Answers
The value of x in this geometric sequence is equal to √2.
How to calculate the nth term of a geometric sequence?In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:
aₙ = a₁rⁿ⁻¹
Where:
aₙ is the nth term of a geometric sequence.r represents the common ratio.a₁ represents the first term of a geometric sequence.For this exercise, we would formulate an equation from the common ratio of this geometric sequence as follows:
r = a₂/a₁ = a₃/a₁
Substituting the given parameters into the common ratio formula, we have;
1/√X + 1 = √x - 1/1
Next, we would take the square of both sides, we have:
1/x + 1 = x - 1/1
Cross-multiplying, we have:
(x + 1)(x - 1) = 1
x² - x + x - 1 = 1
x² - 1 = 1
Adding 1 to both sides, we have:
x² - 1 + 1 = 1 + 1
x² = 1 + 1
x² = 2
x = √2
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Related Questions
Malia put 12 photos into an album. She split the photos evenly among p pages. Write an expression that shows how many photos are on each page.
Answers
All of the following expressions represent the sum of n and itself, except.
O2n
On²
On+n
Answers
All of the following expressions represent the sum of n and itself, except n²
To solve his problem, we need a brief idea about algebraic operations like summation, multiplication, etc.
When we add two or more same algebraic digits we have to just add their coefficients. Otherwise, it remains the same.
Example :
x + 2x + 4x = 6x [ 1 + 2 + 4 = 7; as 1,2,4 are the coefficient of x, 2x, 4x ] x + 2y + z = x + 2y + z ( remains unchanged as they all are different numbered )Here 2n = n + n, the sum of n and itself but n² = n × n, which is the multiplication of n and itself,
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what is the equation of a line that is parallel to line y=3x+5 and goes through the point (6,-7)
Answers
The equation of a line that is parallel to line y=3x+5 and goes through the point (6,-7) is y = 3x + 2
What is equation of line ?A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system. The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line. Any line's equation can be used to determine whether a given point is on the line or not.A linear equation with a degree of one is the equation for a line.
Given that : the equation of a line is parallel to line y=3x+5 and goes through the point (6,-7)
y=3x+5 is the equation for the given line.
This type of line is called a slope intercept. The line has a slope of m=3.
The slope of parallel lines is equal. As a result, all lines with slope m=3 will be perpendicular to one another.
y=3x+2 is an example of a line that is parallel to the supplied line.
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Toilet rolls come in a pack of 4 and 9 the 4-pack is priced at £2.04 and the 9- pack is priced at £4.68 . By calculating the price per roll, determine which pack is better value
Answers
4pack price plus 9pack price
so it implies that 2.o4+4.68=6.72
Pls help!!
Using the following graph, write the equation of a line that is parallel to the given line and passes through the point (0, 0).
(Write your answer is slope intercept form. The y= is already typed for you, so only type the remainder of the equation using NO spaces!)
Answers
Answer:
0
Step-by-step explanation:
because the rule says have u understand
Find the measure of each arc. For each arc, write two or more complete sentences explaining which theorem or postulate you used to find your answer. Include your equations and calculations in your final answer.
m arcRPQ
Answers
Answer:
arc RPQ = 305°
Step-by-step explanation:
• the angle at the centre is equal to the measure of the arc that subtends it.
arc RP = ∠ ROP = 125°
∠ QOS and ∠ ROP are vertically opposite angles and are congruent, so
∠ QOS = 125° and so arc SQ = 125°
RS is a straight angle , then
∠ POS = 180° - 125° = 55°
arc PS = 55° ( arc subtending the angle at centre
Then
arc RPQ = RP + PS + SQ = 125° + 55° + 125° = 305°
i need help with this question 20 points
Answers
Answer:
I think the answers are the last two.
Step-by-step explanation:
A rational number is any faction with a denominator not being 0. For example, 1/2, 1/5, 3/6, etc. Also, the number 0 is also a rational number.
