# Math Homework Help

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• Math
What you need to do is put this equation that is currently in "general form" (y=ax^2 +bx+c) into what is called "vertex form" (y-k=a(x-h)^2) To do this, you must follow these steps: 1) Subtract...

Asked by sj94 on via web

• Math
Let's call the first number N1 and the second number N2. So, let's call N1 the smaller number and N1=x Let's call N2 the larger number and N2=x+4. X(X+4)=45 x^2+4x=45 x^2+4x-45=0 (x+9)(x-5)=0...

Asked by franjess on via web

• Math
Triangle ABC is isosceleswith AB= AC. To find BD^2- CD^2. Let D be the point on AC where the circle onAB as diameter intersects. Now AB = AC by data, The angle ADB is a right angle ,as AB is the...

Asked by issro on via web

• Math
To examine the point x= 1/3 on y(x) = (1/12)(3x+1)^4 - 8x. At x = 1/3, y(1/3)= (1/12)(3/3+1)^4- 8/3= 16/12 - 8/3 = {32-8*32}/12 = -4/3. Therefore y(1/3) = -4/3. Therefore y(1/3) = -4/3. Therefore...

Asked by littlecrumpet on via web

• Math
If 3x^2, x and 2 are subsequent terms of a GP, there is a common ratio between 3x^2 and x and between x and 2. So we have 3x^2 /x = x /2 => 2*3*x^2 = x^2 When we cancel x^2, we get => 6 = 1,...

Asked by xetaalpha2 on via web

• Math
We have to find x and y given that (8x + yi) / (1 + 4i) = (2x + i)/ (3 + 2i) (8x + yi) / (1 + 4i) = (2x + i)/ (3 + 2i) => (8x + yi) (3 + 2i) = (2x +i) (1+ 4i) => 24x + 16xi + 3yi + 2yi^2 = 2x...

Asked by xetaalpha on via web

• Math
To find the required area we need to calculate the definite integral of the function y = sqrt x, between the limits x = 0 and x = 25. First let us find the indefinite integral of y = sqrt x y =...

Asked by zeezey on via web

• Math
Given the equation:\ 1/8 = 16^x First we will simplify 8 and 16 as powers of the prime number 2. We know that: 8 = 2*2*2 = 2^3 16 = 4*4 = 2*2*2*2 = 2^4 Now we will rewrite into the given equation:...

Asked by swavers on via web

• Math
Let the width of the gravel border be x. Then the rectangle's sides after the gravel is: Length = 10 + x Width = 4 + x The area of the rectangle + the border = (x+10)*(x+4) ==> The area of the...

Asked by jgwirki on via web

• Math
Given the curve y= 50/(2x-1)^2 We need to find the tangent line at the point (3,2) We know that the equation of the tangent line is: (y-y1) = m(x-x1) where (x1,y1) is any point on the line and m is...

Asked by littlecrumpet on via web

• Math
We are given that f(x) = 3x^2 - 2x + 5 and g(x) = 3x - 1. We have to find g(4) - f(-2). g(4) = 3*4 - 1 = 12 - 1= 11 f(-2) = 3*(-2)^(2) - 2*(-2) + 5 = 3*4 + 4 + 5 = 12 + 4 + 5 = 21 Therefore g(4) -...

Asked by doribelle on via web

• Math
We have to solve the equation 9^(x-1)=27^(x+1) for x. 9^(x-1)=27^(x+1) => 9^x/ 9 = 27^x * 27 => 9^x / 27^x = 27*9 => 3^2x / 3^3x = 3^5 => 3^(2x - 3x) = 3^5 As the base 3 is the same we...

Asked by doglove on via web

• Math
We have to solve for x given that : x^(-4/3)-1=15 x^(-4/3) - 1 = 15 => x^(-4/3) = 15 + 1 => x^( -4/3) = 16 Take the log to base 4 of both the sides => log [ x^(-4/3)] = log 4^2 => -...

Asked by mamawhit on via web

• Math
When you raise any square root to the 2nd power, you will get the values inside the square root by itself. For example: If 2= sqrtx , then, we know that x = 4. We can determine the value by...

Asked by becaree on via web

• Math
Using the law of exponentials yields: `a^6 = a^(2*3) => a^(2*3) = (a^2)^3` Reasoning by analogy yields: `b^(2*3) = (b^2)^3` Converting the difference of cubes into a product yields: `(a^2)^3 -...

