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Deffense [45]
3 years ago
12

Someone please help me.

Mathematics
1 answer:
Free_Kalibri [48]3 years ago
3 0
<h3>Explanation:</h3>

1. PQ║TS, PQ ≅ TS, PT and QS are transversals to the parallel lines . . . given

2. ∠P ≅ ∠T . . . alternate interior angles at PT

3. ∠Q ≅ ∠S . . . alternate interior angles at QS

4. ΔPQR ≅ ΔTSR . . . ASA postulate

_____

You can use any pair of angles together with the sides PQ and TS. If you use the vertical angles and one of ∠T or ∠S, then you must invoke the AAS postulate for congruence, as the side is not between the two angles.

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Read 2 more answers
Two bowls and one cup weigh 800 grams. One bowl and two cups weigh 700 grams. Find the weight of the bowl and the cup
antoniya [11.8K]

Answer:

\large \boxed{\textbf{Bowl = 300 g; cup = 200 g}}  

Step-by-step explanation:

 Let b  = the mass of a bowl  

and c = the mass of a cup  

We have two conditions:  

\begin{array}{lrcl}(1) &2b + c  & = & 800\\(2) & b + 2c & = & 700\\\end{array}

Calculations:  

\begin{array}{lrcll}(3) & 4b + 2c &=  & 1600&\text{ Multiplied (1) by 2}\\& 3b & = & 900&\text{Subtracted (2) from (3)}\\(4) & b & = & \mathbf{300}&\text{Divided each side by 3}\\ & 600 + c & = & 800&\text{Substituted (4) into (2}\\ & c & = & \mathbf{200}\\\end{array}\\\text{The mass of a bowl  is $\large \boxed{\textbf{300 g}}$ and that of a cup is $\large \boxed{\textbf{200 g}}$}

Check:

\begin{array}{rlcrl}2(300) + 200& =800 & & 300 + 2(200) & = 700\\600 + 200 & = 800& & 300 + 400 & = 700\\800 & = 800& & 700 & = 700\\\end{array}

OK.

6 0
3 years ago
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