If you think any other ones are also the answer, just use my explanation to help it clear stuff up. :)
help me i don’t know how to do this help me please
Answers
Step by step
We know the two triangles are similar
We are looking for EG (x)
Line AB is similar to EF with ratio 100/90
Line AC is similar to EG with ratio 10/x
So if they are similar we can do our equation as 100/90 = 10/x
Cross multiply
100x = 900
Divide both sides by 100 to solve for x
100/100 x = 900/100
x = 9
My triangles in my attachment are not drawn to size but this is how I find which sides are similar for my equation
I hope this helps
Guys help!!! I have to create a other title for the book The call of the wild. Help me figure out titles I should use and why. Write a well-developed paragraph explaining why the title you have chosen suits the book.
Answers
You do not need to listen to my opinion but I think another excellent title could be Survival (Man Vs Dog).
And so here is an explanation of this title: The book may be for young adults, but it truly shows a dark trip to human nature and a species that can be noble as well as cruel and insensitive. Buck, the protagonist, is a dog who has been kidnapped and placed as a sled dog in the 19 century Klondike Gold Rush. It is Buck's loyalty and instinct that helps him return to his owners which forms the plot of the story and the assumptions are able to make about the inhumanity of humans and the very real loyalty and humanity Buck shows.
Sorry for taking so long:)
Select whether ←→ A B and ←→ C D are parallel, perpendicular, or neither. Graph each line on a separate sheet of paper to verify your answer. A ( − 6 , − 9 ) , B ( 8 , 19 ) , C ( 0 , − 4 ) , D ( 2 , 0 )
Answers
The slope of AB = 2
The slope of CD = 2
Both lines are parallel lines.
How to Determine Parallel and Perpendicular Lines?The lines that are perpendicular to each other have slope values that are negative reciprocal of each other.
For example, if the a line's slope is a, the line that is perpendicular to it will have a slope of -1/a. This is because the negative reciprocal of a is -1/a, and (a)(-1/a) = -1.
On the other hand, the lines that are parallel to each other will have the same slope value.
Given the following:
A(−6 , −9)
B(8, 19)
C(0, −4)
D(2, 0)
Find the slope (m) of AB:
Slope of AB = (19 -(-9))/(8 -(-6))
Slope of AB = 28/14
Slope of AB = 2
Find the slope (m) of CD:
Slope of CD = (0 -(-4))/(2 - 0)
Slope of CD = 4/2
Slope of CD = 2
The graph of both lines are shown below.
Thus, the slope of AB and CD are the same, therefore, we can conclude that lines AB and CD are parallel to each other.
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the number of people arriving for treatment at an emergency room can be modeled by a poisson process with a rate parameter of five per hour. what is the probability that exactly four arrivals occur during a particular ""half an hour""?
Answers
There is a 0.087 = 8.73% chance that four arrivals will occur at the same half-hour.
What is defined as the Poisson's distribution?The Poisson is a discrete distribution that calculates the likelihood of a given number of events occurring in a given time period.The probability that X is the number of successes of a random variable in a Poisson distribution is given by the following formula: P(X = x) = (e∧(-μ)× μˣ) / x!In which case,
x represents the number of successes.
The Euler number is e = 2.71828 = 2.72
μ is the average over the given time interval.
With a rate parameter of five per hour, the Poisson process is used.
So, μ = 5
The likelihood of exactly four arrivals occurring at the same time;
This is known as P(X = 4).
Put the values in the formula;
P(X = x) = (e∧(-μ)× μˣ) / x!
P(X = 4) = (2.72∧(-5)× 5⁴) / 4!
Simplifying the equation;
P(X = 4) = 0.08736
P(X = 4) = 8.73%
0.087 = 8.73% chance that exactly four arrivals happen during a specific half -hour.
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one side of rectangle is 5cm than the other side. its perimeter is 38 cm. find the measure of the sides
Answers
The measure of the sides of rectangle is 14cm.
What is rectangle?Each pair of neighboring sides in a rectangle are perpendicular, making it a special case of a parallelogram. A parallelogram is a specific type of trapezium, also referred to as a trapezoid in North America, in which the lengths of the two pairs of opposite sides are parallel. A quadrilateral with four right angles is a rectangle. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equal sides.
