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2 years ago

Seats at a local entertainment venue sell for $5 each in the lower level and $4 each in the upper level. If all the seats

Mathematics

1 answer:

7nadin3 [17]2 years ago

5 0

Step-by-step explanation:

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The sum of two numbers is 9.9, and the sum of the squares of the numbers is 53.21. What are the numbers?

Snezhnost [94]

Answer:

There are two possibilities:

$x_{1} = 3.5$ and $y_{1} = 6.4$

$x_{2} = 6.4$ and $y_{2} = 3.5$

Step-by-step explanation:

Mathematically speaking, the statement is equivalent to this 2-variable non-linear system:

$x + y = 9.9$

$x^{2} + y^{2} = 53.21$

First, $x$ is cleared in the first equation:

$x = 9.9 - y$

Now, the variable is substituted in the second one:

$(9.9-y)^{2} + y^{2} = 53.21$

And some algebra is done in order to simplify the expression:

$98.01-19.8\cdot y +2\cdot y^{2} = 53.21$

$2\cdot y^{2} -19.8\cdot y +44.8 = 0$

Roots are found by means of the General Equation for Second-Order Polynomials:

$y_{1} \approx \frac{32}{5}$ and $y_{2} \approx \frac{7}{2}$

There are two different values for $x$ :

$y = y_{1}$

$x_{1} = 9.9-6.4$

$x_{1} = 3.5$

$y = y_{2}$

$x_{2} = 9.9 - 3.5$

$x_{2} = 6.4$

There are two possibilities:

$x_{1} = 3.5$ and $y_{1} = 6.4$

$x_{2} = 6.4$ and $y_{2} = 3.5$

5 0

2 years ago

What is the equation of the line that passes through (-3,-1 ) and has a slope of 3/5

vfiekz [6]

The point-slope form:

$y-y_1=m(x-x_1)$

We have the point (-3, -1) and the slope m = 3/5. Substitute:

$y-(-1)=\dfrac{3}{5}(x-(-3))\\\\y+1=\dfrac{3}{5}(x+3)\qquad\text{use distributive property}\\\\y+1=\dfrac{3}{5}x+\dfrac{9}{5}\qqua\text{subtract 1 from both sides}\\\\y=\dfrac{3}{5}x+\dfrac{4}{5}\qquad\text{multiply both sides by 5}\\\\5y=3x+4\qquad\text{subtract 3x from both sides}\\\\-3x+5y=4\qquad\text{change the signs}\\\\3x-5y=-4$