# Posts by Jai

Total # Posts: 1,998

**Calculus**

limit of (sin^2 (x))/(x^2 - 1) as x -> infinity Note that the range of values of sin x is from -1 to 1, for all real values of x. Thus the range of sin^2 (x) is only from 0 to 1 (as any real number squared results to greater than or equal to zero). Now, for the denominator...

**Calculus-correction**

*oops I made a mistake on x->(pi)- means that x approaches pi (=3.14159) at the LEFT side (thus it is SMALLER than pi, for instance 3.140) But the answer & other explanations are still the same. :)

**Calculus (first year uni)**

First, we get the limit of cot(x) as x->(pi) only. Note that cot(x) is also equal to cos(x)/sin(x). Thus, lim cot(x) as x->pi lim (cos(x))/(sin(x)) = cos(pi) / sin(pi) = -1 / 0 = infinity Now we know that it approaches infinity, but we're not sure of the sign whether...

**calculus**

I think you mean f(x) = 3 + e^(4−x) To get the inverse, replace the f(x) by x, and the x by f'(x), then solve for f'(x): f(x) = 3 + e^(4−x) x = 3 + e^(4 - f'(x)) x - 3 = e^(4 - f'(x)) ln(x - 3) = 4 - f'(x) f'(x) = 4 - ln(x - 3) This is the ...

**algebra**

A < C A + C = 27 M = A + 19 Note that from the third relationship, to maximize M, we also have to maximize A. From the second relationship, we want A to be maximize in a way that it is still less than C. Thus the maximum possible integer for A = 13, so that C = 14. Thus, M...

**algebra**

There might have been some typos in your question, so I interpreted it as ((5x^2-16x+3)/(5x^2+24x-5))*((15x^2-8x+1)/(3x^2+14x-5)) We factor each quadratic equation inside the parenthesis, and simplify. ((5x^2-16x+3)/(5x^2+24x-5))*((15x^2-8x+1)/(3x^2+14x-5)) ((5x-1)(x-3)/(5x-1...

**chemistry**

First we get the amount (the mass, specifically) of calcium chloride needed. Mass is related to number of moles. Recall that molarity (M) is just number of moles (n) divided by the volume (V) in liters: M = n/V Therefore, n = MV n = (0.15 M)(0.2 L) n = 0.03 moles Now, to get ...

**algebra**

Note that when (8+9x) and (8-9x) are multiplied, (8+9x)(8-9x) = 64 + 72x - 72x - 81x^2 = 64 - 81x^2 Thus the least common multiple is 64 - 81x^2 hope this helps~ :3

**Calculus**

Both are correct. (The variation in the answers depends on what "u" to be substituted) Integral (sec^2 (x) tan x) dx This can be rewritten as: Integral (sec(x)*sec(x)*tan(x)) dx Here we use substitution. We let u = sec(x) du = sec(x)*tan(x) dx Substituting, Integral...

**Algebra**

Step 1 & 2 are right. She made the first mistake in Step 3, it should be 2 + 10 = 2y 12 = 2y And so the succeeding steps are wrong too. But the earliest was in step 3. hope this helps :3

**Math**

3a^3 + 4 - 4a - 2a^3 + 6 + 12a - b^3 Before we simplify this, I'll just write some terms: *Variable: in this case, the variables are a and b *Numerical coefficient: the number before the variables *Exponent: number raised to certain term *Constant: the numbers (w/o ...

**Geometry**

When it is rotated about its diameter, the shape formed is a sphere. :)

**Calculus**

Yep, not continuous at x = -8. If you graph the function, it approaches (+) and (-) infinity at x = -8. To prove, we get the lim as x -> (-8)+ (approaching -8 from the right side) and as x -> (-8)- (approaching -8 from the left side) lim |x−8| / (x+8) as x -> (-...

**Calculus-correction**

*oops sorry, I mean x = -8.

**Calculus**

f(x)= |x−8| / (x+8) The function is discontinuous only at x = 8 since it will yield a denominator equal to zero: f(8) = |8-(-8)| /-8+8 f(8) = 16/0 x = 8 is an asymptotic discontinuity. Hope this helps~ :3

**Algebra II**

The original function is k(x) = x^2. Provided that c cannot be equal to zero, we'll compare the following to the original position of the given function: 1. k(x+c) = (x+c)^2 The graph moves c units to the left is c is (+) and c units to the right if c is (-). 2. k(x) + c...