Given that,
One side of rectangle is 5cm than the other side.
Its perimeter is 38 cm.
P = 2b +2 h
38= 2b+ 2(5)
38= 2b+ 10
38-10= 2b
28= 2b
b = 28/2
b= 14cm.
Therefore, the measure of the sides is 14cm.
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The graph shows the temperature of ice cream in an ice chest during an overnight trip. What is the domain of this function?
The domain is negative 10 through 30.
The domain is all integers from negative 10 through 30.
The domain is all real numbers 0 through 30.
The domain is all integers from 0 through 30.
Answers
The domain of this function is that: C. the domain is all real numbers 0 through 30.
What is a domain?A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values (numbers) to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.
How to identify the domain of this graph?The horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
By critically observing this graph of a function shown, we can reasonably infer and logically deduce the following:
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Angela, Emily, and Christina are on their school’s soccer team. The table below shows the number of shots each player made and missed.
Answers
The ratio of shots made to the shots missed for each player will be:
Angela = 4:1
Emily.= 3:1
Christina = 7:3
How to illustrate the ratio?It should be noted that from the information given, Angela made 12 shots and missed 3 shots. Therefore the ratio is:
= 12/3
= 4/1
= 4:1
Emily made 15 shots and missed 5 shots. Therefore the ratio is:
= 15/5
= 3/1
= 3:1
Christina made 21 shots and missed 9 shots. Therefore the ratio is:
= 21/9
= 7/3
= 7:3
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"if i flip a coin, i have a 50 percent chance that it will land on heads." in this statement, even after the first coin flip, we still have a 50 percent chance that the next flip will result in a head. this statements interprets "probability" as:
Answers
The probability of getting heads on both occasions will be 0.25.
How to calculate the probability?It should be noted that probability simply means the likelihood that a particular event will happen.
In this case, if I flip a coin, i have a 50 percent chance that it will land on heads and after the first coin flip, we still have a 50 percent chance that the next flip will result in a head.
The probability will be:
= P(head) × P(head)
= 50% × 50%
= 1/2 × 1/2
= 1/4
= 0.25
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write a mathematical sentence that expresses the information below use s as your variable mr.jones algebra class has too many students in it. if each class were split exactly
Answers
When the class were split exactly in equal parts to form 3 be classes each class would have no more than 14 students, the expression is s / 3 <= 14.
What is an expression?It should be noted that an expression is simply used to illustrate the relationship between the variables that are given.
From the mr. Jones algebra class has too many students in it and each class were split exactly in equal parts to form 3 be classes each class would have no more than 14 students.
The expression will be let the total students be represented by s. This will be:
s / 3 <= 14
The expression is s / 3 <= 14.
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Write a mathematical sentence that expresses the information below use s as your variable mr.jones algebra class has too many students in it. if each class were split exactly in equal parts to form 3 be classes each class would have no ore than 14 students
Alice, raul, and jane are baking cookies together, alice brought 2.5 cups of flour, raul brought 1 1/4 cups of flour and jane brought 3/4 cups of flour. how many cups of flour they have all together? show all work.
Answers
The total cups of flour Alice, Raul and Jane have altogether is equal to 6.
We can determine the number of cups of flour they have all together by the addition of the fractions brought by each one of them.
First, we convert the decimal value of 2.5 into fraction form;
2.5 = 2.5/1
Multiplying and dividing both sides by 10;
25/10 = 5/2
Now we add the fractions as follows;
Total number of cups of flour = 5/2 + 11/4 + 3/4
We Multiply 5/2 by 2 to get the same denominator as the other values;
5×2 / 2×2 = 10/4
10/4 + 11/4 + 3/4 = 6
Therefore, the total number of cups of flour they have altogether is calculated to be 6.
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Mia sells headbands for $8.50 each. The
situation can be represented by y = 8.50x
where x is the number of headbands sold and
y is the amount of money collected. Does this
situation represent a function?
