Answer:
x = 2/5
Step-by-step explanation:
Solve for x:
x/3 + 2/3 = 2 x
Hint: | Combine x/3 + 2/3 into a single fraction.
x/3 + 2/3 = (x + 2)/3:
(x + 2)/3 = 2 x
Hint: | Make (x + 2)/3 = 2 x simpler by multiplying both sides by a constant.
Multiply both sides by 3:
(3 (x + 2))/3 = 3×2 x
Hint: | Cancel common terms in the numerator and denominator of (3 (x + 2))/3.
(3 (x + 2))/3 = 3/3×(x + 2) = x + 2:
x + 2 = 3×2 x
Hint: | Multiply 3 and 2 together.
3×2 = 6:
x + 2 = 6 x
Hint: | Move terms with x to the left hand side.
Subtract 6 x from both sides:
(x - 6 x) + 2 = 6 x - 6 x
Hint: | Combine like terms in x - 6 x.
x - 6 x = -5 x:
-5 x + 2 = 6 x - 6 x
Hint: | Look for the difference of two identical terms.
6 x - 6 x = 0:
2 - 5 x = 0
Hint: | Isolate terms with x to the left hand side.
Subtract 2 from both sides:
(2 - 2) - 5 x = -2
Hint: | Look for the difference of two identical terms.
2 - 2 = 0:
-5 x = -2
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of -5 x = -2 by -5:
(-5 x)/(-5) = (-2)/(-5)
Hint: | Any nonzero number divided by itself is one.
(-5)/(-5) = 1:
x = (-2)/(-5)
Hint: | Simplify the sign of (-2)/(-5).
Multiply numerator and denominator of (-2)/(-5) by -1:
Answer: x = 2/5
Answer: [tex]x=2/5[/tex]
Simplify both sides of the equation
[tex]1/3x+2/3=2x[/tex]
Subtract 2x from both sides
[tex]1/3x+2/3-2x=2x-2x\\-5/3x+2/3=0[/tex]
Subtract 2/3 from both sides
[tex]-5/3x=2/3-2/3=0-2/3\\-5/3x=-2/3[/tex]
Multiply both sides by 3/-5
[tex](3/-5)*(-5/3x)=(3/-5)*(-2/3)\\x=2/5[/tex]
Find x and round to the nearest tenth
Answer:
The answer is
x = 38.7°Step-by-step explanation:
Since the triangle is a right angled triangle we can use trigonometric ratios to find the value of x
To find the value of x we use tan
[tex] \tan(\theta) = \frac{opposite}{adjacent} [/tex]
From the question
the opposite is 12
the adjacent is 15
We have
[tex] \tan(x) = \frac{12}{15} \\ x = \tan^{ - 1} ( \frac{12}{15} ) \\ x = 38.659808[/tex]
We have the final answer as
x = 38.7°Hope this helps you
The length of Tom’s rectangular classroom floor is 8 feet longer than 2 times the
width. The perimeter of his classroom floor is 124 feet. Write and solve an
equation to find the length of his classroom.
Answer:
Length= 44 feet
Width= 18 feet
Step-by-step explanation:
Let the length= x
Let the width = y
Length is 8 feet longer than 2 times the
width.
X= 8+2y
The perimeter of his classroom floor is 124 feet
Perimeter= 2(x+y)
124= 2x+2y
But x= 8+2y
124= 2x+2y
124= 2(8+2y) +2y
124= 16 +4y +2y
124-16= 6y
108= 6y
18 = y
Width= 18 feet
X= 8+2y
X= 8 +2(18)
X= 8+36
X= 44
Length= 44 feet
Find the circumference of a circle with radius of 18 in. Leave your answer in terms of pi.
A. 18 pi in.
B. 324 pi in.
C. 54 pi in.
D. 36 pi in.
Answer:
36pi. in. answer is D
Step-by-step explanation:
C = 2(18)pi= 36pi in
Tecside real estate, inc. is a research firm that tracks the cost of apartment rentals in southwest virginia. in mid-2002, the regional average apartment rental rate was $895 per month. assume that, based on the historical quarterly surveys, it is reasonable to assume that the population standard deviation is $225. in a current study of apartment rental rates, a sample of 180 apartments in the region provided the apartment rental rates.a. do the sample data enable tecside real estate, inc. to conclude that the population mean apartment rental rate now exceeds the level reported in 2002? the sample mean is $915 and the sample standard deviation is $227.50. make your decision based on α=0.10.b. what is the p-value?
