In a game show, players play multiple rounds to score points. Each round has 3 times as many points available as the previous round.
Round 0 1 2 3 n
Points 25 75 225 675
Which equation shows the number of points available, p, in round n of the game show?
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
Plz look at the photo for geometry
Answer: m<C = 45, m<M = 50, m< B = 85.
Step-by-step explanation:
Adjacent angles on a line sum to 180 degrees.
m<C + m<M + m<B = 180. 45 + (8x+10) + (12x+25) = 180. Combine like terms. 80+ 20x =180. Subtract 89 from both sides. 20x = 100. Divide both sides by 20. X = 5. Substitute x back into the angle measures. m<C = 45, m<M = 50, m< B = 85.
A total of 150 tickets were sold for the annual concert. Student tickets were $4 and non-students $8. If the total revenue was $840, how many tickets of each type were sold ?
Answer:
x = 90
y = 60
Step-by-step explanation:
Let x = student
Let y = non-student
x + y = 150
4x + 8y = 840 <—— Use elimination/addition ethos for both equations
8 (x + y = 150)
-1 (4x + 8y = 840) <—— Let’s eliminate y
8x + 8y = 1200
+ -4x - 8y = -840
—————————————
4x = 360
x = 90
x + y = 150 <— substitute for x from above
90 + y = 150
- 90 = - 90 <— subtract from both sides
y = 60
Need help pleaseeeee!!
Answer: z 1/2
Step-by-step
:) 100%
5*4 3/10 pls answer I will mark you as brainliest
Answer:
5x4 x 3 /10
20x 3 /10
60/10
6
Answer:
Step-by-step explanation:
[tex]5* 4 \frac{3}{10}=5* \frac{(4*10)+3}{10}\\\\= 5*\frac{43}{10}\\\\= \frac{43}{2}\\\\= 21 \frac{1}{2}[/tex]
jack is making a triangle shaped deck,one side is 5ft and the other is 7ft. he is going to make the third length 14ft. is jack correct about his third length?
Answer:
no
Step-by-step explanation:
brainliest give an explanation to
Answer:
70 caps, 72 hotdogs, 50 paintings, 8 scouts
Step-by-step explanation:
Ms. Myrie gave her class 20 minutes to read. Carrie read 5 1/2
pages in that time. At what rate, in pages per hour, did Carrie read?
Answer:
16.5
Step-by-step explanation:
60 minutes = 1 hour
20 minutes * 3 = 60.
That means, by multiplying by a factor of 3, we can see exactly what Carrier's pg/hr speed is.
5.5 * 3 = 16.5
Answer:3.63 pagers per hour
Step-by-step explanation:
5 1/2 is the same as 5.5
20/5.5=3.63
For what value of k is the expression x^4 + kx^2 + 49 a perfect square?
Answer:
[tex]k=14[/tex]
Step-by-step explanation:
Completing the square gives
[tex]x^4 + kx^2 + 49\\= (x^2+7)^2 - 14x^2 + kx^2[/tex]
So we have to cancel the latter two terms out for the expression to always become a square (otherwise we are dealing with a square plus something else, which doesn't always result in a square), giving us our answer directly.
Answer:
k=± 14
Step-by-step explanation:
[tex]x^4+kx^2+49\\Disc.=b^2-4ac=k^2-4*1*49\\it ~ is ~a ~ perfect ~ square.\\k^2-196=0\\k^2=196\\k= \pm 14[/tex]
1. A storage trunk is 3 feet long and 1 foot wide. The height of the trunk is 2 feet. What is the volume of the trunk?
what is the slope of (-3,-6) and (4,7)
Answer:
13/7
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(7-(-6))/(4-(-3))
m=(7+6)/(4+3)
m=13/7
The discriminant of a quadratic equation is 0. Which statement is true?
a. there are two real solution
b. there are no real solution
c. there is one real solution
Answer:
A
Step-by-step explanation:
two real solutions! hope this helped!!
Solve - 12x ≤ 72 and then plot the solution set on the number line.
Answer:
(6,0)
Step-by-step explanation:
Used Desmos Scientific calculator.
