# algebra1 Homework Help

### Showing All Questions Answered Popular Recommended Unanswered Editor's Choice in algebra1

• Math
We wish to evaluate the expression `10^(((x+y)/2) - 3z)` First, simplify the power into seperate terms involving each of `x`, `y` and `z` only: `10^(((x+y)/2) - 3z) = 10^(x/2 + y/2 - 3z)` Then...

Asked by inquire123 on via web

• Math
First evaluate the expression under the square root sign: `x^2 + 2x + (y-1)^2 - 2xy = x^2 + 2x + y^2 - 2y + 1 - 2xy` `= x^2 + y^2 -2xy + 2(x-y) + 1` Now `(x-y)^2 = x^2 + y^2 - 2xy` So that...

Asked by phanpal999 on via web

• Math
a) We want the roots of `x^3 +3x^2 -4x + d=0` If we are given that two of the roots are opposites then we have that `x^3 + 3x^2 - 4x + d = (x-a)(x+a)(x-b)` `= (x^2 -a^2)(x-b)` Multiply this out...

Asked by konkonz on via web

• algebra1
y-3=3(x+1)If we are going to express this in slope-intercept form y=mx+b, then we have todistribute 3 to x+1.y-3=3x+3And, isolate the y by adding 3 on both sides of the...

Asked by asmamanasrah on via web

• algebra1
the answer is NOT 5! C(a,b) may also be written as aCb, implying a!/b!(a-b)! Hence, (n+1)C3 = (n+1)!/3!(n+1-3)! But (n+1)! = (n+1)n! And (n+1-3)! = (n-2)! Therefore, (n+1)C3= (n+1)n!/3!(n-2)! Also,...

Asked by myt123 on via web

• algebra1
We have to prove that a^2 - 4a + b^2 + 10b + 29>=0, for real values of a and b. a^2 - 4a + b^2 + 10b + 29 => a^2 - 4a + 4 + b^2 + 10b + 25 => (a - 2)^2 + (b + 5)^2 The sum of squares of...

Asked by maisaphie on via web

• algebra1
k! = 1*2*3*...*k (k - 1)/k! = k/k! - 1/k! => 1/(k - 1)! - 1/k! The sum of (k - 1)/k! for k = 1 to n is: 1/0! - 1/1! + 1/1! - 1/2! + 1/2! - 1/3! + ... + 1/(n - 1)! - 1/n! => 1/0! - 1/n!...

Asked by anneenna on via web

• algebra1
We'll apply the quotient rule of logarithms: log (a/b) = log a - log b According to this rule, we'll get: log (2x-5)/(x^2+3) = log (2x-5) - log(x^2+3) We'll re-write the equation: log (2x-5) -...

Asked by anneliese94 on via web

• algebra1
We'll replace the result of the difference x - y by z, at the numerator of the 1st option. (x-y)/2z = z/2z We'll simplify and we'll get: (x-y)/2z = 1/2 Since the result is not equal 2, we'll reject...

Asked by jungbac on via web

• algebra1
The absolute value of the complex number can be evaluated when we know the rectangular form of z: z = x + i*y |z| = sqrt(x^2 + y^2) We'll identify the real part and the imaginary part of z: x =...

Asked by deuxtoi on via web

• algebra1
We'll multiply the first fraction by (3x - 5) and the 2nd by (4x-1)[3x(3x - 5) + 2x(4x-1)]/(4x-1)(3x-5)We'll remove the brackets:(9x^2 - 15x + 8x^2 - 2x)/(12x^2 - 20x - 3x + 5)(17x^2 - 17x)/(12x^2...

Asked by gudeapp on via web

• algebra1
To determine the expression of f(x^2), we'll simply replace x by x^2 in the expression of the function: f(x^2) = 4*(x^2)^2 - 3 f(x^2) = 4x^4 - 3 The found expression of f(x^2) is f(x^2) = 4x^4 - 3

Asked by undoitu on via web

• algebra1
The linear function put in standard form is: f(x) = ax + b Since the graph of the function is passing through the points (1,2) and (3,1), that means that if we'll substitute the coordinates of the...

Asked by greynose on via web

• algebra1
We'll apply quadratic formula to determine the roots: b1 = [-(-21)+sqrt((-21)^2 + 4*108)]/2*1 b1 = (21+sqrt9)/2 b1 = (21+3)/2 b1 = 12 b2 = (21-3)/2 b2 = 9 We can write the quadratic expression as a...

Asked by noralbbig on via web

• algebra1
We'll re-write g as a product of linear factors, using it's roots. x1 = [1 + sqrt(1 + 8)]/2 x1 = (1+3)/2 x1 = 2 x2 = (1-3)/2 x2 = -1 Therefore, g = (x-2)(x+1) Since f is divisible by g, it means...

Asked by lexijuly on via web

• algebra1
We'll determine the inverse of g(x) in this way. Let g(x) = y y = -2/(x+1) Now, we'll find x with respect to y. F y(x+1) = -2 We'll remove the brackets and we'll get: yx + y = -2 We'll isolate x to...