Answers
Answer:
Yes
Step-by-step explanation:
This is a linear function, which you can see if you graph it. It is in the form of y = mx + b where be = 0 and the slope is 8.5.
29 less than -10 times a number is equal to -18 times the number plus 91
Answers
Answer:
-10x - 29 = -18x + 91
x = 15
Step-by-step explanation:
29 less than -10 times a number is equal to -18 times the number plus 91:
-10x - 29 = -18x + 91
add 21 to both sides:
-10x - 29 + 29 = -18x + 91 + 29
-10x = -18x + 120
add 18x to both sides:
-10x + 18x = -18x + 120 + 18x
8x = 120
divide both sides by 8:
8x/8 = 120/8
x = 15
A bike was reduced by 20% in a sale. If it was £520 what was the original price
Answers
Answer:416
Step-by-step explanation:520x.8=416
Answer:
Original price = 416.
i hope this helps
complete the table of values for y = 1 over x
Answers
The table of values for the given equation, y = 1/x, is
x y
-3 -1/3
-2 -1/2
-1 -1
0 ∞
1 1
2 1/2
3 1/3
Table of values of an equationFrom the question, we are to determine the table of values for the given function
The given equation is y = 1/x
We will determine the values of y for certain values of x
When x = -3
y = 1/x
y = 1/-3
y = -1/3
When x = -2
y = 1/x
y = 1/-2
y = -1/2
When x = -1
y = 1/x
y = 1/-1
y = -1
When x = 0
y = 1/x
y = 1/0
y = ∞
When x = 1
y = 1/x
y = 1/1
y = 1
When x = 2
y = 1/x
y = 1/2
When x = 3
y = 1/x
y = 1/3
Thus,
The table of values is
x y
-3 -1/3
-2 -1/2
-1 -1
0 ∞
1 1
2 1/2
3 1/3
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15≥3x-3>-12
What would the answer to this be
Answers
Answer:
-3 < x ≤ 6
(-3, 6]
Step-by-step explanation:
15 ≥ 3x - 3 > -12
+3 +3 +3
------------------------
18 ≥ 3x > -9
÷3 ÷3 ÷3
-------------------
6 ≥ x > -3
-3 < x ≤ 6
(-3, 6]
I hope this helps!
Use the Law of Detachment to make a conclusion. If a person wants to get a car, that person must buy car insurance. Jayla wants to get a car. A. Jayla has car insurance. B. Jayla has her driver's license. C. Jayla must get her driver's license. D. Jayla must buy car insurance.
Answers
According to the law of detachment, if a person wants to get a car, that person must buy car insurance, since Jayla wants to get a car, D. Jayla must buy car insurance.
What is the law of detachment?It should be noted that the law of detachment states that if P leads to Q and Q is true, then Q must be true.
In this case, if a person wants to get a car, the person must buy car insurance. Without this it's impossible to buy the car. Therefore, this illustrates that the correct option is that Kayla must also get the insurance.
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Use the following function rule to find f(2).
f(x) = 4 + x
f(2)=
Answers
4 + x = 4 + 2 = 6
Answer = 6
4+2=6
Please quickly help me figure this out
Answers
The final expression of the simplified version is 28x + 8y + 2.
What is the simplified version?We know that, to simplify means to obtain the lowest possible form of the of the expression. The expression is written in its simplest form when there are no more ambiguities left in the way that it is written.
Given the expression;
-2(3x + 12y - 5 - 17x - 16y + 4)
We can now expand the expression to have;
-6x - 24y + 10 + 34x + 32y - 8
This could further simplify to
-6x + 34x - 24y + 32y + 10 - 8
To obtain the final simplified expression, we have;
28x + 8y + 2
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hey yall my question is: how do u divide 5 600 in the ratio:
4: 5: 7
:)
Answers
explanation
4/16×5600=1400
5/16×5600=1750
7/16×5600=2450
therefore first ratio over total ratio multiplied by number. use the same approach for the others
Kylie just accepted a job at a new company where she will make an annual salary of $67000. kylie was told that for each year she stays with the company, she will be given a salary raise of $3000. how much would kylie make as a salary after 3 years working for the company? what would be her salary after tt years?