**Math!!!**

#32. n is any nonzero number. n*n = n^2 Therefore it is always (+), regardless of the sign of n. #33. If y is (-), (-y)(-y)(-y) = (-1)^3 * (y^3) = -(y^3) Therefore the sign is (-). #41. Since it is depth (it went down), from the origin it is: -40,230 I think you can do the ...

**chemistry**

First, we get the molar masses to the CuCl2 and H2O. Just get a periodic table and add the individual masses of elements in the chemical formula: CuCl2: 63.55 + 2*35.45 = 134.45 H2O: 2*1 + 1*16 = 18 Then we get their moles. We divide the mass by the molar mass to get the moles...

**Pre algebra**

Let x = number It was said in the first statement that the number is multiplied by itself and then by itself again. Thus, it was multiplied by itself thrice: x*x*x = -1000 x^3 = -1000 We get the cuberoot of this, so that we can get x alone on the left side: cuberoot(x^3) = ...

**math**

Formula for getting an interior angle of a regular polygon with n sides: I = 180(n-2)/n Substituting, I = 180(18-2)/18 I = 160 degrees Hope this helps~ :3

**Calculus**

Your answer is actually correct. :) d/dx (6/ln(x)) d/dx (6*(ln(x))^(-1)) = 6(-1)(1/x)(ln(x))^2 = -6/(x*(ln(x))^2)

**chemistry**

First, we have to get the molar mass of aniline. Just get a periodic table and add the individual masses of the elements in the chemical formula: C6H5NH2: 6*12 + 5*1 + 1*14 + 2*1 = 93 g/mol Then we get the mass of aniline using the given density and volume. Recall that density...

**Chemistry**

Nope, you can't directly convert the 1.27 g sample to moles of Mg because it is impure or not 100% Mg. Since there is some HCl left after the reaction, the impure Mg is the limiting reactant and HCl is in excess. Note that the Mg used was impure. To get the number of moles...

**Math**

#1. Not necessarily. For example, a = -5 and b = -3 |a| = 5 |b| = 3 |a| is greater than |b|, but -5 is NOT greater than -3. #2. Opposites are numbers which have the same distance (numerical value) from zero but different in directions (opposite signs). An example would be -5 ...

**Calculus**

lim (x^4-5x^3+7x^2-6x+3)/(x-1) as x->1 Note that if we substitute 1 to the function, the denominator becomes zero (and we don't want that). But take note that the numerator can be factored: lim (x-1)(x^3 - 4x^2 + 3x - 3) / (x-1) Thus the x-1 will be cancelled, and we&#...

**math**

If that's already the question, then yes. :3

**8th G-Math**

This means that the number of students did not exactly fill the total capacity of the 7 buses, because there are 6 who had to travel in cars. What we'll do here is first, we subtract the 6 "extra" students from the 405, so that we'll know the exact, total ...

**Math**

Represent the unknown with variable. Let x = time that Steve's brother travelled Recall that distance is equal to speed multiplied by time. We get their distances travelled and equate them (since it's said that they followed the same route and they'll overtake at ...

**maths**

Note that you can factor out a(a+b) from the two terms: a(a+b) * (a+b - 2b) Thus, a(a+b)(a-b) Hope this helps~ :3

**Algebra Answer Check**

Yup, they are all correct. :)

**Chemistry stoch1**

First we write the balanced chemical reaction involved: 3Fe + 4H2O -> Fe3O4 + 4H2 Since we have 18 g of steam, we have to convert this to moles and use the stoich ratios from the reaction to get amount of Fe needed to react with it. To convert mass to moles, we get the ...

**a**

0 > x^2 + 5x - 2 We can also rewrite this as x^2 + 5x - 2 < 0 First thing to do is find the roots of the equation. Since the quadratic equation is not factorable in just one look, we use the quadratic formula: x = ( -b +/- sqrt(b^2 - 4ac) ) / 2a Therefore, x = ( -5 +/- ...

**Math**

Note that when two lines are parallel, their slopes are equal. The given equation is 4x - 5y = 8. To get its slope, we change it to the form y = mx + b where m is the slope and b is the y-intercept. Therefore, 4x - 5y = 8 -5y = -4x + 8 y = (4/5)x - 8/5 The slope is equal to 4/...

