All categories

2 years ago

Graph each equation. Determine the solution of the system of equations

Mathematics

1 answer:

ivann1987 [24]2 years ago

5 0

Answer:

Step-by-step explanation:

Explanation: Equation 1: 3 x − 2 y = 10 Equation 2 : 5 x + 2 y = 6 Both equations are in the standard form for a linear equation. This form makes it easy to determine the x- and y-intercepts. We can use those two points to graph each equation. X-intercept: value of x when y = 0 Substitute 0 for y and solve for x . Y-intercept: value of y when x = 0 Substitute 0 for x and solve for y . Equation 1 3 x − 2 y = 10 X-intercept: Substitute 0 for y and solve for x . 3 x − 2 ( 0 ) = 10 3 x = 10 Divide both sides by 3 . x = 10 3 or ≈ 3.333 x-intercept: ( 10 3 , 0 ) or ( ≈ 3.333 , 0 ) Plot this point. Y-intercept: Substitute 0 for x and solve for y . 3 ( 0 ) − 2 y = 10 − 2 y = 10 Divide both sides by − 2 . y = 10 − 2 y = − 5 y-intercept: ( 0 , − 5 ) Plot this point. Draw a straight line through the two points. This is the graph for Equation 1. Equation 2 5 x + 2 y = 6 X-intercept: Substitute 0 for y and solve for x . 5 x + 2 ( 0 ) = 6 5 x = 6 Divide both sides by 5 . x = 6 5 or 1.2 x-intercept: ( 6 5 , 0 ) or ( 1.2 , 0 ) Plot this point. Y-intercept: Substitute 0 for x and solve for y . 5 ( 0 ) + 2 y = 6 2 y = 6 Divide both sides by 2 . y = 6 2 y = 3 y-intercept: ( 0 , 3 ) Plot this point. Draw a line between the two points. This is the graph of Equation 2. The lines intersect at a single point, therefore the system of equations is consistent. graph{(3x-2y-10)(5x+2y-6)=0 [-10, 10, -5, 5]}

You might be interested in

What function is it when an objective function is maximized.

Leokris [45]

Answer:

Linear Objective Function

7 0

2 years ago

3) Write in expanded form: 12, 245

spin [16.1K]

Twelve, two hundred and fourty five

5 0

3 years ago

Read 2 more answers

Rewrite each fraction with a denominator of 10. a 7 - IN 2 3 IN 5

PolarNik [594]

Answer:

7/2 = 35/10

3/5 = 6/10

Step-by-step explanation:

To get a common denominator of 10, simply multiply the current denominator by any number to equal 10. The first fraction has a denominator of 2. If we divide 10 by 2, we get the answer 5. This means 2 can be multiplied by 5 to get a denominator of 10. However, what we do to the denominator we must also do to the numerator (multiply by 5).

7/2

7 × 5 / 2 × 5

35/10

3/5

3 × 2 / 5 × 2

6/10

brainliest pls

6 0

2 years ago

Solve 73 make sure to also define the limits in the parts a and b

Aleks04 [339]

73.

$f(x)=\frac{3x^4+3x^3-36x^2}{x^4-25x^2+144}$

$\lim_{x\to\infty}f(x)=\lim_{x\to\infty}(\frac{3+\frac{3}{x}-\frac{36}{x^2}}{1-\frac{25}{x^2}+\frac{144}{x^4}})=3$ $\lim_{x\to-\infty}f(x)=\lim_{x\to-\infty}(\frac{3+\frac{3}{x}-\frac{36}{x^2}}{1-\frac{25}{x^2}+\frac{144}{x^4}})=3\cdot\frac{1}{2}=3$

Since we can't divide by zero, we need to find when:

$x^4-2x^2+144=0$

But before, we can factor the numerator and the denominator:

$\begin{gathered} \frac{3x^2(x^2+x-12)}{x^4-25x^2+144}=\frac{3x^2((x+4)(x-3))}{(x-3)(x-3)(x+4)(x+4)} \\ so: \\ \frac{3x^2}{(x+3)(x-4)} \end{gathered}$

Now, we can conclude that the vertical asymptotes are located at:

$\begin{gathered} (x+3)(x-4)=0 \\ so: \\ x=-3 \\ x=4 \end{gathered}$

so, for x = -3:

$\lim_{x\to-3^-}f(x)=\lim_{x\to-3^-}-\frac{162}{x^4-25x^2+144}=-162(-\infty)=\infty$ $\lim_{x\to-3^+}f(x)=\lim_{x\to-3^+}-\frac{162}{x^4-25x^2+144}=-162(\infty)=-\infty$

For x = 4:

$\lim_{x\to4^-}f(x)=\lim_{n\to4^-}\frac{384}{x^4-25x^2+144}=384(-\infty)=-\infty$ $\lim_{x\to4^-}f(x)=\lim_{n\to4^-}\frac{384}{x^4-25x^2+144}=384(-\infty)=-\infty$

4 0

1 year ago

What is the area of the figure below?

Mashutka [201]

The answer to your question is 67

4 0

2 years ago

Read 2 more answers