The arithmetic sequence has a 2nd term of -2 and a 7th term of 18 has the following answers.
What is arithmetic progression?
An progression or arithmetic sequence may be a sequence of numbers specified the difference between the consecutive terms is constant.
Main body:
General formula for arithmetic sequence
a + (n-1)d = aₙ
arithmetic sequence has a 2nd term of -2 , which means
a+d = -2
a = -(d+2) ---------(1)
7th term of 18 , which means
a+ 6d = 18
substituting value from equation 1,
-(d+2) +6d = 18
-d -2 +6d = 18
5d = 20
d = 5
using d= 5 in equation 1,
a = -(5+2)
a =-7
A) 10th term
=a +9d
= -7+9*5
= 38
B) recursive formula for the sequence = aₙ+1=aₙ+d .
Hence for the given sequence , it is
a₃ = a₂ +d
a₃ = -2+5
a₃ = 3
C) sum of first 10 terms
Sₙ = n/2{2a+ (n-1)d}
S₁₀ = 5 {2*-7 + 9*5}
S₁₀ = 5[ -14 +45]
S₁₀ = 5*31
= 105
Hence the sum of the first 10 terms is 105.\
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Is this a function? Explain, why or why not!
8
6
4
2
0
0
2
4
6
Edit View Insert Format Tools Table
Answer:
Yes
Step-by-step explanation:
Every input has only one output.
Hellllalalap pls happy holidAys
Answer:
Federal Reserve banks
Step-by-step explanation:
Hope it helps!
Find an explicit formula for the following equence, an which tart with a1=23. 23,34,45,56,…
The explicit formula for the given arithmetic sequence is aₙ = 23 + (n - 1)11. Here the first term is a1 = 23 and the common difference is d = 11.
What is the explicit formula for an arithmetic sequence?The explicit formula for an arithmetic sequence gives the nth term of the sequence. I.e.,
aₙ = a1 + (n - 1)d
Here a1 is the first term; d is a common difference, it is calculated by
d = aₙ₊₁ - aₙ = aₙ₋₁ - aₙ
Calculation:The given sequence is 23, 34, 45, 56,...
Here the first term a1 = 23
So, the common difference between the terms in the sequence is
d = 34 - 23 = 11
Then, the explicit formula for the given sequence is
aₙ = a1 + (n - 1)d
⇒ aₙ = 23 + (n - 1)11
Therefore, the nth term of the explicit formula for the given arithmetic sequence is aₙ = 23 + (n - 1)11.
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Timmy received $50 for his birthday. Following the birthday party, his parents promised him $5 each week for completing his chores. Assuming timmy completes all chores, use a linear equation to determine the number of dollars timmy will have 7 weeks after his birthday.
Assuming timmy completes all chores, the number of dollars timmy will have 7 weeks after his birthday is 85 dollars.
What are equations?In mathematics, an equation is a claim that two expressions are equivalent. It is a mathematical expression that employs the equals symbol, "=", to indicate that two quantities have values that are equal. Problems in algebra, geometry, calculus, and other branches of mathematics are frequently solved using equations. In algebra, equations are frequently used to depict the connection between variables and constants, as well as to discover the value of an unknown variable. For example, the equation x + 2 = 5 may be utilised to get the value of x, which is 3. Equations can be linear, quadratic, or higher-degree, and they can involve multiple variables.
How to solve?
Let x be the number of weeks after Timmy's birthday.
The total number of dollars Timmy will have after x weeks is 50 + 5x.
Therefore, Timmy will have 50 + 5(7) =85 dollars after 7 weeks
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Which of the following equations is correct? Select all that apply.
Answer:
option a is correct i.e 6.25 = 25/4
Step-by-step explanation:
= 6.25
= 625 / 100
both being divisible by 5
we get
= 25/4
Suppose you deposit $100 in Account A with
a simple interest rate of 3.4%, and $300 in
Account B with a simple interest rate of 1.8%.
One year later, you get
a bank statement
that
shows the interest for Account A is
$3.40 and the
interest for Account B is $540.00.
a. Which account statement is incorrect?
b. What may have been the bank's error?
The account statement for Account B is incorrect.
What is simple rate of interest?
Simple rate of interest is a type of interest calculation where interest is calculated only on the principal amount of a loan. Simple interest is calculated periodically, usually monthly or annually, as a fixed percentage of the principal. It is different from compound interest, which applies interest to both the principal and the accumulated interest. It is simpler to calculate than compound interest, and is generally used for short-term loans.
Given: Account A: $100, 3.4% and Account B: $300, 1.8%
We know, Simple Interest = Principal × Rate × Time
Interest for Account B = $300 × 1.8%
= $5.40
The bank statement after one year should be $5.40 instead of $540.00.
