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3 years ago

-------100 POINTS------ Complete the proof of the Pythagorean theorem.

Mathematics

2 answers:

KIM [24]3 years ago

7 0

Step-by-step explanation:

Complete the proof of the Pythagorean theorem is given below.

Statement Reason

1. ΔABC is a right triangle, with a 1. Given

right angle at ∠C

2. Draw an altitude from point C 2. From a point not on a line, exactly

to AB one perpendicular can be drawn through the point to the line

3. ∠CDB and ∠CDA are right 3. Definition of altitude

angles

4. ∠BCA ≅ ∠BDC 4. All right angles are congruent

5. ∠B ≅ ∠B 5. $Reflexive\:Property$

6. ΔCBA ~ ΔDBC 6. AA Similarity Postulate

7. $\frac{a}{x}\:=\:\frac{c}{a}$ 7. $Polygon\:Similarity\:Postulate\:\:\:$

8. $a^{2} = cx$ 8. $Cross\:Multiply\:and\:Simplify$

9. ∠CDA ≅ ∠BCA 9. $All\:Right\:Angles\:are\:Congruent$

10. ∠A ≅ ∠A 10. $Reflexive\:Property$

11. ΔCBA ~ ΔDBA 11. AA Similarity Postulate

12. $\frac{b}{y}\:=\:\frac{c}{b}=$ 12. $Polygon\:Similarity\:Postulate$

13. $b^2\:=\:cy$ 13. $Cross\:Multiply\:and\:Simplify$

14. $a^2\:+\:b^2\:=\:cx\:+cy$ 14. $Addition\:Property\:of\:Equality$

15. $\left(CB\right)^2+\left(CA\right)^2=\left(AB\right)\left(DB+BA\right)$ 15. Distributive Property

16. $x + y = c$ 16. $Segment\:Addition\:Postulate$

17. $a^2\:+\:b^2\:=\:c^2$ 18. $Substitution\:Property$

Marina CMI [18]3 years ago

6 0

Answer:

Step-by-step explanation:

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3 years ago

The measure of b is..

sladkih [1.3K]

Answer:

b =21

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

20^2 + b^2 = 29^1

400 + b^2 =841

Subtract 400 from each side

b^2 = 441

Take the square root of each side

sqrt(b^2) = sqrt(441)

b =21

7 0

3 years ago

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Solve: x^4-34x^2=-225

dangina [55]

X
4
−34x
2
+225=0

2 Factor
x
4
−
34
x
2
+
225
x
4
−34x
2
+225.
(
x
2
−
25
)
(
x
2
−
9
)
=
0
(x
2
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3 Solve for
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8 0

3 years ago

Harry is trying to solve the equation 0 = 2x2 − x − 6 using the quadratic formula. He has made an error in one of the steps belo

bija089 [108]

<h3><u>Given</u> - </h3>

➙ a quadratic equation in which Harry lagged due to an error made by him, 2x² - x - 6= 0

<h3><u>To solve</u> - </h3>

➙ the given quadratic equation.

<h3><u>Concept applied</u> - </h3>

➙ We will apply the quadratic formula as given in the question. So, let's study about quadratic equation first because we are supposed to apply the formula in equation.

What is quadratic equation?

➙ A quadratic equation in the variable x is an equation of the form ax² + bx + c = 0, where a, b, c are real numbers, a ≠ 0.

Now, what is quadratic formula?

➙The roots of a quadratic equation ax + bx + c = 0 are given by $\sf{\:\frac{-b \pm\: \sqrt {b ^ 2 - 4ac}}{2a}}$ provided b - 4ac ≥ 0.

<h3><u>Solution</u> - </h3>

here as per the given quadratic equation,

a = 2, b = -1 and c = -6

putting in the formula,

$\implies\sf{x=\frac{-(-1) \pm\: \sqrt {(-1)^2 - 4(2)(-6)}}{2(2)}}$

$\implies\sf{x=\frac{1 \pm\: \sqrt {1+48}}{4}}$

$\implies\sf{x=\frac{1 \pm\: \sqrt {49}}{4}}$

$\implies\sf{x=\frac{1 \pm\: 7}{4}}$

Solving one by one,

$\implies\sf{x=\frac{1 + \: 7}{4}}$

$\implies\sf{x=\frac{8}{4}}$

$\implies{\boxed{\bf{x=2}}}$

________________

$\implies\sf{x=\frac{1 - \: 7}{4}}$

$\implies\sf{x=\frac{-6}{4}}$

$\implies{\boxed{\bf{x=\frac{-3}{2}}}}$

________________________________

<em><u>Note</u> - Hey dear user!! You haven't provided the solution which was solved by Harry (A.T.Q). Please go through the solution as it will help you to find the error done by Harry.</em>

Hope it helps!! (:

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2 years ago

In disgustAng math :D

zalisa [80]

Answer:

Step-by-step explanation:

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2 years ago

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