Asked by she16 on via web

• Math
The algebraic form of an imaginary root is `z = x + i*y` , where x represents the real part and y represents the imaginary part. A polynomial can only have an even number of comeplex roots since if...

Asked by bookofhth on via web

• Math
Yest it is important. When we know that location of the angle, we can determine the values of the trigonometric identities. For example: We will compare the angle pi/3 into the first, second,...

Asked by siteulove on via web

• Math
The value of cos 30 is usually known to all students. cos 30 = (sqrt 3)/2. Now we use the formula for cos 2x, which is: cos 2x = (cos x)^2 - (sin x)^2 => cos 2x = 2 (cos x)^2 - 1 Now substitute...

Asked by mwin002 on via web

• Math
Let the distance where the defender and the prisoner met be D. Then the distance the defender ran = D Then, the distance the prisoner ran = D-27 The number of steps that the defender ran to D is x...

Asked by funkygrace on via web

• Math
We have the vectors u = 3i - 4j and v = 2i + j. Now the cosine of the angle between two vectors A = a1*i + b1*j and B = a2*i + b2*j is given by cos...

Asked by starshippiy on via web

• Math
You have to be a little bit more specific. If you are referring to the constraints of existence imposed by the denominators of the fraction, the value of the given expression has to be different...

Asked by electrika on via web

• Math
We need to find the antiderivative of f(x)=x*e^4x We solve this problem using Integration by parts: Int [f(x)g'(x) dx = f(x)g(x)- Int [ f'(x)g(x) dx] Let f(x) = x and g'(x)= e^4x => g(x) =...

Asked by for3cast on via web

• Math
We have a + b = 9 and a – b= 2. The easiest way to find a^4 + b^4 would be to first use the given values of a + b and a – b to determine a and b. a + b = 9 … (1) a – b = 2 … (2) (2) +...

Asked by xetaalpha on via web

• Math
We have the function f(x) = cos 2x /(sin x)^2*(cos x)^2 cos 2x = (cos x)^2 - ( sin x)^2 => cos 2x /(sin x)^2*(cos x)^2 => [(cos x)^2 - ( sin x)^2] / (sin x)^2*(cos x)^2 => 1/ (sin x)^2 -...

Asked by agneslund on via web

• Math
We have to find x given that 26|2x+1|=52. 26|2x+1|=52 cancel 26 from both the sides. => |2x + 1| = 2 Now |x| represents the absolute value of x and has the same value for x as well as -x. =>...

Asked by singwriter on via web

• Math
We have to solve : (1/5)[(1/5)(a -1/5) - (1/5)] = 2/5 and determine the value of a. (1/5)[(1/5)(a -1/5) - (1/5)] = 2/5 => [(1/5)(a -1/5) - (1/5)] = 2 open the brackets => (1/5)a - (1/5)(1/5)...

Asked by lesoir on via web

• Math
We have to verify if cos^4x + 2sin^2x - sin^4x = 1. Now cos^4x + 2sin^2x - sin^4x => [(cos x)^2]^2 + 2sin^2x - sin^4x Now use the relation (cos x)^2 = 1 - (sin x)^2 => [1 - (sin x)^2]^2 +...

Asked by mantov on via web

• Math
We have the curve y=x^2 - 2x + ln e^2. Now we need to find the extreme point of the curve. For this, we first find the first derivative of the curve. y = x^2 - 2x + ln e^2 => y = x^2 - 2x + 2...

Asked by sokolof on via web

• Math
We have to solve 13^(13x+1)=3^x for x. Looking at 13^(13x+1)=3^x, the bases are not the same, so we cannot equate the exponential. Therefore, we can only solve the problem using logarithms. Take...

Asked by articsonia on via web

• Math
We have to prove that 1/cos^2x+tan^2y=1/cos^2y+tan^2x Now 1/( cos x)^2 + ( tan y )^2 - 1/ (cos y)^2 - (tan x)^2 => [(sin y)^2/ (cos y)^2] + 1/ (cos x)^2 - 1/ (cos y)^2 - [(sin x)^2/ (cos x)^2]...

Asked by orlovolga on via web

• Math
We'll re-write the function: f(x) = 1/(x+1)(x+2) The function is continuous over the interval [1;2] (the function is discontinuously for x = -1 and x = -2, that are the roots of the denominator)....

Asked by riverwave on via web

• Math
We have to find the sum of the terms An = n^2 + 12n Now Sum [ An], of n terms => Sum [ n^2 + 12n ] , of n terms => Sum [ n^2] + Sum [ 12n] , of n terms => n(n+1)(2n+1)/6 + 12* n(n+1)/2...