Answer:
The decision is to fail to reject the null hypothesis
This means that the population mean apartment rental rate now does not exceeds the level reported in 2002
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = \$895[/tex]
The population standard deviation is [tex]\sigma = \$225[/tex]
The sample size is [tex]n = 180[/tex]
The sample mean is [tex]\= x = \$ 915[/tex]
The sample standard deviation is [tex]s = \$ 227.50[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \mu \le \$ 895[/tex]
The alternative hypothesis is [tex]H_a : \mu > \$895[/tex]
The test statistics is evaluated as
[tex]t = \frac{\= x- \mu}{\frac{\sigma }{\sqrt{n} } }[/tex]
=> [tex]t = \frac{ 915 - 895}{ \frac{225}{ \sqrt{180} } }[/tex]
=> [tex]t =1.193[/tex]
So from z-table the p-value is obtained, the value is
[tex]p-value = P(Z > t) = P(Z > 1.193 ) = 0.11643[/tex]
So From the value obtained we see that
[tex]p-value > \alpha[/tex] so we fail to reject the null hypothesis
Simplify: Negative two and one-third minus negative ten and one-sixth(20 points)
Negative twelve and one-half -12 1/2 Twelve and one-half 12 1/3 Seven and five-sixths 7 5/6 Negative seven and five-sixths -7 5/6
Given:
The expression is
[tex]-2\dfrac{1}{3}-\left(-10\dfrac{1}{6}\right)[/tex]
To find:
The value of the expression.
Solution:
We have,
[tex]-2\dfrac{1}{3}-\left(-10\dfrac{1}{6}\right)=-2\dfrac{1}{3}+10\dfrac{1}{6}[/tex]
Convert the mixed fraction in improper fraction.
[tex]=-\dfrac{2\times 3+1}{3}+\dfrac{10\times 6+1}{6}[/tex]
[tex]=-\dfrac{6+1}{3}+\dfrac{60+1}{6}[/tex]
[tex]=-\dfrac{7}{3}+\dfrac{61}{6}[/tex]
Taking LCM, we get
[tex]=\dfrac{-2(7)+61}{6}[/tex]
[tex]=\dfrac{-14+61}{6}[/tex]
[tex]=\dfrac{42}{6}[/tex]
Convert it into mixed fraction.
[tex]=\dfrac{6(7)+5}{6}[/tex]
[tex]=7\dfrac{5}{6}[/tex]
Therefore, the correct option is C.
Consider the region bounded by the curves y=x2 and y=9. Find the volume of the solid formed when this region is rotated around the x-axis.
Answer:
V = 36Π cubic Centimetres
Step-by-step explanation:
Step(i):-
Volume of the solid
The Volume of the solid formed by revolving the region bounded by the curve y = f(x) and rotated around the x-axis defined by
[tex]V = \pi \int\limits^a_b {[f(x)]^{2} } \, d x[/tex]
Step(ii):-
Given two curves are y = x² and y = 9
The point of intersection of two curves
y = x²...(i)
and y = 9 ...(ii)
Equating both equations , we get
x² - 9 =0
⇒ x² - 3² =0
⇒ (x+3)(x-3) =0
⇒ x+3=0 and x-3=0
x = 3 ⇒ y = 9
x = -3 ⇒y = 9
The point of intersection ( -3,9) and (3,9)
Step(iii):-
[tex]V = \pi \int\limits^a_b {[(f(x)]^{2} } \, -[g(x)]^{2})d x[/tex]
The limits x- varies from -3 to 3
[tex]V =\pi (\int\limits^3_3 {x^{2} } \, dx +\int\limits^3_3{9} \, dx[/tex]
[tex]V =\pi (\frac{x^{3} }{3} -9 x)^{3} _{-3}[/tex]
[tex]V= \pi ( \frac{27}{3} - 9(3) - (\frac{-27}{3} -9(-3))[/tex]
V = π ( |-36| = 36Π cubic Centimetres
Final answer:-
The volume of the solid
V = π ( |-36| = 36Π cubic Centimetres
Decide whether the set S = {−1, 0 ,1} is closed under each of the following operations. Be sure to justify
each of your conclusions.
