Maxematics

Step one: Find the negative reciprocal of the line where it passes through A

The negative reciprocal of y = x+3 is y = -x+b, and to find b, we can plug in x and y. Doing so gets us "7 = -1 + b", so b is 8. Therefore, the line we were looking for is "y = -x+8"

Step two: Find the point of intersection of the lines.

To find the point of intersection, we simply find what value of x makes both equations true, or, in our case, what value of x makes "x + 3 = -x + 8". Solving for x, we get x = 2.5, so y = 5.5. Therefore, our lines intersect at (2.5, 5.5).

Step three: Find the point's distance from intersection, then flip that.

To go from (2.5, 5.5) to (7, 1), you must move right 4.5 units, then down 4.5 units. We then do the opposite of this, and move up 4.5 units and left 4.5 units from the intersection, bringing us to (2.5 - 4.5, 5.5+4.5) = (-2, 10), which is what we're looking for.

After following all these steps, we can now see that the coordinates of B are (-2, 10).

\(\frac{1}{1 \times 4} + \frac{1}{4 \times 7} + \frac{1}{7 \times 12}\)

\(\frac{1}{4}+\frac{1}{28}+\frac{1}{84}\)

\(\frac{21}{84}+\frac{3}{84}+\frac{1}{84}\)

\(\mathbf{\frac{25}{84}}\)

\(1 + \frac{3}{6} + \frac{5}{6^2}\)

\(\frac{6}{6}+\frac{3}{6}+\frac{5}{36}\)

\(\frac{9}{6}+\frac{5}{36}\)

\( \frac{54}{36}+\frac{5}{36}\)

\(\mathbf{\frac{59}{36}}\)

Since all sides of a square are equal, the top side of the square is one. Since the sides of equilateral triangles are also the same, all of the sides on the equilateral triangles are also one. The bases of two of these equilateral triangles almost make up the side length of the large square, but there is a gap. If we continue the horizontal line made up by those two bases, we can see that the shape to the right of the last equilateral triangle is another equilateral triangle, just cut off halfway. This means that the whole length of the side of the square is 2 sides of the equilateral triangle plus one half of the side, which is 1 + 1 + 1/2 = 5/2. To find the area of the large square, we just square the side length, getting (5/2)^2 = 25/4 square units.

You might want to double check the question, because there is no real pair of numbers that holds those properties. There are, however, complex numbers that do:

\(y = 10 - x\)

\(x^3 + (10-x)^3 = 162 +x^2 + (10-x)^2\)

\(x^3 + (10-x)^2(10-x) = 162 + x^2 + (100 - 20x + x^2)\)

\(x^3 + (100-20x+x^2)(10-x) = 2x^2-20x+262\)

\(x^3 + (1000 -200x+10x^2-100x+20x^2-x^3) = 2x^2-20x+262\)

\(30x^2-300x+1000 = 2x^2 - 20x + 262\)

\(15x^2-150x+500=x^2-10x+131\)

\(14x^2-140x+369 = 0\)

\(x^2-10x+\frac{369}{14} = 0\)

\(x^2 - 10x +\frac{350}{14} = -\frac{19}{14}\)

\(x^2 - 10x + 25 = -\frac{19}{14}\)

\((x-5)^2 = -\frac{19}{14}\)

\(x-5 = \sqrt{\frac{19}{14}}i\)

\(x = 5 + \sqrt{\frac{19}{14}}i\)

\(y = 10 - (5 + \sqrt{\frac{19}{14}}i)\)

\(y = 5 - \sqrt{\frac{19}{14}}i\)

Therefore, one ordered pair of complex numbers that works is 5 + sqrt(19/14)i and 5 - sqrt(19/14)i

Please let me know if I had made any errors!

The dimensions of the wall in feet are 15 / 0.3048 = 49.2126 ft and 60 / 0.3048 = 196.8504 ft. This means that the area of the wall is 49.2126 * 196.8504 = 9.687.52 feet. Since 9600 (400 * 24) < 9687.52 < 10000 (400 * 25), you will need 25 gallons of paint to paint the wall.

If an equation has a minimum value of zero, then it only has one solution, meaning that it can be written as (x + y)^2. The only way to write the given equation as (x+y)^2 is (x + 1)(x - 2(-0.5)) = (x + 1)(x - (-1)) = (x + 1)(x + 1) = (x + 1)^2. Therefore, the only real value for p is -(1/2)

Let's use the "distance = rate (or speed) times time". Let's suppose that d represents the distance to the beach and t represents the time taken to drive to the beach at 40 mph.Then we can represent what we said as these equations:

\(d = 40 \times t\)

\(d = 55 \times (t - 5/12)\)

We can now simplify these equations and solve for d like this:

\(d = 55t - 275/12\)

\(55t - 275/12= 40t\)

\(15t= 275/12\)

\(t = 55/36\)

\(d = 55/36 \times 40\)

\(d = 550/9\)

So the distance you will drive will be 550/9 miles.