
Explicit Formulas:
A formula that allows you to find the nth term of the sequence by substituting known values in the expression.
Formula : an = a1 + d( n - 1)
a1= first term in the sequence
an = current term in the sequence
d = constant difference
n = term number
Solution:
Write the explicit formula of the sequence 4, 7, 10, 13, 16 ….
Formula for explicit term:
an = ___ + ___( n - 1)
Simplify: an = ___ + ___n
In the sequence 4, 7, 10, 13, ….
To find the 11th term explicitly, I plug in the into the formula I just made:
an = 1 + 3n
a11 = 1 + 3(11)
a11 = 34
Find the 15th term of the sequence using the formula: an = 1 + 3n
Write the recursive formula of the sequence 4, 7, 10, 13, ….
Recursive formula:
a1 =
an = a n - 1
In the sequence 4, 7, 10, 13, 16 ….
To find the 5th term recursively, I plug it into the formula I just made:
an = an-1 + 3
a5 = a5-1 + 3 in words: 5th term equals the 4th term plus 3
a5 = 13 + 3
a5 = 16
Recursive and Explicit Formulas for Arithmetic (Linear) Sequences
in a club there are 10 women and 10 men. A comittee of 3 men and 2 women is to be chosen. how many different possibilities are there?
In a circle with a radius of 6 m, an arc is intercepted by a central angle of 7π4 radians.
What is the arc length?
Use 3.14 for π .
Answer:
Arc length = 32.97 m .
Step-by-step explanation:
Given : In a circle with a radius of 6 m, an arc is intercepted by a central angle of 7π/4 radians and use 3.14 for π .
To find : What is the arc length.
Solution : We have given a circle of radius = 6 m
Central angle = 7π/4
Formula of arc length = radius × central angle .
Arc length = 6 × ([tex]\frac{7(3.14)}{4}[/tex]).
Arc length = 32.97 m .
Therefore, Arc length = 32.97 m .
after earning $17 in interest bob bank account has $143 how many dollars were in the account to start with
Devin borrowed $1,058 at 13 percent for nine months. What will he pay in interest?
A. 103.16
B.105.80
C.137.54
D.122.40
Devin borrowed $1,058 at 13 percent for nine months.
We have to calculate the interest paid.
Interest = [tex] \frac{P \times R \times T}{100} [/tex]
Substituting the values of
Principal = $1058
Rate = 13%
Time = 9 months = [tex] \frac{9}{12} [/tex] year
Interest = [tex] \frac{1058 \times 13 \times 9}{12 \times 100} [/tex]
Interest = 103.155
= 103.16
So, Devin will pay 103.16 as the interest.
Therefore, Option A is the correct answer.
1. What is the value of x?
sin(x+22)°=cos(2x−7)°
2.Given cosx=1213 and sinx=513
.
What is ratio for tanx
?
leave answer as a fraction in simplest form
the sine and cosine are co-functions
So
sin (theta) = cos (90 - theta)------> This implies that the angles sum to 90°
therefore
( x + 22) + (2x - 7) = 90 simplify
3x + 15 = 90 subtract 15 from both sides
3x = 75 divide both sides by 3
x = 25
The answer Part 1) is x=25°
Part 2) Given cos x=12/13 and sin x =5/13
What is ratio for tanx ?
we know that
tan x = sinx / cos x
tan x = (5/13) / (12/13) = (5/13) * (13/12) = 5/12
the answer Part 2) is 5/12
what is the fourth term of the expansion of the binomial (2x+5)^5
when expanded from left to right the powers of x decrease from 5 to 0 and powers of y increase from 0 to 5
substitute x =2x and y = 5
(2x + 5)⁵ = (2x)⁵ + 5(2x)⁴5 + 10(2x)³5² + 10(2x)²5³ + 5(2x)5⁴ + 5⁵
= 32x⁵ + 400x⁴ + 2000x³ + 5000x² + 6250x + 3125
An amount of $27,000 is borrowed for 11 years at 8.25%
interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?
Use the calculator provided and round your answer to the nearest dollar.
What is the area of the shaded region of the following figure?
446 in.2
5,760 in.2
4,788 in.2
5,274 in.2
Answer:
5,274 in.2
Step-by-step explanation:
Find the area of both the shaded and not shaded regions.
Shaded: 8 ft x 12 in = 96 5 ft x 12 in = 60
Then: 96 in x 60 in = 5760
Not Shaded: 27 in x (36 / 2) 18 in = 486
Then Subtract The Not Shaded Region From The Shaded Region:
5,760 - 486 = 5,274
How many solutions does the system have?
X+y=5
X+y=6
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
x + y = 5
x + y = 6
5 ≠ 6
The system of equations has many solutions.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 is an equation.
2x + 4 - 5x is an equation.
