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3 years ago

16) through: (1,1), slope = 6

Mathematics

2 answers:

Anton [14]3 years ago

7 0

the correct answer is D

krok68 [10]3 years ago

4 0

Answer:

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here slope m = 6, thus

y = 6x + c ← is the partial equation

To find c substitute (1, 1) into the partial equation

1 = 6 + c ⇒ c = 1 - 6 = - 5

y = 6x - 5 → D

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3 years ago

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balu736 [363]

It looks like we're told that

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$T\left(\dfrac12x+3\right)=-3x^2+3x-4$

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We use the fact that $T$ is linear to find $T(1),T(x),T(x^2)$ . First, we notice that

$T(-2x^2)+T(2x^2-1)=T(-2x^2+2x^2-1)=T(-1)=-T(1)$

We also have

$T\left(\dfrac12x+3\right)=T\left(\dfrac12x\right)+T(3)=\dfrac12T(x)+3T(1)$

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So once we find $T(1)$ , we can determine $T(x)$ and $T(x^2)$ . We have

$T(1)=-\left(T(-2x^2)+T(2x^2-1)\right)\implies T(1)=-3x^2-x-4$

and using this we find

$T(x)=12x^2+12x+16$

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Then

$T(ax^2+bx+c)=T(ax^2)+T(bx)+T(c)=aT(x^2)+bT(x)+cT(1)$

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