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Lapatulllka [165]
3 years ago
14

Suppose ΔDEF has an exterior angle at vertex D. The measure of the exterior angle is (8x−2)º, m∠E=(3x−8)°, and m∠F=(4x+13)°. Wha

t is the measure of the exterior angle at vertex D?
A. 7°
B. 13°
C. 41°
D. 54°
Mathematics
1 answer:
miv72 [106K]3 years ago
7 0

The measure of the exterior angle at vertex D is: D. 54°

<em><u>Recall:</u></em>

  • The exterior angle theorem of a triangle states that the measure of an exterior angle equals the sum of the measures of two opposite interior angles of the triangle.

<em><u>Thus:</u></em>

In ΔDEF, (8x−2)º is an exterior angle at vertex D.

m∠E = (3x−8)° (interior angle)

m∠F = (4x+13)° (interior angle)

<em>Therefore:</em>

(8x−2)º = (3x−8)° + (4x+13)°

  • Solve for x

8x - 2 = 3x - 8 + 4x + 13

  • Combine like terms

8x - 2 = 7x + 5

8x - 7x = 2 + 5

x = 7

Exterior angle at vertex D = (8x−2)º

  • Plug in the value of x

= 8(7) - 2

= 54º (option D)

Learn more about exterior angle theorem on:

brainly.com/question/24756010

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Answer:

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Step-by-step explanation:

Given that the roots are x = 3 and x = - 1, then the factors are

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f(x) = a(x - 3)(x + 1) ← a is a multiplier

Here a = 5, thus

f(x) = 5(x - 3)(x + 1) ← expand factors using FOIL

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Thus equation is

5x² - 10x - 15 = 0

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brilliants [131]

Answer:

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Range: {4,5}

Step-by-step explanation:

A function is a relation where each input has its own output. In other words if the x value has multiple corresponding y values then the relation is not a function

For the relation given {(3, 4), (3, 5), (4, 4), (4, 5)} the x value 3 and 4 have more than one corresponding y value therefore the relation shown is not a function

Now let's find the domain and range.

Domain is the set of x values in a relation.

The x values of the given relation are 3 and 4 so the domain is {3,4}

The range is the set of y values in a relation

The y value of the given relation include 4 and 5

So the range would be {4,5}

Notes:

The values of x and y should be written from least to greatest when writing them out as domain and range.

They should be written inside of brackets

Do not repeat numbers when writing the domain and range

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