Answer:
[tex]a_n=100 \left(\dfrac15\right)^{n-1}[/tex]
Step-by-step explanation:
General equation of geometric sequence: [tex]a_n=ar^{n-1}[/tex]
Given:
a₁ = 100a₂ = 20a₃ = 4[tex]\implies a_1=a=100[/tex]
[tex]\implies a_2=100 \cdot r=20[/tex]
[tex]\implies a_3=100 \cdot r^2=4[/tex]
Common ratio:
[tex]r=\dfrac{a_3}{a_2}=\dfrac{4}{20}=\dfrac15[/tex]
Therefore:
[tex]a_n=100 \left(\dfrac15\right)^{n-1}[/tex]
Is the point (11,5) on the parabola? Show or explain your work.
Answer:
The point (11, 5) is NOT on the parabola.
Step-by-step explanation:
Let [tex](x_0,y_0)[/tex] be any point on the parabola
Let [tex](a, b)[/tex] be the focus
Let [tex]y=c[/tex] be the the directrix
Distance between [tex](x_0,y_0)[/tex] and the focus: [tex]\sqrt{(x_0-a)^2+(y_0-b)^2}[/tex]
Distance between [tex](x_0,y_0)[/tex] and the directrix is [tex]|y_0-c|[/tex]
Given:
focus (6, 4)directrix y = 0Therefore:
Distance between [tex](x_0,y_0)[/tex] and the focus: [tex]\sqrt{(x_0-6)^2+(y_0-4)^2}[/tex]
Distance between [tex](x_0,y_0)[/tex] and the directrix is [tex]|y_0-0|[/tex]
Equate the two expressions and solve for [tex]y_0[/tex]:
[tex]\sqrt{(x_0-6)^2+(y_0-4)^2}=|y_0-0|[/tex]
[tex]\implies (x_0-6)^2+(y_0-4)^}=(y_0-0)^2[/tex]
[tex]\implies {x_0}^2-12x_0+36+{y_0}^2-8y_0+16={y_0}^2[/tex]
[tex]\implies {x_0}^2-12x_0-8y_0+52=0[/tex]
[tex]\implies 8y_0={x_0}^2-12x_0+52[/tex]
[tex]\implies y_0=\dfrac18{x_0}^2-\dfrac{12}{8}x_0+\dfrac{52}{8}[/tex]
[tex]\implies y_0=\dfrac18{x_0}^2-\dfrac32x_0+\dfrac{13}{2}[/tex]
Now rewrite with (x, y):
[tex]\implies y=\dfrac18x^2-\dfrac32x+\dfrac{13}{2}[/tex]
Therefore, this is the equation of the parabola
To determine if the point (11, 5) is on the parabola, input x = 11 into the equation:
[tex]\implies y=\dfrac18(11)^2-\dfrac32(11)+\dfrac{13}{2}[/tex]
[tex]\implies y=\dfrac{41}{8}[/tex]
So the point (11, 5) is NOT on the parabola.
Ryan walked 2 1/2 miles in 3/4 hours find unit
Answer:
2/3
Step-by-step explanation:
Divide 1/2 by 3/4 to get 1/2 x 4/3 = 2/3 mph
what are the missing numbers?
whats 2+2 its so hard
Answer:
4!
Step-by-step explanation:
Please rate 5 stars and give brainlest.
What is the value of x in the equation −6 + x = −5? (1 point)
1
11
-1
-11
Answer:
1
Step-by-step explanation:
-6 + 1 = -5
which statements are true when solving x^2=81
Answer: x
2
=
81
can be written as
x
2
−
81
=
0
by property ,
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
The expression becomes
x
2
−
(
9
)
2
=
0
(
x
−
9
)
(
x
+
9
)
=
0
equating each of the terms with zero we obtain the solution
x
−
9
=
0
and
x
+
9
=
0
the solutions are
x
=
9
or
x
=
−
9
Step-by-step explanation:
Answer:
A) Take the square root of both sides to solve
E) x = ±9
Step-by-step explanation:
Can someone help me pleeeease
Answer:
2 Possible Outcomes
Step-by-step explanation:
This is because you can only get the (x,y) coordinates.
Hello!
