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Daniel [21]
3 years ago
6

*BRAINLIEST* (EASY QA: Warm UP) Find a positive solution to each equation: x2 = 1/4

Mathematics
2 answers:
Kay [80]3 years ago
6 0

Answer:

C. x = 1/2

Explanation:

\sf \rightarrow x^2 = \dfrac{1}{4}

\sf \rightarrow x=\sqrt{\dfrac{1}{4}},\:x=-\sqrt{\dfrac{1}{4}}

\sf \rightarrow x=\dfrac{1}{2},\:x=-\dfrac{1}{2}

<u>As asked for positive solution (+)</u>

\sf \rightarrrow \sf \rightarrow x=\dfrac{1}{2}

Georgia [21]3 years ago
4 0

\qquad\qquad\huge\underline{{\sf Answer}}

\textbf{Let's get it solved :}

  • \sf{x² = \dfrac{1}{4}}

  • \sf{x = \sqrt{\dfrac{1}{4}}}

  • \sf{x= \pm{\dfrac{1}{2}}}

  • \sf{x ={\dfrac{1}{2}} }

\textsf{[ since we need positive solution ]}

\textsf{Correct choice is C}

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A mixture of 12 liters of chemical A, 16 liters of chemical B, and 26 liters of chemical C is required to kill a destructive cro
VMariaS [17]

Answer:

  • From Commercial spray X: 4 liters from Chemical A, 8 liters from Chemical B and 8 liters from Chemical C.
  • From Commercial spray Y: 18 liters of Chemical C
  • From Commercial spray Z: 8 liters of Chemical A and 8 liters of Chemical B.

Step-by-step explanation:

Since we need a lot of chemical C, we are going to leave Commercial spray Y   for last in case we lack in case we need more Chemical C, which is supplied by spray Y.

We need to cover the demand of both chemical A and B. For each liter of Chemical A we get 2 liters of Chemical B by using Commercial spray X. And for each liter of Chemical A we get 2 liters of Chemical B by using spray Z.

We will  call X the number of units of Commercial spray X used, where each unit contains 1 liter of Chemical A, 2 liters of Chemical B and 2 iters of Chemical C. Y is the number of units of Commercial spray Y used, containing each of them 1 liter of Chemical C, and Z the number of units of commercial spray Z used, on units containing both 1 liter of Chemical A and Chemical B.

We can represent the amount of liters we have for each chemical on a vector of the form <em>(a,b,c)</em> where a reresents the amount of Chemical A, b the amount of chemical B, and c the amount of chemical C. We want<em> (a,b,c)</em> to be equal to (12,16,26), in other words, we want a to be 12, b to be 16 and c to b 26. Furthermore we can obtain <em>(a,b,c) </em>by using this equation

(a,b,c) = X * (1,2,2) + Y * (0,0,1) + Z * (1,1,0) = (1*X+0*Y+1*Z,2*X+0*Y+1*Z,2*X+1*Y+0*Z) = (X+Z,2*X+Z,2*X+Y)

Thus, we have

  • a = X+Z = 12
  • b = 2*X+Z = 16
  • c = 2*X+Y = 26

We can substract the second equation with the first one to obtain the value of X:

X = b-a = (2*X+Z)-(X+Z) = 16-12 = 4

Replacing X by 4, we obtain on the first expression that 4+Z = 12, hence, Z = 8. Since X is 4, 2*X+Y = 8+Y = 26. This gives us that Y must be 18.

We conclude that we need the following amount of Chemical A, B and C:

  • From Commercial spray X: 4, 4*2 = 8 and 4*2 = 8 liters respectively
  • From Commercial spray Y: 18 liters of Chemical C
  • From Commercial spray Z: 8 liters of Chemical A and 8 liters of Chemical B.

I hope i could help you!

6 0
3 years ago
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