**Geometry**

Note that we can form a right triangle here, with base equal to 100 ft and angle between hypotenuse and base equal to 48°. Let h = height of triangle, which is also equal to total height of statue minus the 5 ft elevation of the device. Thus, tan 48° = h / 100 h = 100...

**Geometry**

To get the distance, use the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2) Assuming the point where the home lies is at the origin (0,0), thus the beach lies at (120, -30). Substituting, d = sqrt((120 - 0)^2 + (-30 - 0)^2) d = sqrt(14400 + 900) d = sqrt(15300) d = 123....

**Geometry**

Angle of depression is the angle below the horizontal that an observer must look in order to see an object below him. If you draw the figure, you can actually see that the hot-air balloon is located 25° above the horizontal. We actually formed a triangle here, with height ...

**Geometry**

It's easier if you drew the figure, but it's hard to draw figures here so I'll just describe it. :3 Note that the woman is 15 ft from the statue, and she looks up at an angle of 60° in order to see the top of statue. From here we can actually form a right ...

**MATH**

Let x = the stones that Eunice must take from Esther in the third round in order to be declared winner At start, Eu: 20 Es: 20 After first round, Eu: 20 + 5 = 25 Es: 20 - 5 = 15 After second round, Eu: 25 - 3 = 22 Es: 15 + 3 = 18 After third round, Eu: 22 + x = 30 Therefore, x...

**geometry**

I think we need to see the figure, but looking at the given, I think the point FG bisects and intersects BT at point O. Therefore we can say the lengths of segments BO and OT are equal, or 7x - 6 = 5x + 10 7x - 5x = 10 + 6 2x = 16 x = 8 Susbtituting, BO = 7x - 6 BO = 7(8) - 6 ...

**MATH**

Mira: 20 Noreen: 20 Olivia: 20 After they give pretzels, M: 20 - p N: 20 + p + q O: 20 - q What we can do here is add all of them and equate them to the sum of the ratio multiplied by a certain factor, say x: (20 - p) + (20 + p + q) + (20 - q) = (5+9+6)x The p's and q'...

**calculus**

y = (5e^x)/(cos x) Since 1/cos(x) = sec(x), we can also rewrite this as (5e^x)(sec(x)) Since two terms which are both functions of x are multiplied, we use the chain rule. Thus it becomes: (5e^x)(sec(x)) + (5e^x)(tan(x) * sec(x)) Simplifying, dy/dx = (5e^x)(sec(x))(1 + tan(x...

**calculus**

y = (sin x)^-1 This can also be rewritten as y = 1/(sin x) y = csc x Therefore, dy/dx = -cot(x) * csc(x) Hope this helps~ :3

**pre calcalus**

(x+4)^(2/3) = 9 To do this, we raise both side by 3/2, so that the exponent 2/3 of the term on the left side will be cancelled: (x + 4)^(2/3 * 3/2) = 9^(3/2) (x + 4)^(1) = 3^3 x + 4 = 27 x = 27 - 4 x = 23 To check, substitute the x value to the original equation: (23 + 4)^(2/3...

**math**

(4x)^(2/3) = (30x+4)^(1/3) To do this, note that it's much easier to work with whole number exponents. This we raise both side terms by 3, so that the denominator 3 will be cancelled: (4x)^(2/3 * 3) = (30x+4)^(1/3 * 3) (4x)^2 = (30x+4)^1 16x^2 = 30x + 4 Solving for x, 8x^2...

**AP Calculus**

f(x) = | (x)(x-3) / (9 - x^2) | (a) Domain & Zeroes of f? Domain is the set of all possible values of x. In the given function, note that the denominator can not be equal to zero, because any number divided by zero results to indeterminate (if 0/0) or infinity (if any non-zero...

**Physics**

R = a*t, or a = R/t Units of R = m^3 / s Units of t = s Thus, a = (m^3 / s) / s a = m^3 / s^2

**Math :(**

2b = b + 2 + b 2b = 2b + 2 We can see here that the 2b will be cancelled from both sides, and we're left with, 0 = 2 which is not possible. Thus there is no solution. Hope this helps~ :3

**math**

Recall that the perimeter of a square is equal to P = 4*s where s = length of one side Therefore, 80 = 4*s s = 80/4 s = 20 meters We need to find the area. Recall that the area of a square is just A = s^2 Substituting, A = 20^2 A = 400 m^2 Hope this helps~ :3

**Algebra Homework**

First we find the slope of the given points: m = (y2 - y1)/(x2 - x1) Substituting, m = (0 - (-2))/(-5 - k) m = 2/(-5 - k) Then, we get the slope of the given line. y = (5/9)x − 2 Note that it follows the form y = mx + b, where m is the slope and b is the y-intercept. ...

