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2 years ago

X - 2y = 3 5x + 3y = 2 The lines whose equations are shown intersect at which point?

Mathematics

1 answer:

Lady_Fox [76]2 years ago

8 0

The point of intersection of the two lines is at (1,-1)

<h3>System of equation</h3>

The given system of expression is shown below

x - 2y = 3

5x + 3y = 2

The solution to the system of equation is the point of intersection

From equation 1

x = 3 + 2y

Substitute into 2

5(3+2y) + 3y = 2

15 +10y + 3y = 2

13y = -13

y = -1

Substitute y = -1 into 3

x = 3 + 2y

x = 3+(-2)

x = 1

Hence the point of intersection of the two lines is at (1,-1)

Learn more on system of equation here: brainly.com/question/25976025

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3 years ago

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antiseptic1488 [7]

Answer:

8. Domain: (-∞, -15) ∪ (-15, -5) ∪ (-5, ∞)

9. Domain: [7/13, ∞)

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Step-by-step explanation:

Question 8

Given rational function:

$f(x)=\dfrac{x}{x^2+20x+75}$

Factor the denominator of the given rational function:

$\implies x^2+20x+75$

$\implies x^2+5x+15x+75$

$\implies x(x+5)+15(x+5)$

$\implies (x+15)(x+5)$

Therefore:

$f(x)=\dfrac{x}{(x+15)(x+5)}$

Asymptote: a line that the curve gets infinitely close to, but never touches.

The function is undefined when the denominator equals zero:

$x+15=0 \implies x=-15$

$x+5=0 \implies x=-5$

Therefore, there are vertical asymptotes at x = -15 and x = -5.

Domain: set of all possible input values (x-values)

Therefore, the domain of the given rational function is:

(-∞, -15) ∪ (-15, -5) ∪ (-5, ∞)

---------------------------------------------------------------------------------

Question 9

Given function:

$f(x)=\sqrt{13x-7}+1$

Domain: set of all possible input values (x-values)

As the square root of a negative number is undefined:

$\implies 13x-7\geq 0$

$\implies 13x\geq 7$

$\implies x\geq \dfrac{7}{13}$

Therefore, the domain of the given function is:

$\left[\dfrac{7}{13},\infty\right)$

Range: set of all possible output values (y-values)

$\textsf{As }\:\sqrt{13x-7}\geq 0$

$\implies \sqrt{13x-7}+1\geq 1$

Therefore, the range of the given function is:

[1, ∞)

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3 years ago

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Answer:

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Step-by-step explanation:

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And we want to find the value of each variable.

To solve this system, first look at it and consider what you should try to do.

So we can see that the second and third equations both have an x.

Therefore, we can isolate the variables for the second and third equation and then substitute them into the first equation to make the first equation all xs.

Therefore, let's first isolate the variable in the second and third equation.

Second Equation:

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