Answer:
Turning point has coordinates 
Step-by-step explanation:
Gandalf the Grey started in the Forest of Mirkwood at a point P(3, 0) and began walking in the direction of the vector 
The coordinates of the vector v are (-3,2). Then he changed the direction at a right angle, so he was walking in the direction of the vector 
(vectors u and v are perpendicular).
Let B(x,y) be the turning point. Find vectors PB and BQ:
Note that vectors v and PB and vectors u and BQ are collinear, so
Hence
Now solve the system of two equations:
Multiply the first equation by 3, the second equation by 2 and add them:
Substitute it into the first equation:
Turning point has coordinates
Answer:
2.89, rounded to the nearest hundredth
Step-by-step explanation:
Given that GPA is weighted by credits, we must first multiply each grade by its credit amount and sum those up to weigh the credits. Then, we divide by the total amount of credits to get the GPA per credit.
So, we start with math,
3.7 *5 + 1.8 *3 + 2.8 * 5 + 2.8 * 4 = 49.1 as the total GPA weighted per credit.
Then, to find the average per credit, we divide by the total amount of credits, which is 5 + 3 + 5 + 4 = 17.
Our answer is 49.1/17 = 2.89, rounded to the nearest hundredth
Answer:
Step-by-step explanation:
<u>Question 1</u>
Two isosceles triangles with repeat 72°.
- x = 180° - 2*72°
- x = 180° - 144°
- x = 36°
<u>Question 2</u>
Isosceles triangle with repeat x/2 angle and a x angle.
- 2(x/2) + x = 180°
- 2x = 180°
- x = 90°
Answer: Scale factor of -1/2
Step-by-step explanation:
B=A*(-2)
A=B/(-2)
A=-(B/2)
A=B*(-1/2)
Scale factor of -1/2
The system of equations is
n + d = 27
n + 5d = 55
Step-by-step explanation:
The given is:
- Kiran has 27 nickels and quarters in his pocket
- They worth a total of $2.75
- We need to write a system of equations to represent the relationships between the number of nickels n, the number of quarters d, and the dollar amount in this situation
∵ The number of nickles is n
∵ The number of quarters is d
∵ There are 27 nickles and quarters
∴ n + d = 27 ⇒ (1)
∵ 1 nickel = 5 cents
∵ 1 quarter = 25 cents
- Multiply n by 5 and d by 25 to find their value
∴ They worth = 5n + 25d
∵ They worth a total of $2.75
- Chang the dollar to cent
∵ 1 dollar = 100 cents
∴ $2.75 = 2.75 × 100 = 275 cents
- Equate their value by 275
∴ 5n + 25d = 275
- Simplify it by divide each term by 5
∴ n + 5d = 55 ⇒ (2)
The system of equations is
n + d = 27
n + 5d = 55
Learn more:
You can learn more about the system of equations in brainly.com/question/2115716
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