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3 years ago

Helppppppppppppppppppppppp

Mathematics

1 answer:

lbvjy [14]3 years ago

4 0

Answer:

no, yes, no

Step-by-step explanation:

Translating the points up 2 units adds 2 to the y-coordinate.

(x, y) ⇒ (x, y+2)

T(4, 2) ⇒ T'(4, 2+2) = T'(4, 4) . . . . matches 2nd table entry

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3 years ago

Amir throws a stone off of a bridge into a river. The stone's height (in meters above the water) ttt seconds after Amir throws i

Harrizon [31]

Answer:

1) The vertex form of $h(t) = -5\cdot t^{2}+20\cdot t +160$ is $h -180 = -5\cdot (t-2)^{2}$ , 2) The stone reaches its maximum height 2 seconds after being thrown.

Step-by-step explanation:

1) Given that height of the stone is represented by a second-order polynomial, which depicts a parabola as graph. The best approach to determine the instant when stone reaches its highest is by vertex form, whose form is:

$h-k = C\cdot (t-r)^{2}$

Where:

$r$ , $k$ - Instant and maximum height of the stone, measured in seconds and meters.

$C$ - Vertex constant, which must be negative as there is an absolute maximum, measured in meters per square second.

Let be $h(t) = -5\cdot t^{2}+20\cdot t +160$ , which is transformed into vertex form:

i) $h = -5\cdot t^{2}+20\cdot t +160$ Given

ii) $h = -5\cdot (t^{2}-4\cdot t -32)$ Distributive property/ $(-a)\cdot b = -a\cdot b$

iii) $h = -5\cdot [(t^{2}-4\cdot t +4)+(-36)]$ Existence of additive inverse/Definitions of addition and subtraction

iv) $h = (-5)\cdot (t-2)^{2}+180$ Distributive property/ $(-a)\cdot (-b) = a\cdot b$ /Perfect square binomial

v) $h -180 = -5\cdot (t-2)^{2}$ Compatibility with addition/Existence of additive inverse/Modulative property/Definition of subtraction/Result

The vertex form of $h(t) = -5\cdot t^{2}+20\cdot t +160$ is $h -180 = -5\cdot (t-2)^{2}$ .

2) The time can be extracted from previous results, which indicates that stone reaches its maximum height 2 seconds after being thrown.

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kolbaska11 [484]

Answer:

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