A geometric sequence is shown below.
2, – 6, 18, – 54, 162, ...
Part A:
Write a recursive relationship for this sequence. Explain how you determined your answer.
Part B:
Write an explicit formula for this sequence.
The diameter at the center of the tower is_ meters. The center of the tower is _meters above the ground
Answer:
think 5 meters
Step-by-step explanation:
Answer:
The diameter at the center of the tower is 4 meters. The center of the tower is 8 meters above the ground.
Step-by-step explanation:
4x^2-y^2+16y-80=0
Completing squares in variable "y": Common factor -1:
4x^2-(y^2-16y)-80=0
4x^2-[(y-16/2)^2-(16/2)^2]-80=0
4x^2-[(y-8)^2-(8)^2]-80=0
4x^2-[(y-8)^2-64]-80=0
Eliminating the brackets:
4x^2-(y-8)^2+64-80=0
Adding like terms (constants):
4x^2-(y-8)^2-16=0
Adding 16 both sides of the equation:
4x^2-(y-8)^2-16+16=0+16
4x^2-(y-8)^2=16
Dividing all the terms by 16:
4x^2/16-(y-8)^2/16=16/16
Simplifying:
x^2/4-(y-8)^2/16=1
The hyperbola has the form:
(x-h)^2/a^2-(y-k)^2/b^2=1
Then:
h=0
k=8
a^2=4→sqrt(a^2)=sqrt(4)→a=2
The diameter (d) at the center of the tower is:
d=2a→d=2(2)→d=4 meters
The center of the tower is 8 (k) meters above the ground.
What is the solution set of the equation j+4/j+2=2−1/j ? Note: j≠0, −2
Answer:
values of j are: 2 , -1
Step-by-step explanation:
In the given case, The solutions are j = -4 and j = 1, and the solution set is {-4, 1}.
The given equation is:
j+4/j+2=2−1/j
We can solve for j by cross-multiplying:
(j+4)(j) = (j+2)(2-1/j)
Expanding the left side and right side, we get:
[tex]j^2 + 4j = 2j + 4 - 2/j[/tex]
Moving all the terms to the left side of the equation, we get:
[tex]j^2 + 2j - 4 = 0[/tex]
We can factor the left side of the equation as:
(j+4)(j-1) = 0
Therefore, the solutions are j = -4 and j = 1.
Note that the given equation is defined when j ≠ 0 and j ≠ -2. Therefore, the solutions are j = -4 and j = 1, and the solution set is {-4, 1}.
Here is a step-by-step solution:
n first move the constant term to the right side of the equation.
j² + 2j = 4
We can then factor the left side of the equation.
(j+4)(j-1) = 0
The solutions are j = -4 and j = 1.
We check that these solutions are valid by substituting them back into the original equation.
j+4/j+2=2−1/j
When j = -4, the left side of the equation is 0/-2 = 0, and the right side of the equation is 2 - 1/-4 = 2 + 0.5 = 2.5.
The equation is satisfied.
When j = 1, the left side of the equation is 5/3, and the right side of the equation is 2 - 1/1 = 2 - 1 = 1. The equation is satisfied.
Therefore, the solutions are j = -4 and j = 1, and the solution set is {-4, 1}.
Learn more about solving equations here:
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in 2 years i will be twice as old as i was 20 years ago how old am I?
Answer:
I am 42 years old
Step-by-step explanation:
Given : In 2 years i will be twice as old as i was 20 years ago.
To Find : Current age
Solution :
Let the current age be x years.
After two years i will be (x+2) years
20 years ago i was (x-20)years
Since we are given that in 2 years i will be twice as old as i was 20 years ago.
⇒[tex]x+2 = 2 (x-20)[/tex]
⇒[tex]x+2 = 2x-40[/tex]
⇒[tex]40+2 = 2x-x[/tex]
⇒[tex]42 = x[/tex]
Thus my current age 'x' = 42 years.
