# Math Homework Help

### Showing All Questions Answered Popular Recommended Unanswered Editor's Choice in Math

• Math
We have to find the roots of : x^3 – 2x^2 – 23x + 60 x^3 – 2x^2 – 23x + 60 = 0 As the equation has a highest power of x, we will have 3 roots. From the numeric term equal to 60 we know that...

Asked by alrightstudent on via web

• Math
We have to prove the sum of the squares of the first n numbers is given by n(n+1)(n+2)/6 We know that (x+1)^3 = x^3 + 3x^2 + 3x + 1, now if we write the cubes of the numbers 1 to n+1, we get 1^3 =...

Asked by aristokid on via web

• Math
We have f(x) = 5x - 2 and g(x) = x^(1/3) [ I have assumed by cubed sqrt you mean raised to the power (1/3)] We have to find fog( - 8) fog(x) = f(g(x)) = f( x^(1/3)) =5 * x^(1/3) - 2 For x = -8...

• Math
We have to solve the system of equations: y=x^2+4 y=2x+7 Equate the value of y => x^2+4 = 2x+7 => x^2 - 2x - 3 = 0 solving the quadratic equation we get two values of x. => x^2 - 3x + x -...

Asked by tahiraha on via web

• Math
The rate of depreciation is given as 30%. This means that the value of the car reduces by 30% every year. Or the value of the car after a year is 1 - 30% = 70% of its value in the previous year....

Asked by sammysoso on via web

• Math
The man can make the trip from city A t city B at a rate inversely proportional to the time he takes. Let the distance between the two cities be D. When he travels at 60 kilometers per hour he...

Asked by mandabearbaybe on via web

• Math
Given f(x) = ax+bx Since wee need to differentiate with respect to a, then we will assume that b is a constant. ==> f'(x)= (ax)' +(bx)' = a'*x + a*x' + bx' = a'x + a...

Asked by mohsin1234 on via web

• Math
Let the amount that the manufacturer gets per chocolate be C. The supermarket marks up the price by 3% and it is sold at \$3. So, we have C *( 1 + 3%) = 3 => C* (1 + 0.03) = 3 => C*( 1.03) =...

Asked by thomas666 on via web

• Math
Use cross multiple: y(2x+1) = 6x-8 2yx +y = 6x - 8 2yx - 6x = -y-8 2x(y-3) = -(y+8) x = -(y+8)/2(y-3) If y = 2, x = 5 This is the only one meeting the requirement.

Asked by lipiciuc on via web

• Math
We have to solve: 6(7^(2x-1) + 7^(x-1) - 1 = 0. Note : I am not sure where the initial brackets that you have started ends, so I'm solving the following equation 7^2(x-1) + 7^(x-1) - 1 = 0 Take...

Asked by rosemin on via web

• Math
We have to simplify : 6 (log c/log a) + 5 log(a) d - 7 log(a) b Now we use the relation that log(a)b = log b / log a 6 (log c/log a) + 5 log(a) d - 7 log(a) b => 6(log c/ log a) + 5( log d/ log...

Asked by rosemin on via web

• Math
We have to solve : | x - 4| = | 2x- 7| Now the absolute value |x| of x as well as -x is equal to x. | x - 4| = | 2x- 7| gives us x - 4 = 2x - 7 and -( x - 4) = 2x - 7 x - 4 = 2x - 7 => x - 2x =...

Asked by carolinesmiths on via web

• Math
We have to solve x^2 - 19x = 90 x^2 - 19x = 90 we use the relation that the roots of a quadratic equation ax^2+ bx + c = 0 are given by [-b + sqrt (b^2 - 4ac)]/2a and [-b + sqrt (b^2 - 4ac)]/2a...

Asked by xetabeta on via web

• Math
We are given that f(x) = x^2 - 3x + 8. f(x-2) can be found by replacing x by (x – 2) in f(x) = x^2 - 3x + 8 => (x – 2)^2 – 3*(x – 2) + 8 Similarly for f(x + 2) replace x with (x + 2) in...

Asked by xetaalpha2 on via web

• Math
The average age of 10 men initially is 20. So the total age of the men is 10*20 = 200. When the two men join the group later, the average age of the group increases by 3. So the total age of all...

Asked by xetaalpha on via web

• Math
We have to express [5x^2 + 10 x + 3] / [x^3 + 2x^2 – x – 2] as partial fractions. First, we factorize the denominator [5x^2 + 10 x + 3] / [x^3 + 2x^2 – x – 2] => [5x^2 + 10 x + 3] /...