Answer:
There are only 2 outcomes
Step-by-step explanation:
This is because when solving a system of equations, your answer will be coordinates (For example>>(x,y)) so you will be getting two numbers, which means two outcomes.
Wish you luck!!
Which of the following is an example of how self-awareness can affect communication?
a.
Self-awareness can help you choose who to communicate with.
b.
Self-awareness can help you decide how to communicate.
c.
Self-awareness can help you choose when to communicate.
d.
All of the above
Answer:
d all if these things are a part of self awareness
Answer:
d. All of the above
Step-by-step explanation:
E2020
A torch and a battery cost £2.50 altogether.
The torch costs £2.00 more than the battery.
What fraction of the total price is the battery's price?
Give your answer in its simplest form.
Answer:
1/10
Step-by-step explanation:
2.50-2=0.5
0.5/2=0.25
0.25+2=2.25
2.5-2.25=0.25
0.25/2.5= 0.1
0.1 = 1/10
x < 1 is the solution to which of the following compound inequalities?
a) x > 3 OR x < 1
b) x < 4 OR x > 1
c) x < 4 AND x < 1
d) x > 3 AND x < 1
As vrea sa încep sa cant îmi place foarte mult muzica Românească
| 3х – 9| = 24
??????????????????????????????????
Answer:
X=11
Step-by-step explanation:
|3x-9|=24
is the same as
3x-9=24
which becomes
3x=33 because you add 9 to both sides
which is
x=11 because you divide by 3
Anita read 150 pages in 5 hours. What is her reading rate in pages per minute?
Answer:
Answer = 0.5 pages per minute.
Step-by-step explanation:
150 ÷ 5 = 30 pages an hour
30 ÷ 60 ( Minutes in an hour ) = 0.5 Pages/ Minute.
Hope this helps.
565, 961, 867, 517, 627, 714, 517, 728
What is the range of these areas in square feet?
Answer:
No Clue
Step-by-step explanation:
Austin works as an electrician. If a job requires Austin to work on weekends, the function C(t)=54t+75 represents the customer's cost, C, in dollars of working t hours on the job. What is the interpretation of the y-intercept?
Answer:
He charges a flat rate of 75, and any extra work will be 54 dollars per hour.
Step-by-step explanation:
Answer:
he charges $75
Step-by-step explanation:
The treasurer counted that there was $200 in the bank account he decided to use 1/2 of the money
Answer:
That means he will have $100
Step-by-step explanation:
Half of 200 is 100
Passes through 0,2 and has a slope of -5/3
Answer:
y = - 1 2/3x + 2
Step-by-step explanation:
Step 1:
y = mx + b Slope intercept Form
Step 2:
y = - 5/3x + b Input Slope
Step 3:
2 = - 5/3 ( 0 ) + b Input x and y
Step 4:
2 = b Multiply
Answer:
y = - 1 2/3x + 2 Input b
Hope This Helps :)
Solve for x
Show work please
Answer:
[tex]\tt x=5[/tex]
Step-by-step explanation:
[tex]\tt 18x-5=13x+4x+1-11[/tex]
[tex]\tt 18x-17x=15-10[/tex]
[tex]\tt x=5[/tex]
~
Divide 300 among Ravi and Isha in the ratio 2:3.
Answer:
Ravi: 120
Isha: 180
Step-by-step explanation:
Think of the ratio as parts. Ravi gets 2 parts while Isha gets 3.
But, we don't know how much each gets. This is written as X.
The ratio of 2:3 can be set up in an equation as 2x and 3x.
We know that the total is 300.
[tex]2x+3x=300\\5x=300\\x=60[/tex]
Ravi has 2 parts:
[tex]2(60)=120[/tex]
Isha has 3 parts:
[tex]3(60)=180[/tex]
The radius of a circle is 7 kilometers. What is the circle's circumference? Use 3.14 for .
Answer:
A circle of radius = 7 or diameter = 14 or circumference = 43.98 kilometers has an area of: 153.9 square kilometers (km²) 1.539 × 10 8 square meters (m²)
Step-by-step explanation:
I need helppp pleaseeeeee!!!!!!!!!!!!!!
Answer:
$5.55
Step-by-step explanation:
Circle the irrational number in the list below. 7.27, 5, 9215, 2196
Answer:
7.27 is the irrational number
Step-by-step explanation:
7.27 can not turn into a fraction because it keeps on repeating
There are no Irrational numbers in the list.