Hence i am 42 years old
Consider parallelogram ABCD. Choose all of the statements which MUST be true.
∠ADB ≅ ∠CBD
ADC + DCB = 180
∠CED ≅ ∠DEA
AE = EC AC = DB
Answer:
The first one is correct the rest are not
Step-by-step explanation:
I don't know if you need an explanation or not.
Answer:
it 1,2,and 4 just took it
Step-by-step explanation:
It takes Francisco 15 minutes to ride his bicycle 4km ,which is the distance from home to school . What is the average speed
Answer:
16 KMH is the correct answer
Step-by-step explanation:
Work out the area of the lawn.
Answer:
68 m^2
Step-by-step explanation:
Area of The entire enclosure ( rectangle)
Area rectangle = L * WL = 7 + 7 = 14W = 10 Area rectangle = 10*(7 + 7)Area of rectangle = 10 * 14Area of rectangle = 140 square meters.Area of the triangle
Area of the triangle = 1/2 b*hArea of the triangle = 1/2 * 8 * 3Area of the triangle= 12 square meters.Area of the Trapezoid
h = 10b1 = 5b2 = 7Formula
Area = (b1 + b2)*h /2Solution
Area = (5 + 7)*10/2Area = 12*10/2Area = 60Area of the Lawn
Area of the Lawn = rectangle area - triangle area - trapezoid areaArea of the lawn = 140 - 12 - 60Area of the lawn = 68 m^2Write the first five terms of the the sequence defined by the explicit formula an=72(1/3)^n-1
[tex]a_n=72\left(\dfrac{1}{3}\right)^{n-1}\\\\\text{Put}\ n=1,\ n=2,\ n=3,\ n=4,\ n=5\ \text{to the equation}:\\\\n=1\to a_1=72\left(\dfrac{1}{3}\right)^{1-1}=72\left(\dfrac{1}{3}\right)^0=72(1)=72\\\\n=2\to a_2=72\left(\dfrac{1}{3}\right)^{2-1}=72\left(\dfrac{1}{3}\right)^1=72\left(\dfrac{1}{3}\right)=\dfrac{72}{3}=24\\\\n=3\to a_3=72\left(\dfrac{1}{3}\right)^{3-1}=72\left(\dfrac{1}{3}\right)^2=72\left(\dfrac{1}{9}\right)=\dfrac{72}{9}=8\\\\n=4\to a_4=72\left(\dfrac{1}{3}\right)^{4-1}=72\left(\dfrac{1}{3}\right)^3=72\left(\dfrac{1}{27}\right)=\dfrac{72}{27}=\dfrac{8}{3}\\\\n=5\to a_5=72\left(\dfrac{1}{3}\right)^{5-1}=72\left(\dfrac{1}{3}\right)^4=72\left(\dfrac{1}{81}\right)=\dfrac{72}{81}=\dfrac{8}{9}\\\\Answer:\ \boxed{72,\ 24,\ 8,\ \dfrac{8}{3},\ \dfrac{8}{9}}[/tex]
Answer:
The first five terms are as follows:
72, 24, 8, 2.66, 0.88
Step-by-step explanation:
1) Explicit formula:
[tex]72 * 1/3^{n-1}[/tex]
2) Simply replace "n" with 2,3,4 and 5 in order to find the numbers associated with these terms.
a(1) = 72
a(2) = 24
a(3) = 8
a(4) = 2.66
a(5) = 0.88
Note:
In the explicit formula the first term is already provided, so you do not have to find the first term if it has already been given.
A recursive rule for a geometric sequence is a1=3;an=1/2an−1.
What is the explicit rule for this sequence?
Enter your answer in the box.
