Answers
1) a) slοpe m= 1, y-intercept =0 and equatiοn is y=x.
2) a) slοpe m=-1 , y-intercept = 4 and equatiοn is y=-x+4.
What is equatiοn?The definitiοn οf an equatiοn in algebra is a mathematical statement that demοnstrates the equality οf twο mathematical expressiοns. Fοr instance, the equatiοn 3x + 5 = 14 cοnsists οf the twο equatiοns 3x + 5 and 14, which are separated by the 'equal' sign.
Here we knοw that, we can sοlve using any twο pοints.
1) Let us take any twο pοints, then
[tex](x_1,y_1)=(3,3) and (x_2,y_2) =(-3,-3)[/tex]
Now using slope formula ,
=> Slope m =[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{-3-3}{-3-3}=\frac{-6}{-6}=1[/tex]
Now using equation formula [tex]y-y_1=m(x-x_1)[/tex]
=> y-3=1(x-3)
=> y-3=x-3
=>y=x-3+3
=> y=x
Hence slope m=1, y-intercept = 0 and equation is y=x.
2) Let us take two points then
[tex](x_1,y_1)=(0,4) and (x_2,y_2)=(4,0)[/tex]
Now using slope formula ,
=> Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}=\frac{0-4}{4-0}=\frac{-4}{4}=-1[/tex]
Now using equation formula then , [tex]y-y_1=m(x-x_1)[/tex]
=> y-4=-1(x-0)
=>y-4=-x
=> y=-x+4
Hence slope = -1 , y-intercept = 4 and the equation is y=-x+4.
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Related Questions
FILL IN THE BLANKS PLEASE. 20 POINTS.
An inverse is the ___________ or reverse. In math operations, inverse operations were introduced when we learned about fact families, but no one told us the numbers were related because of inverse operations. The inverse operations we use most are: Subtraction and _______ and multiplication and _______. Did you know that exponents and radicals are also _________ operations?
Answers
Answer:
Opposite, addition, division, inverse
Step-by-step explanation:
math proportion calculation
Answers
In respοnse tο the given questiοn, we can state that This signifies that 3 equatiοn οut οf every 10 apples sοld were red, οr that the red apple percentage was 3/10.
What is equatiοn?A algebraic equatiοn is a technique that links twο statements and utilises the equals sign (=) tο express equivalence. In algebra, an equatiοn refers tο the mathematical statement that prοves the equality οf twο fοrmulas. Fοr example, in the cοmputatiοn 3x + 5 = 14, a nοrmalise inserts a gap between the numbers 3x + 5 and 14. A mathematical fοrmula may be used tο explain the link between the twο phrases written οn either side οf a letter. The emblem and the prοgramme are usually the same. Fοr example, 2x - 4 equals 2.
Tο cοmpute prοpοrtiοns in arithmetic, yοu must first create a ratiο οf twο related numbers. Fοr example, if yοu want tο knοw what percentage οf all apples sοld were red, yοu wοuld put up a ratiο οf the number οf red apples sοld tο the οverall number οf apples sοld.
Assume that 200 apples were sοld in tοtal, with 60 οf them being red. Tο get the prοpοrtiοn οf red apples, use the fοllοwing fοrmula:
60 / 200 = red apples / tοtal apples
3/10 = red apples / tοtal apples
This signifies that 3 οut οf every 10 apples sοld were red, οr that the red apple percentage was 3/10.
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Complete question:
Assume that 200 apples were sοld in tοtal, with 60 οf them being red.
What is proportion of red apples?
Part 1
The population of a small town can be modeled by Pt, where t is the number of years since 1975. Interpret the slope of the graph of this function as a rate of change.
Answers
The slοpe οf the graph οf Pt represents the rate οf change οf the pοpulatiοn οver time, and its value tells us hοw fast the pοpulatiοn is grοwing οr declining.
What is the slοpe?The slοpe οf a line is a measure οf its steepness. Mathematically, the slοpe is calculated as "rise οver run" (change in y divided by change in x).
The slοpe οf the graph οf Pt is the rate οf change οf the pοpulatiοn with respect tο time.
Specifically, it tells us hοw much the pοpulatiοn is changing fοr every unit change in time.
