Answer:
[tex]p = 25(3)^n[/tex]
Step-by-step explanation:
Given
Round 0 1 2 3
Points 25 75 225 675
Required
Determine the equation
Let n = rounds and p = points.
So, we have:
[tex](n_1,p_1) = (0,25)[/tex]
[tex](n_2,p_2) = (1,75)[/tex]
[tex](n_2,p_2) = (3,225)[/tex]
The above shows a geometric progression.
So, we solve using
[tex]p = ab^n[/tex]
In [tex](n_1,p_1) = (0,25)[/tex]
n = 0 and p = 25
Substitute these values in [tex]p = ab^n[/tex]
[tex]25 = ab^0[/tex]
[tex]25 = a*1[/tex]
[tex]25 = a[/tex]
[tex]a = 25[/tex]
In [tex](n_2,p_2) = (1,75)[/tex]
n = 1 and p = 75
Substitute these values in [tex]p = ab^n[/tex]
[tex]75 = ab^1[/tex]
[tex]75 = ab[/tex]
Substitute 25 for a
[tex]75 = 25*b[/tex]
Make b the subject
[tex]b = \frac{75}{25}[/tex]
[tex]b = 3[/tex]
So, we have:
[tex]a = 25[/tex] and [tex]b = 3[/tex]
The equation [tex]p = ab^n[/tex] becomes
[tex]p = 25(3)^n[/tex]
Equation representing the number of points 'P' in 'n' games will be [tex]P=25(3)^{n}[/tex].
Explicit formula of the Geometric sequence:a, ar, ar², ar³........arⁿ
There is a common ratio of 'r' in each successive term to the
previous term.
Therefore, it's a geometric sequence.
Explicit formula of a geometric sequence is given by,[tex]T_n=ar^{n-1}[/tex] (For n ≥ 1)
Here, [tex]a=[/tex] First term
[tex]r=[/tex] Common ratio
[tex]n=[/tex] nth term
Given in the table,
Common ratio (r) of any successive term to the previous term,[tex]r=\frac{75}{25}=3[/tex]
First term of the sequence 'a' = 25Explicit formula of the sequence will be,
[tex]P=25(3)^{n}[/tex] [For n ≥ 0]
Therefore, equation representing the number of points 'P' in 'n' games will be [tex]P=25(3)^{n}[/tex].
Learn more about the geometric sequence here,
https://brainly.com/question/11385300?referrer=searchResults
Solve for r in terms s, t, u, v.
su=rtv
Answer:
r = su/tv
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityStep-by-step explanation:
Step 1: Define
su = rtv
Step 2: Solve for r
[Division Property of Equality] Divide tv on both sides: su/tv = rRewrite/Rearrange: r = su/tva(-6)=-42
solve for a
Answer:
7
Step-by-step explanation:
Answer:
A = 7
Step-by-step explanation:
You would take -42/-6 because that will tell you what x -6=-42
-42/-6 = 7
Also. you have to remember that a negative divided or multiplied by a negative = a positive
please help my friend, he's struggling on math
Answer:
question 1 = 37 covers , 535 dollars
question 2 = 32 covers , 460 dollars
Expression = 69 covers , 995 dollars
Step-by-step explanation:
You would take the number of covers and multiply it by 15 because 15 dollars is how much they sold each cover for.
and then for the expression wasnt sure what to do but from what i could see you added up the totals.
Hope this helped him :)
also tell me what his snap is BAHA okay lemme stop.
Ryan ordered some books online and spent a total of . Each book cost and he paid a total of for shipping. How many books did he buy?
Answer: 12 books
Step-by-step explanation:
First you need to remove the cost of shipping from the total amount:
= 75 - 3
= $72
The above is the total amount spent on the books without shipping.
If each book cost $6, the total number of books bought is:
= 72 / 6
= 12 books
Work out the size of angle X
Answer:
117
Step-by-step explanation:
180-101 = 79
180-(79+38)
180-117
63
180-63=117
PLEASE HELPPPPPPPP....?.......
