Answer:
73°
Step-by-step explanation:
Given: BD=BE
∠DBE= 50°
∠EAC= 42°
DE//AC and AE=CD
Attach is the new drawn diagram with M point.
∵ we know BD=BE, ∴ ∠BDE=∠BED= x ( taking x as unknown angle)
Remember, sum of triangle= 180°
Now, ∠BDE+∠BDE+∠DBE= 180°
⇒ 
⇒ 
Subtracting both side by 50, then dividing both side by 2
∴
°
We know, ∠MAC= ∠MCA= 42° (∵AM=MC)
Next, ∠EDC=DCA= 42° ( ∵ Alternate interior angle as we know DE//AC )
Now, we have ∠EDC= 42°, ∠BDE= 65°
∴
° (∵sum of straight line= 180°)
⇒
°
⇒
°
Subtracting both side by 107
∴∠ADC=
°
∴∠ADC= 73°
Answer:
b. 4:35 p.m
Step-by-step explanation:
Her speed in t minutes after 4:30 p.m. is modeled by the following equation:

In which v(0) is her speed at 4:30 pm and a is the acceleration.
At 4:30 p.m. she looks down at her speedometer and notices that she is going 45 mph.
This means that 
Ten minutes later she looks down at the speedometer again and notices that she is going 55 mph.
This means that 
So




So

When was she moving exactly 50 mph?
This is t minutes after 4:30 p.m.
t is found when v(t) = 50. So



5 minutes after 4:30 p.m. is 4:35 p.m.
So the correct answer is:
b. 4:35 p.m
Ok so total distance is 22 cm. And 2 sides r equal and third side is 6cm. So we can currently put this in the equation: 22=x+x+6 (x represents the two sides) they can be the same variable since they are equal too.
Steps for solving the equation: 22=2x+6
16=2x
x=8.
The two equal lengths of the triangle are 8 cm long.
Parallel = same slope
Slope = 1/2
Y = 1/2x + b
Plug in the point
0 = -1/2 + b, b = 1/2
Solution : y = 1/2x + 1/2
The answer is A
First, you add the two parts of the ratio together. 8+5=13. Then you do 390 divided by 13 which is 30. After this, you multiply 30 by each side to get the ratio to be equal. 30x8=240, and 30x5=150. This can now be put into the ratio 240:150. As you said it was in the ratio adults to children, it must stay in that order. The part of the ratio for children is 150.
<em>The answer to your question is 150. You can double-check your answer by adding up the two parts again. 240=150=390 so you can be assured that your answer is truly correct. Thank you for uploading this question. I hope my explanation was helpful enough for you
</em>
<em><u>PencilandPaper21</u></em>