The nth term of the following sequence is: 5n²
What is arithmetic sequence?Arithmetic sequence is a sequence where each consequtive term has a common constant difference.
An arithmetic sequence, therefore, is defined by two parameters, viz. the starting term and the common difference.
We are given the sequence are;
5, 20, 45, 80, 125
The quadratic sequence formula : an²+bn+c
2nd difference 2a = 10
a = 5
1st difference 3a+b = 15
Then substitute 5
3(5)+b = 15
b = 0
The nth term rule : a + b + c = 5
Now substitute a and b values into equation
5 + 0 + c = 5
c = 0
The nth term is: 5n²
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Help pls I’ll give extra points
Answer:
1. Gorgeous
2. Tremendous
3. Coarse
4. Crackling
5. Appetizing
Step-by-step explanation:
Those are the only words that make sense in each square.
Answer:
1.) gorgeous
2.) tremendous
3.) crackling
4.) coarse
5.) appetizing
6.) buttery
7.) magnificent
Hope this helps!
Complete the square for the expression. Then factor the trinomial.
x2 - 6x
Expression:
Factored form:
Expression: x² - 6x + 9
Factored form: (x - 3)²
Using the concept of factorization.
What is factorization?The breaking or breakdown of an entity (such as an integer, a matrix, or even a polynomial) into such a combination of some other unit, or factors, whose multiplication yields the original number, matrix, etc., is known as factorization or factoring in mathematics.
Similarly to this, factoring is a very useful technique in algebra that is utilized at all levels. Additionally, to, of course, simplify complex expressions, it offers a standard way for solving quadratic equations. Graphing functions also makes advantage of it.
Factor the expression, put each factor equal to 0, and then solve each equation to solve a quadratic equation by factoring. To do this, rearrange all terms on one side of the equation such the other side equals 0.
Given that,
x² - 6x
Now, to find the value of c = (b/2)²
divide the coefficient of x by 2.
So, divide 6 by 2 we get: ( -1.3)²
Next, multiply -1 by 3: (-3)²
Now, raise -3 to the power of 2, we get: 9
So, the expression becomes: x² - 6x + 9
Factorized form: (x - 3) (x -3)
or we can write (x - 3)²
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Dan is training his puppy, Lola, to sit. Dan holds a treat 5 feet above the ground until Lola
sits. As soon as she does, he drops the treat, and Lola catches it in her mouth 1.5 feet above
the ground.
To the nearest tenth of a second, how long does the treat fall before Lola catches it?
Hint: Use the formula h = -16t² + s.
Answer:
t = 0.5 seconds
Step-by-step explanation:
Given formula:
[tex]h=-16t^2+s[/tex]
where:
h = height above the ground (in feet)t = time after dropping the treat (in seconds)Dan drops the treat 5 feet above the ground.
Therefore, when t = 0, h = 5 ft.
To find the value of s, substitute these values into the given formula:
[tex]\implies -16(0)^2+s=5[/tex]
[tex]\implies s=5[/tex]
Therefore:
[tex]h=-16t^2+5[/tex]
To calculate how long the treat falls before Lola catches it, substitute h = 1.5 into the formula:
[tex]\implies -16t^2+5=1.5[/tex]
[tex]\implies -16t^2=-3.5[/tex]
[tex]\implies t^2=0.21875[/tex]
[tex]\implies t=\sqrt{0.21875}[/tex]
[tex]\implies t=\pm0.467707173...[/tex]
[tex]\implies t=\pm0.5\; \; \sf (nearest\;tenth)[/tex]
As time is positive, t = 0.5 seconds (nearest tenth) only.
Therefore, it took 0.5 seconds for Lola to catch the treat after it fell.
Simplify the difference. (2w2 – 8w – 8) – (5w2 + 3w – 5)
Answer:
-3w2-11w-3
Step-by-step explanation:
take w2 and w as variables. you can substitute it as w2=y and w=X then expand brackets
2y-8x-8-5y-3x+5
note that the signed changed at the second part because it was expanded with the minus sign which is basically like -1, so it changes the signs
then you collect like terms:
2y-5y-8x-3x-8+5= -3y-11x-3
now put substitute back w2=y and w=X
-3w2-11w-3
if it won't be a problem solving with w2 and w, then you skip the substitution part and solve the same
PLEASE HELP!!
