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4 years ago

Which expression is equivalent to 3^4 ⋅ 3^−9? 1/3^13 1/3^5 3^5 3^13

1 answer:

3 0

${3}^{4} \times {3}^{ - 9} = {3}^{4} \times (1/ {3}^{9}) = {3}^{4} \div {3}^{9} \\ {3}^{(4 - 9)} = {3}^{ - 5} = 1/( {3}^{5} )$
So the 2nd answer is correct: 1 / 3^5

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Step-by-step explanation:

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3 years ago

In the diagram, AD=CD=CB and measure of angle A=40°. How many degrees are in angle DCB?

Ad libitum [116K]

Answer:

$20^{\circ}$

Step-by-step explanation:

Consider triangle ACD. This triangle is isosceles triangle, because AD = DC. Angles adjacent to the base AC are congruent abgles, so

$m\angle DAC=m\angle DCA=40^{\circ}$

The sum of the measures of all interiror angles in the triangle is always $180^{\circ},$ then

$m\angle DAC+m\angle DCA+m\angle ADC=180^{\circ}\\ \\40^{\circ}+40^{\circ}+m\angle ADC=180^{\circ}\\ \\m\angle ADC=180^{\circ}-40^{\circ}-40^{\circ}=100^{\circ}$

Angles ADC and BDC are supplementary angles (add up to $180^{\circ}$ ), then

$m\angle BDC=180^{\circ}-100^{\circ}=80^{\circ}$

Consider triangle BCD. This triangle is isosceles triangle because BC = DC. Angles adjacent to the base BD are congruent abgles, so

$m\angle BDC=m\angle DBC=80^{\circ}$

The sum of the measures of all interiror angles in the triangle is always $180^{\circ},$ then

$m\angle DBC+m\angle BDC+m\angle BCD=180^{\circ}\\ \\80^{\circ}+80^{\circ}+m\angle BCD=180^{\circ}\\ \\m\angle BCD=180^{\circ}-80^{\circ}-80^{\circ}=20^{\circ}$

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3 years ago