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Hi Sabrina, Let's take each part of this multipart problem one step at a time and all will be clear.  Part (a): We can set up 2 equations using the distance formula:  D = RT Our formula tells us that the distance (D) is the product of the rate or speeed (R) and...

Hi Adin, We can establishing new Trig identities by making use of the known Trig identities. Let's apply this approach with our first Trig identity, we need to prove:  csc * cos = cot We can replace the csc on the left side of the equation with the known reciprocal...

Hi Betsy, Let's begin by writing the ratio of our larger object to our smaller object (the larger object will be the one with the greater power of 10): larger object / smaller object = 1.31 x 108 / 3.2 x 105 Now let's reduce our ratio to a fraction with a denominator of 1 and, thereby,...

Hi Shauntia, Factoring a quadratic equation only works when the solution has roots which are rational numbers - meaning that each root is a quotient of 2 integers.  Otherwise, the solution can only be found by using the quadratic formula or by completing the square.  The quadratic...

Hi Tanesha, Let's begin by putting both equations into slope-intercept form (y = mx + b): 3x + y = -4 becomes y = -3x - 4 (slope (m) = -3 and y-intercept (b) = -4) x + 2y = 2 becomes 2y = -x + 2 and then y= -0.5x + 1 (slope (m) = -0.5 and y-intercept...

Hi CiJi, Let's begin by writing out our equation as you indicated (the 6x^2 and -3/2 terms being under the square root sign):  sqrt(6x^2) + 2x - sqrt(3/2) = 0 Now let's isolate the sqrt(6x^2) term on the left side by moving the other two terms to the right side (reversing...

Hi Erika, Let's begin by writing out the expression we need to simplify:  (2x - 3)^2 First, we know that squaring an expression is the equivalent of multiplying the expression by itself. So we can rewrite our exprssion as:  (2x - 3)(2x - 3) Now we can use FOIL to multiply...

Hi Grace, Let's begin by writing out our equation:  x/5 = -7 This will be an easy one step operation to solve for x. We will get rid of the fraction on the left side by multiplying both sides by the denominator of the fraction (5): (5)(x/5) = (5)(-7) After multiplying both...

Hi Grace, Let's begin by writing out our equation as you typed it in (3 divided by 2b = 14 and 1/2):  3/2b = 14 1/2 First, we want to convert the mixed number 14 1/2 to an improper fraction: (whole number x denominator + numerator) / denominator (14 x 2 + 1) / 2...

Hi Grace, Let's begin by writing out our equation:  1 / 3y = 18 First, we want to get rid of the fraction on the left side of the equation by multiplying both sides of the equation by the denominator (3y), which will cancel out the denominator (3y): (3y) (1 / 3y) = (3y)(18)...

Hi Dani, Let's begin by defining a sector of a circle - it's a portion (fraction) of the circle expressed as a ratio:  number of degrees in arc of sector / number of degrees in circle (360 degrees).   For example, if the arc marked out by our sector...

Hi Jessica, Let's begin by writing out our equation:  9 / (2x + 1) = 4 / x First, we can see that our equation is actually a proportion - 2 ratios (fractions) set equal to each other. In a proportion, the cross products (numerator x denominator diagonally across the equal sign...

Hi Lakeyshia, Let's begin by writing our equation:  3(4z - 1) - 2(2 + 8) = 3(2 + 1) First, we'll combine all like numeric terms in the parentheses on both sides of the equation: 3(4z - 1) - 2(10) = 3(3) Next, we'll do the multiplication operation indicated...

The coordinate plane consists of a vertical (up and down) line called the y axis and a horizontal (left and right) line called the x axis. The center of the coordinate plane (also called the origin) is the point both the horizontal horizontal x coordinate and the vertical y coordinate are both...

The answer to this question is false, because a line of best fit (also called a "trend line") should pass thru as many data points as possible to show a linear correlation.  It should also be noted that scatter plots can also show non-linear (curved) correlations between variables...