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Georgia [21]
3 years ago
8

Find the x and y intercepts of the function f (x) = 2x^2 - 7x + 5

Mathematics
1 answer:
ololo11 [35]3 years ago
8 0

Answer:

x-intercepts at x = 1 and 2.5

y-intercept at y = 5

Step-by-step explanation:

Given: f(x) = 2x² - 7x + 5

It is required to find x and y intercepts.

x-intercept ⇒ the value of x when y = 0

y-intercept ⇒ the value of y when x = 0

So, to find x intercepts of the given function put f(x) = 0

∴ 2x² - 7x + 5 = 0

a = 2 , b = -7 and c = 5

Using the general rule to find the roots:

x=\frac{-b \pm \sqrt{b^2-4ac}  }{2a} =\frac{-(-7) \pm \sqrt{(-7)^2-4*2*5}  }{2*2} =\frac{7 \pm \sqrt{49-40}  }{4}=\frac{7 \pm \sqrt{9}  }{4}=\frac{7 \pm 3  }{4}

∴ x = (7+3)/2 = 10/2 = 2.5

OR x = (7-3)/4 = 4/4 = 1

So, x-intercepts at x = 1 and 2.5

===========================================

To find y intercepts of the given function put x = 0

∴ y = 2x² - 7x + 5 = 2 * (0)² - 7 * 0 + 5 = 5

So, y-intercept at y = 5

============================================

See the attached figure which represents x and y intercepts of the function f(x) using the graph.

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What is the longest line segment that can be drawn in a right rectangular prism that is 15 cm​ long, 11 cm​ wide, and 10 cm​ tal
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Answer:

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Step-by-step explanation:

The longest dimension of a rectangular prism is the length of the space diagonal from one corner to the opposite corner through the center of the prism. The Pythagorean theorm tells you the square of its length is the sum of the squares of the dimensions of the prism:

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_____

<em>Additional comment</em>

The square of the face diagonal is the sum of the squares of the dimensions of that face. The square of the space diagonal will be the sum of that square and the square of the remaining prism dimenaion, hence the sum of squares of all three prism dimensions.

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