The next number in the Fibonacci sequence after 34 (found by adding 21 and 34) is 55.
The Fibonacci sequence is a series of numbers where each number is the sum of the two numbers preceding it. The sequence starts with 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... and continues infinitely. The number 34 is found by adding the two numbers before it (13 and 21), and the next number in the sequence is 55, which is the sum of 34 and 21. This pattern continues, with each subsequent number being the sum of the two numbers before it.
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what is the inverse of the function f (x) = 1/3x-5
Solve. Write both set-builder notation and interval notation for the answer.
X/5+4≤3
The solution set is {x|_}
(Type an inequality. Use integers or fractions for any numbers in the inequality.)
The solution set is
(Type your answer in interval notation. Use integers or fractions for any numbers in the expression
Answer: We can solve for x by subtracting 4 from both sides of the inequality:
X/5 + 4 <= 3
X/5 <= -1
Multiplying both sides of the inequality by 5:
X <= -5
The solution set for x can be expressed in set-builder notation as:
{x | x <= -5}
And in interval notation as:
(-∞, -5]
Step-by-step explanation:
The value of x is x≤ -5
What is inequality?inequality, In mathematics is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
greater than is >
less than is <
greater then or equal to is ≥
less than or equal to is ≤
x/5 +4 ≤ 3
collect like terms
x/5 ≤3-4
x/5 ≤ -1
multiply both sides by 5
x ≤ -5
therefore the value of x≤ -5
in interval notation
= infinity < x ≤ -5
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A map has a scale of 1:250 000. How many centimeters on the map is a journey of 40 km?
Answer: I believe its 4.16 centimeters
Step-by-step explanation:
I do not have an explanation, but I hope the answer is correct.
ASAP I NEED THIS ASAP
b. Measure the length of the side DF.
c. Measure the height of the triangle, XF.
d. Describe in words the locus of the point that is 2cm from E and draw this onto your diagram.
e. Use compasses to bisect the angle D. You must leave your construction arcs in.
According to the mathematical calculations made, the results are as follows: the length of DF is 3.87 cm, the length of XF is 4.89 cm. The point 2cm from E is 5cm from X and the angle of D is 60°.
What is the length of DF?In this problem, we have to apply the Pythagorean theorem to find the lenght of DF line.
a² + b² = c²
7² + b² = 8²
49 + b² = 64
b² = 15
b = 3.87
How to calculate side XF?In this problem, we have to apply the Pythagorean theorem to find the lenght of XF line.
a² + b² = c²
3² + 3.87² = c²
9 + 14.97 = c²
23.97 = c²
4.89 = c
According to the information of the graph we can conclude that the point 2cm from E is on the line EX, and it is located 2cm from E and 5cm from X.
What is the angle of D?We know that F has a angle less than D so we can infer that F has an angle of 30° and D has an angle of 60° which we can check with a compass.
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Solve -8(c-1)=-(-3) what is the solution of c?
Answer:
c = [tex]\frac{5}{8}[/tex]
Step-by-step explanation:
First, expand the brackets by applying the Distributive Law:
[tex]= -8c + 8 = 3[/tex]
Then bring all the like terms together and isolate c. Move '3' to the left and '8c' to the right: of the equation:
[tex]= 8 - 3 = 8c[/tex]
= [tex]5 = 8c[/tex]
= [tex]c = \frac{5}{8}[/tex]
A film show lasted for 3 3/2 hours. Out of this ,1 1/3 hours were spent on advertisements. What was the actual duration of the film
3 3/2 hours as a decimal= 4.5
1 1/3 hours as a decimal = 1.3
Duration of the film show = 4.5 hours
Hours spent on advertisements = 1.3 hours
Actual duration of the film = 4.5 - 1.3 hours
= 3.2 hours
3.2 hours as a fraction = 3 1/5 hours.
Therefore, the actual duration of the film was 3 1/5 hours.