We have,
x + y = 5 _____(1)
x + y = 6 ______(2)
Now,
Solving (1) and (2) we get,
5 = 6
This is not true.
This means that,
We have many solutions.
If we get,
x = y
0 = 0
n = n ( n can be any value)
The system of equations will have no solutions.
Thus,
x + y = 5
x + y = 6
5 ≠ 6
The system of equations has many solutions.
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The surface area of a rectangular prism is 792 units2. The length of the prism is 2 times the width, and the width is 4 times the height. What is the volume of the prism?
Answer:
The real answer is 846 ^-^ I got it right
The volume of the rectangular prism is 105.57
What is the volume of a rectangular prism?A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.
The volume of a rectangular prism=Length X Width X Height
Where l, h and w represent the length, height and width respectively.
Given that;
Length of the prism is 2 times the width L = 2w
the width is 4 times the height w = 4h
Now let’s plug these values;
the surface area equation, it becomes;
A = 2(2w(w) + w(w/4) + w/4(2w))
A = 2(2w^2 + w^2/4 + w^2/2)
A = 1/2(7w^2)
792 x2 = 7w^2
w = 15.04
The volume of a rectangular prism=Length X Width X Height
V = 2w x w x w/4
V x 2 = w³
V = 15.04³/2
V = 105.57
Thus, the volume is 105.57.
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Charley wants to have $950,000 when he retires in a year. If he currently has $900,000 to put in a 1-year CD, which of these APRs and compounding periods will allow him to reach his goal?
A. An APR of 5.44% compounded semiannually
B. An APR of 5.42% compounded monthly
C. An APR of 5.34% compounded daily
D. An APR of 5.43% compounded quarterly
Charley needs an APR of 5.44% compounded semiannually to reach his goal of $950,000 in a year.(A)
Given:
Final Amount (A) = $950,000
Principal Amount (P) = $900,000
Time (t) = 1 year
We use the compound interest formula: A = [tex]P(1 + r/n)^{(nt)[/tex]
Option A: 5.44% APR compounded semiannually
APR (r) = 0.0544
Compounding periods per year (n) = 2
Plugging in the values, we get: A = 900,000[tex](1 + 0.0544/2)^{(2*1)[/tex]≈ $949,999 (which is approximately $950,000)
Option B: 5.42% APR compounded monthly
APR (r) = 0.0542
Compounding periods per year (n) = 12
Plugging in the values, we get: A = 900,000[tex](1 + 0.0542/12)^{(12*1)[/tex] ≈ $949,941 (less than $950,000)
Option C: 5.34% APR compounded daily
APR (r) = 0.0534
Compounding periods per year (n) = 365
Plugging in the values, we get: A = 900,000[tex](1 + 0.0534/365)^{(365*1)[/tex] ≈ $949,591 (less than $950,000)
Option D: 5.43% APR compounded quarterly
APR (r) = 0.0543
Compounding periods per year (n) = 4
Plugging in the values, we get: A = 900,000[tex](1 + 0.0543/4)^{(4*1)[/tex] ≈ $949,980 (missing the goal by a small amount)
Conclusion: The correct option is 5.44% compounded semiannually as it allows Charley to reach his goal of $950,000.
PLEASE HELP
8.07a, part 1
1. Find the vertex, focus, directrix, and focal width of the parabola. (1 point)
negative 1 divided by 40 x squared equals y
A) Vertex: (0, 0); Focus: (0, -10); Directrix: y = 10; Focal width: 160
B) Vertex: (0, 0); Focus: (-20, 0); Directrix: x = 10; Focal width: 160
C) Vertex: (0, 0); Focus: (0, -10); Directrix: y = 10; Focal width: 40
D) Vertex: (0, 0); Focus: (0, 10); Directrix: y = -10; Focal width: 10
2. Find the standard form of the equation of the parabola with a focus at (0, -2) and a directrix at y = 2.
A)y2 = -2x
B) y2 = -8x
C) y equals negative 1 divided by 8 x squared
D) y equals negative 1 divided by 2 x squared
3. Find the standard form of the equation of the parabola with a focus at (-8, 0) and a directrix at x = 8.
A) y equals negative 1 divided by 32 x squared
B) y2 = 16x
C) 16y = x2
D) x equals negative 1 divided by 32 y squared
4. A building has an entry the shape of a parabolic arch 84 ft high and 42 ft wide at the base, as shown below.
A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 84 feet and its width from left to right is 42 feet.
Find an equation for the parabola if the vertex is put at the origin of the coordinate system.
A) y2 = -21x
B) x2 = -21y
C) x2 = -5.3y
D) y2 = -5.3x
5. Find the center, vertices, and foci of the ellipse with equation x squared divided by 81 plus y squared divided by 225 equals 1 .