1. Multiplication
2. Addition
3. Subtraction
4. Division
5. Squaring
6. Square rooting
7. Averaging 2 numbers
8. Averaging 3 numbers
Answer:
Explained below
Step-by-step explanation:
Sol: 1. Multiplication
Multiply the set S; the answer should also belong to the set S. For example, -1 x 0 = 0 Є S and -1 x 1 = -1 Є S, Hence the set S is closed under multiplication.
2. Addition
When we add two sets S elements, the answer should also belong to the set S, for example, 1 + 0 = 1 Є S but 1 + 1 = 2, which does not belong to set S; hence S is not closed under addition.
3. Subtraction
The set S is not closed under subtraction because -1 – 1 = -2, -2 is not the set S.
4. Division
The set S is not a closed division because when we divide one S element to another element, the answer does not belong to the set S, for example -1/0 = undefined.
5. Squaring
The set is closed under squaring if we square an element of the set S, and the result also belongs to the set S, for example, (0)2 = 0 and (-1)2 = 1, which belongs to the set S. Hence set S is closed under squaring.
6. Square rooting
The set S is not closed under square rooting because when we take the square root of an element of set S, the answer does not belong to the set S. √-1 = undefined.
7. Averaging two numbers
Averaging two numbers mean the sum of two numbers of set S is divided by two. For example, 1 + 0/2 = 1/2, which is not belongs to set S. hence set is not closed under averaging two numbers.
8. Averaging three numbers
The sum of three numbers of set S is divided by 3; the answer should belong to the set S.
-1 + 0 + 1 / 3= 0, 0 belongs to set. Hence the set S is closed under averaging three numbers.
Answer is explained below. We can say that Subtraction is not closed under the set.
Given set S = {−1, 0 ,1} we have to check the given set is closed or not.
1. Multiplication
Multiply the set S; the answer should also belong to the set S. For example, [tex]-1\times 0=0[/tex], 0 Є S and [tex]-1\times 1 = -1[/tex] , -1 Є S, so the set S is closed under multiplication.
2. Addition
On adding the any two values of the set, the result belong to the set itself, for ex if we add [tex]-1+0=-1\\[/tex] Є S but 1. so we can say that the given set is closed under addition.
3. Subtraction
The set S is not closed under subtraction because -1 – 1 = -2, -2 is not the set element S.
4. Division
The set S is not belongs to closed division because when we divide one S element to another element, the answer does not belong to the set S, for example -1/0 = undefined.
5. Squaring
The set is closed under squaring,since we square an element of the set S, and the result also belongs to the set S. for example, [tex]0^{2} =0[/tex] and[tex]-1^{2} =1[/tex] which belongs to the set S. Hence set S is closed.
Hence We can say that Subtraction is not closed under the set.
For more details on Set follow the link below:
https://brainly.com/question/8053622
20 POINTS AND BRAINLIEST Ed has 93 marbles. In which sequence can he arrange them in to use all the marbles?
Answer:
A.) asequence with six terms that starts with 1 and has a common ratio of 2
The area of a triangle is 25 square Inches, base Inches. What is its helght (a) ? Use the formula A triangle = 1/2 ba
50 inches
5 inches
62.5 inches
10 inches
125 inches
Answer:
50/b in
Step-by-step explanation:
Use the area formula A = (1/2)(base)(height).
Here the area A is given and is 25 in^2; the base is not given, so use 'b.'
Then, since A = (1/2)(base)(height),
(height) = 2A/(base) = 2(25 in^2)/b = 50/b in
A company says their cough syrup, called Cough-Up, is real effective and that 7 out of 10 doctors prefer it over any competitors. Using the given ratio, answer the following questions If there are 40 doctors, how many prefer Cough-Up? Your answer
Answer:
40÷10=4
7×4=28
18 doctors
Is 8.73 a rational number
Answer:
Yes
Step-by-step explanation:
8 73/ 100=8.73
What are the subsets of real numbers -7
The subsets of real numbers are known as:
rational numbers (decimals that don't repeat)irrational numbers (decimals that repeat)integers (a number that isn't a fraction)whole numbersnatural numbers (a positive number)Best of Luck!
