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klemol [59]
3 years ago
13

What is m angle A B E?

Mathematics
1 answer:
sattari [20]3 years ago
6 0

Answer:

  • ∠ABE = 60°
  • ∠DBE = 40°
  • ∠FBA = 47°
  • y = 2

Step-by-step explanation:

The various markings tell you that ...

  GH = GI

  5x -10 = 3x

  2x = 10

  x = 5

and

  ∠ABD ≅ ∠DBC

  10y° = (8y+4)°

  2y = 4

  y = 2

The markings on GH and GI tell you that ΔGBI ≅ ΔGBH, so ...

  ∠CBE ≅ ∠DBC ≅ ∠ABD = 10y° = 20°

__

A) m∠ABE = 60° . . . matches choice D

__

B) m∠DBE = 40° . . . matches choice C

__

C) m∠FBA = 7(5) +6(2) = 35 +12 = 47 . . . matches choice C

__

D) The value of y is 2. . . . matches choice A

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The formula c = √a^2 + b^2 represents the length of the hypotenuse of a right triangle with side lengths a and b. Solve the equa
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Answer:

b = √(c^2 - a²)

Step-by-step explanation:

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Taking the square root of both sides, we get:

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and so:

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What is the distance between two points with coordinates (32,12,5) and (20,3,13) in space?​
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The distance between two points with the given coordinates in space is;

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We are given the coordinates;

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(20, 3, 13)

  • Formula for the distance between two points that have (x, y, z) coordinates is;

d = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)

From the equation given to us, we can see that;

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2 years ago
Factor the expression using the two different techniques listed for Parts 1(a) and 1(b).
Natalija [7]

Answer:

9a^4 b^10(2 +3a^6 b^5)  (2 -3a^6 b^5)

see work below

Step-by-step explanation:

36a^4b^10 - 81a^16b^20

A)  find the GCF

36a^4b^10 = 4*9 a^4b^10  = 2*2*3*3 a*a*a*a*b*b*b*b*b*b*b*b*b*b

81a^16b^20= 9*9a^16b^20= 3*3*3*3* a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a                *b*b*b*b*b*b*b*b*b*b*b*b*b*b*b*b*b*b*b*b

The terms that appear in both terms is the GCF.  The terms that remain are inside the parentheses.

The GCF is 3*3 a*a*a*a*b*b*b*b*b*b*b*b*b*b

36a^4b^10 - 81a^16b^20 = 3*3 a*a*a*a*b*b*b*b*b*b*b*b*b*b *

( 2*2 - 3*3a*a*a*a*a*a*a*a*a*a*a*a b*b*b*b*b*b*b*b*b*b)

Combining like terms

36a^4b^10 - 81a^16b^20 = 9a^4b^10(4-9a^12b^10)

The expression inside the parenthesis can be factored using the difference of squares

let x^2 =4   x =2  

y^2 = 9a^12 b^10   y = 3a^6b^5

(x^2 -y^2) = (x+y)(x-y)

9a^4b^10(4-9a^12b^10) = 9a^4b^10 ( 2+3a^6b^5) ( 2-3a^6b^5)

b) difference of squares  a^2 – b^2 = (a + b)(a – b)

let a^2 = 36a^4b^10

so a = 6a^2b^5

b^2 = 81a^16b^20

b = 9a^8 b^10

a^2 – b^2 = (a + b)(a – b)

36a^4b^10 - 81a^16b^20 = (6a^2b^5 +9a^8 b^10) (6a^2b^5 -9a^8 b^10)

We can factor a 3 a^2 b^5 out of the first term

3 a^2 b^5 (2 +3a^6 b^5) (6a^2b^5 -9a^8 b^10)

3 a^2 b^5 (2 +3a^6 b^5) 3 a^2 b^5 (2 -3a^6 b^5)

Multiply the terms outside the parentheses together

9a^4 b^10(2 +3a^6 b^5)  (2 -3a^6 b^5)

4 0
3 years ago
Read 2 more answers
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