We have a set of numbers - 7.27, 5, 9215, 2196.
We have to circle out the Irrational ones.
What are Irrational Numbers?Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction - p/q where p and q are integers.
According to the question, we have -
7.27, 5, 9215, 2196
Now -
7.27 = [tex]$\frac{727}{100}[/tex] → It is Rational.
5 = [tex]$\frac{5}{1}[/tex] → It is Rational.
9215 = [tex]$\frac{9215}{1}[/tex] → It is Rational.
9215 = [tex]$\frac{2196}{1}[/tex] → It is Rational.
All the numbers are Rational as they can be expressed in the form of p/q.
Hence, there are no Irrational numbers in the list.
To solve more questions on Rational and Irrational numbers, visit the link below-
https://brainly.com/question/20400557
#SPJ2
find the area of the hexagon with a perimeter of 240
Answer:
5985.97
Step-by-step explanation:
A=33
2a2=3·3
2·482≈5985.96759
that describes a way to solve the equation x – 23 = 18
Answer:
One of the ways you could describe the solution is 18+23=x x=41.
Step-by-step explanation:
Answer:
X = 41
▬▬▬▬▬
41 - 23 = 18
23 + 18 = 41x
▬▬▬▬▬
Hope it helps!
Please Mark Brainliest.
Help pleaseeeeeeeeeee
Answer:
angle relationship is co-interior
x = 3.94
Step-by-step explanation:
(34x - 1 ) + 45 = 180 [co-interior angles add up to 180 degrees]
34x - 1 = 135
34x = 134
x= 134/34 =3.94
What kind of shape is created from the cross section seen here on the square pyramid?
HELP IMAGE INCLUDED
a triangle.........................................
Answer:
a rectangular pyramid
Step-by-step explanation:
carry out this experiment
get a sheet of paper, create a square from the sheet, after that divide the square in half. Which shape is formed.
Do mark brainliest
PLZ HELP ASAP! I will mark you brainliest!
Answer:
c for first page. b for second. d for third page
Step-by-step explanation:
The LaSalle High School senior class raised funds for an end of the year cruise getaway. The city gave them a special package for the port fees and taxes - a flat fee of $1,500 for the entire class's port fees and taxes. It costs $367 per student to board the cruise. If your class raised $16,600, how many students can attend?
HELP ME ASAP if ure not sure please dont answer
Answer:
Depends on what you think your instructor is looking for either it is 45 students, or the answer is 41.
Step-by-step explanation:
41 is the answer if you subtract the port fees from the amount raised then divided the remainder by cost per student .
Kenji is playing the video game Dragon Tamer, where players go on adventures finding and training dragons. In the first level of the game, he gets 10 points for finding a Silverthorn Dragon but gets – 6 points when it scorches him with fire. What is Kenji's score at the end of the first level?
Answer:
[tex]Final\ Score = 4\ points[/tex]
Step-by-step explanation:
Given
[tex]Silverthorn\ Dragon = 10\ points[/tex]
[tex]Fire\ Scorches = -6\ points[/tex]
Required
Determine the final score
Final score is calculated as follows:
[tex]Final\ Score = Silverthorn\ Dragon + Fire\ Scorches[/tex]
[tex]Final\ Score = 10\ points -6\ points[/tex]
[tex]Final\ Score = 4\ points[/tex]
Answer:
4
Step-by-step explanation:
Hi, I can use some help wiTh this thanks!
Answer:
Square root of 9 = 3 ! ^^
Step-by-step explanation:
[tex]3*3=9 \\3^{2}=9\\\sqrt{9} = 3[/tex]
^^
Hello everyone good morning may I get ur help in the first attachment~ marking brainliest for the right answer
Answer:
x=1.5
Step-by-step explanation:
triangle JLM is similar to triangle QST
so we know that similar triangles have proportionate sides
so..
JM/LM=QT/ST
4/(6x-3)=2/3
3*4=2(6x-3)
12=12x-6
12x=18
x=1.5
X = 1.5
On paper, I worked it out. Despite the fact that answers have already been offered, this might be used as confirmation that the answers given by other members are correct.
Have a wonderful day.