Answer:
<CFD =62°
<AFB= 90°
Step-by-step explanation:
here you have a vertical angle, so to simply put it the answer on one side of the angle is the same answer for the opposite side of the angle. knowing this, angle <AFE is 62° and <CFD is on the opposite side making the angle the same(62°). the opposite angle of <AFB is <EFD which is 118° but both <AFB and <AFC equal 118° so you subtract 118° to <AFC degree which is 28° and you get 90°.
i hope this makes sense im not good at explaining. if anyone has a better explanation feel free to correct me.
These are two questions and two answers.
Question 1) Which of the following polar equations is equivalent to the parametric equations below?
<span>
x=t²
y=2t</span>
Answer: option <span>A.) r = 4cot(theta)csc(theta)
</span>
Explanation:
1) Polar coordinates ⇒ x = r cosθ and y = r sinθ
2) replace x and y in the parametric equations:
r cosθ = t²
r sinθ = 2t
3) work r sinθ = 2t
r sinθ/2 = t
(r sinθ / 2)² = t²
4) equal both expressions for t²
r cos θ = (r sin θ / 2 )²
5) simplify
r cos θ = r² (sin θ)² / 4
4 = r (sinθ)² / cos θ
r = 4 cosθ / (sinθ)²
r = 4 cot θ csc θ ↔ which is the option A.
Question 2) Which polar equation is equivalent to the parametric equations below?
<span>
x=sin(theta)cos(theta)+cos(theta)
y=sin^2(theta)+sin(theta)</span>
Answer: option B) r = sinθ + 1
Explanation:
1) Polar coordinates ⇒ x = r cosθ, and y = r sinθ
2) replace x and y in the parametric equations:
a) r cosθ = sin(θ)cos(θ)+cos(θ)
<span>
b) r sinθ =sin²(θ)+sin(θ)</span>
3) work both equations
a) r cosθ = sin(θ)cos(θ)+cos(θ) ⇒ r cosθ = cosθ [ sin θ + 1] ⇒ r = sinθ + 1
<span>
b) r sinθ =sin²(θ)+sin(θ) ⇒ r sinθ = sinθ [sinθ + 1] ⇒ r = sinθ + 1
</span><span>
</span><span>
</span>Therefore, the answer is r = sinθ + 1 which is the option B.
<span>15 - 13(2x + 6) < 15 - 3(6x - 7)
15 - 26x - 78 < 15 - 18x + 21
-26x -63 < -18x + 36
-8x < 99
x > -99/8
or
x > - 12.375
</span>
Answer:
$1.5
Step-by-step explanation:
Solve by graphing the system of equations where x = the number of hot dogs and y = the number of hamburgers
> 3x + 2y = 8
> 2x + 3y = 8.25
The solution is (1.5, 1.75)
-- Check attachment for graph
3.7kg is also equal to 3700 grams
3700+620 grams
= 4320 grams
= 4320/1000 kg
= 4.32 kg
