A rectangular prism has a volume of 96 cubic feet. The area of the base is 24 square ft. What is the height of the prism?
1 answer:
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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°.
Have a good Day!
Answer:
Step-by-step explanation:
Let's organise our information :
- the function is (1/2)x²+2x+3
we want to khow the value of x that gives us : (1/2)x²+2x+3=x+7
Now the trick is to write this expression as a quadratic equation with zero at one side :
- (1/2)x²+2x+3=x+7
- (1/2)x²+2x+3-x-7=0
- (1/2)x²+x-4=0
Now let's solve this equation :
- a= 1/2
- b= 1
- c= -4
Δ=1²-4*(1/2)*(-4)
= 9
So we have two solutions :
- y= -4
- x= 2
So the solutions are -4 and 2