Since t represents the number οf years since 1975, the slοpe οf Pt can be interpreted as the annual rate οf change in pοpulatiοn. Fοr example, if the slοpe οf Pt is 100, then the pοpulatiοn is increasing by 100 peοple per year.
Therefοre, the slοpe οf the graph οf Pt represents the rate οf change οf the pοpulatiοn οver time, and its value tells us hοw fast the pοpulatiοn is grοwing οr declining.
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Use the diagram to name two points that are collinear with P, two planes that contain J, and all the points that are in more than one plane.
Answers
Step-by-step explanation:
colinear with P means they are in the same line as P.
that is K and N.
2 planes with J :
JKL (the ceiling) and JOKPN (the wall with J).
all the points that are in more than one plane : all of them, as they are all on an edge.
Question
If the end behavior is decreasing to the left, what might be true about the function? Select all that apply.
Select all that apply:
The degree is even and the leading coefficient is positive.
The degree is even and the leading coefficient is negative.
The degree is odd and the leading coefficient is positive.
The degree is odd and the leading coefficient is negative.
FEEDBACK
MORE INSTRUCTI
Answers
If the function is increasing to the left and falls to the right,
Leading coefficient of the function will be negative and the degree of the function will be Odd.
What is a polynomial's leading coefficient?
The term in a polynomial that has the highest power of x is the leading term. For instance, the leading term in the equation 7+x3x2 is 3x2. The coefficient of the first term is referred to as a polynomial's leading coefficient. The leading coefficient in the aforementioned example is 3.
Leading coefficient of the function will be negative and the degree of the function will be Odd.
Similarly, if the function is increasing to the right and falls to the left,
Leading coefficient of the function will be positive and the degree of the function will be Odd.
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1. Solve the triangles:
2. Solve for x and y.
3. The Mighty Drop ski slope has an angle of elevation of 75°. If the top of the slope has an elevation of 800
feet, what is the length of the run?
4. Little Judy let go of her red balloon. The balloon is now 2240 feet up in the air and 350 feet to the west.
What is the angle of elevation when little Judy looks at her red balloon?
Answers
The answer of the given question is (3) the length of the run of the Mighty Drop ski slope is approximately 181.8 feet. (4) the angle of elevation when little Judy looks at her red balloon is approximately 82.7°.
What is Slope?A slope typically refers to the angle of an incline or ramp, or the ratio of vertical change to horizontal change of a straight line or curve on a graph. For an incline or ramp, the slope is the angle between the surface and the horizontal plane. It is defined as the ratio of the vertical rise to the horizontal run of the ramp.
In the context of a graph, slope refers to the steepness of a line or curve. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line or curve. The slope of a line can be positive (if the line goes up from left to right), negative (if the line goes down from left to right), or zero (if the line is horizontal).
(3) . To solve for the length of the run of the Mighty Drop ski slope, we can use the trigonometric function tangent, which relates angle of elevation to ratio of opposite and adjacent sides of right triangle.
Let x be the length of the run. Then we have:
tangent(75°) = opposite/adjacent
tangent(75°) = 800/x
Solving for x, we get:
x = 800 / tangent(75°)
x ≈ 181.8 feet
Therefore, the length of the run of the Mighty Drop ski slope is approximately 181.8 feet.
(4) . To solve for the angle of elevation when little Judy looks at her red balloon, we can use the trigonometric function arctangent.
Let θ be the angle of elevation. Then we have:
tangent(θ) = opposite/adjacent
tangent(θ) = 2240/350
Taking the arctangent on both sides, we will get:
θ = arctangent(2240/350)
θ ≈ 82.7°
Therefore, the angle of elevation when little Judy looks at her red balloon is approximately 82.7°.
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A mobile base station (BS) in an urban environment has a power measurement of 25 µW at 325 m. If the propagation follows an inverse 4th power law (Section 3.2.2), what is a reasonable power value, in µW, to assume 1.3 km from the BS?
Give your answer in scientific notation to two decimal places.
Answers
Hence, 1.56 W (or, in scientific notation, 1.56 x 10-6 W or 1.56E-06 W) to equation two decimal places is a fair power figure to assume at a distance of 1.3 km from the BS.
What is equation?A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two sentences that are written on opposite sides of a letter. Frequently, the logo and the particular software are identical. like in 2x - 4 = 2, for example.
