tertre

The coordinates of point Y(name this point Y) can be found by: \((\frac{x_1+\gamma x_2}{1+\gamma}, \frac{y_1+\gamma y_2}{1+\gamma})\), where gamma(\(\gamma\)) is the ratio of the coordinates(1:3).

\((\frac{7+\frac{1}{3}*2}{1+\frac{1}{3}},\frac{4+\frac{1}{3}*5}{1+\frac{1}{3}})\)=\((\frac{23}{4}, \frac{17}{4}).\)

Since the area of a parallelogram is the base times it's height, we have (2x+1)(x+3)=42

2x^2+6x+x+3=42, 2x^2+7x=39, 2x^2+7x-39=0

x=3 or x=-13/2, yet x cannot equal to a negative number, so it x has to be equal to three(3).

Base of the parallelogram: 2(3)+1=7 units

Height of the parallelogram: 3+3=6 units

Another way:

Rearrange the equation mn=2m+4n as mn-2m-4n=0

Notice that this equation is close to (m-4) * (n-2) is eight is added to both sides.

(m-4) * (n-2) = 8

8=2^3, so four factors.

2(4)=8-total ordered pairs(negative and non-negative)......

@CalTheGreat, it should be 6^2=4x, 4x=36, x=9

log_9 27, change everything into powers of three.

The answer should be 3/2.

1. The answer is (D). You are correct !

2. -4-2+0+2=-4. You are correct !

3. 4(5)(9) /  6  = 30 2*30=60....

4. 5 * 6  /  2  = 15 ,,,, 3*15=45.

Subtract 35 from every number to get a total of 93-35=58 numbers that are in the list.

1,2,3,4,5,6,....56,57,58

Assign coordinates to each of the points.

A(0,0)

B(6,0)

M(3,3)

C(6,-6)

D(0,-6)

By the Distance Formula, \(\sqrt{(6-3)^2+(-6-3)^2}=\sqrt{3^2+9^2}=\sqrt{90}=3\sqrt{10}\)

Side Length of the Square: 48/4=12 units.

1/2*x*48=144

24x=144

x=6

Assume the diameter of the first circle is two and the second circle is four.

Thus, pi and 4pi are the respective areas.

1/4.

Slope-Intercept form: y=mx+b.

x+5y=10

5y=-x+10

y=-1/5x+2

-1/5 * m = -1

m= 5

Thus, y=5x+b

Contains the point (2,5), and 5=10+b, b=-5, thus, y=5x-5