Choose the explanation that shows why ΔADE is similar to ΔABC.

Mathematics

1 answer:

Elan Coil [88]3 years ago

8 0

Hello,

First of all,
C. and D. are both incorrect because they apply translations to ABC; translations will misalign ADE with ABC.

Next,
A. is incorrect because a dilation of 1/2 will place D at (0,3) from its original point of (0,2). Also, the dilation will place E at (6,0) from its original point of (4,0). The triangle ADE would be too small to map ABC.

Finally,

B. Is the correct answer because a dilation of 2 will place D at (0,4)—where B is—and will place E at (8,0), where C is.
Choice B. maps ADE onto ABC

Sorry for that much information, but I think it’s useful. XD

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Find the line of symmetry equation for the function f(x )=x −2x −3.

andriy [413]

Answer:

x = 1

Step-by-step explanation:

The line of symmetry is defined as the x value of the vertex of a parabola.

To find the vertex of a parabola, we need to convert to vertex form.

Vertex form looks like this:

$y=a(x-h)^2+k$ , where -h is the x value of the vertex and k is the y value of the vertex.

H is also defined as $\frac{-b}{2a}$ where a is the coefficient of x squared and b is the coefficient of the x term.

The coefficient of the x squared term is 1 and the coefficient of b is -2.

Plugging in, we get $\frac{-(-2)}{2(1)}$ , which is equal to 1. This can then be plugged into the equation as

$y=1(x-1)^2+k$ , but k doesn't matter because all we need is the x-term. Now, our x-term is negative h, which is negative negative one, which is positive one. Therefore, our answer is x = 1.