[tex]\text{The explicit rule of geometric sequence}\\\\a_n=a_1 r^{n-1}\\------------------------------\\\text{We have the recursive form}\ a_1=3,\ a_n=\dfrac{1}{2}\cdot a_{n-1}.\\\\\text{Therefore}\ r=\dfrac{1}{2}.\ \text{Substitute:}\\\\\boxed{a_n=3\left(\dfrac{1}{2}\right)^{n-1}}[/tex]
The probability that a student at certain high school likes art is 36%. The probability that a student who likes art also likes science is 21%. Find the probability that a student chosen at random likes science given that he or she likes art. Round to the nearest tenth of a percent.
Answer: Probability that a student chose at random likes science given that he or she likes art is 58%.
Step-by-step explanation:
Since we have given that
Probability that a student at certain high school likes art =[tex]P(A)[/tex] = 36%
Probability that a student who likes art also likes science= [tex]P(A\cap S)[/tex] = 21%
We need to find the value of probability that a student chosen at random likes science given that he or she likes art.
As we know the formula for "Conditional Probability" :
[tex]P(S\mid A)=\frac{P(A\cap S)}{P(A)}\\\\P(S\mid A)=\frac{21}{36}\\\\P(S\mid A)=0.58\\\\P(S\mid A)=58\%[/tex]
Hence, Probability that a student chose at random likes science given that he or she likes art is 58%.
Answer with explanation:
A= Art
S= Science
P(A)= 36%
P (A ∩ S)=21%
We have to find ,[tex]P(\frac{S}{A})[/tex].
[tex]P(\frac{S}{A})=\frac{P(S\cap A)}{P(A)}\\\\P(\frac{S}{A})=\frac{\frac{21}{100}}{\frac{36}{100}}\\\\P(\frac{S}{A})=\frac{21}{36}=\frac{7}{12}[/tex]
In terms of Percentage , Required Probability
[tex]=\frac{7}{12}\times 100\\\\=58.34[/tex]
= 58.34 %
You invest $1,000 in an account at 2.5% per year simple interest. How much will you have in the account after 4 years? Round your answer to the nearest whole dollar
Answer:
1000*(1,025)=1025 $ the 1st year
After 4 years, the account will be 4* 1025=4100
Answer:
Amount after 4 years = 1000+100=$1100
Step-by-step explanation:
To solve this, we will simply use the simple interest formula;
S.I = PRT/100
where p=principal
R=rate and T= time
S.I = simple interest
From the question
Principal=$1000
Rate = 2.5 and time=4
We can now proceed to inert the values into the equation
S.I = 1000×2.5×4 /100
Two zeros at the numerator will cancel-out the two zeros at the denominator, Hence;
S.I = 10×2.5×4
S.I =$100
Amount after 4 years = 1000+100=$1100
To arrive to his appointment on time, Mr. Jones had to drive all the way from his home with the average speed of 60 mph. Due to heavy traffic, he was driving 15 mph slower than he planned and arrived to the appointment 20 minutes later. How many miles from Mr. Jones' home was his appointment?
Answer:
60
Step-by-step explanation:
Mr Jone's home distance is 60 miles away from his appointment place .
Distance = Speed x Time
Distance planned & distance covered is same.
Time covered is 20 minutes more than time planned ; Actual Speed is 15mph lower than planned speed (60 mph) , ie = 45 mph.
Let the planned time be = t , Actual time = t + 20 mints = t + 20 / 60 = t + 1/3 = 4 t / 3
As distance is same : 60 t = 45 ( 4t / 3)
60t = 60t
t = 1 hour
Distance = Speed x Time :
60 x 1 = 45 ( 4/3) = 60 miles
To learn more, refer https://brainly.com/question/9005902
The point located (3,-1) is reflected across the y-axis.What are the coordinates of the reflected point?
