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V125BC [204]
3 years ago
10

On a coordinate grid point P is at (5,8) in point are is a ( -1, -3) points Q and S are a reflection of birth points across the

Y axis. What are the coordinates of Q and S?
Mathematics
1 answer:
makkiz [27]3 years ago
8 0

Answer:

The coordinates of Q and S are;

(-5,8) and (1,-3)

Step-by-step explanation:

When we reflect a point with coordinates (x,y) across the y-axis, we get a new point with the coordinates (-x,y)

So (5,8) becomes (-5,8)

and (-1,-3) becomes (1,-3)

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Are the functions f,g, and h given below linearly independent?
CaHeK987 [17]

Answer:

Linearly independent, x = 0

Step-by-step explanation:

- We are given three functions as follows:

                           f ( x ) = e^4^x\\\\g ( x ) = xe^4^x\\\\h( x ) = x^2e^4^x

- We are to determine the linear - independence of the given functions. We will use the theorem of linear independence which states that:

                           c_1*f(x) + c_2*g(x) + c_3*h(x) = 0

Where,

                       c1 , c2 , c3 are all zeroes then for all values of (x),

- The system of function is said to be linearly independent

- We will express are system of equations as such:

                           c_1*e^4^x + c_2*xe^4^x + c_3*x^2e^4^x = 0\\\\

- To express our system of linear equations we will choose three arbitrary  values of ( x ). We will choose, x = 0. then we have:

                          c_1*( 1 ) + c_2*(0) + c_3*(0 ) = 0\\\\c_1 = 0

- Next choose x = 1:

                          c_2*e^4 + c_3*e^4 = 0\\\\c_2 + c_3 = 0

- Next choose x = 2:

                          2*c_2*e^8 + 4*c_3*e^8 = 0\\\\c_2 + 2c_3 = 0

- Solve the last two equations simultaneously we have:

                          c_1 = c_2 = c_3 = 0     .... ( Only trivial solution exist )

Answer: The functions are linearly independent

- The only zero exist is x = 0.

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3 years ago
Multiply (1.2 ⋅ 1028) ⋅ (3 ⋅ 10−19). Express the answer in scientific notation.
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3 years ago
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AB and BC form a right angle at point B if A = (-3,-1) and B = (4,4) what is the equation if BC
sergejj [24]

Answer:

7x+5y-48=0

Step-by-step explanation:

Refer the attached figure .

We are given a line AB

Point A=(x_1,y_1) = (-3,-1)

Point B=(x_2,y_2) = (4,4)

Formula for slope 'm' when two points are given :

m=\frac{y_2-y_1}{x_2-x_1}

Substituting thew values

m=\frac{4-(-1)}{4-(-3)}

m=\frac{5}{7}

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\Rightarrow \frac{5}{7}\times m_2 =-1

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5y-20=-7x+28

7x+5y-20-28=0

7x+5y-48=0

Hence the equation of line BC : 7x+5y-48=0

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