danielyskim1119

Let us consider the area of this parallelogram. The area of this paralleogram is EG * DC = 18*27 = 486. Another way to calculate the area of this paralleogram is BC * FH. We know that BC = AD = 18. Therefore, 18 * FH = 486, or FH = 27. 

The area of the original figure is 6*10 = 60. The area of the new figure is 5*9 = 45. Let x be the percentage decrease. Then, we know that 60x = 45. Therefore, x = 0.75 = 3/4

Notice that QO:ON = 2:1, since a median is divided into that ratio. (Search this up if you do not know). Therefore, from the given information, we know that ON = 4. Then, we also know that NR = 18/2 = 9. Since ONR is a right triangle, we can use the pythaogorena theorem from here in order to get our final answer:

OR = sqrt(9^2 + 4^2) = sqrt(97)

Since the circumference is 36, we know that the radius of each circle is 9/pi. Then, we can connect the centers of the circles together in order to get an equaliteral triangle, since the circles are the same. From this, we know that the equaliteral triangle will have a side length of 18/pi. We can then find the 60 degree arcs that the equaliteral triangle creates. Therefore, each 60 degree arc is 1/6 * (9/pi)^2 * pi = 27/2pi. 

Now, we can calculate the area of the equaliteral triangle which is simply 81sqrt(3)/pi^2. Then, we can subtract the arcs in order to get the shaded area. Therefore, the region we are looking for is:

\(\frac{81\sqrt{3}}{\pi^2} - (3 \cdot \frac{27}{2\pi}) = \frac{162\sqrt{3}-81\pi }{2\pi ^2}\)

The way I did it is correct, however some of the numbers may be wrong so please double check before submitting this solution. 

Let x be the number. Using algebra, we get that:

5x = x^2 - 6

Then from here, you can use the quadratic formula to find x. (or factoring). Therefore, the number is -1

Think about using similiar triangles. Notice how triangle CHB is similiar to GFB therefore we can set up a ratio like so to find the length of GF:

\(\frac{CH}{GF} = \frac{HB}{FB}, \frac{24}{20} = \frac{GF}{8}, GF = 9.6.\)

Therefore, we know that the area of GFB = 9.6 * 8 divided by 2. Therefore, GFB = 38.4.

Via symmetry, we know that DAE = 38.4. Therefore, the area of CDEFG = (area of entire triangle) - 38.4 * 2 = 480 - 76.8 = 403.2

Use shoelace theorem in order to get the answer of 13

Let our 4 numbers be \(a_1, a_2, a_3, a_4\). Since we know that \(a_1 = a_4\), we replace it, getting us:

\(a_1, a_2, a_3, a_1\)

Therefore, we know that the last three numbers form an arithmetic sequence. We can represent each of the other terms in terms of \(a_2\). We know that the common difference is 6, therefore, we can write our 4 numbers as:

\(a_1, a_2, a_2 + 6, a_2 + 12\)

Since the first number is the same as the last number, we can also replace the first number with the last number, which gets us:

\(a_2 + 12, a_2, a_2 + 6, a_2 + 12\)

Let r be the common ratio between our numbers. Then, we know that:

\(r(a_2 + 12) = a_2,\\ ra_2 = a_2 + 6,\\ \)

Solving this systems of equations by subsitution, we find out that \(a_2 = -4, r = -\frac{1}{2}\). Therefore, our 4 numbers are:

\(8, -4, 2, 8\)

In order to find the area of this region, we have to first conver this equation into the standard circle equation. Moving all terms (except the constant term) to the left handside, and simplifying, we get:

\(x^2 - 6x + y^2 + 14y = 6\)

Then, we can complete the square by using the formula (b/2)^2, and add the coresponding value to both sides. Therefore, we obtain:

\((x-3)^2 + (y + 7)^2 = 64\)

Therefore, this is a circle with center (3, -7), and a radius of 8. Therefore, the area of this circle is \(64 \pi\)

Let us simplify h(x) first. Plugging in the value of g(x) directly into h(x), we get:

h(x) = f(2x + 8)

We then can plug in 2x + 8 into f(x), to get:

h(x) = 3(2x + 8) + 4

h(x) = 6x + 28

In order to find the inverse of a function, we have to switch the x and y values first. Hence, we get:

y = 6x + 28

x = 6y + 28

We then have to solve for y. Solving for y, we get:

x - 28 = 6y

(x-28)/6 = y

Therefore, the inverse function of h(x) is \(h^{-1}(x) = \frac{x-28}{6}\)

We can use completmentary counting here. Let Y stand for Ymir and B stand for Bin and C stand for Charles and D stand for Daria. Then, we get that:

YBCD.

There are a total of 4! ways in order to rearrange this letter. However, let's find the opposite of what we want. We can group the term Y and B together and form a new letter, which we can call X. Hence, we get:

XCD

There are 3! ways for which we can rearrange XCD, however, we have to multiply this by 2 since X can be rearranged in 2! ways. Hence, we get 3! * 2 = 6 * 2 = 12.

We can now subtract this from 4! = 24, and get 12. 

Let x be the length of the shortest triangle. Hence, we know that the length of the longest side is 2x - 4. We also know that the length of the other side is x + 2. Hence:

2x - 4 + x + 2 + x = 16,

4x - 2 = 16,

4x = 18,

x = 9/2

x = 4.5

Hence, the shortest length is 4.5. From this, you should be able to figure out the lengths of the other side on your own.

Let AAAA be the 4 astronomy books, BBB be the biology books, and CC be the chemistry books. We can group the terms into X, Y, Z repsetivley. Hence we get:

XYZ

There are 3! ways to rearrange this. However, each of the X can be rearranged 4! ways, and the Y can be rearranged in 3! ways, and the Z can be rearragned in 2! ways.

Hence, our answer is:

4! * 3! * 3! * 2!

1728

We first combine like terms and get:

\(x^2 + 2x + 9\)

Then, we complete the square to get:

\(x^2 + 2x + 1 + 8\)

\((x+1)^2 + 8\)

Therefore, the minimum value of x is equal to -1

Oops sorry I replaced x with t