Movie lasted 3 hours and 10 minutes
You have to convert 3 3/2 and 1 1/3 to a fraction.You have to multiply 9/2 by 3 and 4/3 by 2 to get the least common multiple of those two numbers.Subtract 8/6 from 27/6 and you get 19/6.Convert 19/6 into a mixed number and you get 3 1/6 which is 3 hours and 10 minutes because the clock has 60 minutes so 1/6 is ten minutes.[tex]3\frac{3}{2} - 1 \frac{1}{3} = \frac{9}{2} - \frac{4}{3} = \frac{27 - 8}{6} = \frac{19}{6} = 3 \: \frac{1}{6} [/tex]
solve the equation 3.6=12n
The equivalent value of the equation is n = 0.3
Given data ,
Let the equation be represented as A
Now , the value of A is
3.6 = 12n be equation (1)
On simplifying , we get
Divide by 12 on both sides , we get
n = 3.6 / 12
On further simplification , we get
n = 0.3
Hence , the expression is n = 0.3
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The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 10. There are two dots above 6, 7, and 9. There are three dots above 8.
Which of the following is the best measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 8.
The median is the best measure of center, and it equals 7.3.
The mean is the best measure of center, and it equals 7.3.
The median is the best measure of center, and it equals 8.
The answer choice that is the best measure of center for the data, and what is its value is D. The median is the best measure of center, and it equals 8.
How to calculate this?A measure of center gives an idea of the central tendency of the data.
The median is a better choice here because it is not affected by extreme values, unlike the mean.
From the dots plotted on the line graph, it is evident that there are more data points around 8 than any other value. Hence, the median of the data would be closest to 8.
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Answer: The median is the best measure of center and it equals 8
Step-by-step explanation:have a good day!
A passenger train and a freight train leave cities 260 mi apart and travel toward each other. The passenger train is traveling
15 mph faster than the freight train. Find the speed of each train if they pass each other after 4 hr.
Step-by-step explanation:
x = speed of the passenger train
x - 15 = speed of the freight train
remember, the passenger train is traveling 15 mph faster than the freight train. that also means the freight train travels 15 mph slower than the passenger train.
we could define the variable also the other way around (x = freight train, x + 15 = passenger train).
speed = distance/time period
distance = speed × time period
so,
x×4 + (x - 15)×4 = 260
because when both trains meet somewhere in the middle, it means that the sum of both of their ways traveled is the whole distance between both cities : 260 miles.
4x + 4x - 60 = 260
8x = 320
x = 320/8 = 40 mph
so, the passenger train traveled at 40 mph.
the freight train traveled at 40-15 = 25 mph.
Prove angle ABC is a right angle
Pleasee help I need ASAP
Answer: A + B = C + D
Step-by-step explanation:
2. A worker is tiling the floor of a rectangular room that is 12 feet by 15 feet. The tiles
are square with side lengths 11
3 feet. How many tiles are needed to cover the entire
floor? Show your reasoning.
165 tiles are needed to cover the entire floor of the room.
First, we need to find out the area of the room in square feet. We do this by multiplying the length and width of the room:
12 feet x 15 feet = 180 square feet
Next, we need to find out the area of one tile in square feet. We do this by squaring the length of one side of the tile:
11 3/11 feet x 11 3/11 feet = 128/121 square feet
Now, we can divide the total area of the room by the area of one tile to find out how many tiles are needed:
180 square feet / (128/121 square feet) = 180 x 121/128 = 165 tiles
So, 165 tiles are needed to cover the entire floor of the room.
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1/2-5/9 please help me I’m struggling so much with it
Answer:
Below
Step-by-step explanation:
To add or subtract fractions they must have a common denominator
you can multiply them together to find A common denominator
2 x 9 = 18
so now yo have to convert the fractions to 18ths
1/2 * 9/9 ( this is just multiplying by '1') = 9/18
5/9 * 2/2 = 10 / 18
now 1/2 - 5/9 then equals 9/18 - 10/18 = (9-10)/18 = - 1/18
Suppose you know that ∠S and ∠Y are complementary and that m∠S = 5(m∠Y) − 240°. Find m∠Y.
The measure of angle Y, according to the stated statement, is 55 degrees.
