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3 years ago

10

Which statement is true about the congruent triangles below? URGENT

1 answer:

VARVARA [1.3K]3 years ago

4 0

Answer:

LN = HJ

Step-by-step explanation:

If you look at the two triangles, you will see each side has a different number of lines on them. Each set of lines corresponds to the same set of lines on the other triangle.

So since side IH has one line the side on the other triangle with one line would be congruent. So that would be line ML.

Also if there are not lines on every side then you could identify the triangle by the red square in the corner meaning that that is a right angle (90 degrees.)

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Identify the vertex, focus, and directrix of the graph. Which of the following equations represents the parabola in the graph?

antoniya [11.8K]

Answer:

Equation: $(x-2)^2=16(y-2)$

Vertex: $(2,2)$

Directrix: $y=-2$

Focus: $(2,6)$

Step-by-step explanation:

<u>Standard Form of Vertical Parabola:</u>

Equation -> $(x-h)^2=4p(y-k)$ where $p\neq 0$
Vertex -> $(h,k)$
Directrix -> $y=k-p$
Focus -> $(h,k+p)$

We know that our vertex is $(h,k)$ -> $(2,2)$ , therefore, we can determine the value of $p$ by selecting a point from the parabola as $(x,y)$ :

$(x-h)^2=4p(y-k)$

$(x-2)^2=4p(y-2)$

$(6-2)^2=4p(3-2)$

$(4)^2=4p(1)$

$16=4p$

$4=p$

<u>Therefore:</u>

Directrix -> $y=k-p$ -> $y=2-4$ -> $y=-2$

Focus -> $(h,k+p)$ -> $(2,2+4)$ -> $(2,6)$

<u>Conclusion:</u>

Equation -> $(x-2)^2=16(y-2)$
Vertex -> $(2,2)$
Directrix -> $y=-2$
Focus -> $(2,6)$

Review the graph for a visual

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