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A version of this answer, with diagrams and notations, is on my blog, at http://mathdoesnthurt.blogspot.com/2014/10/a-question-was-posed-about-following.html.   First, we must understand the problem. What are we asked to find? (Alternately, what is the unknown?) We...

Consider any value of θ in the domain 0 ≤ θ1 ≤ π⁄2 (where θ1 is acute or right).  If we take the distance from θ1 to π⁄2, add that difference to π⁄2, and call that θ2, then sin(θ1) = sin(θ2).     This is just...

You can use the given point together with the slope of the equation to construct the point-slope form.  I have posted a fuller explanation, with equations and plots, at my blog.  See http://p-nichols.blogspot.com/2014/10/finding-linear-equation-given-point-and.html

Look at a calendar for May.  On each of the first 15 days, write 759.  On each of the next 5 days, write 1985; on the next five days, 1410.  On each of the next 6 days, write 348.     Now, we have 31 measurements, each for one day.  Does this look like a...

Note that for any rational number k, y^(m/n) = y^(km/kn).  We know this because y^(m/n) = (y^(m/n))^(1) (Identity property of exponents) k/k = k * 1/k = 1 (Inverse property of multiplication) (y^(m/n))^(1) = (y^(m/n))^(k/k) (Substitution property of equality) [1] (y^(m/n))^(k/k)...

It can be hard to type mathematical expressions here, but the second term in yours is ambiguous.  It could be either -8x - (1/6)x   (where the second term is the product of one sixth and x) or -8x - 1/(6x)   (where the second term is one divided by the product...

Once you're done building the walkway, you'll have two rectangles, one (the garden) inside the other (the outer edge of the walkway). Recall that to find the area of a rectangle we use the formula A = bh, where A is the area, b is the length of the base of the rectangle, and h is the height...

The ladder forms a triangle with the wall and the ground.  The three points of the triangle are (a) at the foot of the ladder, (b) at the base of the wall, and (c) where the top of the ladder touches the wall; the three sides are the ladder itself, the distance on the ground from the foot of...

The graph of this equation is a line.  We know that because each term is either a constant (1.5) or the product of a constant and the first power of a variable (d, 0.8t). Since we have two variables (d and t), the line sits in a two-dimensional plane, with a vertical axis and a horizontal...

There are a number of ways to solve this.  Probably the simplest is to cross-multiply, using the ratios you've already set up. 6/10 = 8/x That implies 6×x = 8×10 6×x = 80 (6×x)/6 = 80/6 (6×x)/6 = 80/6 x = 13 1/3 minutes = 13 minutes, 20 seconds

Let A be the amount invested in Fund A, which earned 7%, and let B be the amount invested in Fund B, which earned 3%. We know that the sum of the amount earned from Fund A (7%×A) and the amount earned from Fund B (3%×B) is \$138, or (7%×A) + (3%×B) = (0.07×A) + (0.03×B) = \$138 [1] We...

To solve this, we also need the other information from your other posting of this question. Up to Algebra 2: 38 Both:9 AP Calculus:? (https://www.wyzant.com/answers/9343/up_to_algebra_2_38__both9___ap_calculus) The students are divided into three groups: (a) those who entered...

Standard form of a linear equation is Ax+By=C, where A, B, and C are all integers.  Your equation is given in slope-intercept form (usually stated as y=mx+b), so we have to isolate the constant term and then multiply through by the least common denominator of any fractions in the coefficients...

We can use the distributive property to factor the right side of the equation for n, and we get A = nz+n = n(z+1) Then, we can use the division property of equality to prepare to move z+1 to the left side of the equation and to isolate n. A/(z+1) = n×(z+1)/(z+1) Now,...