All the angles inside a triangle add up to 180°.
(2x + 15) + (5x + 5) + x = 180
8x + 20 = 180
8x = 180 - 20
8x = 160
x = 160/8
x = 20
the question is asking what angle B is,
B = 2(20) + 15
B = 40 + 15
B = 55°
Answer:
Bill is 9.80 km apart from Concert
Step-by-step explanation:
It's given in the question,
m∠B = 75°
m∠C = 45°
By triangle sum theorem,
m∠A + m∠B + m∠C = 180°
m∠A + 75° + 45° = 180°
m∠A = 180° - 120°
m∠A = 60°
By sine rule,
BC = 
= 9.80 km
Therefore, Bill is 9.80 km apart from Concert.
Answer:
56 music files
Step-by-step explanation:
From the above question:
Let the number of music files
Arely has = x
Valerie has = y
Arely has 4 fewer than twice as many music files as Valerie.
x = 2y - 4
They have a combined number of 86 music files.
x + y = 86
We substitute 2y - 4 for x in the above equation
2y - 4 + y = 86
3y - 4 = 86
3y = 86 + 4
3y = 90
Divide both sides by 3
3y/3 = 90/3
y = 30
Hence, Valerie has 30 music files.
The number of music files that Arely has is calculated as:
x = 2y - 4
x = 2(30) - 4
x = 60 - 4
x = 56
Arely has 56 music files
Answer: 1221
Step-by-step explanation:
Given : A 4-digit number is a palindrome .
If it has remainder 21 when you divide it by 100, then last two digits are 21.
So required palindrome = _ _ 21
since palindrome does not change if you write it backwards, so first two numbers should be reverse of 21 = 12
hence, the complete palindrome = 1221
So the number is 1221.
Answer:
Both boxes have the same amount of work applied to them. The smaller box will get to the end first.
Step-by-step explanation:
For the 400 kg box, we can say,
force = 1 newton
force = mass*acceleration
1 = 400*acceleration
acceleration = 1/400 meters per second^2
acceleration = 0.0025 meters per second^2
Each second, the larger box's velocity is increasing by 0.0025 meters per second.
While the smaller box would have an acceleration of...
force = 1 newton
force = mass*acceleration
1 = 200*acceleration
acceleration = 1/200 meters per second^2
acceleration = 0.005 meters per second^2
Which is twice as much as the larger box.
Put simply: if the force applied is the same for the two boxes, then the smaller box will have larger acceleration. This is because more force is needed to push on the larger mass.
Because the smaller box has more acceleration, it will naturally travel faster compared to the larger box. Therefore, the smaller box reaches the goal line faster.
