Answer:
See below.
Step-by-step explanation:
a.
x = cost of adult ticket
y = cost of student ticket
cost of adult ticket is twice the cost of a student ticket
x = 2y
number of adult tickets = 64
number of student tickets = 132
cost of all adult tickets = 64x
cost of all student tickets = 132y
cost of all adult and student tickets combined: 64x + 132y
cost of all adult and student tickets combined: 1040
This gives us the equation:
64x + 132y = 1040
b.
Use substitution to solve the system of equations. Since x = 2y, where you see x in the second equation, substitute it with 2y.
64(2y) + 132y = 1040
128y + 132y = 1040
260y = 1040
y = 1040/260
y = 4
x = 2y = 2(4) = 8
adult ticket: $8
student ticket: $4
Answer:
one unit vector is ur=(-1/√3 ,1/√3 ,1/√3 )
Step-by-step explanation:
first we need to find a vector that is ortogonal to u and v . This vector r can be generated through the vectorial product of u and v , u X v :![r=u X v =\left[\begin{array}{ccc}i&j&k\\1&0&1\\0&1&1\end{array}\right] = \left[\begin{array}{ccc}0&1\\1&1\end{array}\right]*i + \left[\begin{array}{ccc}1&0\\1&1\end{array}\right]*j + \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]*k = -1 * i + 1*j + 1*k = (-1,1,1)](https://tex.z-dn.net/?f=r%3Du%20X%20v%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Di%26j%26k%5C%5C1%260%261%5C%5C0%261%261%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%5C%5C1%261%5Cend%7Barray%7D%5Cright%5D%2Ai%20%2B%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5C1%261%5Cend%7Barray%7D%5Cright%5D%2Aj%20%2B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D%2Ak%20%3D%20-1%20%2A%20i%20%2B%201%2Aj%20%2B%201%2Ak%20%3D%20%28-1%2C1%2C1%29)
then the unit vector ur can be found through r and its modulus |r| :
ur=r/|r| = 1/[√[(-1)²+(1)²+(1)²]] * (-1,1,1)/√3 =(-1/√3 ,1/√3 ,1/√3 )
ur=(-1/√3 ,1/√3 ,1/√3 )
Answers: Using the process of completing the square:
1. Isolate the constant by <u>adding 7 to</u> both sides of the equation:
x^2-6x-7+7=0+7
x^2-6x=7
2. Add <u>9</u> to both sides of x2 – 6x = 7 to form a perfect square trinomial while keeping the equation balanced:
x^2-6x+9=7+9
x^2-6x+9=16
3. Write the trinomial x2 – 6x + 9 as squared:
<u>(x-3)^2</u> = 16
4. Use the square root property of equality to get x – 3 = ±<u>4</u> .
sqrt[ (x-3)^2 ] = ± sqrt(16)
x-3 = ±4
5. Isolate the variable to get solutions of –1 and 7.
x-3 = ±4
x-3+3 = ±4+3
x = ±4+3
x1=-4+3→x1=-1
x2=+4+3→x2=7
Answer:
Step-by-step explanation:
P + 4.5 = - p + 5
Bringing like terms on one side
P + p = 5 - 4.5
2p = 0.5
p = 0.5/2 = 0.25
In my opinion the answer is one solution
100 + 10h
The 100 represents the $100 and the 10h represents the $10 times the hours