Asked by bookofhth on via web

• Math
To determine the antiderivative, you'll have to evaluate the indefinite integral of the given function y. Int f(x)dx = Int sqrt(25 - x^2)dx (y = f(x)) We'll factorize by 25: Int sqrt[25(1 -...

Asked by pengui on via web

• Math
Given the logarithm equation: log(x) 8e^3 = 2 We need to find the values of x. let us rewrite into the exponent form. ==> x^2 = 8e^3 But we know that 8= 2^3 ==> x^2 = (2^3)(e^3) Now we will...

Asked by alinnne on via web

• Math
Given that: a^2 - b^2 = 8 ............(1) ab = 2..................(2) We need to determine a^4 + b^4 Let us square equation (1). ==> (a^2 - b^2)^2 = 8^2 ==> a^4 - 2a^2 b^2 + b^4 = 64 ==>...

Asked by neefo on via web

• Math
Given the polynomial P(x) = x^3 - 3x^2 - 10x + 24 We are given that x=2 is one of the root. Then we know that (x-2) is one of the factors of P(x). ==> P(x) = (x-2) * Q(x) Now we will divide P(x)...

• Math
Given the number i^231 Let us simplify and determine the values. First we will rewrite the power. ==> i^(231) = i^(3+228) Now we will use exponent properties to simplify. We know that x^(a+b) =...

• Math
Given the quadratic equation f(x) = 2x^2 + 5x -k We need to find the value of k such that f(x) has two real solutions. We will use delta to determine the values of k. We know that the function has...

Asked by jojoogel on via web

• Math
Given the parabola y= x^2 - 5x + 4 and the line y= 2x-2 We need to find the intersection points of the parabola and the line. The intersection points are the values of x and y such that: the...

Asked by roooze on via web

• Math
a = ( 3- sqrt2)^1/2 b = ( 3+ sqrt2)^1/2 We need to find the values of b(1/a - b) First we will rewrite: b*(1/a - b) = b/a - b^2 Now we will calculate each terms. ==> b/a = (3+sqrt2)^1/2 /...

Asked by maisaphie on via web

• Math
Let the width of the perimeter be "w" and the length be "L" Given that the perimeter is 160 cm But the perimeter is given by : P = 2L + 2W = 160 We will divide by 2. ==> L + w = 80...

Asked by rogeryyo on via web

• Math
Given that: x^2 - y^2 = 10..............(1) x+y = 2..............(2) We need to find the values of x and y. First , we will rewrite equation (1) We know that (x^2 - y^2) = (x-y)(x+y) ==>...

Asked by meterya on via web

• Math
1/xy(x+y+z)+1/yz(x+y+z)+1/xz(x+y+z) The least common denominator is xyz(x+y+z) Since this is not a full equation- it does not have "=" sign-, we cannot multiply least common denominator. But, we...

Asked by babysana on via web

• Math
Given the point (-2, k) and the line -3x+3y=4 Use the point (-2, k) and let x=-2 and y=k, and plug into the line -3x+3y=4. -3(-2) + 3(k) = 4 Solve for k. 6 + 3k =4 3k=4-6 3k=-2 k=-2/3

Asked by genieee on via web

• Math
Let us assume that the number is E. ==> E = (1-1/10) ( 1-1/11) ( 1- 1/12) .... (1-1/99)( 1- 1/100) Let us rewrite the terms by using the common denominator. ==> 1- 1/10 = 10/10 - 1/10 = 9/10...

Asked by zaidzoo on via web

• Math
The property is: log (a) + log (b) = log (ab) The bases of the logarithm must be equal. Let us solve an example. Given the logarithm equation: log (x-2) + log x = log 4 We need to solve for x. We...

Asked by merishorverde on via web

• Math
Given the function f(x) = -3(x-10)(x-4) We need to find the maximum value. First we will open the brackets and expand the function. ==> f(x) = -3(x^2 -14x + 40) = -3x^2 + 42x -...

Asked by clara2 on via web

• Math
Let us assume that the width of the field is "W" and the length of the field is "L" We are given that the area of the rectangular field is 300 m^2 But we know that the area = L*W ==> L*W = 300...

Asked by nano75 on via web

• Math
I will explain in an example: We have the equation: 2x + 5 = 9 We will solve the equation by isolating x on the left side. We will subtract 5 from both sides. ==> 2x = 4 ==> x = 2 Then there...

Asked by fairydrink on via web