Which fraction divided by 3/6 is equal to -9/10? A-9/20. B9/20. C-3/2. D9/40
Answer: -9/20 is equal to -9/10 when divided by 3/6 (1/2)
Step-by-step explanation:
Begin by reducing the fraction you're dividing with. In this case 3/6 can be reduced to 1.2, also known as 0.5 Beginning with -9/20, as it is the first answer option, we can put the problem into the following equation: -9/20 * 2/1 = -9/10.It is always good to verify all of your answer options are not possible answers. However, in a question like this, the math evenly works out in most cases, eliminating any other possible answer options.
By submitting this answer and referring to the work and resources given I trust you're in accordance with the Brainly Honor Code and I take no responsibility for any laws or rules broken with you using this platform.
help me please-1 = (5 + x)/6
Answer:
x= -11 I hope this helps!
Step-by-step explanation:
Answer:
x=-11
Step-by-step explanation:
/=division
*=multiplication
-1=(5+x)/6
-1*6=(5+x)/6*6
-6-5=5+x-5
-11=x
Question 13
Find the angle between the given vectors to the nearest tenth of a
degree.
u= <8,4, v = <9.-9> (5 points)
Answer:
71.6 degrees
Step-by-step explanation:
Given the vectors
u= <8,4> v = <9.-9> (5 points)
u*v = (8, 4)*(9, -9)
u*v = 8(9)+(4)(-9)
u*v = 72 - 36
u*v = 36
|u| = √8²+4²
|u| = √64+16
|u| = √80
|v| = √9²+9²
|v| = √81+81
|v| = √162
Using the formula
u*v = ||u||v| cos theta
36 = √80(√162)cos theta
36 = √12960 cos theta
cos theta = 36/√12960
cos theta = 36/113.8
cos theta = 0.3162
theta = arccos(0.3162)
theta = 71.56 degrees
Hence the angle between the given vectors to the nearest tenth of a
degree is 71.6 degrees
how many games have the hawks played?
Describe the transformation from y= x + 4 to y= .5x + 4 Group of answer choices compresses stretches shifts right 4 shifts left 4
Answer:
This type of transformation is a horizontal stretch.
Step-by-step explanation:
Given
[tex]y = x + 4[/tex]
[tex]y = .5x + 4[/tex]
Required
Determine the type of transformation
The first function can be expressed as:
[tex]f(x) = x + 4[/tex]
While the second function is:
[tex]g(x) = f(0.5x)[/tex]
Solving f(0.5x), we have to substitute 0.5x for x in [tex]f(x) = x + 4[/tex]
[tex]f(0.5x) = 0.5x + 4[/tex]
So:
The second function is:
[tex]g(x) = 0.5x + 4[/tex]
This type of transformation is a horizontal stretch.
i.e. f(x) stretched to g(x)
pls Help I hate math
Answer:
C
Step-by-step explanation:
Remark
There are three rectangles all the same size.
There are two triangles both the same size
Triangles.
Givens
b = 7.5 cm
h = 6.5
Solution
Area 1 triangle = 1/2 * 7.5 * 6.5
Area 1 triangle = 24.375
Area 2 triangles = 2*24.375 = 48.75
Rectangles
Givens
L = 13.5
w = 7.5
Solution
Area one rectangle = L*w
Area one rectangle = 13.5*7.5
Area one rectangle = 101.25
Area three rectangles = 3*101.25
Area three rectangles = 303.75 Add
Total Area = 352.5
TWVU is a trapezoid with midsgment FG find the value of x please help
Answer:
Find each measure.
1.
SOLUTION:
The trapezoid ABCD is an isosceles trapezoid. So,
each pair of base angles is congruent. Therefore,
ANSWER:
101
2. WT, if ZX = 20 and TY = 15
SOLUTION:
The trapezoid WXYZ is an isosceles trapezoid. So, the
diagonals are congruent. Therefore, WY = ZX.
WT + TY = ZX
WT + 15 = 20
WT = 5
ANSWER:
5
COORDINATE GEOMETRY Quadrilateral
ABCD has vertices A(–4, –1), B(–2, 3), C(3, 3),
and D(5, –1).
3. Verify that ABCD is a trapezoid.
SOLUTION:
First graph the points on a coordinate grid and draw
the trapezoid.
Use the slope formula to find the slope of the sides of
the trapezoid.
The slopes of exactly one pair of opposite sides are
equal. So, they are parallel. Therefore, the
quadrilateral ABCD is a trapezoid.
ANSWER:
ABCD is a trapezoid.
4. Determine whether ABCD is an isosceles trapezoid.
Explain.
