Let us find the slopes of the two lines
ax+by=c, slope m1 = -a/b
bx-ay=c, slope m2 = b/a
m1*m2 = (-a/b)(b/a) = -1
Therefore the two lines are perpendicular so the answer is D
Hello :
<span> sin 2x = sin x and 0 ≤ x ≤ 2π.
all solutions :
2x= x +2k</span>π or x= π -x +2kπ ..... k in : Z
x = 2kπ or : x = π/2 + kπ
but :
<span>0 ≤ x ≤ 2π
</span><span>all values of x such that sin 2x = sin x and 0 ≤ x ≤ 2π are :
</span>k = 0 : x=0 , x= π/2
k=1 : x=2 π , x=3π/2
Answer: C
Step-by-step explanation: You want to find the square root of each number given. The square root of 400 is 20, and the square root of 100 is 10
Number of days Val rented the bicycle is 8
<h3><u>Solution:</u></h3>
Given that val paid a flat rental fee of $55.00 plus $8.50 each day
The total cost was $123
To find: number of days she rented the bicycle
Let "a" be the number of days she rented the bicycle
Rental fee = $55.00
Fee for one day = $ 8.50
So total cost is equal to rental fee and fee for "a" days
Total cost = rental fee + (number of days she rented the bicycle x Fee for one day)
123 - 55 = 8.50a
8.50a = 68
Thus number of days she rented the bicycle is 8
Y = -(1/2)(x-2)² +8
Re write it in standard form:
(y-8) = -1/2(x-2)² ↔ (y-k) = a(x-h)²
This parabola open downward (a = -1/2 <0), with a maximum shown in vertex
The vertex is (h , k) → Vertex(2 , 8)
focus(h, k +c )
a = 1/4c → -1/2 = 1/4c → c = -1/2, hence focus(2, 8-1/2) →focus(2,15/2)
Latus rectum: y-value = 15/2
Replace in the equation y with 15/2→→15/2 = -1/2(x-2)² + 8
Or -1/2(x-2)² +8 -15/2 = 0
Solving this quadratic equation gives x' = 3 and x" = 2, then
Latus rectum = 5