I’m rlly struggling with my hw rn
There you have it, your answer
Step-by-step explanation:
Easy
7 time a number , increased by 4
Answer:
7 times a number increased by 4 times the number
Let a number and the number be an arbitrary variable. Let's call it x. We have an algebraic expression. Let's take it in pieces:
7 times a number: 7x
4 times the number: 4x
The phrase increased by means we add 4x to 7x:
7x + 4x
Simplifying, we get: (7 + 4)x
11x
Step-by-step explanation:
Find the slope of the line 6x - 2y = -16
Answer:
The slope is 3
Step-by-step explanation:
Find the radius of the circle, if the big square is 30 square units more than the area of the small square.
Answer:
The area of a square is equal to the side length of the square squared. If the side length of the small square is "s" and the side length of the big square is "b", then we can write the following two equations to represent the area of the two squares:
Area of small square = s^2
Area of big square = b^2
Since the area of the big square is 30 units more than the area of the small square, we can write the equation:
b^2 = s^2 + 30
To find the radius of the circle, we need to find the side length of the small square. To do this, we can rearrange the equation above to solve for s:
s^2 = b^2 - 30
s = sqrt(b^2 - 30)
Now we just need to find the value of "b", which is the side length of the big square. To do this, we can use the fact that the big square is inscribed in the circle, so the side length of the big square is equal to the diameter of the circle. Let's call the diameter of the circle "d". Then we can substitute "d" for "b" in the equation above:
s = sqrt(d^2 - 30)
To find the radius of the circle, we just need to divide the diameter of the circle by 2, so the radius is equal to "d" divided by 2. Therefore, the radius of the circle is:
r = d/2 = sqrt(d^2 - 30)/2
So to find the radius of the circle, we just need to know the diameter of the circle. Can you provide the diameter of the circle in the question?:
The radius of the circle is: r = d/2 = sqrt(d^2 - 30)/2
What is area of circle?The area of a circle is π multiplied by the square of the radius. The area of a circle, (A) when the radius 'r' is given is πr2. π is approximately 3.142
Here, we have,
The area of a square is equal to the side length of the square squared. If the side length of the small square is "s" and the side length of the big square is "b", then we can write the following two equations to represent the area of the two squares:
Area of small square = s^2
Area of big square = b^2
Since the area of the big square is 30 units more than the area of the small square, we can write the equation:
b^2 = s^2 + 30
To find the radius of the circle, we need to find the side length of the small square. To do this, we can rearrange the equation above to solve for s:
s^2 = b^2 - 30
s = sqrt(b^2 - 30)
Now we just need to find the value of "b", which is the side length of the big square. To do this, we can use the fact that the big square is inscribed in the circle, so the side length of the big square is equal to the diameter of the circle. Let's call the diameter of the circle "d". Then we can substitute "d" for "b" in the equation above:
s = sqrt(d^2 - 30)
To find the radius of the circle, we just need to divide the diameter of the circle by 2, so the radius is equal to "d" divided by 2. Therefore, the radius of the circle is:
r = d/2 = sqrt(d^2 - 30)/2
So to find the radius of the circle, we just need to know the diameter of the circle.
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A cone has a volume of 602.88 cm3 and a radius of 8 cm. What is the height of the cone
Answer:
h≈9cm
Step-by-step explanation:
V=
π
r
2
h
3 h=
3
V
π
r
2
=
3
602.88
π
8
2
≈
8.99544cm
Explain how to write a quadratic equation given the following three points on the graph (5,31) (3,11) (0,11)
Given:
The graph of a quadratic function passes through the points (5,31) (3,11) (0,11).
To find:
The equation of the quadratic function.
Solution:
A quadratic function is defined as:
[tex]y=ax^2+bx+c[/tex] ...(i)
It is passes through the point (0,11). So, substitute [tex]x=0,y=11[/tex] in (i).
[tex]11=a(0)^2+b(0)+c[/tex]
[tex]11=c[/tex]
Putting [tex]c=11[/tex] in (i), we get
[tex]y=ax^2+bx+11[/tex] ...(ii)
The quadratic function passes through the point (5,31). So, substitute [tex]x=5,y=31[/tex] in (ii).