If a+b=15 and ab=54 then find
1)
[tex] {a}^{2} + {b}^{2} [/tex]
2)
[tex](a - b )^{2} [/tex]
3)
[tex]a ^{2} - {b}^{2} [/tex]
Answer:
a = 9
b = 6
I hope you can do the rest yoyrself, as I coulsnt find how to type it out ;-;
Answer:
1) 117
2) 9
3) 45 or -45
Step-by-step explanation:
a=9
b=6
1) a²+b²=9²+6²=81+36=117
2) (a-b)²=(9-6)²=3²=9
3) a²-b²=81-36=45
It’s also possible that a=6 and b=9, in which case
1) (same)
2) (same)
3) 36-81=-45
I WILL MARK BRAINLIEST PLEASE HELP ASAP!!!!! Sketch a new graph of this relationship. The equation is y=7/4x
Answer:
Step-by-step explanation:
Find the value of x.
Answer:
Step-by-step explanation:
8/18=x/24
18x=192
x=10.667(correct to three decimal places)
Find all of the roots of the following quartic equation:
h(x)= x^4 - 2x^3 - 9x^2 + 18x
please help me on this will give you brainliest!!
Answer:
0.926
Step-by-step explanation:
Since it ask as decimal you will have to 0. and then the number which 926. Hope this helps, thank you !!
Dan was thinking of a number. Dan adds 10 to it, then doubles it and gets an answer of 56.6. What was the original number
Answer:
23.3 is the answer to this question
19.- Según la gráfica ¿Cuál es la rapidez media entre 4 s y 8 s?
A. 8 m/s
B. 1 m/s
C. 0,5 m/s
Answer:
B. 1m/s es la respuesta correcta
-10(d+1)=-14
What is the value of d
Answer:
[tex]d=\frac{2}{5}[/tex]
Step-by-step explanation:
-10 (d+1) = -14
-10d -10 = -14
-10d = -14 + 10
-10d = -4
d = 4/10
d= 2/5
v
8
IZ
13
10
U
What is the LCM (least common multiple) of 2 and 7
Answer:
14
Step-by-step explanation:
Answer: 14
Step-by-step explanation:
The greatest common multiple of 2 and 7 is 1, because they are both prime numbers (numbers that cannot be divided by anything other than one or themselves).
Why bother with the greatest common multiple?
There's a very sneaky formula you can do to calculate the LCM with this.
[tex]lcm(a, b) = \frac{|a * b|}{gcd(a, b)}[/tex]
where lcm(a, b) = the least common multiple of integers a and b (1)
a = integer a (2)
b = integer b (7)
gcd(a, b) = greatest common divisor of integers a and b
So let's use it, we have all the available numbers.
[tex]lcm(a, b) = \frac{|2 * 7|}{1} = 14[/tex]
92 divided by 11 with remainder
Answer:
8 remainder 4
3(2h+5)+4 so i dont get what it is, can someone help please?
Answer:
An linear equation in one variable
Step-by-step explanation:
Variable:h
Equation:6h+19
An isosceles triangle has an angle that measures 56º. Which other angles could be in that
isosceles triangle? Choose all that apply.
HELP PLEASE I NEED THIS
Answer:
The other angles can be 56°, 68°, or 62°.
Step-by-step explanation:
If the 56° angle is one of the two congruent angles, then the remaining angles are 56° and 180-2(56) = 68°
If the is 56° Is not congruent to either of the other angles, then each of the remaining two angles is (180-56)/2 = 62°.
The other angles can be 56°, 68°, or 62°.
This another nae for fraction or quotient.It can also be written in the forms 'a:b' and a to b', where a and b are numbers.
Answer:
The answer is "Ratio".
Step-by-step explanation:
A ratio indicates how often a number contains a different number. Whenever the calculation of two quantities, as often happens, is indeed a measurement ratio without dimension. It is called a quotient of two volumes, which is calculated by using various units.
It is the relationship among two or more elements of financial reports is calculated by ratios. These also are efficient when the outcomes are presented several times. It allows you to monitor the performance of your company over time and to detect signs of injury.
Which statement is correct?
O A.
The opposite of the opposite of 6 is 6.
OB.
The opposite of the opposite of 1 is 1.
O C.
The opposite of the opposite of 3 is 0.
O D.
The opposite of the opposite of 5 is.
Answer:
I think its OB but I'm not sure
Step-by-step explanation:
Simplify (6w + 5.2) + (12.2 + 2.3w)
Answer:
The answer is 8.3 W + 17.4
If you click on the image it will show you how to solve the equation and I hope this helps you.