Asked by galbenusa on via web

• algebra1
We'll shift -6 to the left side: -5126+6 = - 5(x+ 22)^(5/3) -5120 = 5(x+ 22)^(5/3) We'll divide by -5 both sides: 1024 = (x+ 22)^(5/3) We'll raise both sides to 3/5 power: 1024^(3/5) = x+22 We'll...

Asked by abigaile on via web

• algebra1
Writing 9 as a power of 3, we'll create matching bases both sides: 9 = 3^2 We'll apply the rule of negative power: a^-b = 1/a^b We'll put a = 9 and b = -3 9^-3 = 1/9^3 = 1/(3^2)^3 = 1/3^6 = 3^-6...

Asked by portoruj on via web

• algebra1
We'll choose to re-write f(x): ( 2x^3 + 2x - 1 )/ (x^2 + 1) = (2x^3 + 2x)/(x^2 + 1) - 1/(x^2 + 1) We'll factorize by 2x the first fraction: (2x^3 + 2x)/(x^2 + 1) = 2x(x^2 + 1)/(x^2 + 1) We'll...

Asked by labrrat on via web

• algebra1
We'll write the rectangular form of any complex number is z = x + y*i. The trigonometric form of a complex number is: z = |z|(cos a + i*sin a) |z| = sqrt(x^2 + y^2) cos a = x/|z| sin a = y/|z|...

Asked by magnet1qu3 on via web

• algebra1
We'll ilustrate the idea with the help of the following example: 3*2^2x - 5*2^x*3^x + 2*3^2x= 0 We'll divide by 3^2x to create matching bases that can be replaced by another variable, later on:...

Asked by zuzuman on via web

• algebra1
Since the composition of 2 functions is not commutative, then (fog)(x) is not the same with (gof)(x) We'll get (fog)(x) for f(x) = x^2 and g(x) = (x-7). (fog)(x) = f(g(x)) We'll substitute x by...

Asked by museinspires on via web

• algebra1
We'll start by imposing the constraint of existence of the square roots: x+2 >=0 x> =-2 2-x>=0 x=<2 The interval of possible values for x is [-2 ; 2]. Now, we'll solve the equation....

Asked by sodelete on via web

• algebra1
We notice that 6^x = (2*3)^x But (2*3)^x = 2^x*3^x We'll subtract 5*2^x*3^x both sides: 3*2^2x + 2*3^2x - 5*2^x*3^x = 0 We'll divide by 3^2x: 3*(2/3)^2x - 5*(2/3)^x + 2 = 0 We'll note (2/3)^x = t...

Asked by for3cast on via web

• algebra1
We'll use the theorem of arithmetic mean to determine the terms of the arithmetic progression. 4 = (x+y)/2 => 8 = x+y (1) y = (4+12)/2 y = 16/2 y = 8 We'll substitute y into (1): 8 = x+8 We'll...

Asked by markusg on via web

• algebra1
To find the local extreme of a function, first we have to determine the critical value of the function. The critical value of the function is the root of the first derivative of the function....

Asked by l0l1 on via web

• algebra1
Before solving the equation, we'll impose conditions of existence of the square root. 5x-6 >= 0 We'll subtract 6 both sides: 5x >= 6 We'll divide by 5: x >=6/5 The interval of admissible...

Asked by albimaia on via web

• algebra1
We'll impose the constraints of existence of logarithm. x>0 The solution has to be in the interval of admissible values (0,+infinite) lgx/(1-lg2) = 2 lgx = 2 - 2*lg2 Well use the power rule of...

Asked by jolyanne on via web

• algebra1
We'll denote the point with that has equal coordinates as M(m,m). Since the point is located on the line y = 0.5x - 0.5, it's coordinates verify the expression of the line. We'll put y = f(x) and...

Asked by ulichh on via web

• algebra1
The complex roots of a polynomial are always found as conjugate pairs. For the root 2 - i, the complex conjugate is 2 + i. The polynomial has the roots 2 - i and 2 + i Irrational roots are also...

Asked by hahaz on via web

• algebra1
We'll establish the constraints of existence of logarithms: x - 24/5>0 x > 24/5 2x>0 x>0 The range of admissible values for x is (24/5 ,+inf.). We'll apply quotient property of...

Asked by labrrat on via web

• algebra1
The function f(x) = x^2 - tx - 3. The point (2, 9) lies on the curve. => 9 = 2^2 - t*2 - 3 => 9 = 4 - 2t - 3 => 8 = 2t => t = 4 The coefficient t = 4

• algebra1
We have the points P(7,11) and Q(-2,4), and we need to find the length, slope and the midpoint of the line segment joining them. The length of the line segment is: sqrt ((7 + 2)^2 + (11 - 4)^2)...

Asked by pavelpimen on via web

• algebra1
We have to simplify: 4t^2- 16/8/t - 2/6 4t^2- 16/8/t - 2/6 => 4t^2- (16/8)/t - (2/6) 16/8 = 2 and 2/6 = 1/3 => 4t^2- 2/t - 1/3 We can simplify 4t^2- 16/8/t - 2/6 as 4t^2- 2/t - 1/3.