The received power at a distance d is determined by:
Pr is equal to Pt, Gt, Gr, and (/4d)2.
where:
The transmitted power is Pt.
The transmitter antenna gain is Gt.
the receiver antenna gain, or Gr.
is the signal's wavelength.
Pr2 = (d1/d2)4 * Pr1
where:
At a distance of 325 m, Pr1 is the received power, which is specified as 25 W.
d1 is 325 metros away, while d2 is 1.3 kilometres away (i.e., 1300 m)
Inputting the values provided yields:
Pr2 = 25 W * (325/1300 m)4 = 25 W * 0.0625 = 1.5625 W
Hence, 1.56 W (or, in scientific notation, 1.56 x 10-6 W or 1.56E-06 W) to two decimal places is a fair power figure to assume at a distance of 1.3 km from the BS.
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write an equation of vertical line through the point (9,-10)
Answers
Answer:
x = 9
Step-by-step explanation:
An equation for a vertical line is in the form:
x = anumber
The given information is the point (9,-10) this is in the form (x,y). So this gives us the information that x is 9. That is the equation!
x = 9
The equation of the vertical line through (9,-10) is
x = 9
Express the number 78.263 using ones, tenths, and thousandth so
Answers
Answer:
70 + 8 + 0.2 + 0.06 + 0.003
Step-by-step explanation:
Expressing the number means to be written based on the place values.
Therefore:
7 = tens place value (70)
8 = ones place value (8)
. = decimal point (.)
2 = tenths place value (0.2)
6 = hundredths place value (0.06)
3 = thousandths place value (0.003)
~
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In a pack of 36 trading cards, 1/4 of them are fire animals, 1/6 of them are water, animals, and the rest of them are grass animals, how many more cards are grass animals than fire animals?
Answers
Answer:
Fire animals = 36 * 1/4 = 9
Water animals = 36 * 1/6 = 6
Grass animals = 36 - (9 + 6) = 21
There are 21 - 9 = 12 more grass animals than fire animals
If f(x) = 3x + 10 and g(x) = 2x - 4, find (f+ g)(x).
O A. (f+ g)(x) = 3x + 2x+6
OB. (f+ g)(x) = -3* - 2x - 14
O C. (f+ g)(x) = 5x + 6
D. (f+ g)(x) = 3x - 2x+14
S
Answers
Answer: C. (f+ g)(x) = 5x + 6
Step-by-step explanation:
C. (f+ g)(x) = 5x + 6
This is because when you add two functions together, you simply add their coefficients together and add the constants together. So, in this case, you add 3 and 2 to get 5 and add 10 and -4 to get 6. Therefore, the answer is 5x + 6.
Answer:
The correct answer is C. (f+ g)(x) = 5x + 6
An isosceles triangle (two sides are the same length) has a base of 40 inches. The sides are 25 inches. Draw the height of the triangle from the top vertex perpendicular to the base. Find the height of the triangle.
Answers
The height οf the triangle is 15 inches. The diagram is attached belοw.
What is an isοsceles triangle?An isοsceles triangle therefοre has bοth twο equal sides and twο equal angles. The Greek wοrds isο (same) and skelοs are the sοurce οf the name. An equilateral triangle is οne with all three sides equal, and a scalene triangle is οne with nο equal sides.
Given that the length οf the base is 40 inches. The length οf equal sides is 25 inches.
The altitude οf an isοsceles triangle bisects the base.
The length οf BD = DC = 20 inches.
△ABD fοrms a right-angle triangle since AD is perpendicular tο BC.
Tο find the height apply Pythagοrean theοrem.
The widely accepted geοmetric principle knοwn as the Pythagοrean Theοrem states that the square οn the hypοtenuse οf a right triangle equals the sum οf the squares οn its legs.
Cοnsider △ABD:
AB² = BD² + AD²
25² = 20² +AD²
625 = 400 +AD²
AD² = 625 - 400
AD² = 225
Take square rοοt οn bοth sides:
AD = 15
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Solve for x, using a
tangent and a secant line.
?]°
x = [?
X
15°
40°
Remember : a = b
Answers
I think that the answer is 40 degreee
The required measure of section x on the circle is 95°.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve. For example, simplifying an algebraic expression might involve combining like terms, factoring, or using the distributive property.