**Math**

2(4m + 6) = 8m + 6 8m + 12 = 8m + 6 Note that from here, we can see that there is no solution. The 8m will be cancelled from both sides, and we are left with 12 = 6 which is impossible. Thus, there is no solution, or there is no value of m that can satisfy the equation. Hope ...

**math**

If you mean √(2x - 7) + 8 = 11 Then, first we isolate the whole squareroot term on one side of equation: √(2x - 7) = 11 - 8 √(2x - 7) = 3 Then we square both sides: 2x - 7 = 9 2x = 9 + 7 2x = 16 x = 8 Note that if we're dealing with squareroots, we always...

**algebra**

What do you want to solve specifically? If you want to solve for x, V = 4/3 πx^3 4/3 πx^3 = V x^3 = V(3/(4π)) x = cuberoot( 3V/(4π))

**algebra**

I'm not sure if this is the same with the other post, but I'll just paste it here. If you mean √(2x - 7) + 8 = 11 Then, first we isolate the whole squareroot term on one side of equation: √(2x - 7) = 11 - 8 √(2x - 7) = 3 Then we square both sides: 2x...

**Math simplifying mixed radicals**

To do this, you have to factor the radicand (or the number inside the radical sign) and look for perfect squares. For instance, 2 * √(48) 2 * √(16*3) 2 * √(4*4*3) Express the repeating factors using exponents, so it's easier to see. Since four is ...

**Math simplifying mixed radicals**

To do this, you have to factor the radicand (or the number inside the radical sign) and look for perfect squares. For instance, 2 * √(48) 2 * √(16*3) 2 * √(4*4*3) Express the repeating factors using exponents, so it's easier to see. Since four is ...

**Math simplifying mixed radicals**

Hi! Just to clarify, are those numbers on the left (the 2, 3, 6, 3, etc.) are multiplied with the squareroot terms or are written as small number which is therefore part of the radical sign?

**Math**

Represent the unknowns with variables. Let x = total amount of Muffins sold in dollars Let (4 1/2)x = total amount of Doughnuts sold in dollars (according to the first statement) Then we set up the equation. Since their total is $44,000: x + (4 1/2)x = 44000 Then we solve for ...

**chemistry**

First, we write the balanced chemical equation involved. Since the reaction is synthesis of NH3, N2 + 3 H2 -> 2 NH3 Since N2 is excess, H2 is limiting and we therefore use its moles to determine the amount of NH3 produced. In the equation, there are 2 moles of NH3 produced ...

**math**

Domain of what? If the required is their individual domains: 1. For f(x) = 1/(x^2 - 8x - 9) Note that domain is the set of all possible values of x. In the function, note that the denominator must not be equal to zero because 1/0 is infinity. Therefore, we find the values of x...

**math**

What is required to find? :3

**Radius Question Geometry(college level)**

I'm not sure if there is a given figure for this problem, but if the three separate circles are tangent with the other with their centers aligned (or can be connected by a straight line), then yes, you get 60 cm for the diameter of the new, bigger circle which ...

**calculus**

lim (x^2 + 6x + 5)/(x^2 - 3x - 4) as x-> -1 Not that we can factor both numerator & denominator, lim (x+5)(x+1) / (x-4)(x+1) We can thus cancel the x+1, leaving lim (x + 5)/(x - 4) as x-> -1 Substituting x = -1, = (-1 + 5) / (-1 - 4) = 4 / -5 = -4/5 Hope this helps~ :3

**Math**

Recall the point-slope form of an equation: y - y1 = m(x - x1) where m = slope (x1, y1) = point on the line Substituting, y - 6 = -8(x - 4) y - 6 = -8x + 32 y = -8x + 38 (slope-intercept form), or 8x + y = 38 (standard form), or 8x + y - 38 = 0 (general form) Hope this helps~ :3

**MATH**

Recall the formula for slope of a line: m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the points on the line Substituting, m = (4 - 2) / (3 - (-1)) m = 2 / (3+1) m = 2/4 m = 1/2 Hope this helps~ :3

**Math**

Recall the formula for slope of a line: m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the points on the line Substituting, m = (9 - 5) / (4 - 3) m = 4/1 m = 4 Hope this helps~ :3

**Maths**

Hmm not sure if this can be accepted: 4 + (4-4)/4 ..but at least it has four 4's. XD

**Maths**

9*9+9+9+(9/9) ...six 9's. XD I'm not sure how if only four 9's should be used with normal math operations. Hmm...

