9514 1404 393
Answer:
no
Step-by-step explanation:
The slope formula is ...
m = (y2 -y1)/(x2 -x1)
We can use the values ...
(x1, y1) = (1, -19)
(x2, y2) = (-2, -7)
Putting these into the formula gives ...
m = (-7 -(-19))/(-2 -1) = 12/-3 = -4
The slope is -4, not -1/4. Mark is incorrect.
The correct answer is 1.414 or 1
You have two 30-60-90 triangles, ADC and BDC.
The ratio of the lengths of the sides of a 30-60-90 triangle is
short leg : long leg : hypotenuse
1 : sqrt(3) : 2
Using triangle ADC, we can find length AC.
Using triangle BDC, we can find length BC.
Then AB = AC - BC
First, we find length AC.
Look at triangle ACD.
DC is the short leg opposite the 30-deg angle.
DC = 10sqrt(3)
AC = sqrt(3) * 10sqrt(3) = 3 * 10 = 30
Now, we find length BC.
Look at triangle BCD.
For triangle BCD, the long leg is DC and the short leg is BC.
BC = 10sqrt(3)/sqrt(3) = 10
AB = AC - BC = 30 - 10 = 20
9514 1404 393
Answer:
24°
Step-by-step explanation:
The angle between the vertical line AB and the horizontal dashed line at A is 90°. That is, ...
66° + ? = 90°
? = 90° -66° = 24°
The angle of depression is 24°.
_____
<em>Additional comment</em>
The sum of angles in the triangle is 180°, so the angle at C (the angle of elevation) is the same as the angle we just figured:
∠C + 90° +66° = 180°
∠C +66° = 90° . . . . . . . subtracting 90°; shows C is complementary to 66°
∠C = 90° -66° = 24°
As a rule, the angle of elevation and the angle of depression are the same.
Let’s start with “five more than a number x.” This translates to:
x + 5
This is “less than” 17, so we insert the corresponding symbol and add 17 to the right side of the equation:
x + 5 < 17
This is the translation of the inequality. Now we have to solve it. To do so, simply subtract 5 from both sides of he equation:
x + 5 ( – 5 ) < 17 ( – 5 )
x < 12
This is the solution to the translated inequality.
I hope this helps!