Hence, Account B's statement is incorrect.
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In the diagram, ∠4 ≅ ∠5 and SE — bisects
∠RSF. Find m∠1. Explain your reasoning.
Answer:
60°
Step-by-step explanation:
You want the measure of angle 1 in the given diagram.
Angle relationsTransversal TR creates corresponding angles 1 and 5, so those are congruent.
It is given that angles 4 and 5 are congruent.
Transversal SE creates alternate interior angles 2 and 4, so those are congruent.
Angle bisector SE creates angles 2 and 3 congruent.
Now we have ∠1≅∠5≅∠4≅∠2≅∠3.
Hence all of the angles are congruent to each other, and angle 1 is 1/3 of 180°.
m∠1 = 60°
Graph y=-4x+8 please.
Answer:
attached is the graph and other data
Step-by-step explanation:
In Exercises 7-10, find the zeros of the function. Then sketch a graph of the function.
7. f(x) = - 5x ^ 4 + 20x ^ 3 + 60x ^ 2
8. g(x) = - x ^ 3 - x ^ 2 + 30x
9. k(x) = x ^ 3 + x ^ 2 - 4x - 4
10. f(x) = x ^ 1 - 4x ^ 2 - 9x + 36
Answer:
Step-by-step explanation:
7 1+1
8 2+2
9 4+4
10 1+1+2+2+4+4=69
which of the following represents 3 square root x^2 in exponential form?
Answer:
D
Step-by-step explanation:
the numerator of the exponent is the exponent of x
the denominator is the the index of the root
a retired biologist withdraws money from a retirement account at a constant rate. 15 months after she starts withdrawing money, she has $785,000 in the account. she has $630,000 in her account 40 months after she starts withdrawing money. let a(t) represent the dollar amount in the account t months after she begins withdrawing money from the account. a. find the linear function that gives a(t), the dollar amount in the account t months after she starts withdrawing money. (8 points) b. how much money is in the account 80 months after she starts withdrawing money? (2 points)
The linear function that gives a(t), the dollar amount in the account t months after she starts withdrawing money is [tex]a(t)=785000-3875t[/tex]
The money in the account 80 months after she starts withdrawing money is [tex]a(80) & =\$ 475000\end{aligned}$$[/tex]
The amount of money she withdraw in 40 months
[tex]& \Rightarrow \$(785000-630000) \\& =\$ 155000\end{aligned}$$[/tex]
She withdraw money per month at constant rate
[tex]=\frac{155000}{40}$$[/tex]
The amount of money a(t) in t months.
[tex]a(t)=785000-\frac{155000 t}{40}$$[/tex]
[tex]a(t)=785000-3875t[/tex]
Therefore the linear function that gives a(t), the dollar amount in the account t months after she starts withdrawing money is [tex]a(t)=785000-3875t[/tex]
(b) The money in the account after 80 months.
[tex]$$\begin{aligned}a(80) & =785000-3875(80) \\& =785000-310000 \\a(80) & =\$ 475000\end{aligned}$$[/tex]
Therefore the money in the account 80 months after she starts withdrawing money is [tex]a(80) & =\$ 475000\end{aligned}$$[/tex]
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nearly a quarter of the texas gulf coast is national seashore or state park. At 372 miles long, it is undergoing a seaward advance at the rate of about .0095 mile per year. find the length of the texas shoreline in km. 1 mile = 1.61 km
If one quarter of the Texas Guff coast is national seashore or state park at the given figures, the length of the Texas shoreline is 0.8835km
How to determine the length?The length is the measure of how long the shoreline is.
The given parameters sare
mileage of the seashore = 372 miles
Advancement of 0.0095 miles per year.
1/4 taken as gulf coast
Applying these parameters we have
372*0.0095*1/4*12
⇒ 96.102 miles
= 96.102/1000 = 0.96102 km
1000 miles = 1km
Therefore divide the value by 1000 to get
Therefore the length is 0.96102km
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n is m% of what? Help please :)
Answer:
Step-by-step explanation:
m% = m/100
what = a variable ... "x". for example.
"is" means "="
"of" means multiply
n = (m/100)•x
The circumference of a circle is 11π cm. What is the area, in square centimeters? Express your answer in terms of π.
Answer:
The area of the circle is 30.25π cm^2.
Step-by-step explanation:
The circumference of a circle is equal to the diameter of the circle times π. Therefore, if the circumference of the circle is 11π cm, the diameter must be 11 cm.
The formula for the area of a circle is A = πr^2, where r is the radius of the circle. The radius of the circle is half the diameter, so the radius is (1/2) * 11 cm = 5.5 cm.
