Posts by Quidditch
Total # Posts: 512
for g(x) = x-7 only allowing real numbers... Yes, C is the answer.
(a-b)^2(a+b)+ab(a+b) multiply and combine like terms: First multiply--shown in two steps... =(a^2 - 2ab + b^2)(a + b) + (a^2)b + a(b^2) =a^3 - 2(a^2)b + a(b^2) + (a^2)b - 2a(b^2) + b^3 + (a^2)b + a(b^2) Now combine terms.
Let x = Adam's points Imram's ponts = x - 3 Shakeel's points = 2(Imram's points) or 2(x-3) totaling x + (x - 3) + 2(x-3) = 39
Check your work. When you multiplied (2x) times (3x) you got 6x. It should be 6x^2
math (am i correct)
1 is not 46.9. Question 1 asks you to find a linear function that fits the data. Find a function f(t) where t is the number of years since 1920. There are two points given. 1920, 46.9s 1990, 45.5s Or, for t expressed as years since 1920... 0 years, 46.9s 70 years, 45.5s for a ...
A quick check of your answer for b shows a problem. The second equation is: 2x + 5y = 10 Substituting the answer (10,2)... 2(10) + 5(2) = 10 or 20 + 10 = 10 Not correct
Checking (a) only, (1, 0) is not correct. To check your answer, substitute the values into either equation. So, y = 4x + 6 substituting your (1,0) answer... 0 = 4(1) + 6 or 0 = 10 which is not equal
for (a), one method: y = 4x + 6 y = -x + 1 For the standard equation, y = mx + b, m is the slope. If m is the same for both equations, the lines are the same or parallel. If parallel, the will not intersect. This is not the case here. The lines do intersect. There are two ...
For the standard line equation, y=mx+b m is the slope of the line b is the y intercept (where x=0) Take the derivative of the equation. Use that to find the slope of the tangent at (0,8). Once you have the slope and one point (0,8) you can solve for the b.
Given: sin(x+y)=sin(x)cos(y) + cos(x)sin(y) For the case y=x: sin(x+x) = sin(x)cos(x) + cos(x)sin(x) =sin(2x) = 2sin(x)cos(x) or, just to make it easier 2sin(x)cos(x) = sin(2x) so, what does 4sin(x)cos(x) = ?
11th grade Algebra 2/ Trig
recall that log x^y = y log x rewriting... (x+2)(log 10) - (x)(log 10) =(2)(log 10) IF the base is 10 then log 10 = 1. In that case the above reduces to: =2
Slope = rise/run Let x = run in feet 1/10 = (5 1/2 feet)/x multiply both sides by x x(1/10) = 5 1/2 feet multiply both sides by 10 x = (10) (5 1/2 feet) You do the last step.
Yes, you're right! I missed the last part that stated "through the 20.0 resistor". Sorry about that
That's not what I got. The equivalent resistance of the 20 ohm and 15 ohm resistors in parallel is, in ohms, (20 * 15)/(20 + 15). Add that to the 5 ohm resistor connected in series. Finally divide the applied voltage, 100 volts, by the total resistance to get the current.
one more elgebra problem...
The standard equation for a line is: y = mx + b where m = the slope of the line b = the y intercept putting y - 3x = 6 in standard form: y = 3x + 6 Therefore the slope of the line is 3. For lines to be parallel, the slope must be the same. Which of the possible answers has the...
Check rounding--I got slightly different values that rounded to different numbers. Given: C = 90 degrees A = 32 degrees AB = 42 units Therefore, B = 180 - 90- 32 = 58 degrees Sine rule: BC/sin(A) = AC/sin(B) = AB/sin(C) BC/sin(32) = AC/sin(58) = 42/sin(90) BC/(0.5299) = AC/(0....
gradeCounter is defined as Integer. Try: If(gradeCounter = 0)...
For the first problem: Let x = lesser number let y = greater number (x) (y) = 273 The problem states that y = x + 8. substituting for y: (x) (x+8)=273 x^2 + 8x=273 so x^2 + 8x - 273 = 0 Solve for x. Then, y = x + 8
Uh-oh, You need to reverse the inequality sign when you multiply or divide both sides by a negative number! should be: y < (1/3)x + 5
Take your step: x^2 + 5x + 6 = 90 Now: x^2 + 5x - 84 = 0 Factor by inspection or use the quadratic formula to solve for x. A hint is what two factors of 84 differ by 5?
Algebra, PLEASE help!
One approach is to just use the quadratic formula to solve it. But, you could probably do it by inspection if you write the equation as: 0.25x^2 + 0.3x + 0.09 =(10^(-2))(25x^2 + 30x + 9)
What do you think the answer is?