What does the term "complementary" mean?An adverb used to describe something which goes together with something else and improves or completes it is complimentary (as in complementary colors)
The total of two complimentary angles is 90 degrees. As a result, we have:
m∠S + m∠Y = 90
Substituting the given equation m∠S = 5(m∠Y) − 240°, we get:
5(m∠Y) − 240° + m∠Y = 90
By merging like variables in the equation, we can reduce it to:
6(m∠Y) - 240° = 90
Adding 240 to both sides, we get:
6(m∠Y) = 330
Dividing both sides by 6, we get:
m∠Y = 55
Therefore, the measure of angle Y is 55 degrees.
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A survey organization conducted telephone interviews in December 2008 in which 1,009 randomly selected adults in the United States responded to the following question: At the present time, do you think television commercials are an effective way to promote a new product?
Yes, television commercials are an effective way to promote a new product.
The survey organization conducted a telephone survey in December 2008 to gauge the effectiveness of television commercials in promoting new products among a sample of 1,009 randomly selected adults in the United States.
The survey asked the respondents whether they believed that television commercials were an effective way to promote a new product at the time of the survey. The results of the survey can provide insights into the public's perception of television commercials as a tool for promoting new products, as well as how this perception may have changed over time.
The findings can also be useful for marketers and advertisers who want to understand consumer attitudes toward television commercials and use this information to guide their advertising strategies. However, it's important to note that the results of this survey are limited to the specific time and population studied and may not be generalizable to other populations or time periods.
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Car X travels 174 miles in 3 hours.
a. Write the equation of the line that describes the relationship between distance and time. Use x for the time in hours and y for the distance in miles.
b. What is the graph that represents the relationship between distance and time for Car X? Explain.
Answer:
Step-by-step explanation:
a. The equation of the line that describes the relationship between distance and time for Car X can be found by using the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
To find the slope (m), we can use the formula: m = (change in y) / (change in x) = (distance traveled) / (time elapsed) = 174 miles / 3 hours = 58 miles per hour.
Since the car starts at time x = 0 and has traveled 174 miles at time x = 3, the y-intercept (b) can be found by setting x = 0 and solving for y: y = 58x + b, and y = 174 when x = 3, so b = 174 - 58(3) = -160.
Putting it all together, we get the equation: y = 58x - 160.
b. The graph that represents the relationship between distance and time for Car X is a line that passes through the point (0, -160) and has a slope of 58. This line represents the linear relationship between the distance traveled and the time elapsed for Car X.
The y-intercept of -160 represents the distance traveled when time is equal to 0. The slope of 58 represents the rate of change of the distance traveled with respect to time. This means that for every hour that passes, Car X travels 58 miles.
To indirectly measure the distance across a lake, Dominic makes use of a couple landmarks at points � B and � C. He measures � � AD, � � DB, and � � DE as marked. Find the distance across the lake ( � � ) (BC), rounding your answer to the nearest hundredth of a meter.
The distance across the lake is approximately 62.5 meters, rounded to the nearest hundredth of a meter.
To find the distance across the lake (BC), we can use the following formula based on triangle similarity:
BC/AD = DB/DE
Where BC is the distance across the lake, AD is the known direct measurement made by Dominic, DB is the known measurement from point B to the landmark, and DE is the known measurement from point D to the landmark.
Let's assume that AD = 100 meters, DB = 50 meters, and DE = 80 meters. Then we can calculate BC as follows:
BC = (BC/AD) * AD = (DB/DE) * AD
BC = (50/80) * 100
BC = 62.5 meters
So, the distance across the lake is approximately 62.5 meters, rounded to the nearest hundredth of a meter.
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Please Help ASAP. No links or files. I will report!
The value of x is 7.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
∠TUV = 9x + 1
∠TUW = 7x - 9
∠WUV = 5x - 11
Now,
∠TUV = ∠TUW + ∠WUV
Substituting the values.
9x + 1 = 7x - 9 + 5x - 11
Adding like terms.
9x + 1 = 12x - 20
1 + 20 = 12x - 9x
21 = 3x
Dividing 3 on both sides.
x = 21/3
x = 7
Thus,
x is 7.
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. If gcd(a, b)-p, a prime, what are the possible values of gcd(a2, b2), gcd(a2, b), and gcd(a3, 2)?
The possible values are -
(a²,b²) = p
(a²,b) = p if p|-r and (a²,b) = p² if p|r
(a²,b³) = p² if p|-r and (a²,b³) = p³ if p|r
What is gcd?
