Answer:
Marry = $17
Ravi = $11
Alan = $34
Step-by-step explanation:
Let us assume
Mary be X
Ravi be Y
Alan be Z
So, the equation in total is
X + Y + Z = 62
It is given that
X = Y + 6
Z = 2X
Now we put the Z value in the total equation, so it would be
X + Y + 2X = 62
3X + Y = 62 .................................... (1)
And can we write
X = Y + 6
X - Y = 6 ................................. (2)
Now substitution these two equations,
3X + Y = 62
X - Y = 6
2X = 68
X = $17
So, Z = 2 × 17 = $34
And, Y
$17 + Y + $34 = $62
So, Y = $11
sin(x+y)=sin(x)cos(y)-cos(x)sin(y)
also, remember pythagorean rule, 
given that sin(Θ)=4/5 and cos(x)=-5/13
find sin(x) and cos(Θ)
sin(x)
cos(x)=-5/13
using pythagorean identity
(sin(x))^2+(-5/13)^2=1
sin(x)=+/- 12/13
in the 2nd quadrant, sin is positve so sin(x)=12/13
cos(Θ)
sin(Θ)=4/5
using pythagrean identity
(4/5)^2+(cos(Θ))^2=1
cos(Θ)=+/-3/5
in 1st quadrant, cos is positive
cos(Θ)=3/5
so sin(Θ+x)=sin(Θ)cos(x)+cos(Θ)sin(x)
sin(Θ+x)=(4/5)(-5/13)+(3/5)(12/13)
sin(Θ+x)=16/65
answer is 1st option
We have been given an equation
. We are asked to fill in the blanks using our given equation.
The axis of symmetry will be the vertical line passing through vertex.
First of all, we will convert our given equation in standard vertex form of parabola as:
Standard vertex form of parabola:
, where (h,k) is vertex of parabola.

Upon comparing our function with standard vertex form, we can see that vertex of parabola is at
.
The axis of symmetry will be vertical line passing through point
. The vertical line will pass through
, therefore, the axis of symmetry is
.
Since our given parabola is an upward opening parabola, so it has a minimum at
. This means that parabola will intersect the x-axis at two points. Therefore, there are two real solutions for the given function.
Answer:
A
Step-by-step explanation:
So,
The skateboard cost $67.
The protective helmet cost $25.
To find the percent that the price of the skateboard was out of the total amount, add 67 and 25 and divide 67 by the result.
Step 1:
67 + 25 = 92
Step 2:
67/92 = 0.728 or 72.8%.
The correct option is B.