Central Angles and Arc Measures Practice What is X?

Mathematics

1 answer:

myrzilka [38]3 years ago

7 0

Answer: $5^{\circ}$

Step-by-step explanation:

Given

$\angle DIE=(18x-2)^{\circ}\\\angle DIH=15^{\circ}\\\angle FIG=103^{\circ}$

from the figure

$\angle HIE=\angle GIF\quad [\text{vertically opposite angles}]\\\angle HID+\angle DIE=\angle GIF\\15^{\circ}+(18x)^{\circ}-2^{\circ}=103^{\circ}\\(18x)^{\circ}=103^{\circ}-13^{\circ}\\\\x=\dfrac{90^{\circ}}{18}\\\\x=5^{\circ}$

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Is (x+5) a factor of f(x)=x^3 - 4x^2 + 3x + 7? use either the remainder theorem or the factor theorem to explain your reasoning.

Rufina [12.5K]

Answer:

Step-by-step explanation:

<u>Use synthetic division</u>

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How do I solve these problems?

lesya [120]

$Domain:\\D:x > 0\\\\\ln x=5.6+\ln(7.5)\ \ \ \ |-\ln(7.5)\\\\\ln x-\ln7.5=5.6\ \ \ |Use\ \log x-\log y=\log\dfrac{x}{y}\\\\\ln\dfrac{x}{7.5}=5.6\ \ \ \ |use\ \log_ab=c\iff a^c=b\\\\\dfrac{x}{7.5}=e^{5.6}\ \ \ \ |\cdot7.5\\\\\boxed{x=7.5e^{5.6}}\in D$

$\log x=5.6-\log7.5\ \ \ \ |+\log7.5\\\\\log x+\log7.5=5.6\ \ \ \ |use\ \log x+\log y=\log (xy)\\\\\log(7.5x)=5.6\ \ \ \ |use\ \log_ab=c\iff a^c=b\\\\7.5x=10^{5.6}\ \ \ \ |:7.5\\\\\boxed{x=\dfrac{10^{5.6}}{7.5}}\in D$