**Maths**

9+9+(9+9)/9 lol there are five 9's. XD I'm not really sure how if there are only four 9's. :3

**Math**

If you mean that the a regular 40-sided polygon, recall that the formula for total number of diagonals of a polygon with n sides is, D = n(n-3)/2 Therefore, D = 40(40-3)/2 D = 740 diagonals Hope this helps~ :3

**Math - Factoring**

I think you forgot to type the choices. But anyway, you just have to apply some exponential rules and division rules: *When 2 is raised with an integer (greater than 1), the last digit of the number has a repeating pattern of 2, 4, 8, 6. *A number is divisible by 10 if the ...

**Math - Polygons**

Recall that the formula to find the measure of one interior angle of a polygon with n sides is, I = 180(n-2)/n Substituting, 150 = 180(n-2)/n 150n = 180n - 360 -30n = -360 n = 12 sides Hope this helps~ :3

**mathssssSsssss**

#1. Note that if you draw a broken line corresponding to the height of the parallelogram, you would form a right triangle in which the hypotenuse is 10 cm and one of the angles is 55 degrees. We can actually solve for the height, which is equal to 10 * sin (55) = 8.19 cm A of ...

**Math - Quadrilaterals**

Note that the sum of interior angles of a quadrilateral is equal to 360 degrees. Therefore, 63 + 4s + 5s + 2s = 360 We then find the value of s: 4s + 5s + 2s = 360 - 63 11s = 297 s = 27 Finally, we solve for the remaining angles, 4s = 4*27 = 108 degrees 5s = 5*27 = 135 degrees...

**Math - Polygons and Quadrilaterals**

Recall that the length of a diagonal of a rectangle can be calculated by, D^2 = W^2 + L^2 or simply, we'll use the Pythagorean theorem. Substituting, 125^2 = (7x)^2 + (24x)^2 15625 = 49x^2 + 576x^2 15625 = 625x^2 x^2 = 25 x = 5 (this is the multiplier for the ratio) ...

**Chemistry**

Note that density is just mass per unit volume, or d = m/V Substituting, d = 24.5 grams / 3.4 Liters d = 7.21 g/L Hope this helps~ :3

**Chemistry**

I'll give you the steps on how to solve: (1) Get the molecular weights (MW) of MgCO3 and MgO. -> I think you know how to do this one, you just go to periodic table and find the masses of the individual atoms and add them according to the chemical formulas. (2) Let x = ...

**Math**

(a) If the number is even, it is divisible by 2. If the number ends with 0 or 5 (the last digit), it is divisible by 5. If the number ends with 0, it is divisible by 10. (b) If the sum of the digits of a number is divisible by 3, it is divisible by 3. For instance, 4320: 4+3+2...

**MATHS**

True. One way to check is of course to plot the given function. You'll see it has an axis of symmetry at y-axis. Another way is to replace x with -x. If the resulting function is the same as the original, it has an axis of symmetry at the y-axis. Like, in the given ...

**calculus 2**

*sorry I forgot to add + C on the answer. ^^; Anyway, in your answer that you showed us, there's no x multiplier in the second term. I think that's the only wrong term and the other terms are correct. :3

**calculus 2**

∫ (63x(cos(x))^2) dx 63 ∫ x(cos(x))^2 dx Recall that cos^2 x is also equal to (1/2)(1+cos(2x)): 63/2 ∫ x(1+cos(2x)) dx 63/2 ∫ x + x cos(2x) dx First term is easy, it becomes: 63/2 ∫ x dx = (63/4)x^2 For the second term, we use integration by parts...

**CHEMISTRY HELP! D;**

Br2 + 2 H2O + SO2 -> 2 HBr + H2SO4

**Chemistry**

I think this was asked before: w ww.jiskha.c om/display.cgi?id=1375933614

**Chemistry**

63.15 % Carbon 5.30 % Hydrogen 100 - (63.15+5.30) = 31.55 % Oxygen To do this, divide each mass percentages with the corresponding weights of the elements to get the moles of each: 63.15 / 12 = 5.26 5.30 / 1 = 5.30 31.55 / 16 = 1.97 Now, divide all by the smallest, in this ...