Substituting this value for r into the formula for the area of a circle, we get:
A = π * (5.5 cm)^2
= π * 30.25 cm^2
= 30.25π cm^2
Therefore, the area of the circle is 30.25π cm^2.
6√-48
please help with this question
Answer:
24i√3
Step-by-step explanation:
simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
I tried.
If ur good at geometry can u help Solve for m given that the perimeter of the triangle is 19 centimeters.
Answer:
m = 7cm
Step-by-step explanation:
Perimeter of a triangle is all the sides added up, so a+ b + c.
Given that a= 6 and b= 6, that's 12cm together. So just subtract the perimeter 19cm by 12cm to get your answer of 7cm.
Norberto received the following scores on his last five spelling tests: 88, 76, 93, 85, and 98. Which of the following statements is
true?
The median of the set of scores is 93.
The mean and median of the set of scores are the same.
The mode of the set of scores is 88.
The mean of the set is less than the median.
What is the value of x? Please give steps on how you did it. Please, Hurry it is due at 11:59 pm.
Answer:
51/3
Step-by-step explanation:
Angles opposite congruent sides of a triangle are congruent.
[tex]x+17=4x-34 \\ \\ 17=3x-34 \\ \\ 51=3x \\ \\ x=51/3[/tex]
Could Someone Help Me with this rewrite dis equation into y=mx+b
y< -3/4x+2 pls help me
The equation written in slope-intercept form is y = -(3/4)x +2.
What is the slope-intercept form of a line?The slope-intercept form of a line is y = mx +c where m is the slope of the line and c is the y-intercept.
The given inequality is y < -3/4x + 2
Rewrite the inequality as an equation in slope-intercept form:
y < (-3/4)x + 2
y = (-3/4)x + 2
Where m = -3/4 and b = 2
Hence, the equation written in slope-intercept form is y = -(3/4)x +2.
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A state seal, which is round, hangs in the capitol building. It has a radius of 2 yards. What is the seal's diameter?
Step-by-step explanation:
you do understand that the diameter of a circle is simply 2 times the radius, yes ?
imagine a circle and you draw a radius line (from the center of the circle to the circle arc).
and now imagine to draw another radius line, just in the opposite direction.
when you look at the result, you have 1 straight line going from the circle arc to the circle arc and passing through the center of the circle. that is what a diameter is.
how long is it ? well, we drew 2 radius lines to create this line. so, it is 2×radius long.
so, the diameter of the seal is
2×2 = 4 yards
the initial population of a town is 100,231 and it grows with a doubling time of 98 years. what will the population be in 31 years?
If the initial population of a town is 100,231 and it grows with a doubling time of 98 years, the population after 31 years is 124803
The initial population of the town = 100231 people
The doubling time = 98 years
We have to find the population in 31 year
The exponential function will be
f(t) = fo(2)^(t/98)
f(t) is the population of the town in t years
fo is the population of the town in t = 0 years
t is the number of years
2 because it doubling time
The value of t = 31 years
Substitute the values in the function
f(31) = 100231×(2)^(31/98)
Do the arithmetic operations
f(31) = 100231 × 1.245
f(31) = 124803.23
f(31) ≈ 124803
Therefore, the population after 31 years is 124803
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Find y she c=10 if y=8 when’s=20
The value of x=10 is y=4 if y=8 if x=20.
What is an algebra?Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Mathematics has several different subfields, including algebra. Algebra is the study of mathematical symbols and the rules for using them in formulas; it is a common thread that runs through practically all of mathematics. It is also used to name specific types of algebraic structures, such as an algebra over a field, which is frequently referred to as an algebra. The word algebra is used to name both a mathematical field and some of its subfields.
When x=20, y=8
The value of y is 0.4 times of x.
y=0.4×20
y=8
So, when x=10
y=0.4×10
y=4
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What answer is the best one? Pls help me
we know ,
the probability=no of repeated value/total number
factorial of 3 and 2
and factorial of total number
=3ḷ×2ḷ/7ḷ
=3×2×1×2×1/7×6×5×4×3×2×1
=1/7×5×4×3
=1/420
=0.23809
or
=0.238
what is Probability?
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means.
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Which statement about 56 – 34 is true?
A The least common denominator is 6.The least common denominator is 6.
B The difference is a whole number.The difference is a whole number.
C The least common denominator is 12.The least common denominator is 12.
D The difference is a mixed number.The difference is a mixed number.
Since, Both the numbers used for the difference calculation are whole numbers, The answer is B) The difference is a whole number.
