How many solutions does the system of equations have?

1 answer:

3 0

First, simplify this system:

2x = -10y + 6 and x + 5y = 3

by dividing the first equation by 2. Result: x = -5y + 3

Subbing this into the 2nd equation, -5y + 3 + 5y = 3

This equation is always true, so this system has infinitely many sol'ns.

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What is the equation of the line that passes through (-5, 7) and is parallel to the line y = 4x + 5?

Marysya12 [62]

Answer:

y=4x+27

Step-by-step explanation:

If a line is parallel, it would have the same slope, so you already have that.

Now, you need the y-intercept of the second line. You already have one point, so use that point and the slope to find the y-int. What you can do (since you know you have to go up 4 and over 1, add a 1 to the -5 until you get to zero. your y-int would be 7+20 since you've gone up 5x4)

your final answer (i think) should be y=4x+27, but I could be wrong :))

6 0

2 years ago

The coordinates of quadrilateral PQRS are P(–3, 0), Q(0, 4), R(4, 1), and S(1, –3). What best describes the quadrilateral?

denis-greek [22]

Answer:

Square

Step-by-step explanation:

Plot the vertices of the quadrilateral PQRS on the coordinate plane (see attached diagram). The diagram shows that this is a square. Let's prove it.

1. Find all sides lengths:

$PQ=\sqrt{(-3-0)^2+(0-4)^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5\\ \\QR=\sqrt{(0-4)^2+(4-1)^2}=\sqrt{(-4)^2+(3)^2}=\sqrt{16+9}=\sqrt{25}=5\\ \\RS=\sqrt{(4-1)^2+(1-(-3))^2}=\sqrt{(3)^2+(4)^2}=\sqrt{9+16}=\sqrt{25}=5\\ \\SP=\sqrt{(1-(-3))^2+(-3-0)^2}=\sqrt{(4)^2+(-3)^2}=\sqrt{16+9}=\sqrt{25}=5$

All sides have the same lengths.

2. Find the slopes of all lines:

$PQ:\ \dfrac{4-0}{0-(-3)}=\dfrac{4}{3}\\ \\QR:\ \dfrac{1-4}{4-0}=-\dfrac{3}{4}\\ \\RS:\ \dfrac{-3-1}{1-4}=\dfrac{4}{3}\\ \\SP:\ \dfrac{0-(-3)}{-3-1}=-\dfrac{3}{4}$