Suppose a change of coordinates t: r2→r2 from the uv-plane to the xy-plane is given byx=−4v−3u−1, y=3−4u−5v.(a) find the absolute value of the determinant of the jacobian for this change of coordinates.∣∣∣∂(x, y)∂(u, v)∣∣∣=∣∣∣det⎡⎣⎢⎢⎤⎦⎥⎥∣∣∣= (b) if a region d∗ in the uv-plane has area 7.25, find the area of the region t(d∗) in the xy-plane.

How many solutions does the nonlinear system of equations graphed bellow have?

Match each whole number with a rational, exponential expression 3 square root 27^2find the domain and range of the exponential function h(x)=125^x. explain your findings. as x decreases does h increase or decrease? explain. as x increases does h increase or decrease? explain.

Which two transformations are applied to pentagon abcde to create a'b'c'd'e'? (4 points) translated according to the rule (x, y) ? (x + 8, y + 2) and reflected across the x-axis translated according to the rule (x, y) ? (x + 2, y + 8) and reflected across the y-axis translated according to the rule (x, y) ? (x + 8, y + 2) and reflected across the y-axis translated according to the rule (x, y) ? (x + 2, y + 8) and reflected across the x-axis