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4 years ago

Danielle plans to graph the linear equation 5x-2y=10 by plotting the x-intercept and y-intercept.

Mathematics

1 answer:

lesya692 [45]4 years ago

4 0

x-intercept is (2,0)

y-intercept is (0,-5)

Step-by-step explanation:

Danielle plans to graph the linear equation 5x-2y=10 by plotting the x-intercept and y-intercept.

Finding x-intercept

X-intercept: Substitute 0 for y and then solve for x. Write your answer in the form (__, 0)

Putting y=0

$5x-2y=10\\5x-2(0)=10\\5x=10\\x=10/5\\x=2$

So, x-intercept is (2,0)

Finding y-intercept

Y-intercept: Substitute 0 for x and then solve for y. Write your answer in the form (0, __)

Putting x=0

$5x-2y=10\\5(0)-2y=10\\-2y=10\\y=10/-2\\y=-5$

So, y-intercept is (0,-5)

Keywords: Solving Equations

Learn more about solving equations at:

#learnwithBrainly

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Read 2 more answers

Given a rectangle with length of (2x+9)cm and width of (3x+1)cm.Two squares, each with sides x cm is removed from the rectangle.

il63 [147K]

Answer: The length is 13cm and the width is 7cm

Step-by-step explanation:

For a rectangle of length L and width W, the area is:

A = W*L

In this case we have:

L = (2*x + 9) cm

W=(3*x + 1) cm

Then the area of the rectangle is:

A = (2*x + 9)*(3*x + 1) cm^2

A = (6*x^2 + 2*x + 27*x + 9) cm^2

A = (6*x^2 + 29*x + 9) cm^2

now we remove two squares with sides of x cm

The area of each one of these squares is (x cm)*(x cm) = x^2 cm^2

Then the area of the figure will be:

area = (6*x^2 + 29*x + 9) cm^2 - (2*x^2 ) cm^2

area = (4*x^2 + 29*x + 9) cm^2

Now we know that the area of this shape is 83 cm^2, then we need to solve:

83 cm^2 = (4*x^2 + 29*x + 9) cm^2

0 = (4*x^2 + 29*x + 9) cm^2 - 83 cm^2

0 = (4*x^2 + 29*x - 74) cm^2

Then we need to solve:

0 = 4*x^2 + 29*x - 74

Here we can use Bhaskara's equation, the solutions of this equation are given by:

$x = \frac{-29 \pm \sqrt{29^2 - 4*4*(-74)} }{2*4} = \frac{-29 \pm 45}{8}$

Then the two solutions are:

x = (-29 - 45)/8 = -9.25 (for how the length and width are defined, we can not have x as a negative number, then this solution can be discarded).

The other solution is:

x = (-29 + 45)/8 = 2

x = 2

Then the length and width of the rectangle are:

Length = (2*2 + 9)cm = 13 cm

Width = (3*2 + 1)cm = 7cm

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