2. 25°
3. 155°
4. 25°
8. 90°
7. 25°
9. 65°
Using the slope concept, it is found that the angle of elevation to the top of the bridges is of 57.7º.
<h3>What is a slope?</h3>
The slope is given by the <u>vertical change divided by the horizontal change</u>.
It's also the tangent of the angle of depression.
In this problem:
- The horizontal change is of 60 m.
- The vertical change is of 100 - 5 = 95 m.
Hence:
![\tan{\alpha} = \frac{95}{60}](https://tex.z-dn.net/?f=%5Ctan%7B%5Calpha%7D%20%3D%20%5Cfrac%7B95%7D%7B60%7D)
![\alpha = \arctan{\left(\frac{95}{60}\right)}](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Carctan%7B%5Cleft%28%5Cfrac%7B95%7D%7B60%7D%5Cright%29%7D)
![\alpha = 57.7](https://tex.z-dn.net/?f=%5Calpha%20%3D%2057.7)
The angle of elevation to the top of the bridges is of 57.7º.
More can be learned about the slope concept at brainly.com/question/18090623
Answer:
The two angles ADB and BDC are congruent since they are both right angles.
The segment AD and CD are congruent since D is the midpoint of AC.
Segment BD is in common for the two triangles.
The triangles ABD and BCD are congruent by SAS. In particular, Angle A is congruent to angle C (they are opposite to congruent sides), QED
To simplify this expression, we can combine like terms.
= 11x - 7 - 3x + 4
= (11x - 3x) + (-7 + 4)
= 8x - 3
Best of Luck!
Answer: c 12 pounds of the $5.50-per-pound coffee, 8 pounds of the $9.20-per-pound coffee
Step-by-step explanation:
Let x = Number of pound of first king.
y= Number of pound of second kind.
As per given , we have
![x+y=20\Rightarrow\ y= 20-x (i)\\\\\\9.20x +5.50 y= 6.98(20) \\\Rightarrow\ 9.20x +5.50 y=139.6 (ii)](https://tex.z-dn.net/?f=x%2By%3D20%5CRightarrow%5C%20y%3D%2020-x%20%28i%29%5C%5C%5C%5C%5C%5C9.20x%20%2B5.50%20y%3D%206.98%2820%29%20%20%5C%5C%5CRightarrow%5C%209.20x%20%2B5.50%20y%3D139.6%20%20%28ii%29)
substitute value of y from (i) in (ii), we get
![9.20x +5.50(20-x) =139.6\\\\\Rightarrow\ 9.20x +5.50(20)-5.50x =139.6\\\\\Rightarrow\ 9.20x-5.50x +110 =139.6\\\\\Rightarrow\ 3.7x =139.6-110\\\\\Rightarrow\ 3.7x =29.6\\\\\Rightarrow\ x=\dfrac{29.6}{3.7}=\dfrac{296}{37}\\\\\Rightarrow\ x=8](https://tex.z-dn.net/?f=9.20x%20%2B5.50%2820-x%29%20%3D139.6%5C%5C%5C%5C%5CRightarrow%5C%209.20x%20%2B5.50%2820%29-5.50x%20%3D139.6%5C%5C%5C%5C%5CRightarrow%5C%209.20x-5.50x%20%2B110%20%3D139.6%5C%5C%5C%5C%5CRightarrow%5C%203.7x%20%20%3D139.6-110%5C%5C%5C%5C%5CRightarrow%5C%203.7x%20%20%3D29.6%5C%5C%5C%5C%5CRightarrow%5C%20x%3D%5Cdfrac%7B29.6%7D%7B3.7%7D%3D%5Cdfrac%7B296%7D%7B37%7D%5C%5C%5C%5C%5CRightarrow%5C%20x%3D8)
Put this in (i), we get y= 20-8 = 12
Hence, he should blend 12 pounds of the $5.50-per-pound coffee, 8 pounds of the $9.20-per-pound coffee.
So the correct option is c.