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# X + y = 3. x - y = 7 (answer)

x + y = 3 +     x - y = 7      2x = 10 ----> x = 5   5 + y = 3 ----> y = - 2 5 + (- 2) = 3  5 - (- 2) = 7

# Can I reduce an equation when it is set up like x= -2(+ or -) 2i(square root 3)/ 2 (answer)

- 2 ± 2 i √3   ---------------- =         2    2( - 1 ± i √3)  ------------------- =            2    - 1 ± i √3

# Which inequalities represent the possible lengths for the third side, x? (answer)

Rule for Δ ABC: any two sides added together must be greater than the third side. If       AB = c       BC = a       AC = b, then     a + b > c     a + c > b     b + c > a ~~~~~~~~~~~~ If one side of triangle is 6 units, second side is 16 units and...

# Solve root 5x-1=1+root x+2 (answer)

√(5x - 1) = 1 + √(x + 2) √(5x - 1) - √(x + 2) = 1 [√(5x - 1) - √(x + 2)]2 = 12 [√(5x - 1)]2 - 2√(5x - 1) * √(x + 2) + [√(x + 2)]2 = 1  5x - 1 - 2√[(5x - 1)(x + 2)] + x + 2 = 1 - 2√[(5x - 1)(x + 2)] + 6x + 1 = 1  - 2√[(5x - 1)(x + 2)] = -...

# Ratio problem - Solve ASAP NEED SERIOUS HELP (answer)

(1)  ...  x : y = 5 : 2  (2)  ...  y : z = 8 : 11 Let's rewrite (1) as            x : y = 20 : 8 , and            y : z = 8 : 11 Now, both ratios we can rewrite as one:           x : y : z = 20 : 8 : 11           20 + 8 + 11...

# Solve for x and check any extraneous roots : root 5x-1=1 root x+2 (answer)

√(5x - 1) = 1 [√(5x - 1)]2 = 12 5x - 1 = 1  5x = 2 x = 2/5   Let's check solution in the original equation √(5 * 2/5 - 1) = 1 √(2 - 1) = 1 √1 = 1   1 = 1 Thus, x = 2/5 is not an extraneous root.

# solve system of equations. (answer)

x2 - 4y2 + 7 = 0  ..... (1)  3x2 + y2 = 31      ..... (2)  Let's multiply (2) by 4 and add two equations:       x2 - 4y2 = - 7   +   12x2 + 4y2 = 124     13x2 +  0  =  117      x2 = 117 / 13     x2 = 9     x = ± 3 Lets plug...

# prove the following trigonometric identity (answer)

sin2 x + cos2 x = 1               1 csc x = ------             sin x               1 sec x = ------             cos x ~~~~~~~~~~~               1                       1  sin x ÷ ------ + cos x ÷ ------ = 1            sin x                 cos x  sin...

# what is the square root of (6a) times the square root of (3a) plus the square root of (2a)? (answer)

In the set of real numbers for any a ≥ 0 and b ≥ 0 : √(ab) = √a * √b  ~~~~~~~~~~~~~~  √(6a)√(3a) + √(2a) (a ≥ 0) √(18a2) + √2 * √a = √(9a2) * √2 + √2 * √a =  3a√2 + √2 * √a =  √2(3a + √a)

(C) a = 0 produces a counter example. If a = 0, then we have f(x) = 0x + b or f(x) = b , which is a horizontal line. Thus, the range (all possible values of "y") is limited to whatever "b" is.

3x2 - 2x + 1 = 5  3x2 - 2x - 4 = 0 . Let's multiply this equation by 3 9x2 - 6x - 12 = 0 9x2 - 6x = 12 (3x)2 - 2*3x*1 + 1 = 12 + 1 (3x - 1)2 = 13 3x - 1 = ±√13  3x = 1 ± √13         1 ± √13 x = -----------...

# Given functions f and g, perform the indicated operations: (answer)

(a ± b)2 = a2 ± 2ab + b2   (f o g)(x) = f(g(x)) ~~~~~~~~~~~~~~  f(x) = 8x2 - 7x g(x) = 8x - 4 (f o g)(x) = f[g(x)] = 8(8x - 4)2 - 7(8x - 4) = 8(64x2 - 64x + 16) - 56x + 28 = 512x2 - 512x + 128 - 56x + 28 = 512x2 - 568x...

# Use the properties of logarithms to write the expression as a single logarithm: (answer)

logcan = n*logca                                 a logca - logcb = logc ---                                  b logca + logcb = logc(ab)  ~~~~~~~~~~~~~~~~~~~  7 ln x  - (1/4) ln y = ln x7  -  ln y1/4 =        x7             x7   ln...

# find the equation of the line passing through (-3,5) with an undefined slope (answer)

Vertical line has undefined slope. Thus, the equation will be x = - 3 , or for any value of "y" value of "x" is always "- 3"

# If each of the dimensions of a rectangle is increased by 100% by what percent is the area increased (answer)

100% = 1 A = length * width "... if each of the dimensions of a rectangle is increased by 100% ..." Let length of new rectangle be "l1" and width - "w1" l1 = l + l * 100% = l + l * 1 = 2l w1 = w + w * 100% = w + w * 1 = 2w  A1 = 2l * 2w = 4lw...

# if the three segments below were used to form a triangle, what could the values for the length of the third side be? check all that apply. (answer)

Rule for Δ ABC: any two sides added together must be greater than the third side. If    AB = c    BC = a    AC = b, then    a + b > c    a + c > b    b + c > a ~~~~~~~~~~~~ a = 12 b = 3 c = ? 1.)  12 + 3 > c...

# hello i need help with my homework for geometry it's about triangles and properties (answer)

Angles ACB and DGC are on opposite sides of transversal line AC and two parallel lines DF and HI. Thus, angle ACB and DGC are alternate interior angles, therefore measure of angel ACB = measure of angel DGC  m < ACB = m < DGC = 58.6o < CGD and < AGD are supplementary angles ----->...