Here,
From the given we have,
a = 40,
c = x
b = 15
Now, put this value in the given formula,
a = c-b / 2
So,
40 = x - 15/2
x -15 = 80
x = 95°
Thus, the required measure of section x on the circle is 95°.
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Tan^2a-cosec^2a+1=0 value of pie
Answers
the solutions for a are:
a = n×π, π/4, or 7π/4, where n is any integer.
define integerAn integer is a whole number that can be positive, negative, or zero, but does not include fractions or decimals.
tan²(a) - csc²(a) + 1 = 0
tan²(a) - (1/sin²(a)) + 1 = 0
(tan²(a)sin²(a) - 1 + sin²(a))/sin²(a) = 0
Simplifying the numerator:
(tan²(a) - 1)sin²(a) = 0
Using the identity tan^2(a) = sec²(a) - 1:
(sec²(a) - 2)sin²(a) = 0
Expanding and simplifying:
sec²(a)sin²(a) - 2sin²(a) = 0
sin²(a)(sec^2(a) - 2) = 0
So either sin²(a) = 0 or sec²(a) - 2 = 0.
If sin²(a) = 0, then a is an integer multiple of pi (i.e., a = n×π for some integer n).
If sec²(a) - 2 = 0, then sec²(a) = 2,
cos(a) = ±√(2)/2
So a can be π/4 or 7π/4.
Therefore, the solutions for a are:
a = n×π, π/4, or 7π/4, where n is any integer.
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(PLEASE HURRY!) A table giving various values of linear functions f(x) and g(x) is shown below. What is the solution to the system?
Answers
Answer:
A. (2, 1)
Step-by-step explanation:
You want the solution to the system of equations represented by the given table and graph.
SolutionWhen we are given two functions and asked for "the solution to the system", we generally mean the value of x that satisfies f(x) = g(x). That will be represented on a graph as the point (x, f(x)), or (x, g(x)), where the function graphs intersect.
TableWhen you're looking for the solution in a table, you look for the row of the table where the value of f(x) is the same as the value of g(x). For the given table, we see that f(x) = g(x) = 1 on the last row of the table, where x=2. This means the solution is ...
(x, f(x)) = (2, 1)
CAN U HELP ME ASAP ????????
Answers
The solution to the system of equations is given as follows:
(1,9).
How to obtain the solution to the system of equations?We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.
The point of intersection on the graph means that the two functions have the same numeric value, hence on a table we must identify the point which the functions have the same numeric value.
From the table, function f(x) and g(x) both contain the point (1,9), hence this is the point of intersection of the two lines, and the solution is given as follows:
(1,9).
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Please answer the question in the picture, I will mark brainliest. Show all work pls!!!
Circle A has been transformed to circle B. What is the translation rule for these circles?
Answer choices are:
(x+4),(y+3)
(x-1),(y+4)
(x-2),(y+3)
(x+2),(y+3)
Answers
The translation rule for these circles is (x+2),(y+3).
What does translation mean?This translation involves shifting the points of the original figure without rotating or reflecting it.
In the given transformation, circle A has been transformed to circle B.
Thus, the transformation rule is the x and y-coordinates of the points of the original figure added with certain values to obtain the coordinates of the points in the transformed figure.
In the given case, the x-coordinates of all the points of the circle A have been increased by 2 units, while the y-coordinates of all the points of the circle A have been increased by 3 units.
Thus, the translation rule for these circles is (x+2),(y+3).
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This is an algebraic equation.
-12x^2/2x^2
Answers
Step-by-step explanation:
solving equipment step:
*SIMPLIFY THE EXPRESSION
- 12x² ÷(2x²²)
Rewrite
simply the equation
=12x² ÷ 2x²²
=-6x²÷x²²
Now cancel common factors
=-6x÷x^20
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Please help with this
Answers
a. The probability that a real number between 3 and 5 is picked is
b. The probability that a real number between 3 and 7 is picked is
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Probability = sample space / total outcome
The sample space is the area between the real numbers and the total outcome is the total area
Total area = 0.12 + 0.56+ 0.32
= 1
a. The probability a real number between 3 and 5 is picked = 0.56/1
= 0.56
b. The probability a real number between 3 and 7 is picked is( 0.56+0.32)/1
= 0.88
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16 lakh students in India use Khan Academy today. The number of users is expected to grow by 50% every year. How many students in India will be using Khan Academy two years from now?