The greatest common factor (GCF) that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor is another name for it (HCF).
Since (a, b) = p it can be written a = pr and b = ps where r and s are integers such that (r, s) = 1.
Then a² = p²r².
Then by Theorem 1.7, (a²,b) = (p²r²,ps) = p(pr²,s).
By Theorem 1.8, (r²,s) = 1 .
Thus, there are two cases to consider: if p|s then, (a²,b) = p², and if p|-s then (pr²,s) = 1 (Again by Theorem 1.8) so that (a²,b) = p in that case.
Thus, there are two cases for (a²,b): namely p or p².
The same analysis shows that (a³,b) must be either p, p² or p³ depending on the power of p that divides b.
Analyze (a²,b³) as follows.
Using the notation already introduced, and
Theorem 1.7, it is obtained that (a²,b³) = (p²r²,p³s³) = p²(r²,ps³).
Since, (r, s) = 1, Theorem 1.8 shows that (r²,s³) = 1.
Therefore, there are two possibilities for (a²,b³) -
(a²,b³) = p² if p|-r and (a²,b³) = p³ if p|r.
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this is from khan academy help...
The simplified form of the expression is given by 4⁹/y³
What are exponents?Exponent is a mathematical operation, written as an. Here the expression an involves two numbers, the base 'a and the exponent or power 'n'. Exponents are used to simplify algebraic expressions.
Given here : The exponents (4³/y)³
Simplifying we get
(4³/y)³
When multiplying two bases of the same value, keep the bases the same and then add the exponents together to get the solution.
4³ ˣ ³ / y³
4⁹/y³
Thus the simplified form of the expression is given by 4⁹/y³
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mr . france wants to have a party they want to celebrate . out of all the students in the class , 5 wants a ice cream part , 7 want a movie party , 10 want a costume party , and the rest are undecided , if 20% want a ice cream party , how many students are in the class
Answer:
there is 27 percent In the class
Step-by-step explanation:
you need black bla bla times bla = ur racist
(8h - 4) + (4h to the third power - 8h squared +9h +7)
Answer:
4h^3 - 8h^2 + 17h + 3
Step-by-step explanation:
I put it into my calculator, let me know if that helped!
Daniel has 53 paintbrushes in his art drawer. This is 25% of the total number of paintbrushes he has. How many paintbrushes does he have in all?
Answer:
Total number of paintbrushes
= 53 ÷ 25%
= 53 ÷ 0.25
= 212
Answer:
If 53 paintbrushes represent 25% of the total number of paintbrushes Daniel has, we can use the following formula to find the total:
total number of paintbrushes = (number of paintbrushes / percentage) x 100
Plugging in the values we know, we get:
total number of paintbrushes = (53 / 25) x 100
Simplifying, we get:
total number of paintbrushes = 212
Therefore, Daniel has a total of 212 paintbrushes in all.
Let the variable s represent the amount of videos streamed and let the variable c represent the cost.
For how many video streams will the cost be the same for both companies?
Which system of equations can be used to solve this problem?
A. c=40+2*8
c=24*8
B. c=42*8
c=24*
C. c=40*8+2
c=20*8+4
D. c=40*8- 2
c=20-4*8
The system of equations for cost of company A and B is c = 40 + 2s and c = 40 + 4s respectively.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The amount of videos streamed is = s
The cost of streaming each video is = c
The amount of money charged by company A as membership fee is = $40.
The amount of money charged by company A per video stream is = $2.
The equation for cost of company A will be -
c = 40 + 2s
The amount of money charged by company B as membership fee is = $40.
The amount of money charged by company B per video stream is = $4.
The equation for cost of company A will be -
c = 40 + 4s
Therefore, the equations are c = 40 + 2s and c = 40 + 4s.
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Video streaming company A charges a one-time $40 membership fee and $2 per video stream
Video streaming company B charges a one-time $20 membership fee and $4 per video stream.
Let the variable s represent the amount of videos streamed and let the variable c represent the cost
For how many video streams will the cost be the same for both companies?
Which system of equations can be used to solve this problem?
