Chang needs at least $125. he has saved & 45 and he makes $7 an hour. what is the minimum number of complete hours he must work to have enough money

He needs to work 12 hours

Step-by-step explanation:

45+7+7+7+7+7+7+7+7+7+7+7+7=129

Yes

ΔDEF can be mapped to ΔRPQ by a 180° rotation about the origin followed by a translation 2 units down

Step-by-step explanation:

The coordinates of the vertices of the triangles are;

F(1, 0), D(1, 3), and E(5, 0), and Q(-1, -2), R(-1, -5), and P(-5, -2),

Length of FD = √((3 - 0)² + (1 - 1)²) = 3

Length of DE = √((5 - 1)² + (0 - 3)²) = 5

Length of FE = √((5 - 1)² + (0 - 0)²) = 4

For triangle QRP, we have;

Length of QR = √((-5 - (-2))² + (-1 - (-1))²) = 3

Length of RP = √((-5 - (-1))² + (-2 - (-4))²) = 5

Length of PQ = √((-5 - (-1))² + (-2 - (-2))²) = 4

For a reflection across the x-axis, we have;

For a rotation of 180° about the origin, we have;

For a coordinate of the preimage before reflection of (x, y), the coordinates of the image after reflection is (-x, -y)

When followed by a translation 2 units down, we have the coordinates of the image will be (-x, -y-2)

Therefore;

For the points F(1, 0), D(1, 3), and E(5, 0) on triangle FDE, we have;

Rotation 180° about the origin gives;

F(1, 0) → Rotation by 180° → F'(-1, 0)

D(1, 3) → Rotation by 180° → D'(-1, -3)

E(5, 0) → Rotation by 180° → E'(-5, 0)

For a translation 2 unites of the coordinates of the vertices of the above triangle ΔF'D'E',

F'(-1, 0) → Translation 2 units down → F''(-1, -2)

D'(-1, -3) → Translation 2 units down → D''(-1, -5)

E'(-5, 0) → Translation 2 units down → E''(-5, -2)

The coordinates of the vertices of triangle ΔF''D''E'' are equivalent to the coordinates of the ΔQRP

Therefore, ΔDEF, and ΔRPQ are congruent, because ΔDEF can be mapped to ΔRPQ by a 180° rotation about the origin followed by a translation 2 units down.