[tex]31=a(5)^2+b(5)+11[/tex]
[tex]31-11=a(25)+5b[/tex]
[tex]20=25a+5b[/tex]
Divide both sides by 5.
[tex]4=5a+b[/tex] ...(iii)
The quadratic function passes through the point (3,11). So, substitute [tex]x=3,y=11[/tex] in (ii).
[tex]11=a(3)^2+b(3)+11[/tex]
[tex]11-11=a(9)+3b[/tex]
[tex]0=9a+3b[/tex]
Divide both sides by 3.
[tex]0=3a+b[/tex] ...(iv)
Subtracting (iv) from (iii), we get
[tex]4-0=5a+b-3a-b[/tex]
[tex]4=2a[/tex]
[tex]\dfrac{4}{2}=a[/tex]
[tex]2=a[/tex]
Putting [tex]a=2[/tex] in (iv), we get
[tex]0=3(2)+b[/tex]
[tex]0=6+b[/tex]
[tex]-6=b[/tex]
Putting [tex]a=2,b=-6[/tex] in (ii), we get
[tex]y=(2)x^2+(-6)x+11[/tex]
[tex]y=2x^2-6x+11[/tex]
Therefore, the required quadratic equation is [tex]y=2x^2-6x+11[/tex].
A new car costs $40,000. The value of the car depreciates by 20% per year.
a. Create a formula to determine the value of the car t years from now.
b.when will the car be worth 25,000? Round to 2 decimal places.
Answer:
i think A
Step-by-step explanation:
correct me if I wrong k
3. Selecting three desserts from eight possible choices on a menu. How
many choices are there if you determine a 1st, 2nd and 3rd rank. What are
the possible outcome? Show all evidence of understanding.
Answer:
56 possible outcomes
Step-by-step explanation:
Order does not matter in this case, so we will find all the possible combinations:
8 nCr 3 = 8! / ((8 – 3)! 3!) = 40320 / 720 = 56
Therefore, there are 56 possible outcomes.
classify the angles below as acute, right, obtuse or straight
Answer:
Obtuse - over 90°
Acute - less than 90°
Right - 90°
Straight - 180°
1. Obtuse
2. Acute
3. Right
Manuel's small dog eats
1
8
bag of dog food in 1 month. His large dog eats
5
8
bag of dog food in 1 month.
How many bags do both dogs eat in 6 months?
Answer:
I wanna say 348?? maybe.... I think
How to solve Mathematics techniques
Answer:
you can add them
Step-by-step explanation:
Congratulations! You won a contest sponsored by a local radio station. If you were given the choice of the two payment plans listed below, which plan will pay you more? How much more? Be sure to show all evidence including formulas used for calculations.
A. $1 on the first day, $2 on the second day $3 on the third day etc. for 4 weeks.
B. $0.01 on the first day , $0.02 on the second day , $0.04 on the third day etc.. For 4 weeks.
Plan B pays more $2,683,948.55 more than plan A.
What is arithmetic progression?Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence.
What is geometric progression?A geometric progression is a sequence in which any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r.
The first payment plan forms an arithmetic progression with first term
[tex]a_{1} =[/tex] $1 and common difference d = $1.
The total amount gotten after 4 weeks is the sum of the terms in the arithmetic progression when the number of terms is [tex](4\times7) = 28 days[/tex]
[tex]S_{n}=\frac{a}{2}[2a_{1} +(n-1)d][/tex]
Total payment = [tex]S_{n}=\frac{28}{2}[2(1) +(28-1)1][/tex]
= [tex]14(2+27)[/tex]
= [tex]14(29)[/tex]
= $406
The second payment plans a geometric progression with first term
[tex]a_{1} =[/tex] $0.01 and common difference r = 2.
The total amount gotten after 4 weeks is the sum of the first 28 terms of the geometric progression
[tex]S_{n}=\frac{a_{1}(1-r^{n} ) }{1-r}[/tex]
Total payment = [tex]\frac{0.01(1-2^{28}) }{1-2}[/tex]
= [tex]\frac{-2684354.55}{-1}[/tex]
= $2684354.55
The second plan pays more by
= $2684354.55 - $406
= $2683948.55
Plan B pays more $2,683,948.55 more than plan A.