Lauren took 12 hours to read a 360 page book use the unit rate to determine how many hours it will take her to read 150
HELPP PLEASEE
Answer:
360 divied by 2.4 = 150
Step-by-step explanation:
Kris has 3 daughters who all live in different cities across Georgia. She wants to live somewhere that is an equal distance from each of her daughters. She mapped out the 3 cities and drew a triangle connecting them. How can she find a point on the map that is an equal distance from all 3 cities?
construct the incenter
construct the orthocenter
estimate the best place
construct the circumcenter
===========================================================
Explanation:
Consider triangle ABC. The vertex points are at A,B,C. These represent the three cities in which the three different daughters live. Constructing the circumcenter will produce a circle such that all three points A,B,C are on that circle. Let's say that D is the center of that circle.
This means that AD, BD, CD are all radii of this same circle. Radii of the same circle are the same length, which is why point D is equally distant from A,B,C. If the mother lives at point D, then she will travel the same distance to visit any three of her daughters. See the note below.
To construct the circumcenter, we form perpendicular bisectors to segments AB, BC and AC. Technically you only need two of them. All three of these perpendicular bisectors intersect at point D.
-------------
Note: Keep in mind that roads aren't completely straight, so that means we'll have to factor in the curvature of each road. But to keep things simple, we assume each road is a straight line segment.
Pls help me i need your help to do it pls
Answer: 39°
Step-by-step explanation:
This is a right triangle, meaning one of the angles is a 90° angle. Angle CBA in this case is the 90° angle. In order to figure out the measure of ABD, you subtract the measure of CBA by the measure of CBD, which is 51°.
90 - 51 = 39
Thus, the measure of ABD is 39°
The length, in millimeters of each side of a square shaped electronic chip is a rational number. What statement is true about the length of the diagonal of the chip
Answer:
The diagonal is irrational because it is a product of a rational and an irrational number
Step-by-step explanation:
The options are not given. However, the question is still answerable.
Given
Shape: Square
Length: Rational
Since the side length is said to be rational, I'll answer the question based on whether the diagonal is rational or not.
Having said that:
The diagonal (d) of a square with side length (l) is calculated using Pythagoras theorem.
[tex]d^2 = l^2 + l^2[/tex]
[tex]d^2 = 2l^2[/tex]
Take positive square root of both sides
[tex]d = \sqrt{2l^2}[/tex]
Split:
[tex]d = \sqrt{2} * \sqrt{l^2}[/tex]
[tex]d = \sqrt{2} *l[/tex]
Recall that the side length (l) is rational.
However, [tex]\sqrt 2[/tex] is irrational.
So, the product of l and [tex]\sqrt 2[/tex] will be irrational
Hence:
The diagonal is irrational
What is m_8 if m_4= 50 degrees?
HELP ME RN PLEASEEEE!!!!!!!!
how many 3/8 are in 8, explain how you know
Answer:
exactly 21 sets of 3/8 fit into 8
Step-by-step explanation:
Basically you just draw 8 boxes split them in 8ths and you end up with 21 sets of 3/8
can someone please help its due soon.ill give brainliest!
Answer:
z = 17.5
Step-by-step explanation:
To get the value of z, we use the bisector theorem
7/z = 6/15
6z = 7 * 15
6z = 105
z = 105/6
z = 17.5
what is the appoximate distance between points d and e round your answer to the nearest hundreth
Sam's two new aquariums each hold exactly 200 gallons of water. One aquarium will hold small fish and the other will hold large fish. Now he needs new fish for his aquariums.
•He will buy 5 small fish for every 10 gallons of water in the aquarium.
•He will buy 8 large fish for every 40 gallons of water in the aquarium.
What is the total number of fish Sam will have? What will be the ratio of Sam's small fish to large fish? Show or explain the steps you used to solve this problem.
The length of a rectangle is 3 times as big as the width. If beth increases each dimension by 4, write an expression to represent the new area, a, of the rectangle.
Answer: See explanation
Step-by-step explanation:
Let the width of the rectangle be x.
The length of a rectangle is 3 times as big as the width. Length = 3x
New width = x + 4
New length = 3x + 4
The new area will be:
a = (3x + 4)(x + 4)
a = 3x² + 12x + 4x + 16
a = 3x² + 16x + 16