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3 years ago

Complete the statement of congruence for the triangles.

Mathematics

1 answer:

Hoochie [10]3 years ago

3 0

If you are proving a congruence of triangles then you need to match the corresponding parts to the triangle you are proving congruent.

BAC would then be congruent to MJR because of the corresponding angles

B is the same angle as M

A is the same angle as J

C is the same angle as R

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Find the side in of point a to point c

vladimir1956 [14]

Step 1:

Calculate the measure of angle ∠ABC

$\angle DBC+\angle ABC=180(\text{ sum of angles on a straight line)}$ $\angle ABC=65^0$ $\begin{gathered} \angle DBC+\angle ABC=180 \\ \angle DBC+65^0=180^0 \\ \angle DBC=180^0-65^0 \\ \angle DBC=115^0 \end{gathered}$

From the triangle in the question,

$a=10\operatorname{km},c=15\operatorname{km},B=115^0$

Step 2:

Calculate the value of AB using the cosine rule below

$b^2=a^2+c^2-2\times a\times c\times\cos B$

By substituting the values, we will have

$\begin{gathered} b^2=a^2+c^2-2\times a\times c\times\cos B \\ b^2=10^2+15^2-2\times10\times15\times\cos 115^0 \\ b^2=100+225-300\times(-0.4226) \\ b^2=325+126.78 \\ b^2=451.78 \\ \text{Square root both sides} \\ \sqrt[]{b^2}=\sqrt[]{451.78} \\ b=21.26\operatorname{km} \end{gathered}$

Hence,

The distance of point A to point C is = 21.26km

3 0

1 year ago

The variables x and y are inversely proportional, and y = 2 when x = 3. What is the value of y when x = 9?

Nina [5.8K]

Answer:

$\huge \purple{ \boxed{ y = \frac{2}{3} }}$

Step-by-step explanation:

Since, the variables x and y are inversely proportional.

$\therefore \: y \: \: \alpha \: \: \frac{1}{x} \\ \implies \: y = \frac{k}{x} \\ (k = constant) \\ \implies \: xy = k ...(1)\\ plug \: y = 2, \: \: x = 3 \: in \: equation \: (1) \\ we \: find \\ 2 \times 3 = k \\ k = 6 \\ plug \:k = 6 \: in \: equation \: (1) \\ xy = 6 \\ (this \: is \: the \: equation \: of \: variation) \\ when \: x = 9 \: \: y =? \\ \\ 9y = 6 \\ y = \frac{6}{9} \\ \huge \red{ \boxed{ y = \frac{2}{3} }}$

4 0

3 years ago

2. Simplify the fraction to its simplest form. 54 75

sdas [7]

Answer:

18/25

Step-by-step explanation:

=54÷375÷3=18/25

=18/25

8 0

3 years ago

A messenger entered a building on the ground

sp2606 [1]

He first travels 15 floors. He then travels 12 floors, to get to the 3rd floor. He finally travels 35 floors, for a total of 62 floors.

8 0

3 years ago

The distance between the points (-3,-1) and (-4,0) is the square root of ___?

Galina-37 [17]

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ -3}}\quad ,&{{ -1}})\quad 
% (c,d)
&({{ -4}}\quad ,&{{0}})
\end{array}\qquad 
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}$

6 0

4 years ago