Please Help! 1.
Given: ΔABC is a right triangle
∠A is a right angle
m∠B = 45˚
Prove: ∠B ≅ ∠C
STATEMENT: REASON:

2.
Given: m∠X = 4a + 2
m∠Y = 21a + 3
∠X and ∠Y are a linear pair
Prove: ∠Y is an obtuse angle
STATEMENT: REASON:

3.
Given: ∠A and ∠B are complementary angles
∠B and ∠C are complementary angles
Prove: ∠A ≅ ∠C
STATEMENT: REASON:

4.
Given: ΔMNP is a right triangle
∠M is a right angle
Prove: ∠N and ∠P are complementary angles
STATEMENT: REASON:

1. ∠C ≅ ∠B  by definition of congruency

2. m∠Y by definition of obtuse angle

3. ∠C ≅ ∠A by definition of congruency

4. ∠N and ∠P  are  complementary angles by definition of complementary angles

Step-by-step explanation:

1. The given parameters are;

Statement                                                Reason

ΔABC is a right triangle                           Given

∠A is a right angle                                    Given

m∠B = 45°                                                  Given

m∠A + m∠B + m∠C = 180°                         Sum of interior angles of a triangle

m∠C = 180° - (m∠A + m∠B)                      

m∠C = 180° - (90° + 45°) = 45°                   Substitution property

m∠C = 45° = m∠B                                      Substitution property

∠C ≅ ∠B                                                      Definition of congruency

2. Statement                                              Reason

m∠X = 4·a + 2                                              Given

m∠Y = 21·a + 3                                            Given

∠X and ∠Y are linear pair                          Given

m∠X + m∠Y = 180°                                      Sum of angles of linear pair                  

4·a + 2 + 21·a + 3 = 180°                               Substitution property      

25·a + 5 = 180°                                              

a = (180 - 5)/25 = 7

m∠Y = 21 × 7 + 3 = 150°                               Substitution property      

m∠Y = 150° >  90

m∠Y is an obtuse angle                             Definition of obtuse angle

3. Statement                                                 Reason

∠A and ∠B are complementary angles        Given

∠A + ∠B = 180°                                         Definition of complementary angles

∠B and ∠C are complementary angles        Given

∠B + ∠C = 180°                                         Definition of complementary angles

∠B + ∠C = ∠A + ∠B                                 Transitive property

∠C = ∠A                                            Reverse of addition property of equality

∠C ≅ ∠A                                            Definition of congruency

4. Statement                                        Reason

ΔMNP is a right triangle                        Given

∠M is a right angle                               Given

∠M + ∠N + ∠P = 180°                             Sum of interior angles of a triangle

∠N + ∠P = 180° - ∠M                              Subtraction property of equality

∠N + ∠P = 180° - 90° = 90°                    Substitution property of equality

∠N + ∠P = 90°                                        Substitution property of equality

∠N and ∠P  are  complementary angles    Definition of complementary angles.

24+x=y

step-by-step explanation:

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204