Answer:
(3,1)
Step-by-step explanation
All you have to do is change the y-coordinate to its opposite. Ex- (-2,3) coordinates of reflection. (-2,-3)
if 3y - 7= 23, then y =
Answer:
y=10 is the value of y
Step-by-step explanation:
The given equation is
3y - 7 =23 ..............................(i)
We have to find out the value of y from the equation (i)
Now the equation is
3y - 7 = 23
adding 7 on both sides of the equation
3y - 7 + 7 = 23 + 7
3y = 30
as we need the value of y so
Dividing both sides of the equation by 3
[tex]\frac{3y}{3}=\frac{30}{3}[/tex]
which will lead us to
y = 10
so this is the value of y
Answer:
y=10
Step-by-step explanation:
3y-7 =23
3y = 23+7 -move 7 over
3y=30 -add remaing
3y/3 =30/3 -divide 3
y=10 -answer
check work 3x10-7=23
NEED HELP!! 30 POINTS! HAS TO BE CORRECT AND NEED THE ANSWER NOOW!
Answer: options b and c
Step-by-step explanation:
∠ACD is supplementary to ∠ACE given
∠ACD is supplementary to ∠BCD given
⇒ ∠ACE is supplementary to ∠BCD transitive property
∠ACD ≅ ∠BCE given
⇒ ∠BCE is supplementary to ∠ACE substitution
and ∠BCE is supplementary to ∠BCD substitution
********************************************************************************
multiple choice options:
a) ∠ACE is supplementary to ∠BCD False
b) ∠BCE is supplementary to ∠ACE TRUE
c) ∠BCD is supplementary to ∠BCE TRUE
d) ∠ACE ≅ ∠BCE False
e) ∠BCD ≅ ∠ACE False
IN AN ATHLETIC EVENT 60 STUDENTS OF A SCHOOL PARTICIPATED LAST YEAR . THIS YEARTHE NUMBER OF STUDENTS OF THAT SCHOOLK TAKING PART IS DECREASED BY 5 % . FIND THE NUMBER OF STUDENTS TAKING PART IN THE ATHLETIC EVENT THIS YEAR
Answer: the number of students participating this year is 57.
Step-by-step explanation:
5% of 60 is 3.
60-3=57
I believe this is correct :)
Answer: Number of students participated this year = 57
Step-by-step explanation: Number of student participated last year = 60
Decreased by 5%
Decreased in number = 5% of 60 = 0.05x 60 =3
Number of Students this year = Number of student last year - decreased
= 60 - 3
= 57
The length of a rectangle is three times its width. The perimeter of the rectangle is at most 112cm. Which inequality models the relationship between the width and the perimeter of the rectangle.
Answer: w ≤ 14 cm , L ≤ 42 cm
Step-by-step explanation:
width (w): w
Length(L): 3w
Perimeter (P) = 2w + 2L
P ≤ 112
2w + 2L ≤ 112
2(w) + 2(3w) ≤ 112
2w + 6w ≤ 112
8w ≤ 112
w ≤ 14
If the mass of a material is 45 grams and the volume of the material is 11 cm^3, what would the density of the material be?
I need the answer and than units
Answer:
Density of material would be 4.09 [tex]g/cm^3[/tex]
units is [tex]g/cm^3[/tex]
Step-by-step explanation:
Given: The mass of a material is 45 grams and the volume of the material is 11 cubic centimeter
Density is defined as mass per unit volume.
It is given by:
[tex]p= \frac{m}{V}[/tex] where p is the density , m is the mass and V is the volume of the material respectively.
Here, Density is expressed in grams per centimeter cubed (g/cubic cm)
Here, m = 45 g , V = 11 cubic cm
We get;
[tex]p= \frac{45}{11}[/tex] = 4.09 [tex]g/cm^3[/tex]
therefore, density of a material would be, [tex]4.09 g/cm^3[/tex]
and its units is [tex]g/cm^3[/tex]
the force on an object is given by the equation f=ma. in this equation, F is the force, m is the mass, and a is the acceleration. which answer hows this equation solved for mass?
