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liq [111]
3 years ago
14

In Exercises 37– 40, BD ⃗ bisects ∠ABC. Find m∠ABD,m∠CBD, and m∠ABC.

Mathematics
1 answer:
MrRissso [65]3 years ago
3 0

Answer:

37,  ABD = CBD = 44 degrees, and ABC = 88 degrees

38.  ABD = CBD = 24 degrees, and ABC = 48 degrees

39.  ABD = CBD = 65 degrees, and ABC = 130 degrees

40.  ABD = CBD =67 degrees, and ABC = 134 degrees

Step-by-step explanation:

Recall that when a segment bisects an angle, the angle is divided in equal parts then we have:

37.  

6 x + 14 = 3 x + 29

3 x = 19 - 14 = 15

x = 15/3

x = 5

then ABD = 6 (5) + 14 = 30 + 14 = 44 degrees

CBD must equal ABD , so CBD = 44 degrees

And the total angle ABC = 88 degrees

38.

3 x + 6 = 7 x - 18

24 = 4 x

x = 24/4 = 6

Then ABD = 3 (6) + 6 = 24 degrees. Also CBD = 24 degrees and ABC = 48 degrees

39.

- 4 x + 33 = 2 x + 81

- 6 x = 81 - 33

-6 x = 48

x = - 48/6

x = -8

Then ABD = -4 (-8) + 33 = 32 + 33 = 65 degrees

The also CBD = 65 degrees, and ABC = 130 degrees

40.

8 x + 35 = 11 x + 23

35 - 23 = 11 x - 8 x

12 = 3 x

x = 12/3

x = 4 degrees

Therefore:

ABD = 8 (4) + 35 = 32 + 35 = 67 degrees.

Then also CBD = 67 degrees, and ABC = 134 degrees

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Step-by-step explanation:


4 0
3 years ago
The area of a rectangular piece of cardboard is represented by
Liula [17]

This question is solved applying the formula of the area of the rectangle, and finding it's width. To do this, we solve a quadratic equation, and we get that the cardboard has a width of 1.5 feet.

Area of a rectangle:

The area of rectangle of length l and width w is given by:

A = wl

w(2w + 3) = 9

From this, we get that:

l = 2w + 3, A = 9

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}

x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}

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In this question:

w(2w+3) = 9

2w^2 + 3w - 9 = 0

Thus a quadratic equation with a = 2, b = 3, c = -9

Then

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w_{2} = \frac{-3 - \sqrt{81}}{2*2} = -3

Width is a positive measure, thus, the width of the cardboard is of 1.5 feet.

Another similar problem can be found at brainly.com/question/16995958

5 0
2 years ago
Which equation shows how (-10,8) can be used to write the equation of this line in point-slope from?
NeTakaya

Options :

y – 8 = –0.15(x – 10)

y + 8 = –0.15(x – 10)

y – 8 = –0.2(x + 10)

y + 8 = –0.2(x – 10)

Answer:

y – 8 = –0.2(x + 10)

Step-by-step explanation:

(-10, 8)

General equation in point - slope form:

y - y1 = m(x - x1)

m = slope

Given the points : ( - 10, 8)

x1= - 10 ; y1 = 8

y - y1 = m(x - x1)

Substitute the values of x and y into the equation :

y - 8 = m(x - - 10)

y - 8 = m(x + 10)

The best option which fits is :

y – 8 = –0.2(x + 10)

6 0
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I need help with this homework assignment, NO, I am not looking for answers, just help. Here it is.
shusha [124]
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