SOLUTION:
Refer to the graph of the trapezoid.
Use the slope formula to find the slope of the sides of
the quadrilateral.
The slopes of exactly one pair of opposite sides are
equal. So, they are parallel. Therefore, the
quadrilateral ABCD is a trapezoid.
Use the Distance Formula to find the lengths of the
legs of the trapezoid.
The lengths of the legs are equal. Therefore, ABCD
is an isosceles trapezoid.
ANSWER:
isosceles;
5. GRIDDED REPSONSE In the figure, is the
midsegment of trapezoid TWRV. Determine the value
of x.
SOLUTION:
By the Trapezoid Midsegment Theorem, the
midsegment of a trapezoid is parallel to each base
and its measure is one half the sum of the lengths of
the bases.
are the bases and is the
midsegment. So,
Solve for x.
16 = 14.8 + x
1.2 = x
ANSWER:
1.2
CCSS SENSE-MAKING If ABCD is a kite, find
each measure.
6. AB
SOLUTION
Work out the perimeter of an equilateral triangle with side length 2.7mm
Answer:
, so easy
Step-by-step explanation:
3×2.7mm=8.1mm
Answer:
8.1mm
Step-by-step explanation:
equilateral triangle all sides are equal.
If 1 side is 2.7mm what will be the total of three sides. 2.7+2.7+2.7=8.1mm
Please help...it due ASAP
Show workings please
Answer:
36.5 i believe.
Step-by-step explanation:
you divide 986 by 27 and it equals 36.5.
hope you get it right!
if this is wrong then you can report me i guess. ='(
Find the value of x.
Answer:
[tex]x=64^{\circ}[/tex]
Step-by-step explanation:
We know that sum of angles of a quadrilateral is equal to 360 degrees.
It means,
[tex]\angle X+\angle Y+\angle Z+\angle W=360\\\\100+130+66+x=360\\\\296+x=360\\\\x=360-296\\\\x=64^{\circ}[/tex]
So, the value of x is equal to [tex]64^{\circ}[/tex].
60% of ___ =39
I NEED AN ANSWER ASAP PLEASE HELP
Answer:
The answer is 65
Step-by-step explanation:
Please help answer correctly !!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!!
Answer:
i think its 360.......
Step-by-step explanation:
i hope it helps
what is the answer to this problem
Answer:
-11/12
Step-by-step explanation:
Answer:
-11
12
Step-by-step explanation:
You have to add the numbers, multiply them, subtract them and then finally divide.
ASAP 20 POINTS!!! Students just finished taking test and these are the scores: 75, 80, 62, 98, 90, 86, 55, 86, 92, 66. What is the mean of the scores?
83
86
79
43
Answer:
I do not understand the question?
Step-by-step explanation:
15
Evaluate
T
1 when T-5.
Answer:
T= 6
Step-by-step explanation:
T-5=1
find T
+5 to both sides
T= 6
Is (3,8) a solution to this system of equations? How do you know?
y=7x + 8
y=x + 1
Answer:
yes it is
Step-by-step explanation:
The point (3,8) is not a solution of system of equation. Explanation given below.
What is the system of equation?Simultaneous equations are any equations with the same number of unknowns that may be solved at the same time. The system of equations is a simultaneous equation.
Given system of equation,
y=7x + 8
y=x + 1
To find that the point (3,8) is a solution of system of equation,
we substitute the point to both of these equation and verify if that point is satisfying the equation or not.
In the first equation, x=3 and y =8
we get, 8 = 29
which is contradiction.
In the second equation ;
we get, 8 = 4.
Which is also contradiction.
Therefore, the equations do not have the solution (3 , 8).
To learn more about the system of equation;
brainly.com/question/13729904
#SPJ2
what does 2(3x − 7) + 18 = 10 equal
Answer:
x = 1
Step-by-step explanation:
We have an expression and are asked to find x perhaps?
2(3x - 7) + 18 = 10
To solve this, we need to get x alone.
Distribute :
(2(3x) - 2(7)) + 18 = 10
6x - 14 + 18
Add like terms :
6x + 4 = 10
Subtract 4 from both sides :
6x = 6
Divide 6 from both sides :
x = 1
Answer:
First you do 2x3 and then 2x7 that would be 6x and 14 so add 18 to 14 and that woukd be 32 so Try 32+6x... I would thnk i'm correct Can I also get Branliest..?