Answers
Since the situation can be since as an arithmetic sequence, her salary after 3 years is $73,000. After t years, her salary is a function of t, that is a(t) = 64000 + 3000 t
The given situation can be seen as an arithmetic sequence. The nth term of an arithmetic sequence is given by the formula:
a(n) = a(1) + (n - 1) . d
Where:
a(1) = the first term
d = the common difference.
The problem can be translated into an arithmetic sequence with:
a(1) = $67000
d = $3000
Kylie's salary after 3 years is a(3),
a(3) = a(1) + (3 - 1) . d
a(3) = Kylie's salary + 2 . 3000 = 73000
Hence, after 3 years, Kylie's salary is $73,000
Her salary after t years, means n = t. Therefore,
a(t) = a(1) + (t - 1) . d
a(t) = 67000 + (t -1) . 3000
a(t) = 64000 + 3000 t
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whats the answer to this combined terms
y−(−3y)
Answers
Answer:
Add y and 3y
= 4y
Step-by-step explanation:
The speed limit on a road is listed at 65 miles per hour. The car’s speedometer reads 63 miles per hour. Is it possible that this car is going over the speed limit?
Answers
It is not possible for the car to go over the speed limit as maximum error represent value of speed limit less than 65 miles per hour.
As given in the question,
Maximum error on the reading of speedometer =1.6%
Speed limit on a road is 65 miles per hour
Reading of a speedometer = 63 miles per hour
As per the error in the speedometer it can be more or less by 1.6%
To check speed limit
If it more
Speed limit = 63 + (1.6% of 63)
= 63 + 1.008
= 64.008 miles per hour < 65 miles per hour
If it less
Speed limit = 63 - (1.6% of 63)
= 63 -1.008
= 61.992 miles per hour < 65 miles per hour
Therefore, it is not possible for the car to go over the speed limit as maximum error represent value of speed limit less than 65 miles per hour.
The complete question is:
The reading on a car speedometer has 1.6% maximum error the speed limit on a road is listed 65 miles per hour.
The car’s speedometer reads 63 miles per hour. Is it possible that this car is going over the speed limit?
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5. Please verify correct
Answers
Our function is a parabola, therefore, it has only one critical point which is its vertex. Since the coefficient of the squared term is negative, the vertex is the maximum point.The critical points of a function are given by the zeros of the first derivative. The first derivative of our function is:
[tex]f^{\prime}(x)=-6x-18[/tex]The solutions for the following equation are the critical points of the original function:
[tex]-6x-18=0\implies x=-3[/tex]The maximum point happens at x = - 3.
To find the corresponding value, we just have to evaluate x = - 3 into our function:
[tex]f(-3)=-3(-3)^2-18(-3)-26=1[/tex]The maximum value of the function is 1, and it occurs at x = - 3.
Answer: The function has a maximum value
The function's maximum value is 1
The function's maximum value occurs at x=-3
Step-by-step explanation:
Given equation: [tex]g(x) = -3x^ - 18x - 26[/tex]
We shall use the differentiation method to find the answer.
Differentiating the equation, we get [tex]g'(x) = - 6x - 18[/tex]
equating g'(x) = 0,
[tex]-6x - 18 = 0\\-6x = 18 \\x = -3[/tex]
Hence the minimum/ maximum value of the function lies in x = -3
on equating x>-3, g'(x) is negative
on equating x<-3, g'(x) is positive
this proves that first, the function was increasing and after x = -3, the function started to decrease hence at x=-3, the function g(x) was at its maximum value
The function's maximum value at x=-3 is
[tex]g(x) = -3x^2 - 18x - 26\\g(-3) = -3(-3)^2 - 18(-3) - 26\\g(-3) = -3(9) +54 -26\\g(-3) = 54 - 27 -26\\g(-3) = 1[/tex]