A triangle has sides with lengths of 2x - 7, 5x - 3, and 2x - 2. What is the perimeter of the triangle
Answer:
3x
Step-by-step explanation:
What information can you obtain about the scores in a regular frequency distribution table that is not available from a grouped table.
A. The number and width of the class intervals
B. The exact frequency for each category on the scale of measurement
C. The overall frequency for each class interval
Answer: B. The exact frequency for each category on the scale of measurement
Step-by-step explanation: The main difference between a grouped table and regular frequency distribution exists in the fact that ; grouped table takes in a defined range of (X) values, that is takes more than one individual value per group and takes the frequency of all scores or values in the group, hence giving the frequency of the scores in the interval rather than the frequency of each individual score. On the other hand, the regular frequency distribution treats values or scores individually and then takes the frequency of each score. This way a regular frequency distribution enables us to know the exact number or distribution of each individual score.
The information in a regular frequency distribution table that is not available from a grouped table is (b) the exact frequency for each category on the scale of measurement
There are several similarities between a regular frequency table, and a grouped frequency table.
However, both frequency tables have a major difference.
This difference is in the frequency of the data they represent
While a regular frequency table shows the exact frequency of each data element, a grouped frequency table cannot show the exact frequency of each data element.
Hence, the true option is (b)
Read more about frequency distribution table at:
https://brainly.com/question/1094036
How do I factor 4x^2-12x^3?
A cafeteria worker knows that it takes 3 bottles of juice to serve a table of 18 students. How many bottles of juice are needed for 24 students? How many bottles of juice are needed for 42 students?
Answer:7
Step-by-step explanation:
quik math
a bucket full of milk is 80cl,how many litres are in 15 of such
Answer:
1.2 liters
Step-by-step explanation:
1 bucket has a volume of 80 cL.
15 buckets have a volume of 15 * 80 cL = 120 cL
1 L = 100 cL
120 cL * (1 L)/(100 cL) = 1.2 L
16. The difference of two numbers is 3 and the
difference of their square is 69. Find the
numbers.
Make a system of equations.
[tex]x-y=3[/tex]
[tex]x^2-y^2=69[/tex]
[tex]x=y+3[/tex]
[tex](y^2+6y+9)-y^2=69[/tex]
[tex]6y+9=69[/tex]
[tex]6y=60[/tex]
[tex]y=10[/tex]
[tex]x=10+3[/tex]
[tex]x=13[/tex]
[tex]x=13,y=10[/tex]
Hope this helps.
頑張って!
For the given functions f and g find the indicated composition. f(x) = -2x + 2, g(x) = 3x + 2 A. - 6x - 4.B. - 6x + 8.C. 6x + 8.D. - 6x + 6.Find the Inverse of the one-to-one function. f(x) = 4x + 8
Answer:
i'm not sure if it is right
Step-by-step explanation:
1, B
g(f(x)) --> g(-2x+2)=3x+2
g(-2x+2)=3.(-2x+2)+2=-6x+6+2=-6x+8
2,
#1: Write as a linear equation
y=4x+8
#2: Swap x and y variables
x=4y+8
#3: Solve for y
4y+8=x
4y=x-8
y=[tex]\frac{x-8}{4}[/tex]
#4: Write in inverse notation:
[tex]f^{-1}[/tex](x)=[tex]\frac{x-8}{4}[/tex]= (x/4) - 2
Hi! I really need help with figuring out how to do #2, I just don't get how it's done and really need an explanation! thanks in advance :)
Answer:
18
Step-by-step explanation:
g(3)+f(4)
=3²+1+2×4
=9+1+8
=18
A company assigns to each of its employees an ID code that consists of one or two uppercase letters followed by a digit from 0 through 9. How many employee codes does the company have available?
Answer:
7020 codes
Step-by-step explanation:
For one upper case letter:
There are 26 letters in this scenario
For two upper case letters:
There are 26 * 26 letters in this scenario. Essentially, there are 676 letters in this scenario.
For one upper case letter:
There are 10 digits that can be applied to it. So therefore, there are 26 * 10 codes in this case.
That means, there are 260 codes for one upper case letter.
For two upper case letters:
There are 10 digits that can be applied to it. That is to day, there are 676 * 10 codes in this case.