One method: Use substitution to express an equation in one unknown. Choose a. From the first equation... a + b = 6 So, b = 6 - a From the third equation... c + a = 7.5 So, c = 7.5 - a Now write the second equation substituting the values for b and c in terms of a: b + c = 20 ...
Just to be clear, it is a vertical line at x=1.
Below assumes: y = e^2x means e^(2x) and y = e^5x means e^(5x) The two curves (equations) intersect at x=0, y=1. Then, going in the positive x direction, they diverge. But, the right side of the region is bounded by a line at x=1. So, find the area from x = 0 to x = 1 under ...
1. m/n = 8 is correct. 2. x=2178 is not correct 11x=198 divide both sides by 11 x=198/11 x=?
Area = length * width length = (2x-1)m width = (x+2)m Area = (2x-1)(x+2) m^2 Multiply the two factors (use FOIL).
Let A=Total amount of the stronger (75%) DeMuggle juice potion added in ml. The percent of DeMuggle juice is: (total DeMuggle juice)/(total volume of potion) The final total DeMuggle juice is: 2000ml(30%) + A(%75) =600ml + 0.75A The final total volume of potion is: 2000ml + A ...
Absolute values are always positive. For any t, |3t| will be larger than |2t| . So, the right side is always negative. The absolute value of the left side is always positive.
I think Chopsticks misread the problem. let P=price 20 years ago 49 cents = 4P-(3 cents) 52 cents = 4P P=13 cents
let R = rainfall last year in cm. 18.6cm = (R/2) -3.2cm 21.8cm = R/2 R= ?
Chopsticks is wrong. let W = Juan's weight in kg 6W - 12kg = 486kg 6W = 498kg W = ?
Your are on the right track. You want to get just the variable on one side of the equation. You have done that. Your last step above: 4 - 10 = 10n + 10 - 10 The +10 and - 10 on the right cancel 4 - 10 = 10n Subtract 10 from 4 on the left. Then you something on the left = 10n. ...
Sorry, I am not sure what they are asking. Someone else here might understand it.
Is the problem c^2 - 8c + 16 - y^2 = 0?
OK, (3x^3 - 1) (2x^3 + 5) First Multiply the first terms of the two factors: (3x^3)(2x^3) = 6x^6 Outer Multiply the outer terms of the factors: (3x^3)(5) = 15x^3 Inner Multiply the inner terms of the factors: (-1)(2x^3) = -2x^3 Last Multiply the last terms of the factors: (-1...
Yes. Also, lyne mentioned checking using FOIL (First Outer Inner Last). That is a good acronym for multiplying binomials.
Your step 3: 6u^2 + 13u - 5 What number multiplied give -5? One possibility... (?u - 1) ( ?u + 5) What numbers multiplied give 6? One possibility... (3u - 1)(2u + 5) Now substitute back for u.
Hint: get rid of the denominator (4x^2 + 10)/(x^(1/2)) =4x^(3/2) + 10x^(-1/2)
Check your previous post for the solution to problem 2.
The first line above (where the problems was restated) should have been: 3^(x^3)=9^x The rest of the lines are correct.
For problem 2: 3^(x^3)=9^3 take log of both sides (x^3)log(3)=(x)log(9) divide both sides by x (x^2)log(3)=log(9) 9=3^2 so (x^2)log(3)=2log(3) divide both sides by log(3) x^2=2 x=sqrt(2)
[SQRT(2x^2 + 5x +6) = x square both sides 2x^2 + 5x + 6 = x^2 subtracting x^2 from both sides... x^2 + 5x + 6 = 0 Factor by inspection or use the binomial theorem to solve for x. The second problem is similar.
7x + 13x = 140 Combine all the x terms: 20x = 140 Solve for x.
6th grade Math
night 1=1 night 2=5 night 3=14 night 4=30 difference from 1 and 2 = 4 difference from 2 and 3 = 9 difference from 3 and 4 = 16 Do you see anything special in the differences?
First convert the number to a decimal number. Remember that percent is expressed in "hundredths". So multiply the decimal number by 100 to get the percent value. Example: 3 1/16 = 3.0625 = 306.25 percent = 306.25%
Yes, it is correct.
Disregard my answer. I assumed that the stationary block was fixed. I don't think that is the case. DRWLS has the correct approach. He is very good.