A. m=a/f
B. m=fa
C. m=f/a
D. m= m/f
Answer:
C. mass = force / accellaration
Step-by-step explanation:
Find a polynomial f(×) with leading coefficient 1 such that the equation f(×)=0 has The given roots and no others . Root 1, -5 multiplicity 2,1
Answer:
[tex]x^{3} +3x^{2}-9x+5 = 0[/tex]
Step-by-step explanation:
We are given that the only roots of the given polynomial f(x) are 1 and -5 with multiplicity (the number of times the roots are repeating) 2 and 1 respectively.
Also, it is provided that the function satisfy that f(x)=0.
So, comparing the two information we have that,
f(x) = 0 and 1, -5 are the roots of f(x),
i.e [tex](x-1)^{2} \times (x+5) = 0[/tex]
i.e. [tex](x^{2} +1-2x) \times (x+5) = 0[/tex]
i.e. [tex]x^{3} +3x^{2}-9x+5 = 0[/tex]
Also, we can see that ths polynomial has leading co-efficient 1 i.e. the co-efficient of highest degree variable i.e. x^{3}.
Hence, the polynomial having leading co-efficient 1 and roots 1, -5 is [tex]x^{3} +3x^{2}-9x+5 = 0[/tex].
Given that AD and BC bisect each other at E, which of the following justifies ΔABE ≅ ΔDCE? A. Definition of Segment Bisector B. SSS Postulate C. Definition of Congruent Triangles D. SAS Postulate
Answer:
A. Definition of Segment Bisector
Step-by-step explanation:
One have to understand that according to data given in the question, we only know that AD and BC are bisected at the intersection point E. Now two triangles are formed which are ΔABE and ΔCDE.
Now by definition of segment bisector, we know that
AE = DE
BE = CE
Now, what is to understand that this information is based on the clue which is given in the question that AD and BC bisects each other. All the remaining options like SAS postulate, SSS postulate and definition of congruent triangle are not useful here if we don't know that these two lines bisect each other. Because, the fact that
AE = DE
BE = CE
is only derived by the information that AD and BC bisect each other. Now we can derive SSS and SAS postulate both because we know by the theorems of trigonometry that if two sides of two different triangles are equal in length, then their third sides must be equal, or when two lines bisect or intersect each other, vertical angles are always equal. So the answer is A.
The movie theater sold 56 boxes of gummy bears during the week.At this rate how many boxes of gummy bears will the movie theater sell in a 6 week period
Answer:
Step-by-step explanation:
At a sales rate of 56 boxes of gummy bears per week, the movie theater will sell
= 56 × 6
= 336 boxes
This is on the assumption that the rate is sustained.
At that rate (of 56 boxes per week), the company (movie theater) would have sold 336 boxes.
What is the solution to 4+5e^(x+2)=11?
(Answers Below)
Answer:
x = ln (7/5) - 2
Step-by-step explanation:
4+5e^(x+2)=11
Subtract 4 from each side
4-4+5e^(x+2)=11-4
5e^(x+2)=7
Divide by 5 on each side
5/5e^(x+2)=7/5
e^(x+2)=7/5
Take the natural log on each side
ln (e^(x+2))= ln (7/5)
x+2 = ln (7/5)
Subtract 2 from each side
x = ln (7/5) - 2
Answer:
option 1
Step-by-step explanation:
Mackenzie wrote the following paragraph proof for the Vertical Angles Theorem: Line segment NT intersects line segment MR forming four angles. Angles 1 and 3 are vertical angles. Angles 2 and 4 are vertical angles. The sum of angle 1 and angle 4 and the sum of angle 3 and angle 4 are each equal to 180 degrees by the definition of supplementary angles. The sum of angle 1 and angle 4 is equal to the sum of angle 3 and angle 4 _________________. Angle 1 is equal to angle 3 by the subtraction property of equality. Which phrase completes the proof? by construction using a straightedge by the definition of a perpendicular bisector by the transitive property of equality. by the vertical angles theorem
by the transitive property of equality
Answer:
the transitive property of equality
Step-by-step explanation:
What is the solution to this system of equations?