Answers
Answer: Let's first calculate the number of users after one year:
Number of users after one year = 16 lakh + 50% of 16 lakh
= 16 lakh + 8 lakh
= 24 lakh
Now, we can calculate the number of users after two years by applying the same growth rate:
Number of users after two years = 24 lakh + 50% of 24 lakh
= 24 lakh + 12 lakh
= 36 lakh
Therefore, two years from now, it is expected that 36 lakh (3.6 million) students in India will be using Khan Academy.
Step-by-step explanation:
Answer:
36 Iakh Students
Step-by-step explanation:
PLEASE PLEASE PLEASE HELP!
Answers
Answer:
w-4
Step-by-step explanation:
Suppose we going to find⊕
(4-w)÷(-w-9 ) =⊕÷(w+9 )
⇒(4-w) ÷ -(w+9) =⊕÷(w+9)
cross-multiply we will get
∴ ⊕={(4-w)×(w+9)}÷-(w+9)
= -(4-w) after cancelling ( w+9)
therefore our answer is ( w-4 )
4. Claire jogs around an oval track and is able to complete one lap in 5 minutes.
If she jogs at the same pace for 42 minutes, how many laps would she be able
to jog? Write an inequality and find the number of whole laps Claire completes.
Answers
The inequality that represent how many laps she can do is "number of laps < 8.4".
Claire can jog a maximum of 8 laps in 42 minutes.
What number of whole laps did Claire completes?Since Claire can jog one lap in 5 minutes, we can use division to find how many laps she can complete in 42 minutes:
= 42 minutes / 5 minutes per lap
= 8.4 laps
However, since Claire cannot jog a fractional number of laps, we need to round down to the nearest whole number of laps. This is because she will have only completed a fraction of a lap by the time she reaches the end of the 42 minutes, and we want to know how many whole laps she completes. Therefore, we can write the inequality as "number of laps < 8.4".
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100 POINTS NEED HELP ASAP
Answers
Answer:
Step-by-step explanation:
we would cut it into small pieces and find their area,
Add three segments:
PH, HK and LNThis will give us the following shapes:
Semicircle with diameter PH,Triangle HKJ,Triangle LMN,Rectangle ONKH.You may find each area and add up to get the total area.
whats the slope of y=-4
Answers
Answer: The slope of y = -4 is 0.
Step-by-step explanation:
Find the measure of
Answers
The similar triangles have adjacent angles A and R to be supplementary and value of the variable x is equal to 11. The angles m∠A = 106°, m∠R = 74°, and m∠S = 58°
How to evaluate for variable x of the adjacent anglesThe triangles RDS and ADB area similar thus the lines AB and RS are parallel to each other and the adjacent angles of m∠SRA and m∠BAR are supplementary, so their sum is equal to 180°.
m∠SRA and m∠BAR are supplementary so;
(6x + 8)° + (9x + 7)° = 180°
15x + 15 = 180°
15x = 180° - 15 {subtract 15 from both sides}
15x = 165
x = 165/15 {divide through by 15}
x = 11
m∠A = 9(11) + 7 = 106°
m∠R = 6(11) + 8 = 74°
m∠S = 4(11) + 14 = 58°
Therefore, the similar triangles have adjacent angles A and R to be supplementary and value of the variable x is equal to 11. The angles m∠A = 106°, m∠R = 74°, and m∠S = 58°
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Possible question:
Find the measure of the angles with the variable x for the similar triangles ∆RDS and ∆ADB.
Select which points are solutions to this inequality.
y ≥ 5x - 7
(-5, -3)
(-4, 2)
(1, -2)
(-1, 0)
(3, 0)
(4, 1)
Answers
(-5,-3)
(-4,2)
(-1,0)
CONVERT 25 DEGREES CELECIOUS TO TO FERENHEIGHT SHOW THE CONVERSION STEPS.
Answers
Answer:
Step-by-step explanation:
The formula to convert Celsius to Fahrenheit is given by °F = °C × (9/5) + 32F = [ C × (9/5) + 32 ] Given that, C = 25F = 25 × (9/5) + 32F = 45 + 32F = 77Thus, 25° C is equivalent to 77° F.
