Answer:
- C.) obtuse triangle
- 39°
- 167°
- D.) 111°
Step-by-step explanation:
1. The sum of angles in a triangle is 180°. The sum of the given angles is less than 90°, so the remaining angle must be more than 90°. When the largest angle is more than 90°, it is an obtuse angle. A triangle with an obtuse angle is classified as obtuse.
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2. The sum of the interior angles is 180°, so we have ...
x° +39° +102° = 180°
x° = 39° . . . . . . . . . . . subtract 141°
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3. The third interior angle is the supplement to the sum of the given interior angles. Likewise, x° is the supplement to the third interior angle, so its value is the same as the sum of the two given interior angles. (The rule is often stated as "an exterior angle is equal to the sum of the remote interior angles.")
x° = 130° +37°
x° = 167°
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4. Same deal as problem 3:
x° = 75° +36°
x° = 111°
Step-by-step explanation:
Angle b + 100 = 180 (angles on the same straight line)

Angle c = Angle b (Vertically opposite angles)
= 80 deg
Answer:
1) the better deal is option 2 the weekend one because you're getting 4 tacos for only 2 more cents.
2) $0.83
3) $0.85
4) 85 cents
Step-by-step explanation:
Answer:
33 ft
Step-by-step explanation:
The image in a mirror is as far behind the reflecting surface as the actual object is in front. When working reflection problems such as this one, it is convenient to mirror the geometry in the line of reflection. This puts the target point at the same distance from the left edge of the room, but 8 feet beyond the reflecting wall. A straight line from the source to the target image will intersect the wall at the appropriate point.
Essentially, we want to know where a line between a point at coordinates (6, 12) and a point at coordinates (45, 38) will intersect the wall at y=30.
The 2-point form of the equation for the line is ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
For the points listed above, this is ...
y = (38 -12)/(45 -6)(x -6) +12 = 26/39(x -6) +12
y = 2/3x +8
The value of x that gives y=30 is ...
30 = 2/3x +8 . . . . . substitute 30 for y
22 = 2/3x . . . . . . . . subtract 8
(3/2)·22 = x = 33 . . . . multiply by 3/2
Zack should shoot at a point 33 feet along the wall in order to hit Patrick.
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In short, Zack should aim at Patrick's reflection in the wall.
Answer:
identify is verified, see work below.
Step-by-step explanation:
Verify following identity
2gh/sin^2θ = 2gh sec^2θ/sec^2θ-1
use identity 1+tan^2(θ) = sec^2(θ) on denominator of right-hand-side
right-hand side
= 2gh sec^2(θ) / (sec^2(θ)-1)
= 2gh sec^2(θ) / (tan^2(θ))
= 2gh sec^2(θ) * (cos^2(θ) / sin^2(θ) ) [note: sec^2(θ) = 1/cos^2(θ)]
= 2gh * 1 / sin^2(θ)
= 2gh / sin^2(θ)
= left-hand side
Therefore identify is verified.