What are real numbers?Both rational and irrational numbers are considered to be real numbers. Real numbers include all rational and irrational numbers, including integers (-2, 0, 1) and fractions (1/2, 2.5).
What are whole numbers?Whole numbers are natural numbers including zero with it.
56 is a whole number
34 is a whole number
the difference, 56-34 = 22 is also a whole number.
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Lillian has a rectangular garden with an area of 10x2 +33x – 7 square feet. Find the expressions that would represent the length and width of the garden. Make sure you show all your work for full credit.
Attempt was made but incorrect
(1 pt)
Correct but no work shown OR less than half the work is correct
(2 pts)
About half of the work is correct
(3 pts)
Most of the work is correct (4 pts)
Fully Correct with all work shown
(5 pts)
If Lillian has a rectangular garden with an area of 10x² +33x – 7 square feet.The expressions that would represent the length and width of the garden will be (5x-1)(2x+7)
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that, Lillian has a rectangular garden with an area of 10x² +33x – 7 square feet.
We have to find the expression representing the length and width of the garden.
[tex]=10x^2+33x-7 \\\\ =\left(10x^2-2x\right)+\left(35x-7\right) \\\\ =2x\left(5x-1\right)+7\left(5x-1\right)\\\\ =\left(5x-1\right)\left(2x+7\right)[/tex]
The area of the rectangular garden is,
A = L × B
Comparing the expression with the obtained expression we get the expressions that would represent the length and width of the garden as,
A= (5x-1)(2x+7)
Thus, if Lillian has a rectangular garden with an area of 10x² +33x – 7 square feet. The expressions that would represent the length and width of the garden will be (5x-1)(2x+7)
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PLEASE HELP!!!! ASAP!!
Answer:
2
Step-by-step explanation:
This question is asking about the multiplication rule of exponents. When you multiply two exponents of the same base, the exponents add. With the parameters x=4, y=6, and z=8, the first one is true because 2+4=6. The third one is true because 6+6=12. The second one isn't true because 6+8=14, not 4.
- 1/4 * (x - 26) = - 200 Solve the equation for x.
Answer:
x=826
Step-by-step explanation:
A model car is 12 inches long. Using a scale of 3 inches : 4 feet ,how long is the actual car
The basic unit of length in the metric system is the meter. All units of length in the metric system are derived from the meter.
What is unit of length?Using measuring instruments like a ruler, measuring tape, etc., one can measure the length of any object. A ruler can be used to determine, for instance, how many inches a pencil is long. A feet scale can be used to gauge the height of each student in a class.The inch, foot, yard, and mile are the fundamental units of length and distance measurement in the English system. The rod, furlong, and chain are additional length units.Length of the car is 12 inches equal to 192 feet.
Given ,
3 inches : 4 feet
3 inches : 4*12
3 inches :48
1 inches : 16 feet
Length of the car is 12 inches = 12 * 16
Length of the car is 12 inches = 192 feet
The measurement or size of something from end to end is referred to as its length. To put it another way, it is the greater of the higher two or three dimensions of a geometric shape or object. For instance, a rectangle's length and width are its dimensions.In the metric system, the SI unit of length is a metre which is defined as: “The length of the path travelled by light in a vacuum within 1⁄299792458 seconds.”The SI unit of length is a metre (m). One metre (m) is divided into 100 equal parts called centimetre (cm). One centimetre (cm) has 10 equal parts called millimetre (mm). For measuring longer distances, we use a larger unit of length called, kilometre (km).To learn more about unit of length refer to:
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Rick bought a photo printer and supplies for $186. 90, which will allow him to print photos for $0. 29 each. A photo store charges $0. 55 to print each photo. How many photos must Rick print before his total cost is less than getting prints made at the photo store? More than 718 photos. Less than 718 photos. More than 900 photos. Not enough information to solve
The 718.85 < x inequality says that : He must print 719 photos or more.
Given,
In the question:
Rick bought a photo printer and supplies for $186. 90, which will allow him to print photos for $0. 29 each.
and, A photo store charges $0. 55 to print each photo.
To find the how many photos must Rick print before his total cost is less than getting prints made at the photo store?
Now, According to the question:
Let the photos be x
Rick bought a photo printer be $186.90
A photo store charges $0. 55 to print each photo.
The question is based on inequality:
Photo Printer < photo store
1.86.90 + 0.29x < 0.55x
- 0.29x - 0.29x
______________________
1.86.90 < 0.26x
Divide by 0.26x on both sides
= 718.85 < x
Hence, The 718.85 < x inequality says that : He must print 719 photos or more.
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kjlklnlkjklnnnnnnnnnnnnnlkhi
Answer:
yes seems like you understand
Answer:
yes
Step-by-step explanation:
yes