**Calculus**

To get the max velocity, first, differentiate the velocity equation with respect to time. Then equate to zero: dv/dt = 3 - 0.4t 0 = 3 - 0.4t 0.4t = 3 t = 7.5 Substitute to the original equation: v = 3t-0.2t^2 v = 3(7.5) - 0.2(7.5)^2 v = ? Or you may also want to plot the ...

**math**

2x^2 - 5x + k What we can do here is to get the discriminant. For a quadratic equation with form ax^2 + bx + c = 0, the discriminant is equal to b^2 - 4ac The value of discriminant for a perfect square (which therefore has equal or double roots) is equal to zero. Substituting...

**maths**

We can further transform the given equation in such a way that the numerical coefficient of x^2 is 1. That is, by dividing all terms by 2. In this form, recall that the sum of roots is equal to negative of the numerical coeff of x, and the product of roots is equal to the ...

**maths-correction**

*sorry I mean sum = -b/a, and thus R = -b/(4a) . But the answer's still the same since it is squared.

**maths**

ax^2 + bx + c = 0 x^2 + (b/a)x + (c/a) = 0 For quadratic equations with this form, the sum & product of roots are: sum = b/a product = c/a Let R = one root Let 3R = the other root (according to the problem) Substituting to sum & product equations, R + 3R = b/a R(3R) = c/a from...

**maths**

Recall that for a quadratic equation that is in the form x^2 + bx + c = 0 the sum of the roots is equal to -b, and the product of roots is equal to c. Therefore, we change the form of the given equation by this form, 4x^2 + px +5 = 0 x^2 + (p/4)x + 5/4 = 0 Then we set up the ...

**maths**

Recall that for a quadratic equation that is in the form x^2 + bx + c = 0 the sum of the roots is equal to -b, and the product of roots is equal to c. Therefore, we change the form of the given equation by this form, kx^2 + 4x + k^2 - 21 = 0 x^2 + (4/k)x + k - 21/k = 0 The ...

**math**

The given equation follows the general equation for circles, which is (x - a)^2 + (y - b)^2 = r^2 where (a,b) = the point where the center of the circle lies r = radius From the equation, (x + 3)^2 + (y + 5)^2 = 16 r^2 = 16 r = 4 units Recall that the circumference of a circle...

**math help**

Let x = the third number It says that the average of 2P, 3Q and x is equal to S. Therefore, (2P + 3Q + x)/3 = S Getting x, 2P + 3Q + x = 3S x = 3S - 2P - 3Q hope it helps :)

**Math**

OMG I'm sorry I'm thinking about x-axis! Sorry about that.

**Math**

First, try plotting (-3,1) on a graphing paper. You'll see it's in the 2nd Quadrant. When you reflect it on the y-axis, the new point will be on the third quadrant (where both x & y coordinates are negative). Therefore the new point is at (-3,-1). Hope this helps~ :)

**Math**

*sorry I mean, V = (2.5)^3

**Math**

V = s^3 SA = 6*s^2 Just substitute the given length of one side of the cube. V = (1.5)^3 = ? (units in cubic inches) SA = 6*(2.5)^2 = ? (units in square inches)

**math**

To do this, you have to work backwards. That is, starting from the $15 left. Note that she spent 2/3 of her money and had $15 left. Therefore, this $15 is actually 1/3 of the money she had: 1/3 of something = 15 To do this, just divide 15 by 1/3: 15 / (1/3) = 15*3/1 = $45 And ...

**Chemistry(science)**

I think you mean "methane"? If it is... Methane's chemical formula is CH4. To get the moles of methane, we first get its molar mass by adding the masses of C and H. There are C atoms and 4 H atom: CH4 = 12 + 4*1 = 16 g/mol Then we divide the given mass by the ...

**math**

Let x = number of Ryan's stickers Let y = number of Tony's stickers From the first statement, (2/3)x = (3/4)y From the second statement, x - 48 = y + 48 Then we solve for x and y. There are many ways to solve this system, but let's do substitution. To do ...

**math**

Represent the unknown with variables: Let x = amount of premium grade gasoline sold in gallons Let x+420 = amount of regular grade gasoline sold in gallons (according to the third statement) Then we set up the equation. We know that the total worth of gasoline sold is 10,957. ...