Provide missing reasons for the proof of the theorem, “A diagonal of a parallelogram separates it into two congruent triangles.”Given: with diagonal Prove:
S1. with diagonal R1.S2. R2.S3. R3.S4. R4.S5. R5.S6. R6.S7. R7.

What will be an ideal response?


R1. Given

R2. The opposite sides of a parallelogram are parallel (definition).

R3. If 2 lines are cut by a trans, the alternate interior angles are congruent.

R4. Same as reason 2

R5. Same as reason 3.

R6. Identity

R7. ASA


Mathematics

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Plot the points representing the following integers on a number line.-8, -6, -4, -2

A.

B.

C.

D.

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Find the axis of symmetry of the quadratic function.f(x) = x2 + 10x + 3

A. x = -22 B. x = 5 C. x = -5 D. x = 10

Mathematics

Graph the function, and state its domain and range.f(x) = -

A. Domain: [0, ?); Range: (-?, -1]

B. Domain: [1, ?); Range: (-?, 0]

C. Domain: [0, ?); Range: (-?, 1]

D. Domain: [-1, ?); Range: (-?, 0]

Mathematics

Solve the problem.Suppose f(x) = 34.1 + 1.3log (x + 1) models salinity of ocean water to depths of  at a certain latitude. x is the depth in meters and f(x) is in grams of salt per kilogram of seawater. Approximate the depth (to the nearest tenth of a meter) where the salinity equals 36.

A. -0.9 m B. -1.0 m C. 29.9 m D. 27.9 m

Mathematics