K1=initial kinetic energy K2=kinetic energy after collision K1 = (1/2)(5.2kg)(9.4m/s)^2 K2 = (1/2)(5.2kg)(1.80m/s)^2 kinetic energy lost is: K1 - K2
If you can't quickly factor the equation, it is generally easier to just use the quadratic equation. As you do more and more, you will probably remember how you factored them previously.
math [ i need help with these.]
The line -0(3) should have been =0(3) See below: For x=0 2x(x+3) =2(0)(0+3) =0(3) =0
math [ i need help with these.]
2x(x+3)=0 I am assuming that you need to find the values of x that will be true for the above. When you multiply several items (each of these is called a factor) together the answer (called the product) is 0 if ANY of them are 0. Example: multiply (a)(b)(c) If any of them, a ...
math [ i need help with these.]
Sorry, I meant to say factor not term. If any "factor" in a product is 0 the whole product is 0. There are 2 "factors".
math [ i need help with these.]
2. 2x(x+3)=0 There are 2 terms: 2x and (x+3). If any term in a product is 0 the whole product is 0. So, what value of x would make 2x=0 and what value of x would make x+3 = 0?
x * y = 7 x - y = 5 One method: express one variable in terms of the other variable and then solve the single variable expression. If x - y = 5 then y = x - 5 substituting back into the first equation: x * (x - 5)=7 Solve for x, then substitue the x value into either equation ...
Answered in your 5:50pm post.
Jessica's answer is not correct. x intercept point = -4,0 y intercept point = 0,2 y = mx + b is the standard line equation where: m = the slope of the line b = the y intercept The problems gives the y intercept as 2. slope = (delta y)/(delta x) = (0 - 2)/(-4 - 0) = -2/(-4...
sorry for the mistake (d g(x)/dx = -6(x^5) SIN (x^6)
(d(cos(u))dx = -sin(u)(du/dx) for g(x)=cos(x^6) (d g(x))/dx = -6(x^5)cos(x^6)
Close, but I believe is should be: 309(t^2)((t^3)+8)^102
N = number of nickles D = number of dimes = N+4 Q = number of quarters = 25-N-D = 25-N-(N+4) = 21-(2N) Add the coins to get $3.20 (N*$0.05) + (D*$0.10) + (Q*$0.25) = $3.20 Expressing D and Q in terms of N: (N*$0.05) + ((N+4)*$0.10) + (21-2N)*$0.25=$3.20 Solve for N. Then plug ...
Check the reply to your 1:15am post.
FOIL is an acronym for First Outer Inner Last used when multiplying binomials. 1. Multiply the FIRST terms in each binomail. In this problem that would be x^(1/2) * x^(1/2) 2. Multiply the OUTER terms: x^(1/2) * 4 3. Multiply the INNER terms: -2 * x^(1/2) 4. Multiply the LAST ...
Multiplication is distributive over addition. Division can be performed by multiplying by the inverse of the divisor. So, yes, division is distributive over addition.
Here the vector angles are relative to the X axis. So, east would be 0 degrees, north is 90 degrees, west is 180 degree, and south is 270 degrees. So, SE is 270 + 45 = 315. -45 degrees could also be used.
Break the 3 vectors into components and solve for the unknown vector. For this choose North is positive y East is positive x First vector, 2.00km east represented by (2.00km)x + 0(km)y Second vector, 3.50km SE represented by (3.50)(cos(315))(km)x + (3.50)(sin(315))(km)y Third ...
Let x = first number Let y = second number x +(2x-1) = y 3x-1=y so x = (y+1)/3
3 - 8 difference = 5 4 - 11 difference = 7 5 - 14 difference = 9 etc. In each case the difference is: 2 x (first number) - 1
Let x be the number. (1/3)(x) + 5 = -2 multiply both sides by 3: x + 15 = -6 subtract 15 from both sides to solve for x.
You are CORRECT on #2. Also There is no parenthesis in the problem. I copied it down and added it.
I got the same for #1. For #2 (-6)^-2 =1/((-6)^2) =1/(36
physics please help!
A handy equation for an object with 0 initial velocity and constant acceleration is: v^2 = (2*a*s) where v = final velocity a = acceleration (in this problem it is gravity) s = distance
Passenger height = 2.5m + vt = 2.5m + (2.2m/s)t Camera height = (11.6m/s)t + (1/2)(-g)t^2 The camera reaches the passenger when Passenger height = Camera height solve t for equal height, then plug t into either equation for the height. You will find 2 answers for equal height...
For the problem (4m-7)/2 = 18 To solve for m: The object is to get a single m on one side of the equation. 1. get rid of the denominator (2) on the left side by multiplying both sides of the equation by 2. That gives: 4m-7 = 36 Now add 7 to both sides to get just a term with n...
