How many gallons of 20% antifreeze should be mixed with 10 gallons of 92% antifreeze to obtain a 65% antifreeze mixture?
1 answer:
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Answer:
<em>The solution of the equation </em>
<em>( 0.4 ,-3)</em>
Step-by-step explanation:
<u><em>Explanation</em></u>:-
<u><em>Step(i):</em></u>-
Given system of equations
10 x+3 y = −5 ...(i)
- 5 x - 4 y = 10 ...(ii)
Multiply (i) with '5'
10 × 5 x + 3×5 y = - 25
50 x + 15 y = 25 ...(iii)
Multiply (ii) with '10'
-5 × 10 x - 4×1 0 y = 100
- 50 x - 40 y =100 ...(iv)
<u><em>Step(ii)</em></u>:-
Solving (iii) and (iv)
50 x + 15 y =- 25
<u> - 50 x - 40 y =100</u>
- 25 y = 75
Dividing ' - 25' on both sides, we get
<em> y = -3</em>
<em>substitute y = -3 in equation (i) , we get</em>
<em> </em> 10 x+3 y = −5
10 x - 9 = - 5
10 x = -5 + 9
<em> x = 0.4 </em>
<u><em>Final answer</em></u>:-
<em>The solution of the equation ( 0.4 ,-3)</em>
Answer:
x = 125
Step-by-step explanation:
Tangents from an external point to a circle are congruent , that is
CA = CB
Then Δ ABC is isosceles with base angles being congruent
∠ BAC = ∠ ABC = =
= 55°
∠ ABC and x are adjacent angles on a straight line and sum to 180° , so
x = 180° - 55° = 125°
Then x = 125