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Mathematics

1 answer:

Zolol [24]4 years ago

3 0

Answer:27/5

Step-by-step explanation:It just is that

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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

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

6 0

3 years ago

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o-na [289]

The answer in simplest form is 7/30

4 0

2 years ago

Read 2 more answers

WILL MARK BRAINLIEST FOR THE BEST ANSWER. PLEASE SHOW FULL SOLUTIONS. THANK YOU AND GOD BLESS. THE QUESTION IS ATTACHED. :)

Anuta_ua [19.1K]

9514 1404 393

Answer:

(x, y) = (34/5, -4/5) = (6.8, -0.8)

Step-by-step explanation:

Subtract the first equation from the second to eliminate x.

$\left(\dfrac{x}{3}-\dfrac{y}{2}\right)-\left(\dfrac{x-5}{3}+\dfrac{y+2}{3}\right)=\left(\dfrac{8}{3}\right)-(1)\\\\y\left(-\dfrac{1}{2}-\dfrac{1}{3}\right)+\left(\dfrac{5}{3}-\dfrac{2}{3}\right)=\dfrac{5}{3} \qquad\text{partially simplify}\\\\-\dfrac{5}{6}y=\dfrac{2}{3} \qquad\text{subtract 1}\\\\y=-\dfrac{4}{5} \qquad\text{multiply by $-\dfrac{6}{5}$}$

Substituting for y in the second equation, we can find x.

$\dfrac{x}{3}-\dfrac{1}{2}\left(-\dfrac{4}{5}\right)=\dfrac{8}{3}\\\\5x +6=40 \qquad\text{multiply by 15}\\\\5x=34\qquad\text{subtract 6}\\\\x=\dfrac{34}{5}$