10
If you treat the number as x, then
.
Answer:
So the Point of intersection is (-4,-2)
Which is option A
Step-by-step explanation:
The given system of equations is
-0.1x - 0.8y = 2 ...................(i)
0.6x - 0.5y = -1.4 ...................(ii)
Let us take equation (i) and use method of substitution for solving it
the equation (i) is
-0.1 x - 0.8y = 2
Adding 0.8y on both sides
-0.1 x + 0.8 y - 0.8 y = 2 + 0.8 y
-0.1 x = 2 + 0.8 y
Dividing both sides -0.1

x = -8 y - 20 ..........................(iii)
Now we will use this value and put it into equation (ii) to find the value of y
Equation (ii) is
0.6 x - 0.5 y = -1.4
Put value of x
0.6(-8 y - 20) - 0.5 y =-1.4
It becomes
-4.8 y - 12 - 0.5 y = -1.4
adding 12 on both sides
-4.8 y - 0.5 y - 12 + 12 = -1.4 + 12
it becomes by solving
-5.3 y = 10.6
Dividing both sides by -5.3

So
y = -2
Now we have the value of y putting it in equation (iii)
Equation (iii) is
x = -8 y - 20
Putting value of y
x = -8*(-2) - 20
x = 16-20
x=-4
So the Point of intersection is (-4,-2)
Answer:
Elena's move will lead to the solution of the problem
Step-by-step explanation:
To solve the equation 7.5d=2.5d, Lin divides each side by 2.5d, and Elena subtracts 2.5d from each side. Will both moves lead to the solution? Explain your reasoning
Given:
7.5d = 2.5d
Lin divides each side by 2.5d, Lin:
7.5d / 2.5d = 2.5d / 2.5d
3 = 1
This can not be the solution to the problem because 3 can not be Equal to 1
Elena subtracts 2.5d from each side
7.5d = 2.5d
7.5d - 2.5d = 2.5d - 2.5d
5d = 0
This can lead to the solution of the problem
Elena's move will lead to the solution of the problem
Let z = sin(x). This means z^2 = (sin(x))^2 = sin^2(x). This allows us to go from the equation you're given to this equation: 7z^2 - 14z + 2 = -5
That turns into 7z^2 - 14z + 7 = 0 after adding 5 to both sides. Use the quadratic formula to solve for z. The only solution is z = 1 (see attached image). Since we made z = sin(x), this means sin(x) = 1. All solutions to this equation will be in the form x = (pi/2) + 2pi*n, which is the radian form of the solution set. If you need the degree form, then it would be x = 90 + 360*n
The 2pi*n (or 360*n) part ensures we get every angle coterminal to pi/2 radians (90 degrees), which captures the entire solution set.
Note: The variable n can be any integer.