A ball is dropped from 2 meters and rises up by 75%
When a ball is droped from 2m heights and rises by 75%, then the height of ball after forth bounce is equals to 0.632 meters.
If an object is thrown from high and has a bouncing feature, each bouncing is less than the initial height until it stops. Each bounce reduces the growth rate until it reaches zero. In order to calculate the height of each bounce, so we can estimate what percentage the object will reach after each bounce. If we get the percentage of each bounce, we can easily determine the height of each bounce. We have, a ball is droped from 2 meters and bounce up to 75%. That is height of first bounce is determined by using percentage, height is 2 m × 75% = 2 m×0.75 = 1.5 m
In second bounce, height is 1.5 m × 75%
= 1.5 m×0.75 = 1.12 m
In third bounce, 1.12 m× 75%
= 1.12 m×0.75 = 0.843 m
In forth bounce, height is 0.843× 75%
= 0.843× 0.75 = 0.632 m
The height the ball reaches on its forth bounce is 0.632 m.
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Complete question :
A ball is dropped from a height of 2 meters and rises up by 75% of its height on each bounce. How high would the forth bounce be?
Do you have to multiply one or both equations to use elimination? Explain.
Answer: Depends
Step-by-step explanation: When solving a system using elimination, you may have to multiply both equations by a certain value in order to use the method. However, there are a few instances where you will only need to multiply one. This normally happens when there is a higher multiply representing x or y from one equation to another.
A. Neither
B. SSS
C. SAS
Choose SSS,
SAS, or neither
to compare these
two triangles.
No Criteria used to compare the Triangles.
What is Congruence?Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.
Given:
As from the Figure in two Triangles ACB and ECD.
<ACB = <ECD (Vertically Opposite Angle)
AC= CE (Given)
But we do not have any third pair for make it Congruent.
Thus, None of the Rule is used to prove Congruency in Triangles.
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Answer:
Its Neither
Step-by-step explanation:
A department store buys 300 shirts at a cost of $1,800 and sells them for $9 each. What is the percent markup? A department store buys 300 shirts at a cost of $1,800 and sells them for $9 each. What is the percent markup?
The percent markup for the cost of shirt = 50%
Let us assume that the cost of each shirt be x dollars
A department store buys 300 shirts at a cost of $1,800.
Using unitary method the price of each shirt would be,
x = 1800/300
x = 6 dollars
A department store sells 300 shirts for $9 each.
So, Selling price of one shirt = $9
Price markup = Selling price - Cost price
= $9 - $6
= $3
The percent markup would be,
p = (Price markup / cost price) × 100
p = (3/6) × 100
p = 50%
Therefore, the percent markup = 50%
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Identify the figure shown in the front, top, and side views.
Answer: it's C
Step-by-step explanation:
Answer:D
Step-by-step explanation:
Find the value of k if the graph of y=kx passes through the given point.
A(4,-80)
K=?
The value of k from the equation is k = -20
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
y = kx be equation (1)
Let the first point be P ( 4 , -80 )
Substituting the values in the equation , we get
-80 = 4k
Divide by 4 on both sides of the equation , we get
k = - ( 80/4 )
On simplifying the equation , we get
k = -20
Hence , the equation is k = -20
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A particle is moving along a spiral path defined by the equation r = a * e^(b * θ), where a and b are constants. Determine the velocity of the particle at a given value of θ.
Step-by-step explanation:
The velocity of the particle at a given value of θ can be found by taking the derivative of the position vector with respect to time:
v(θ) = dr/dt = dr/dθ * dθ/dt = dr/dθ * ω
where ω is the angular velocity and dr/dθ is the derivative of the position vector with respect to θ.
The position vector r = a * e^(b * θ) * i + a * b * e^(b * θ) * j
Taking the derivative with respect to θ:
dr/dθ = a * b * e^(b * θ) * i + a * b^2 * e^(b * θ) * j
So the velocity of the particle is given by:
v(θ) = a * b * e^(b * θ) * ω * i + a * b^2 * e^(b * θ) * ω * j
Answer:
Step-by-step explanation:
v(θ) = a * b * e^(b * θ) * ω * i + a * b^2 * e^(b * θ) * ω * jj