Which direction does the graph of the equation shown below open?
v^2-4x+4y-4=0
a. right
b. down
c. up
d. left

A. Right

Step-by-step explanation:

Given

y^2-4x+4y-4=0

Isolating x

y^2 + 4y - 4 = 4x

(y^2)/4 + y - 1 = x

Which is a parabola in the single variable y. That means the curve may open to the right or to the left.

The y component of the vertex of the parabola ()is calculated as

where a is the coefficient of the quadratic term and b the coefficient of the linear term. Replacing in the formula:

Replacing this value in the quadratic formula we get the x component of the vertex

Now, we have to get another point in the curve. For example, taking y = 0, we get:

x  = (y^2)/4 + y - 1

x  = (0^2)/4 + 0 - 1

x = -1

Then, the points (-2, -2) and (-1, 0) belong to the parabola, and in consequence, it opens to the right (see figure attached).

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.