• Math
We have to solve 7^(3x) = 8^(2x) Now the base of the two terms are not the same, so we use logarithms. Take the logarithm of both the sides. log( 7^(3x)) = log(8^(2x)) we use the relation log (a^b)...

Asked by rosemin on via web

• Math
We have to find y such that sin y = cos 3y. We know that sin(y) = cos(pi/2-y),so we can convert the given equation to: sin(y) = cos(pi/2-y) = cos(3y) We now equate pi/2 - y and 3y pi/2 - y = 3y...

Asked by rosemin on via web

• Math
Integers are only whole numbers and include both positive as well as negative whole numbers and 0. An integer cannot not have a decimal or a fractional part. The set of integers is {... −2, −1,...

Asked by sampanana on via web

• Math
We have to determine x given that: sin x * sin 2x - cos x * cos 2x > sin 6x We know that cos (a - b) = cos a * cos b - sin a * sin b => - cos ( 2x + x) > sin 6x => -cos 3x > sin 6x...

Asked by mer33 on via web

• Math
x^5-32. We have to factorise this. Solution: Let f(x) = x^5- 32. Put x= 2 in f(x) = x^5- 32. f(2) = 2^5 - 32 = 32-32 = 0. So by remainder theorem, (x-2) is a factor of x^5-32. We know that...

Asked by lemon2 on via web

• Math
When we need to do an operation on two rational numbers, first we need to have a common denominator. If the ddenominators are not the same, then we will have to multiply the denominators by each...

Asked by bibiloi on via web

• Math
The zeroes of a polynomial are simply those values of the variables where the polynomial as a whole equals zero. So, in other words, to find the zeroes of a polynomial, you have to set the whole...

Asked by shoppana on via web

• Math
Given that z is a complex number, then we will rewrite into the complex form z= a + bi We know that the absolute values of z is given by: lzl = sqrt(a^2 + b^2) Then we will write the log of a...

Asked by frontman0 on via web

• Math
A matrix is consisting from rows and columns. These rows and columns contain numbers that are called elements of the matrix. The size of a matrix is m-by-n, where m represents the number of rows...

Asked by hahaz on via web

• Math
We know that (x + y)^2 = x^2 + y^2 + 2xy 9x^2 + 12xy + 4y^2 => (3x)^2 + 2*(3x)*(2y) + (2y)^2 = 49 = (3x + 4y)^2 = 49 => (3x + 4y)^2 = 7^2 => (3x + 4y) = 7 For x = 1 and y = 1 we have 3x +...

Asked by xetaalpha on via web

• Math
To answer this question, split up the line integral into two pieces: intc (x + 2y)dx and intc (x - y)dy. Our parameter is t, 0<=t<=pi/4 (I assume, because your problem statement gives...

Asked by owlstalk on via web

• Math
Notice that the force P acts along x axis, the force Q acts along y axis and the force R acts on a support that expresses the hypotenuse of right triangle that has as legs the supports of P and Q...

• Math
We can write the given polynomial 6*x^4+17*x^3-2*x^2+x-6 as: 6*x^4+17*x^3-2*x^2+x-6 => 6x^4 + 18x^3 - x^3 - 3x^2 + x^2 + 3x - 2x - 6 => 6x^3( x + 3) - x^2(x + 3) + x(x + 3) - 2(x + 3) =>...

Asked by giokarinos on via web

• Math
We'll put the qudratic equal to zero: -3x^2 + 18x - 7 = 0 We'll multiply by -1 both sides: 3x^2 - 18x + 7 = 0 We'll apply the quadratic formula: x1 = [-b + sqrt(b^2 - 4ac)]/2a a,b,c are the...

Asked by giokarinos on via web

• Math
A line is represented mathematically by a "linear" equation, which takes the following standard form: y = mx + b This equation defines the point y given the input x, and parameters m and b. m is...

Asked by salarc17 on via web

• Math
We have the two functions : f(x)=x^2+3x and g(x)=x+3. To determine for what values of x is f(x) = g(x) , equate the two f(x) = g(x) => x^2+3x = x+3 => x^2 + 2x - 3 = 0 => x^2 + 3x - x - 3...

Asked by mamawhit on via web

• Math
Your answer can be derived from an understanding of the unit of current. In your problem, 0.2 A of current is flowing. (We'll assume that this value remains unchanged for the duration of the...