A) Center: (0, 0); Vertices: (-15, 0), (15, 0); Foci: (0, -9), (0, 9)
B) Center: (0, 0); Vertices: (0, -15), (0, 15); Foci: (-9, 0), (9, 0)
C) Center: (0, 0); Vertices: (0, -15), (0, 15); Foci: (0, -12), (0, 12)
D) Center: (0, 0); Vertices: (-15, 0), (15, 0); Foci: (-12, 0), (12, 0)
6. Find the center, vertices, and foci of the ellipse with equation 2x2 + 8y2 = 16.
A) Center: (0, 0); Vertices: the point zero comma negative two square root two and the point zero comma 2 square root two ; Foci: Ordered pair 0 comma negative square root 6 and ordered pair 0 comma square root 6
B) Center: (0, 0); Vertices: (-8, 0), (8, 0); Foci: Ordered pair negative 2 square root 15 comma 0 and ordered pair 2 square root 15 comma 0
C) Center: (0, 0); Vertices: (0, -8), (0, 8); Foci: Ordered pair 0 comma negative 2 square root 15 and ordered pair 0 comma 2 square root 15
D) Center: (0, 0); Vertices: the point negative square root six comma zero and the point square root six comma zero ; Foci: Ordered pair negative square root 6 comma 0 and ordered pair square root 6 comma 0
7. Graph the ellipse with equation x squared divided by 36 plus y squared divided by 49 equals 1 .
A) A horizontal ellipse is shown on the coordinate plane centered at the origin with vertices at the point negative seven comma zero and the point seven comma zero. The minor axis has endpoints at zero comma six and zero comma negative six.
B) A vertical ellipse is shown on the coordinate plane centered at the origin with vertices at the point zero comma seven and zero comma negative seven. The minor axis has endpoints at negative six comma zero and six comma zero.
C) A horizontal ellipse is shown on the coordinate plane centered at (6, 7) with vertices at (–1, 7) and (13, 7) and minor axis endpoints at (6, 13) and (6, 1).
D) A horizontal ellipse is shown on the coordinate plane centered at the point six comma seven with vertices at the point negative one comma seven and thirteen comma seven. The minor axis has endpoints at six comma thirteen and six comma one.
8. Find an equation in standard form for the ellipse with the vertical major axis of length 10 and minor axis of length 8.
A) x squared divided by 25 plus y squared divided by 16 equals 1
B) x squared divided by 5 plus y squared divided by 4 equals 1
C) x squared divided by 4 plus y squared divided by 5 equals 1
D) x squared divided by 16 plus y squared divided by 25 equals 1
9. Find the vertices and foci of the hyperbola with equation quantity x plus 5 squared divided by 36 minus the quantity of y plus 1 squared divided by 64 equals 1 .
A) Vertices: (-1, 3), (-1, -13); Foci: (-1, -13), (-1, 3)
B) Vertices: (3, -1), (-13, -1); Foci: (-13, -1), (3, -1)
C) Vertices: (-1, 1), (-1, -11); Foci: (-1, -15), (-1, 5)
D) Vertices: (1, -1), (-11, -1); Foci: (-15, -1), (5, -1)
Vertex: (0, 0); Focus: (0, -10); Directrix: y = 10; Focal width: 10
2. C) y equals negative 1 divided by 8 x squared
3. D) x equals negative 1 divided by 32 y squared
4. C) x2 = -5.3y
5. C) Center: (0, 0); Vertices: (0, -15), (0, 15); Foci: (0, -12), (0, 12)
6. None from the choices, it should be
Center: (0, 0); Vertices: the point negative two square root two comma zero and the point 2 square root two comma zero; Foci: Ordered pair negative square root 6 comma zero and ordered pair square root 6 comma zero
7. B) A vertical ellipse is shown on the coordinate plane centered at the origin with vertices at the point zero comma seven and zero comma negative seven. The minor axis has endpoints at negative six comma zero and six comma zero.
8. D) x squared divided by 16 plus y squared divided by 25 equals 1
9. D) Vertices: (1, -1), (-11, -1); Foci: (-15, -1), (5, -1)
Answer:
the answer is letter C
Step-by-step explanation:
ALL I NEED YOU GUYS TO DO IS TO EXPLAIN THIS IN THE MOST FANCY WAY POSSIBLE!!!! THIS IS JUST FOR FUN, I WILL MARK BRAINLIEST FOR THE FANCIEST ANSWER!!!!
WHAT IS 5x5?!?!?!?!?!
