Write the equation of the line that passes through (2, 4) and has a slope of –1 in point-slope form.
1 answer:
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9514 1404 393
Answer:
(d) (-2, 6)
Step-by-step explanation:
We can rewrite the function using vertex form.
f(x) = (x^2 +4x) +10
f(x) = (x^2 +4x +4) +10 -4 . . . . . . . add and subtract (4/2)^2
f(x) = (x +2)^2 +6
Compare to vertex form:
f(x) = (x -h)^2 +k
we see that (h, k) = (-2, 6) . . . . the vertex
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<em>Additional comment</em>
The value added and subtracted is the square of half the x-coefficient. Inside parentheses, that value "completes the square". Outside parentheses, that value ensures the overall function remains unchanged.
The correct answer is option A which is ZA = 3 cm
<h3>What is the triangle?</h3>Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.
The triangle is shown below.
From the triangle, A is the concurrency point of angle bisectors of all vertices.
Consider ΔAYD,
Using the Pythagorean theorem,
AD² = AY² + YD²
5² = AY² + 4²
25 = AY² + 16
AY² = 25 - 16
AY² = 9
AY = √9 = 3 cm
Consider triangles ADY and ADZ.
∠AYD ≅∠AZD=90
∠ADY≅∠ADZ ( Angle bisector)
AD ≡ AD (common side)
The two triangles are congruent by the AAS postulate.
Therefore, by CPCTE, AY=ZA=3 cm
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