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arlik [135]
3 years ago
13

Which values of "P" and "Q" result in an equation with no solution.

Mathematics
1 answer:
GenaCL600 [577]3 years ago
4 0

-68x+P=Qx+34\qquad\text{subtract P from both sides}\\\\-68x=Qx+34-P\qquad\text{subtract QX from both sides}\\\\-68x-Qx=34-P\\\\-x(68+Q)=34-P\qquad\text{divide both sides by (68 + Q)}\\\\-x=\dfrac{34-P}{68+Q}\qquad\text{multiply both sides by (-1)}\\\\x=\dfrac{P-34}{68+Q}\\\\\text{The equation has no solution if the numerator is different than 0}\\\text{and the denominator is equal 0.}\\\\P-34\neq0\ \wedge\ 68+Q=0\\\\P\neq34\ \wedge\ Q=-68

Answer:\\A:\ P=68\ and\ Q=-68\\C:\ P=-68\ and\ Q=-68\\D:\ P=-34\ and\ Q=-68\\-------------------\\\\For\ P=34\ and\ Q=-68\ we\ have\ \dfrac{34-34}{68-68}=\dfrac{0}{0}\\\\Then\ the\ equation\ has\ infinitely\ many\ solutions.

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How many real roots does the function
icang [17]

Answer:

Option C is correct i.e. 2.

Step-by-step explanation:

Given the function is f(x) = x² +8x -2.

We can compare it with general quadratic expression i.e. ax² +bx +c.

Then a = 1, b = 8, c = -2.

We can find the number of real root by finding discriminant of the equation ax² +bx +c =0 as follows:-

D = b² -4ac

D = 8² -4*1*-2

D = 64 +8

D = 72.

When D is a positive value, then we have two real roots of the equation.

Hence, option C is correct i.e. 2.

6 0
3 years ago
Hurrrryyyyy plllzzz. Determine the equation of the line that passes through the given points
pashok25 [27]
<h2>Answer:</h2>

y = 2

<h2>Step-by-step explanation:</h2>

To determine the equation of the line that passes through (10,2) and (-3,2), we need to determine the slope of the line. Then substitute the slope and any given point in point slope form to obtain the equation of the line.

<h3>Finding the Slope of the line:</h3>

\implies \text{Slope} = \dfrac{\text{Rise}}{\text{Run}} = \dfrac{y_{2} - y_{1} }{x_{2} - x_{1}  }

\implies \text{Slope} = \dfrac{y_{2} - y_{1} }{x_{2} - x_{1}  }

<u>Substitute the coordinates of the given points:</u>

\implies \text{Slope} = \dfrac{2 - 2}{-3 - 10  }

<u>Simplify the equation to determine the slope:</u>

\implies \text{Slope} = \dfrac{0}{-3 - 10  }

∴ 0 divided by ANY number is ALWAYS 0.

\implies \text{Slope} =0

<h3>Finding the equation of the line:</h3>

Point slope form formula: y - y₁ = m(x - x₁)

  • x₁ and y₁ are the coordinates of any given point.
  • m is the slope

<u>Substitute the values in the point slope form:</u>

\implies \text{Equation of line:} \ y - y_{1}  = m(x - x_{1} )

\implies \text{Equation of line:} \ y - 2  = 0(x - 10)

<u>Simplify the equation to determine the equation of the line:</u>

∴ Any number multiplied by 0 is 0.

\implies \text{Equation of line:} \ y - 2  = 0

\implies \text{Equation of line:} \ y   = 0 + 2

\implies \text{Equation of line:} \ y   = 2

Thus, the equation of the line is y = 2.

5 0
2 years ago
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STatiana [176]


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