It's 25 easy how I got my answer I looked on my fingers and put 5 fingers up and i did it 5 times and got 5.10.15.20.25 that's 5 times
Suppose rebecca needs a dog sitter so that she can travel to her sister's wedding. rebecca values dog sitting for the weekend at $200. susan is willing to dog sit for rebecca so long as she receives at least $150. rebecca and susan agree on a price of $175. suppose the government imposes a tax of $10 on dog sitting. the tax has made rebecca and susan worse off by a total of
The tax has only made Susan worse off by $10 or 5.7% because Rebecca is the one who is going to pay for the dog sitting and not Susan (who is going to have an income of $165 after-tax).
Further Explanation:
Income Tax: It is the additional payment that an individual needs to pay on the amount of income he/she generates. Here $10 is the tax on the income which Susan is going to generate by dog sitting the dog of Rebecca.
Here, it can be seen that Susan is the one who is earning from the transaction and not Rebecca. So, Rebecca is should not bear any tax payable to the government since both of them agree to a price of $175 so that is the only amount which Rebecca is going to pay for dog sitting. Also, if Susan herself pays the whole amount of tax, it still would not bother her because her expectation from dog sitting was $150 which is still lesser than what she expected in the first place.
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Answer details:
Grade: Senior School
Subject: Taxation
Chapter: Tax imposed on various services.
Keywords: Income tax, payment of tax, dog sitting during the wedding, dog sitter, worse off condition of Rebecca and Susan.
If f(x) = 6x - 4, what is f(x) when x = 8?
what is the approximate area of the shaded region
Find the length of JK and the measure of M. A. JK=26, m=33 B. JK=26, M=54. C. JK=33, M=26. D. JK=54, M=33
Answer:
c i would think/suppose
Step-by-step explanation:
Which expressions are equivalent to the one below? Check all that apply. 9x
Answer:
C.),F.),andD.) Are correct
Step-by-step explanation:
Option: C, D and F are the correct options.
C. [tex](\dfrac{36}{4})^x[/tex]
D. [tex]9\cdot 9^{x-1}[/tex]
F. [tex]\dfrac{36^x}{4^x}[/tex]
Step-by-step explanation:We are asked to find the expression which is equivalent to:
[tex]9^x[/tex]
C)
[tex](\dfrac{36}{4})^x[/tex]
We know that:
[tex](\dfrac{36}{4})^x=9^x[/tex]
Since, 36/4=9
Hence, option: C is correct.
D)
[tex]9\cdot 9^{x-1}=9^{1+x-1}[/tex]
Since,
[tex]a^m\cdot a^n=a^{m+n}[/tex]
Hence,
[tex]9\cdot 9^{x-1}=9^x[/tex]
Hence, option: D is correct.
F)
[tex]\dfrac{36^x}{4^x}[/tex]
We know that:
[tex]\dfrac{36^x}{4^x}=(\dfrac{36}{4})^x[/tex]
Since, we know that:
[tex]\dfrac{a^n}{b^n}=(\dfrac{a}{b})^n[/tex]
Hence, we have:
[tex]\dfrac{36^x}{4^x}=9^x[/tex]
Since, 36/4=9
Hence, option: F is the correct answer.
is this a linear function , why or why not ? explain
y=x^2-1
I need help peeps, im having troubles
Raina is fertilizing her garden. The garden is in the shape of a rectangle. Its length is
15 feet and its width is 13
feet. Suppose each bag of fertilizer covers 39
square feet. How many bags will she need to cover the garden?
Answer: 5 bags
Step-by-step explanation:
Please help?
What is m V?
Round only your final answer to the nearest tenth.
The answer would be 53.9
The system shown is____.
equivalent
independent
inconsistent
A seller buys an item from a manufacturer for $9,500 he increases cost by %5 percent.What is the markup value?
markup = original cost x percentage markup
Answer: $475
Step-by-step explanation:
Given : A seller buys an item from a manufacturer for $9,500 he increases cost by %5 percent.
i.e. The original cost of item = $9,500
Mark up percentage = 5% = 0.05
The formula given to find the mark up value is :_
[tex]\text{Mark up}=\text{Original cost * percentage mark up}\\\\\Rightarrow\ \text{Mark up}=9500\times0.05=\$475[/tex]
Hence, the mark up value = $475
A circular test track for cars has a circumference of 2.7km . A car travels around the track from the southernmost point to the northernmost point. What distance does the car travel? (answer 1.35km). Part B !!!!!!!What is the car's displacement from its original position?,
helppppppppppppppppppp
Summer looked at the formula for the Pythagorean Theorem, ashe said that it didn't matter which sides of a right triangle were a, b, and C. Is she correct?
All my smart people click here
Lines are perpendicular when the slopes are _____
The picture below shows a portion of a river dam:
Which of the following can be used to calculate the height of the river dam? (6 points)
220 cos 40°
220 divided by tan 40 degrees
220 sin 40°
220 divided by cos 40 degrees
Answer:
220cos40
Step-by-step explanation:
cos40=x/220
(220)cos40=x/220(220)
220cos40=x