Solve the following system of equations by graphing and select the correct answer below:
2 answers:
Answer: option c
Step-by-step explanation:
Find the x-intercept and y-intercept of each line.
To find the x-intercept, substitute into the equation and solve for "x".
To find the y-intercept, substitute into the equation and solve for "y".
- For the first equation:
x-intercept
y-intercept
Graph a line that passes through the points (7.25, 0) and (0, 9.66)
- For the second equation:
x-intercept
y-intercept
Graph a line that passes through the points (0.5, 0) and (0, -0.33)
Observe the graph attached. You can see that point of intersection of the lines is (5,3); then this is the solution of the system. Therefore:
ANSWER
c)x = 5, y = 3
EXPLANATION
The given system has equations:
and
We graph the above equations using a graphing software to obtain the graph shown in the attachment.
The solution to the given system is the point of intersection of the two straight lines.
From the graph, the two straight lines intersected at (5,3).
This implies that the solution to the system is:
The correct answer is option is C
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Answer:
{1, (-1±√17)/2}
Step-by-step explanation:
There are formulas for the real and/or complex roots of a cubic, but they are so complicated that they are rarely used. Instead, various other strategies are employed. My favorite is the simplest--let a graphing calculator show you the zeros.
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Descartes observed that the sign changes in the coefficients can tell you the number of real roots. This expression has two sign changes (+-+), so has 0 or 2 positive real roots. If the odd-degree terms have their signs changed, there is only one sign change (-++), so one negative real root.
It can also be informative to add the coefficients in both cases--as is, and with the odd-degree term signs changed. Here, the sum is zero in the first case, so we know immediately that x=1 is a zero of the expression. That is sufficient to help us reduce the problem to finding the zeros of the remaining quadratic factor.
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Using synthetic division (or polynomial long division) to factor out x-1 (after removing the common factor of 4), we find the remaining quadratic factor to be x²+x-4.
The zeros of this quadratic factor can be found using the quadratic formula:
a=1, b=1, c=-4
x = (-b±√(b²-4ac))/(2a) = (-1±√1+16)/2
x = (-1 ±√17)2
The zeros are 1 and (-1±√17)/2.
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The graph shows the zeros of the expression. It also shows the quadratic after dividing out the factor (x-1). The vertex of that quadratic can be used to find the remaining solutions exactly: -0.5 ± √4.25.
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The given expression factors as ...
4(x -1)(x² +x -4)