This means, for two upper case letters, there are 6760 codes.
Finally, we add up the number of codes for one upper case letter, and that of two upper case letters together. As such, we have
6760 + 260 = 7020.
The company has 7020 codes available.
Please vote for brainliest.
The following boxplot is of the birth weights (in ounces) of 160 infants born in a local hospital The following boxplot is of the birth weights (in ounces) of 160 infants born in a local hospital
About 40 of the birth weights were below?
A) 92 ounces B) 102 ounces C) 112 ounces D) 122 ounces
This question is Incomplete because it lacks the diagram of the box plot. Please find attached the diagram of the box plot
Answer:
B) 102 ounces
Step-by-step explanation:
Looking at the attached diagram, we can see the box plot it divided into different segment
The median weight of the babies = 110 ounces
The maximum weight of the babies is between = 140 and 130, approximately let's say 135 ounces
The minimum weight is 80 ounces
Then the box in the middle is divided into 3
It has the First Quartile
Median
And third Quartile
Since we have 160 infants born in the local hospital, about 40 of the birthweights we fall into
= 40/160 = 1/4
1/4 represents the first Quartile
Looking at the box plot, 40 of the birthweights were below 102 ounces.
f(x) = 2x2 + 5x + 20
Find f(-9)
Answer: f(-9)=137
Step-by-step explanation:
To find f(-9), you plug in -9 into x.
f(-9)=2(-9)²+5(-9)+20 [solve parenthesis]
f(-9)=2(81)-45+20 [multiply]
f(-9)=162-45+20 [subtract]
f(-9)=117+20 [add]
f(-9)=137
Simplify the expression to a polynomial in standard form:
(3x − 2)(22 - 2x + 1)
Please answer
Answer:
[tex]-6x^2 + 73x - 46[/tex]
Step-by-step explanation:
(3x-2)(22-2x+1)
simplify (22-2x+1)
(3x-2)(23-2x)
distribute
69x - 6x^2 - 46 + 4x
simplify
[tex]-6x^2 + 73x - 46[/tex]
A lab technician needs 60mL of 25% acid solution for a certain experiment , but he has only 10% solution and 40% solution. How many milliliters of the 10% and the 40% solutions should he mix to get what he needs?
Answer:
10%: 30 mL40%: 30 mLStep-by-step explanation:
The needed concentration is exactly halfway between the available concentrations, hence they must be mixed equally.
He should mix 30 mL each of the 10% and 40% solutions.
_____
The first step in solving any problem is to look at the given information, and at what is being asked for. Here, the mix that is being asked for is exactly halfway between the given concentrations, so you know without any further contemplation that the mix will be 50%/50% of each.
__
If the mix were something else, there are several ways the problem can be solved. I like to use a diagram that puts the available concentrations on the left in a column with the highest on top, the needed concentration in the next column in the middle, and the differences of these numbers on the diagonals in the right column.
Example: if the needed mix is 15%, the diagram would look like ...
40 5
15
10 25
The numbers on the right tell you the proportions required (5:25 = 1:5). For this example, you need 1 part 40% solution and 5 parts 10% solution to make a mix that is 15%. That's a total of 6 parts, so each "part" is 10 mL for 60 mL of solution.
We chose this example so every number in the diagram is different, so you could see how the instructions for use apply.
__
Another way to solve this is to let a variable represent the amount needed of the highest concentration. If we let that variable be x, for the given problem, we can write the equation for the amount of acid in the mix as ...
40%(x) + 10%(60 -x) = 25%(60)
0.30x = 9 . . . . . . . . subtract 6, simplify
x = 9/0.30 = 30 . . . . . mL of 40% solution
All 4 questions please
Answer:
π = S/2πrhv = √2E/mb = (-7a+c)/2x =3y-1Step-by-step explanation:
1.
[tex]S = 2\pi rh\\Divide\:both\sides\:of\:the\:equation\:by\:2rh\\\\\frac{S}{2rh} = \frac{2 \pi rh}{2 rh} \\\\\pi = \frac{S}{2rh}[/tex]
2.
