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Andreyy89
3 years ago
8

Trisha noticed that three copies of a certain triangle could be arranged in a way that the three angles of the triangle form a s

traight line. what can she conclude from this observation
a. that each interior angle of the triangle must measure 60*
b.exterior must measure 60*
c.sum of interior angles must be 180*
d.sum of exterior angles must be 180*
show work please and i need it desperately
Mathematics
1 answer:
anyanavicka [17]3 years ago
8 0
C) sum of interior angles must be 180°.

This is because a straight line = 180°, so if the interior angles of a triangle = 180° they can form a straight line if arranged correctly.
You might be interested in
Which set of ordered pairs represent a function? O A {(1,0), (2,1), (2,3)} O B{(1,3), (1,4), (1,5)} O C{(1,5), (2,5), (3,5)} O D
mestny [16]

Answer:

C

Step-by-step explanation:

C is the only answer that doesnt share x-values

7 0
3 years ago
The indicated function y1(x) is a solution of the associated homogeneous equation. Use the method of reduction of order to find
9966 [12]

Answer:

<em>The particular integral of given differential equation</em>

<em>                  </em>y_{p} = \frac{1}{4} ( x - (\frac{-5}{4} ) (1))<em></em>

<em> General solution of given differential equation</em>

<em>      </em>y = y_{c} + y_{p}<em></em>

<em>  </em>Y (x) = C_{1} e^{x} + C_{2} e^{4x} + \frac{1}{4} ( x + (\frac{5}{4} ))<em></em>

<em></em>

Step-by-step explanation:

<u><em>Step(i)</em></u>:-

Given Differential equation  y'' − 5 y' + 4 y = x

Given equation in operator form

        D²y - 5 Dy +  4 y = x

⇒     ( D² - 5 D +  4 ) y =x

⇒    f(D) y = Q

where  f(D) = D² - 5 D +  4 and Q(x) = x

<em>The auxiliary equation  f(m) =0</em>

<em>           m²-5 m + 4 =0</em>

         m² - 4 m - m + 4 =0

        m ( m -4 ) -1 ( m-4) =0

         (m - 1) =0   and ( m-4) =0

        <em> m = 1 and m =4</em>

<em>The complementary function </em>

<em></em>Y_{c} = C_{1} e^{x} + C_{2} e^{4x}<em></em>

<u><em>Step(ii)</em></u>:-

<u><em>particular integral</em></u>

<em>Particular integral</em>

<em>     </em>y_{p} = \frac{1}{f(D)} Q(x) = \frac{1}{D^{2}  - 5 D +  4} X<em></em>

<em>taking common '4' </em>

<em>                          </em>= \frac{1}{4(1 +  (\frac{D^{2}  - 5 D}{4} ))} X<em></em>

<em>                         </em>

<em>                           </em>=\frac{1}{4}  (1 + (\frac{D^{2} -5D}{4})^{-1} )} X<em></em>

<em>applying binomial expression</em>

<em>      ( 1 + x )⁻¹    = 1 - x + x² - x³ +.....       </em>

<em>                          </em>=\frac{1}{4}  (1 - (\frac{D^{2} -5D}{4}) +((\frac{D^{2} -5D}{4})^{2} -...} )X<em></em>

<em>Now simplifying and we will use notation D = </em>\frac{dy}{dx}<em></em>

<em>                        </em>=\frac{1}{4}  (x - (\frac{D^{2} -5D}{4})x +((\frac{D^{2} -5D}{4})^{2}(x) -...}<em></em>

<em>Higher degree terms are neglected</em>

<em>                     </em>=\frac{1}{4}  (x - (\frac{ -5 D}{4}) x)<em></em>

<em>The particular integral of given differential equation</em>

<em>                  </em>y_{p} = \frac{1}{4} ( x - (\frac{-5}{4} ) (1))<em></em>

<u><em>Final answer</em></u><em>:-</em>

<em>          General solution of given differential equation</em>

<em>      </em>y = y_{c} + y_{p}<em></em>

<em>  </em>Y (x) = C_{1} e^{x} + C_{2} e^{4x} + \frac{1}{4} ( x + (\frac{5}{4} ))<em></em>

<em></em>

<em></em>

<em>         </em>

<em> </em>

     

4 0
3 years ago
I need the answer and work plss help
OlgaM077 [116]

Answer:

B

Step-by-step explanation:

x-5+3x-5+90=180 you set it up this way because you need to find what x is equal to and by adding those two equations plus 90 then setting the against 180 you can find x because all three angles in a triagnle add up to 180.

x-5+3x-5+90=180

4x-10+90=180              you combined like numbers

4x+80=180                   combined like numbers

    -80    -80                 subtract 80 from both sides because you are trying to---                                     get x alone

4x=100                          now to get x alone you have to divide 4 from both     ----                                     sides

/4    /4

x=25                              answer

5 0
3 years ago
If x=7 then which answers would I circle? A. X + 7 = 17 b. 7 = 17 - x c. 70 = 10x d. X/35 = 5 e. 15x = 105
disa [49]

Answer:

C. 70 = 10x

E. 15x = 105

Step-by-step explanation:

x = 7

Using method of elimination;

A. X + 7 = 17

Substituting the value of x;

7 + 7 ≠ 17 (Incorrect option)

B. 7 = 17 - x

Substituting the value of x;

7 ≠ 17 - 7  (Incorrect option)

C. 70 = 10x

Substituting the value of x;

70 = 10 * 7  (Correct option)

D. X/35 = 5

Substituting the value of x;

7 / 35 ≠ 5  (Incorrect option)

E. 15x = 105

Substituting the value of x;

15 * 7 = 105  (Correct option)

8 0
3 years ago
HEELP I'll give brainliest ​
andrey2020 [161]

Answer:

28.3

Step-by-step explanation:

12/20 = 17/x

cross multiply

12x=340

divide each side by 12

x=28.3333333333.......

round it to nearest tenth

28.3

7 0
3 years ago
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