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Step-by-step explanation:
nzkaoavdvsoasb xzakoakaidbzbsva
Answer:
See attached
Step-by-step explanation:
Solution is below
3/5 of carl's money is $27.00. how much is 1/2 of his money
Answer:
$22.5
Step-by-step explanation:
$27.00/3/5=45
45*1/2=$22.5
8w - 12 = 44
I need the steps
this is for 30 points
Answer:
so it would be written as:
8w - 12 + 12 = 44 + 12
8w = 56
56 divided by 8 = 7
w = 7
a decrease of 70% in9,600 gal
Answer:
The answer to this question is 6720
. This line plot shows how many miles Maya walked this week.
Answer:
60.5 or 60 1/2
Step-by-step explanation:
7 (2)
8.5 (1)
9 (1)
9.5 (2)
10 (1)
14 + 8.5 + 9 + 19 + 10
60.5
How can the graph of f(x) = 35x be transformed to represent the function g(x) = 35x – 3?
Translate the graph of f(x) - 3 units.
The point is on the graph of g(x).
Answer: Down | ( 8, -1 )
Step-by-step explanation:
Did the assignment
Tell whether the angles are complementary or supplementary. Then find the value of x.
Answer:
Complementary
x = 15
Step-by-step explanation:
Given angles are complementary, because their sum is 90°.Now, let us find the value of x.-> 3x° + 45° = 90°-> 3x° = 90° - 45°-> 3x° = 45°-> x = 45/3-> x = 15How do I even do thissss?
Please provide your question with a math problem in the form of an image or text.
which expression is equivalent to 7.2 x 7.2 x 7.2?
Answer:
The answer is letter B. 7.2^3
Answer:
b.)
Step-by-step explanation:
I thought of a number, added 26 to it, and then divided the result by 20.what is my number?
Answer:
Step-by-step explanation:
14 MAY BE
Two parallel lines are crossed by a transversal.
Horizontal and parallel lines b and c are cut by transversal a. At the intersection of lines b and a, the bottom right angle is 50 degrees. At the intersection of lines c and a, the top left angle is y degrees.
What is the value of y?
The value of y is 130°
What are corresponding angles?The angles occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.
Given here:
Horizontal and parallel lines b and c are cut by transversal a. At the intersection of lines b and a, the bottom right angle is 50 degrees. At the intersection of lines c and a, the top left angle is y degrees.
Thus the angle adjacent to the 50-degree angle will be 130
but this angle corresponds to the angle y thus y=130 as corresponding angles are equal when a transversal intersects two parallel lines
Hence, The value of y is 130°
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PLEASE HELP WITH EASY FRACTIONS APPRECIATED MUCH!!!
Answer: 3/4 is right
Step-by-step explanation:
George is building a fence in his backyard. One side of the yard has a row of trees that is 15 feet long. This row of trees will serve as part of the fence. If that side of the fence needs to be 26 feet long, George will need feet of fence to finish that one side.
Answer:
11
Step-by-step explanation:
26-15=11
Give the following number
in Base 10.
F16 = [? ]10
The next decimal number should be changed to hexadecimal. Your final response may contain up to six fractional digits. In decimal 386210, subscript 10 to F16.
How do you write a number in base 10?F16 is 001000011000.1111. 218. F716 is 001000011000.111101112. 710 = (h0)16 = 716 is how the hexadecimal number is represented. It is necessary to add a 1 to the left and modify the number for both to 0. In base-2, the numeral 15 is represented as 1111, and the number 16 is represented as 10000. The greatest value in base-16 is the letter F, in a similar vein. such that 10 is the new value.
Binary 10 equals 1010, thus. Dividing 10 by 2 successively until the quotient equals 0 will yield the decimal to binary equivalent. By writing the remainder in each division step from bottom to top, it is possible to determine the binary equivalent.Base-16 is the definition given to hexadecimal. There are many powers of 16 in each place value in the number. The hexadecimal numbers are: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. 10 through 15 are represented, accordingly, by the letters A through F.
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