• Math
The bicycle's wheel has a diameter of d cm. Th radius of the wheel is d/2 cm. When the wheel rotates once the bicycle moves forward by 2*pi*d/2 = pi*d cm. If the bicycle is travelling at x km/h, x...

Asked by rosemin on via web

• Math
We need to find the area of the concrete borders. The swimming pool is of dimensions 25m by 10m. The concrete border at the sides which are 25 m each is 2.5 m wide and is 5 m wide at the ends of 10...

Asked by lucky092569 on via web

• Math
We have to determine the co-ordinates of points that lie in the locus given the constraint: modulus(z - 2) ≤ modulus(z - 2i) The modulus of an expression x + yi = sqrt ( x^2 + y^2) We have...

Asked by lemon2 on via web

• Math
Let one of the numbers be x. Then the next consecutive number is (x+1) Given that the sum of the squares is 145. ==> x^2 + (x+1)^2 = 145 ==> x^2 + x^2 + 2x + 1 = 145 ==> 2x^2 + 2x - 144 =...

Asked by jude69 on via web

• Math
We have to solve 2a-5 < 5(a-1) for a. 2a-5 < 5(a-1) open the brackets => 2a - 5 < 5a - 5 => 2a - 5a < -5 + 5 => -3a < 0 => -a < 0 => a > 0 Therefore a > 0

Asked by feres on via web

• Math
We are given that f'(x) = 8x^3 + 3x^2 + 2. To find f(x) we need to find the integral of f'(x). Int[f'(x)] = Int [ 8x^3 + 3x^2 + 2] => 8x^4 / 4 + 3x^3 / 3 + 2x + C => 2x^4 + x^3 + 2x + C Also,...

Asked by totoo on via web

• Math
We have cosec x = 1/sin x. sin (-x) = -sin x. Now sin x * cosec(-x) => sin x * (1 / sin (-x)) => sin x * ( -1 / sin x) => -1 * (sin x / sin x) = -1 Therefore we prove that sin x *...

Asked by meterya on via web

• Math
We have the two functions h(x) = x^3+ x and g(x) = 2x + 3. Now we need to find g(h(2)). h(2) = 2^3 + 2 = 8 + 2 = 10 g(h(2)) = g(10) = 2*10 + 3 = 20 + 3 = 23 Therefore g(h(2)) = 23.

Asked by lalooo on via web

• Math
So simplify 5/k + (k+3)/(k+5), we make the denominator the same for all the terms 5/k+(k+3)/(k+5) => [5(k + 5) + k(k+3)]/ k(k+5) => [5k + 25 + k^2 + 3k]/k(k+5) => (k^2 + 8k + 25)/k(k+5)...

Asked by yasmin130 on via web

• Math
Given the set of numbers 14 , 8, 16, 14 , and x We know that the mean = the median. Let us arrange the numbers from smallest to largest. ==> 8, 14, 14, 16, x Since we so not know that value of x...

Asked by nano75 on via web

• Math
At the x-intercept the value of the y-coordinate is 0. So to find the x-intercept of y = x^2 – 4x + 4 we can substitute y = 0 and solve. x^2 – 4x + 4 = 0 => (x - 2)^2 = 0 we get x = 2....

Asked by neefo on via web

• Math
Given that the center of the circle is the point (0,0). We know that the equation of the circle is given by : (x-a)^2 + (y-b)^2 = r^2 where (a,b) is the center and r is the radius. ==> x^2 + y^2...

Asked by rogeryyo on via web

• Math
The rectangle has a perimeter of 30 cm. Its length is twice its width. Let us denote length by L and width by W. So we have L = 2W Perimeter = 2L + 2W = 30 => 2* 2W + 2W = 30 => 4W + 2W =...

Asked by jojoogel on via web

• Math
We have the set of numbers {2, 3, 7, 12, 15, 22, 72, 108}. Here we see there are 8 terms in total out of which 12 , 72 and 108 or three terms are divisible by both 2 and 3. So the probability of...

• Math
When looking at the clock, we notice that the circumference is divided into 12 equal sections. These sections represents the hours. When the clock is exactly 1:00, the hands will be on the numbers...

• Math
Given that the original price of the DVD player is \$210. First we need to calculate the cost of the DVD player after the 30% off. ==> The sale price = original price - discount ==> Sale price...

Asked by alinnne on via web