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3 years ago

8

Instructions : state what additional information is required in order to know that the triangles in the image below are congruen

t for the reason given
Reason: AAS Postulate

1 answer:

Travka [436]3 years ago

7 0

Answer:

∠ACB ≅ ∠AGB

Step-by-step explanation:

AAS Postulate is angle-angle-side, which means that both triangles are congruent if 2 angles and a side are congruent.

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Answer:

c).$24.80

Step-by-step explanation:

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4 years ago

the Pythagorean Theorem formula to find the missing side length. You must round your answer to the nearest tenth place (e.g. 10.

Rashid [163]

Answer:

I'm assuming we're solving for the hypotenuse, which is 21.5

Step-by-step explanation:

If a^2+b^2=c^2

Then 19^2+10^2 =461

This is c^2 so we must find the square root of 461

the square root of 461 is 21.47, or 21.5 rounded to the nearest tenth

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3 years ago

4 9 16 25 36 nth term of the quadratic sequence

Bingel [31]

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3 years ago

Simplify -9(1-10n) - 2(3n+9)

agasfer [191]

Answer:

3 (28 n - 9)

Step-by-step explanation:

Simplify the following:

-9 (1 - 10 n) - 2 (3 n + 9)

-9 (1 - 10 n) = 90 n - 9:

90 n - 9 - 2 (3 n + 9)

-2 (3 n + 9) = -6 n - 18:

90 n + -6 n - 18 - 9

Grouping like terms, 90 n - 6 n - 18 - 9 = (90 n - 6 n) + (-9 - 18):

(90 n - 6 n) + (-9 - 18)

90 n - 6 n = 84 n:

84 n + (-9 - 18)

-9 - 18 = -27:

84 n + -27

Factor 3 out of 84 n - 27:

Answer: 3 (28 n - 9)

4 0

3 years ago

Please dont ignore, Need help!!! Use the law of sines/cosines to find..

Ket [755]

Answer:

16. Angle C is approximately 13.0 degrees.

17. The length of segment BC is approximately 45.0.

18. Angle B is approximately 26.0 degrees.

15. The length of segment DF "e" is approximately 12.9.

Step-by-step explanation:

<h3>16</h3>

By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.

For triangle ABC:

$\sin{A} = \sin{103\textdegree{}}$ ,
The opposite side of angle A $a = BC = 26$ ,
The angle C is to be found, and
The length of the side opposite to angle C $c = AB = 6$ .

$\displaystyle \frac{\sin{C}}{\sin{A}} = \frac{c}{a}$ .

$\displaystyle \sin{C} = \frac{c}{a}\cdot \sin{A} = \frac{6}{26}\times \sin{103\textdegree}$ .

$\displaystyle C = \sin^{-1}{(\sin{C}}) = \sin^{-1}{\left(\frac{c}{a}\cdot \sin{A}\right)} = \sin^{-1}{\left(\frac{6}{26}\times \sin{103\textdegree}}\right)} = 13.0\textdegree{}$ .

Note that the inverse sine function here $\sin^{-1}()$ is also known as arcsin.

<h3>17</h3>

By the law of cosine,

$c^{2} = a^{2} + b^{2} - 2\;a\cdot b\cdot \cos{C}$ ,

where

$a$ , $b$ , and $c$ are the lengths of sides of triangle ABC, and
$\cos{C}$ is the cosine of angle C.

For triangle ABC:

$b = 21$ ,
$c = 30$ ,
The length of $a$ (segment BC) is to be found, and
The cosine of angle A is $\cos{123\textdegree}$ .

Therefore, replace C in the equation with A, and the law of cosine will become:

$a^{2} = b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}$ .

$\displaystyle \begin{aligned}a &= \sqrt{b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}}\\&=\sqrt{21^{2} + 30^{2} - 2\times 21\times 30 \times \cos{123\textdegree}}\\&=45.0 \end{aligned}$ .

<h3>18</h3>

For triangle ABC:

$a = 14$ ,
$b = 9$ ,
$c = 6$ , and
Angle B is to be found.

Start by finding the cosine of angle B. Apply the law of cosine.

$b^{2} = a^{2} + c^{2} - 2\;a\cdot c\cdot \cos{B}$ .

$\displaystyle \cos{B} = \frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}$ .

$\displaystyle B = \cos^{-1}{\left(\frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}\right)} = \cos^{-1}{\left(\frac{14^{2} + 6^{2} - 9^{2}}{2\times 14\times 6}\right)} = 26.0\textdegree$ .

<h3>15</h3>

For triangle DEF:

The length of segment DF is to be found,
The length of segment EF is 9,
The sine of angle E is $\sin{64\textdegree}}$ , and
The sine of angle D is $\sin{39\textdegree}$ .

Apply the law of sine:

$\displaystyle \frac{DF}{EF} = \frac{\sin{E}}{\sin{D}}$

$\displaystyle DF = \frac{\sin{E}}{\sin{D}}\cdot EF = \frac{\sin{64\textdegree}}{39\textdegree} \times 9 = 12.9$ .

7 0

3 years ago