Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function. f(x) = -2x4 + 4x3 + 3x2 + 18

1 answer:

Nookie1986 [14]2 years ago

6 0

$f(x) = -2x^4 + 4x^3 + 3x^2 + 18$

$18:\{\pm1;\ \pm2;\ \pm3;\ \pm6;\ \pm9;\ \pm18\}\\2:\{\pm1;\ \pm2\}\\\\Answer:\boxed{\{\pm\frac{1}{2};\ \pm1;\ \pm\frac{3}{2};\ \pm2;\ \pm3;\ \pm\frac{9}{2};\ \pm6;\ \pm9;\ \pm18\}}$

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In the figure, ray OB bisects ∠TOY.

Levart [38]

Answer:

∠BOY = 38°

Explanation:

From the diagram, we can note that:

m∠TOY = m∠TOB + m∠BOY ...................> equation I

We are given that ray OB bisects the angle

Therefore:

m∠TOB = m∠BOY

Substitute in equation I:

m∠TOY = m∠TOB + m∠TOB = 2m∠TOB ............> equation II

We are given that:

m∠TOY = 8x-36

m∠TOB = x+24

Substitute with the givens in equation II and solve for x:

m∠TOY = 2m∠TOB

8x - 36 = 2(x + 24)

2(4x-18) = 2(x+24)

4x - 18 = x + 24

3x = 42

x = 14

This means that:

m∠TOB = x + 24 = 14 + 24 = 38°

Since

m∠TOB = m∠BOY

Therefore:

m∠BOY = 38°

Check:

m∠TOY = 8x - 36 = 8(14) - 36 = 76° which is twice m∠TOB

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