Paint thickness multiplied by area covered should equal the volume of paint. Let T = thickness of paint. T = (volume of paint) / (area covered) T = (231 in^3) / (450 ft^2) Convert 450 ft^2 to its equivalent in in^2, divide, and you have the answer in inches.
Check the answer for the similar problem you posted. It is solved the same way.
For the problem, a value of x which makes a factor 0 is a solution. (x^2-9)(2x-1) = 0 factoring (x^2-9) further (x+3)(x-3)(2x-1) = 0 For each factor, what value of x will make the term 0? The first term, (x+3), will be 0 for x=-3. The second term is 0 for x=? The third term is...
Math - Imaginary Numbers
Remember that i^2 = -1 3(-2i)^2 =3(-2)^2(i^2) =? -i(isqrt(5))^2 =-i(i^2)(sqrt(5))^2 =?
Math - Imaginary Numbers
Remember that i represents the square root of (-1). So, i^2 = -1 i^5 = (i^2)(i^2)(i) =(-1)(-1)(i) =?
Multiply out all the terms -4(k-2) + 3(k+1)=7 -4k + 8 + 3k + 3 = 7 Now combine like terms (all k's and all numbers) -1k + 11 = 7 11 - 7 = k So, k = ?
The volume of the hole will be the length X width X depth. It's always good to be sure that units for each dimension are the same. In this problem, they are all in meters. Volume = length X width X depth Volume = 6m X 2m X 1m Multiply the right side to get the volume. ...
Let B = the number of balloons in each bag. The problem says that each bag has the same number of balloons. Also, after all the bags are used, 18 more balloons are still needed to get to 138. The equation would be: 5B + 18 = 138 To solve for B first subtract 18 from each side...
To clarify the previous posting Number, Square Root: 9, 3 16, 4 23, 4.796 (approximately)
The square root of a number is the number which multiplied by itself results in the original number. Number Square Root 9 3 16 4 23 4.796 (approximately) There are methods to calculate the square root without a calculator, but they are a bit involved. google: calculating ...
Check Work (Math)
That is correct!
Your answer for the first question (b) is correct. I don't think you copied the second question correctly.
Let's look at this: The original value is 18/7. You want to find an equivalent value that has a denominator of 28. To get that value, you need to multiply the denominator by 4. To "multiply by 1" to not change the value, you need to also multiply the numerator by...
(x+4)log3 = (x+2)log5 (x+4)(0.47712) = (x+2)(0.69897) 0.47712x + 1.90848 = 0.69897x + 1.39794 0.22185x = 0.51054 x=2.301 Checking you will probably find a small rounding error. If you carry the calculations to a lot of decimal places it will be more exact.
See reply to your 6:51pm posting below.
Oops! An error on my part! The last line should be: =((2y+7)^5)x((y-2)^4)x[5x(2y+7)+6x(y-2)x2]
I changed the variable to y to avoid confusion with the x used for multiplication. [(2y+7)^6 x 5(y-2)^4] + [(y-2)^5 x 6(2y+7)^5 x 2] (2y+7)^5 and (y-2)^4 are common to both terms. bring the common factors outside: =((2y+7)^5)x((y-2)^4)x[(2y+7)+(y-2)x2] There are 2 terms in the...
There is an error in the second line. Should be: 10x - 35 < -8
square both sides, collect like terms and solve. Here's the first step: (k+3)^2 = (2k-1)^2 k^2 + 6k + 9 = 4k^2 - 4k + 1 Combine all the like terms. You might factor it out, but I would suggest using the quadratic equation.
I don't think you copied the first question correctly. Did you intend 2 equal signs?
Also, because of the (p+1) term remember that p=-1 will be a solution.
Hint. Each term on both sides has a factor (p+1). Divide all terms on both sides by (p+1). This will simplify it for you.
(x + a ) (x + b) = x^2 + 7x + 10 Think what two number multiplied give 10, and when added give 7?
let x = speed of first part of trip in mph let x-5 = speed of second part of trip in mph 5 hours = 63 miles/x + 6/(x-5) Solve for x. If you solve a quadratic, ignore the answer which would cause the slower speed to be negative (non-real case).
point A f(x) = 1/(x^2) point B f(x+deltaX) = 1/((x+deltaX)^2) The slope of the line between these points is: [f(x+deltaX) - f(x)]/[(x+deltaX - x] The slope of the tangent is given when deltaX->0. to get you started... [(1/(x+deltaX)^2) - 1/x^2]/[x+deltaX - x] Get rid of the...