Answer: No solutions
The two lines are parallel. They never intersect. You need a point of intersection to have a solution. Note how the lines have the same slope (2) but different y intercepts (3 and -4). This fact backs up the idea the lines are parallel.
The system has no solution, so we consider this system to be inconsistent. If we were to convert each equation into standard form, then we would have 2x-y = -3 and 2x-y = 4. If we made z = 2x-y, then z = -3 and z = 4 at the same time; but z is only one number at a time. This is one way to see the inconsistency.
Which input value produces the same output value for the two functions on the graph?
X= -3
X= -1
X= 1
X= 3
Answer:
D. [tex]x=3[/tex]
Step-by-step explanation:
We have been graph of two functions on coordinate plane. We are asked to find the input value that produces the same output value for the two functions.
To find the input value that produces the same output value for the two functions, we need to find x-value for which both functions has same y-value.
Upon looking at our given graph, we can see that at [tex]x=3[/tex], the value of both functions is [tex]-1[/tex].
Therefore, our required input value is [tex]x=3[/tex] and option D is the correct choice.
If leo is 6 years old and max is 12 years, how many years would it be until max is 3 times as old as leo
Answer:
Step-by-step explanation: max is already 3 times older than max. 6*3=18 and 6+12=18
Final answer:
Max cannot be 3 times as old as Leo based on the given information.
Explanation:
To find out how many years it will be until Max is 3 times as old as Leo, we can set up an equation.
Let's assume that it takes x years for Max to be 3 times as old as Leo.
So, Max's age in x years will be 12 + x, and Leo's age in x years will be 6 + x. According to the problem, Max will be 3 times as old as Leo, so we can write the equation as: 12 + x = 3(6 + x).
To solve for x, we can start by simplifying the equation: 12 + x = 18 + 3x. Now, let's isolate the variable x by moving all the x terms to one side and the constant terms to the other side. Subtracting x from both sides gives us: 12 = 18 + 2x. Subtracting 18 from both sides gives us: -6 = 2x. Finally, dividing both sides by 2 gives us: -3 = x.
This means that it will take -3 years for Max to be 3 times as old as Leo. However, since time cannot be negative, we can conclude that it is not possible for Max to be 3 times as old as Leo based on the given information.
Johns house is 12 miles away from school he is 2/3 the way there how many miles has he walked
Please help & explain 4th grade math
Answer:2/9
Step-by-step explanation:
If you count the lines form zero like 0/9 1/9 2/9 3/9 4/9 5/9 6/9 7/9 8/9 then 1 is the whole so that would be 9/9
Answer:
2/9 is the answer
In an effort to control vegetation overgrowth, 139 139 rabbits are released in an isolated area free of predators. After 2 2 years, it is estimated that the rabbit population has increased to 556 556 . Assuming exponential population growth, what will the population be after another 6 6 months? Round to the nearest rabbit.
Answer:
197
Step-by-step explanation:
Initial population of rabbit is 139
after 2 years , rabbit population is 556
For exponential growth use y=ab^x
where a is the initial population
x is the time period
b is the growth rate, y is the final population
a= 139 is already given
when x=2, the value of y = 557
plug in all the values in the formula and find out 'b'
[tex]y=ab^x[/tex]
[tex]557=139(b)^2[/tex]
Divide both sides by 139
[tex]\frac{557}{139} =b^2[/tex]
take square root on both sides
b=2.00180 and b=-2.00180
growth factor cannot be negative
So b= 2.0018
The equation y=ab^x becomes
[tex]y=139(2.0018)^x[/tex]
To find population after 6 months
1 year = 12 months
so 6 months = 0.5 years
we plug in 0.5 for x
[tex]y=139(2.0018)^{0.5}[/tex]
y= 196.66
so population after 6 months = 197