[tex]E = \frac{1}{2} mv^2\\\\E = \frac{mv^2}{2} \\\\Cross\:multiply\\\\2E =mv^2\\Divide\:both\:sides\:of\:the\:equation\:by\:m\\\frac{2E}{m} = \frac{mv^2}{m} \\\\\frac{2E}{m} =v^2\\Square\:root\:both\:sides\:of\:the\:equation\\\sqrt{\frac{2E}{m} } = \sqrt{v^2} \\\\\sqrt{\frac{2E}{m} } =v\\\\v =\sqrt{\frac{2E}{m} }[/tex]
3.
[tex]7a+2b =c\\Isolate\:b\\\\2b =c-7a\\2b= -7a+c\\Divide\:both\:sides\:of\:the\:equation\:by \:2\\\frac{2b}{2} =\frac{-7a+c}{2} \\\\b = \frac{-7a+c}{2}[/tex]
4.
[tex]y = \frac{1}{3} (x+1)\\\\y = \frac{x+1}{3}\\\\Cross\:multiply \\3y =x+1\\Isolate \:x\\3y -1=x\\\\x =3y-1[/tex]
On the game show « the price is right », the highest winning amount was $262,743. The next largest winning amount was only 81.4012% of the highest. What was the second highest winning amount rounded to the nearest dollar?
Answer:
The second highest winning amount was of $213,876
Step-by-step explanation:
Given that the main prize of "The price is right" won is $ 262,743, and that the second highest prize in the history of said program is 81.4012% of said value, to obtain said number the following calculation must be performed:
(262,743 / 100) x 81.4012 = X
2,627.43 x 81.4012 = X
213,875.95 = X
Therefore, rounded to the nearest dollar, the second highest prize in the program was $213,876.
Solve and check the solution 5/8 = 1/2(a + 2) please help me
Answer:
[tex]a=-\frac{3}{4}[/tex]
Step-by-step explanation:
[tex]\frac{5}{8}=\frac{1}{2}\left(a+2\right)\\\\Switch\: sides\\\frac{1}{2}\left(a+2\right)=\frac{5}{8}\\\\\mathrm{Multiply\:both\:sides\:by\:}2\\2\times\frac{1}{2}\left(a+2\right)=\frac{5\times\:2}{8}\\\\Simplify\\a+2=\frac{5}{4}\\\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\a+2-2=\frac{5}{4}-2\\\\Simplify\\a=-\frac{3}{4}[/tex]
Check[tex]\frac{5}{8} = \frac{1}{2}\left(-\frac{3}{4}+2\right) \\\\\mathrm{Multiply\:fractions}:\\\\\quad \:a\times\frac{b}{c}=\frac{a\:\times \:b}{c}\\\\\frac{5}{8}=\frac{1\times \left(-\frac{3}{4}+2\right)}{2}\\\\\frac{5}{8}=\frac{1\times\left(-\frac{3}{4}+2\right)}{2}\\\frac{5}{8}=\frac{-\frac{3}{4}+2}{2}\\\\\mathrm{Join}\:-\frac{3}{4}+2:\quad \frac{5}{4}\\\frac{5}{8}=\frac{\frac{5}{4}}{2}\\\\\frac{5}{8}=\frac{5}{4\times\:2}\\\\\frac{5}{8}=\frac{5}{8}[/tex]Please help what is the area?
Answer: 70 square units
Which equation has no solution?
4(x + 3) + 2x = 6(x + 2)
5+2(3 + 2x) = x + 3(x + 1)
5(x + 3) + x = 4(x + 3) + 3
4 + 612 + x) = 2(3x + 8)
Answer:
[tex]4(x + 3) + 2x = 6(x + 2)[/tex][tex]5 + 2(3 + 2x) = x + 3(x + 1)[/tex]Step-by-step explanation:
[tex]5(x + 3) + x = 4(x + 3) + 3 \\ 5x + 15 + x = 4x + 12 + 3 \\ 5x + x - 4x = 12 + 3 - 15 \\ 2x = 0[/tex]
Divide both sides of the equation by 2
2x/2 = 0/2
x = 0
(4+612+x)=2(3x+8)
4+612+x=6x+16
4+612-16=6x-x
600=5x
Divide both sides of the equation by 5
600/5 = 5x
120 = x
Answer:
Its B. 5+2(3 + 2x) = x + 3(x + 1)
Step-by-step explanation:
I just took the test on edge