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hammer [34]
3 years ago
15

Help please!!!

Mathematics
1 answer:
marysya [2.9K]3 years ago
4 0

Answer:

see explanation

Step-by-step explanation:

Given the 2 equations

y = x² + 2x + 7 → (1)

y - 7 = x → (2)

Rearrange (2) expressing y in terms of x by adding 7 to both sides

y = x + 7 → (3)

Substitute y = x + 7 into (1)

x + 7 = x² + 2x + 7 ( subtract x + 7 from both sides )

0 = x² + x ← factor out x from each term

0 = x(x + 1)

Equate each factor to zero and solve for x

x = 0

x + 1 = 0 ⇒ x = - 1

Substitute these values into (3) for corresponding values of y

x = 0 → y = 0 + 7 = 7

x = - 1 → y = - 1 + 7 = 6

The solutions are

(- 1, 6 ) and (0, 7 )

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in the given figure ,o is the centr of the circle, ab is the diameter and do is perpendicular to ab. prove that angle AEC= ANGLE
maksim [4K]

The given triangles ΔDOA and ΔABC are right triangles that have a

common vertex at point <em>A</em>.

  • <u>ΔDOA is similar to ΔABC, and </u><u>∠AEC</u><u> is equal to </u><u>∠ABC,</u><u> therefore, ∠AEC = ∠ODA</u>

Reasons:

The given parameters are;

The diameter of the circle with center <em>O</em> = AB

DO ⊥ AB (DO is perpendicular to AB)

Required:

Prove that ∠AEC = ∠ODA

A two column proof is presented as follows;

Statement {}                                                 Reason

1. AB is the diameter of circle     <em> </em>{}                 1. Given

2. DO is perpendicular to AB <em> </em>{}                     2. Given

3. ∠DOA = 90° <em> </em>{}                                             3. Definition of DO ⊥ AB

4. ∠BCA = 90°  <em> </em>{}                                             4. Thales theorem

5. ∠BCA ≅ ∠BCA <em> </em>{}                                         5. Reflexive property

6. ΔDOA ~ ΔABC  <em> </em>{}                                        6. AA similarity postulate

7. ∠ABC ≅ ∠ODA  <em> </em>{}                                       7. CASTC

8. ∠ABC = ∠ODA  <em> </em>{}                                        8. Definition of congruency

9. ∠AEC ≅ ∠ABC  <em> </em>{}                                        9. Angles in the same segment

10. ∠AEC = ∠ABC  <em> </em>{}                                       10. Definition of congruency

11. ∠AEC = ∠ODA  <em> </em>{}                                        11. Transitive property of equality

In statement 6, ΔDOA is similar to ΔABC by Angle-Angle, AA, similarity

postulate, therefore, the three angles of ΔDOA are congruent to the three

angles of ΔABC.

Therefore ∠ABC ≅ ∠ODA by Corresponding Angles of Similar Triangles

are Congruent, CASTC.

Learn more about circle theorem here:

brainly.com/question/16879446

7 0
3 years ago
How do I find this help please
KIM [24]
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3 years ago
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bazaltina [42]
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4 years ago
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-3 1/2

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