A tree is standing next to a 80 foot high building. At the same time of day, the tree has a 36 foot shadow, while the building h
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Answer: x = +35
Explanation: In this equation, our first step is to isolate the x-term by adding 4 to both sides of the equation. On the left -4 and +4 cancel and we're left with 2/5x and on the right 10 + 4 simplifies to 14.
Now, in order to get <em>x</em> by itself, we must multiply both sides of the equation by the reciprocal of that fraction. The reciprocal of a fraction is just that fraction flipped so the reciprocal of 2/5 is 5/2 so we multiply both sides of the equation by 5/2.
So as we multiply 5/2 times 5/2x, our 5's cancel and our 2's cancel so we are simply left with <em>x</em>. On the right side, 14 and 2 reduce to 7 and 1 so we have 7 times 5 which is 35 so <em>x = 35</em>.
Answer:
15°.
Step-by-step explanation:
1. Angles ADC and CDB are supplementary, thus
m∠ADC+m∠CDB=180°.
Since m∠ADC=115°, you have that m∠CDB=180°-115°=65°.
2. Triangle BCD is isosceles triangle, because it has two congruent sides CB and CD. The base of this triangle is segment BD. Angles that are adjacent to the base of isosceles triangle are congruent, then
m∠CDB=m∠CBD=65°.
The sum of the measures of interior angles of triangle is 180°, therefore,
m∠CDB+m∠CBD+m∠BCD=180° and
m∠BCD=180°-65°-65°=50°.
3. Triangle ABC is isosceles, with base BC. Then
m∠ABC=m∠ACB.
From the previous you have that m∠ABC=65° (angle ABC is exactly angle CBD). So
m∠ACB=65°.
4. Angles BCD and DCA together form angle ACB. This gives you
m∠ACB=m∠ACD+m∠BCD,
m∠ACD=65°-50°=15°.
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