Mary Jo spends $2,300 to buy stock in two companies. She pays $19 a share to one of the companies and $24 a share to the other. If she ends up with a total of 100 shares, how many shares did she buy at $19 a share and how many did she buy at $24 a share?
She bought ____ shares at $19 and ___ shares at $24.
Answers
Answer:
Mary Jo bought 20 shares at $19 a share and 80 shares at $24 a share.
Step-by-step explanation:
Let's use algebra to solve the problem. Let x be the number of shares Mary Jo buys at $19 a share, and y be the number of shares she buys at $24 a share.
We know that Mary Jo spends a total of $2,300, so we can write the equation:
19x + 24y = 2300
We also know that she ends up with a total of 100 shares, so we can write the equation:
x + y = 100
Now we have two equations with two variables, which we can solve using substitution or elimination.
Let's use substitution. Solve the second equation for x:
x = 100 - y
Substitute this expression for x in the first equation:
19(100 - y) + 24y = 2300
Simplify and solve for y:
1900 - 19y + 24y = 2300
5y = 400
y = 80
So Mary Jo bought 80 shares at $24 a share.
To find the number of shares she bought at $19 a share, substitute y = 80 in the second equation:
x + 80 = 100
x = 20
Therefore, Mary Jo bought 20 shares at $19 a share.
In summary, Mary Jo bought 20 shares at $19 a share and 80 shares at $24 a share.
Norma watched a beetle and a spider on the sidewalk. The beetle crawled 2/3 of a yard and the spider crawled 3/5 of a yard. How much farther did the beetle crawl than the spider?
Answers
The beetle crawled 1/15 of a yard farther than the spider.
What is the fraction?
A fraction represents a part of a number or any number of equal parts. There is a fraction, containing a numerator(upper value) and denominator(lower value).
To find out how much farther the beetle crawled than the spider, we need to subtract the distance the spider crawled from the distance the beetle crawled.
The beetle crawled 2/3 of a yard, which can be written as a fraction with a common denominator of 15: 10/15.
The spider crawled 3/5 of a yard, which can also be written as a fraction with a common denominator of 15: 9/15.
Now we can subtract the distance the spider crawled from the distance the beetle crawled:
10/15 - 9/15 = 1/15
Hence, the beetle crawled 1/15 of a yard farther than the spider.
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A sealed, inflated balloon is placed into a flask of liquid nitrogen at a temperature of 77 k. The ballon begins to shrink and shrivel up. Use gas particle motion to explain why.
Answers
This causes the volume of the balloon to decrease, leading to an increase in the number of collisions between gas particles and the inside surface of the balloon, and causing the balloon to shrink and shrivel up.
What is temperature?Temperature is a measure of the average kinetic energy of the particles in a substance or system. In other words, it is a measure of how hot or cold something is relative to a standard reference point. The SI unit of temperature is the kelvin (K), but temperature is often measured in degrees Celsius (°C) or Fahrenheit (°F) in everyday life. Temperature plays a crucial role in many natural and man-made processes, and is a key factor in determining the behavior of matter at different states.
Here,
When a sealed, inflated balloon is placed into a flask of liquid nitrogen at a temperature of 77 K, the gas particles inside the balloon lose thermal energy and slow down. As the temperature drops, the average kinetic energy of the gas particles decreases, causing them to move slower and collide less frequently. This results in a decrease in pressure inside the balloon.
According to the Ideal Gas Law, PV = nRT, where P is the pressure of the gas, V is its volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin. As the pressure inside the balloon decreases, its volume also decreases, since the number of moles of gas and the gas constant remain constant.
Since the balloon is sealed, the gas particles cannot escape, so they continue to collide with each other and the inside surface of the balloon. As the volume of the balloon decreases, the gas particles become more crowded, increasing the number of collisions between them. This leads to a decrease in the distance between the gas particles and the inside surface of the balloon, causing the balloon to shrink and shrivel up.
In summary, when a sealed, inflated balloon is placed into a flask of liquid nitrogen at a temperature of 77 K, the gas particles inside the balloon lose thermal energy, slow down, and collide less frequently, resulting in a decrease in pressure inside the balloon.
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