Asked by ggenius on via web

• algebra1
We have to solve 13/20-7/10x=0.5 for x 13/20-7/10x=0.5 => 13x/20x - 14/20x = 1/2 => (13x - 14)/20x = 1/2 => 13x - 14 = 10x => 3x = 14 => x = 14/3 The value of x = 14/3

Asked by realcomplexnr on via web

• algebra1
To solve 2x - y = 5 ...(1) 3x - 2y = 9 ...(2) using substitution take (1) 2x - y = 5 => y = 2x - 5 substitute in (2) 3x - 2(2x - 5) = 9 => 3x - 4x + 10 = 9 => -x = -1 => x = 1 y = 2x -...

Asked by sixpenpencil on via web

• algebra1
A polynomial has complex roots in pairs of conjugates. As the polynomial has roots 2 and 2i, it also has -2i as a root. The polynomial is: (x - 2)(x - 2i)(x + 2i) => (x - 2)(x^2 - 4i^2) => (x...

Asked by fairydrink on via web

• algebra1
Consecutive terms of a GP have a common ratio. if 2, x, y, 16 form a GP. => 16/y = x/2 => x = 32/y y/x = x/2 Substitute x = 32/y => y/(32/y) = (32/y)/2 => 2y = (32/y)^2 => 2y^3 =...

Asked by gudeapp on via web

• algebra1
We have to solve x^4 - 3x^2 + 2 = 0 x^4 - 3x^2 + 2 = 0 => x^4 - 2x^2 - x^2 + 2 = 0 => x^2(x^2 - 2) - 1(x^2 - 2) = 0 => (x^2 - 1)(x^2 - 2) = 0 x^2 = 1 => x = 1 , x = -1 x^2 = 2 => x =...

Asked by printsaltr on via web

• algebra1
We have to find the complex number z given that (3z - 2z')/6 = -5 Let z = a + ib, z' = a - ib (3z - 2z')/6 = -5 =>(3(a + ib) - 2(a - ib)) = -30 => 3a + 3ib - 2a + 2ib = -30 => a + 5ib =...

Asked by ulichh on via web

• algebra1
We'll write the given expresison as a fraction, using the negative power property: (7x-x^2)^-1 = 1/(7x-x^2) We'll get 2 elementary fractions because we notice 2 factors at denominator. 1/(7x-x^2)...

Asked by greta92 on via web

• algebra1
We'll remove the brackets, using FOIL method: (-2i+5)(i+7) = -2i^2 - 14i + 5i + 35 We know that i^2 = -1 (-2i+5)(i+7) = 2 - 9i + 35 We'll combine real parts: (-2i+5)(i+7) = 37 - 9i The result of...

Asked by andrzej on via web

• algebra1
It is given that 3z -9i = 8i + z + 4 3z -9i = 8i + z + 4 => 3z - z = 4 + 8i + 9i => 2z = 4 + 17i => z = 2 + 17i/2 |z| = sqrt (2^2 + (17/2)^2) => sqrt (4 + 289/4) => sqrt (305/4)...

Asked by starshippiy on via web

• algebra1
It is given that log(72) 48 = a and log(6) 24 = b a = log(72) 48 = log(6) 48/ log(6) 72 => log(6) (6*8)/log(6) 6*12 => [1 + log(6) 8]/[1 + log(6) 12] => [1 + 3*log(6) 2]/[2 + log(6) 2] b...

Asked by solvedphyz on via web

• algebra1
It is given that log x^3- log 10x = log 10^5. To determine x , use the property : log a - log b = log a/b log x^3- log 10x = log 10^5 => log (x^3 / 10x) = 10^5 => x^2 / 10 = 10^5 => x^2 =...

Asked by kamused on via web

• algebra1
The equation to be solved is : (3x+7)(x-1) = 24 (3x+7)(x-1) = 24 => 3x^2 + 4x - 7 = 24 => 3x^2 + 4x - 31 = 0 x1 = -4/6 + sqrt (16 + 372) /6 => -2/3 + (sqrt 97)/6 x2 = -2/3 - (sqrt 97)/6...

Asked by raydusol on via web

• algebra1
We have to solve 3^(3x-9) = 1/81 for x 3^(3x-9) = 1/81 => 3^(3x-9) = 3^(-4) as the base is the same equate the exponent 3x - 9 = -4 => 3x = 5 => x = 5/3 The solution is 5/3

Asked by sirserie on via web

• algebra1
The equation to be solved is (x-4)^1/2=1/(x-4) (x-4)^1/2=1/(x-4) square both the sides => x - 4 = 1 / (x - 4)^2 => (x - 4)^3 = 1 => 1 - (x - 4)^3 = 0 => (1 - (x - 4))(1 + x - 4 + (x -...

Asked by undoitu on via web

• algebra1
We need to solve (log(2) x)^2 + log(2) (4x) = 4 Use the property that log a*b = log a + log b (log(2) x)^2 + log(2) (4x) = 4 => (log(2) x)^2 + log(2) 4 + log(2) x = 4 => (log(2) x)^2 + 2 +...

Asked by pavelpimen on via web