HELP ME, PLEASE. given: the tetrahedron ABCD
m∠BAC = 60°
m∠ CAD = 120°
E is the foot of the inner bisector of ∠A of ΔABD.
prove: ΔACE is a right triangle

1 In the diagram below, ABC ≅ DEF.

Which sequence of transformations maps ABC onto DEF?

2 On the set of axes below, the vertices of PQR have coordinates P(6,7), Q(2,1), and R(1,3).

What is the area of PQR?

3 In right triangle ABC, m∠C = 90°. If cos B = 5/13, which function also equals 5/13?

4 In the diagram below, mABC = 268°.

What is the number of degrees in the measure of ∠ABC?

5 Given MRO shown below, with trapezoid PTRO, MR = 9,MP = 2, and PO = 4.

What is the length of TR?

6 A line segment is dilated by a scale factor of 2 centered at a point not on the line segment. Which statement regarding the relationship between the given line segment and its image is true?

7 Which figure always has exactly four lines of reflection that map the figure onto itself?

8 In the diagram below of circle O, chord DF bisects chord BC at E.

If BC 12 and FE is 5 more than DE, then FE is

9 Kelly is completing a proof based on the figure below.

She was given that ∠A ≅ ∠EDF, and has already proven AB ≅ DE.

Which pair of corresponding parts and triangle congruence method would not prove ABC ≅ DEF?

10 In the diagram below, DE divides AB and AC proportionally, m∠C = 26°, m∠A = 82°, and DF bisects ∠BDE.

The measure of angle DFB is:

I. Diagonals are perpendicular bisectors of each other.

II. Diagonals bisect the angles from which they are drawn.

III. Diagonals form four congruent isosceles right triangles.

correct answer is infinitely many solutions

step-by-step explanation:

2(2x + 3) = -4 + 2(2x + 5)

solving the above equation:

4x + 6 = -4 +4x +10

combining like terms

4x -4x = -4+10-6

0=0

since both sides are 0=0, we end up into true statement it means it has infinite many solutions.

so correct answer is infinitely many solutions

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.