WhyamIdoingthis

Note that WX = YZ and WZ = XY.

WX = 4 by the distance formula (or you can just count squares).

WZ = \(\sqrt{(-3-[-2])^2+(-1-4)^2}=\sqrt{1+25}=\sqrt{26}\)by the distance formula.

WX+XY+YZ+WZ= 4 x 2 + 2\(\sqrt{26}\) = 8 + 2\(\sqrt{26}\)

Pull over terms to the left side:

4x²-4x+1=0

Factor:

(2x-1)²=0

a would be 1/2. b would also be 1/2.

1/a + 1/b would be 4.

AB is the adjacent for B, and BC is the hypotenuse. Since AB/BC = AB/10 = 7/10, AB=7.

Using the Pythagorean theorem, you can deduce that AC = \(\sqrt {51}\)

For C, AB is the opposite and AC is the adjacent, so tan C would be \(7\sqrt{51}\over51\).

My trigonometry skills are... lacking, so I would read this over to see if I made any fundamental mistakes.

Answer: \(24\sqrt {73}\over 73\)

Solution:

The area of the rectangle is 24. The area of BCD is half of that, which is 12. 

Apply the Pythagorean theorem to find that BD²=CD²+BC²=9+64=73. BD is therefore \(\sqrt {73}\).

Multiplying BD by CE and then dividing by two should give the area of BCD (12) because BD is a side and CE is its matching altitude.

\(\sqrt {73} \cdot CE \over 2\)=12

CE=\(24\sqrt {73}\over 73\)

Recognize that the first series has 100 terms and the second one has 101 terms.

The parabola factors like this, because it yields the above coordinates when y is 0:

y=(x+3)(x+5)

Expanding this, you get:

y=x²+8x+15

Can you put that in TeX or at least add parenthesis? I can't tell if you mean \(y=\) \(8ax³+6\over x\), \(8ax³+6/x\) , \(8ax^{3+6/x}\) , or something else entirely.

First, simplify f(x) to 2x²+3x+8.

f(k-x) just reflects f(x) over the y-axis and then translates it to the left by k. The y-intercept of the parent funciton and of f(k-x) would remain the same: 8. The y-intercept would be on the right side of the vertex in f(x) and on the left side in f(-x), so f(-x) has to be shifted left until thegraphs are the same.

2x²+3x+8=8

2x²+3x=0

x(2x+3)=0

x=0 or x=-1.5

Because x=0 would mean the y-inercept, which we already know, the other place the parent y=8 would be at (-1.5, 8), which means k would have to be -1.5 to shift f(k-x) to f(x).

I know this isn't a well-worded at all, but hopefully it helps. I suggest you spend some time on a graphing application looking at how what changes to a function causes what transformations.

Answer: 24

Solution:

Note that XYZ is a right triangle where Y is 90 degrees. Y would be reflected over XZ at the point closest to XZ, which is the foot of the altitude from XZ to Y, which means that YY' would be double that altitude. You may be accustomed to using the altitude of a triangle to find its area, but it can also be derived from the area. Because XYZ is a right triangle, its area can be found by multiplying its legs and then dividing by two.

15 x 20 / 2 = 150

Because the area of the triangle is an altitude multiplied by the side its foot is on over two, the desired altitude would be multiplied by XZ (25) and then divided by two to get the area of the triangle. Set the desired altitude's length to a:

25a / 2 = 150

a = 12

YY' is double this length, YY' is equal to 24. 

Let the three integers be x, y and z, from smallest to largest. A system of equations composed from the information given would look like this:

x+y+z=42

x+5=y

y+2=z

Substitution finds that z= (x+5)+2=x+7, and so x+(x+5)+(x+7)=42.

3x+12=42

3x=30

x=10

y=15

z=17