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Alinara [238K]
1 year ago
5

HELP!

Mathematics
1 answer:
maksim [4K]1 year ago
7 0

<u>Part A</u>

<u />4x^2 -7x-15=0\\\\(4x+5)(x-3)=0\\\\x=-\frac{5}{4}, 3

So, the x-intercepts are \boxed{\left(-\frac{5}{4}, 0 \right), (3,0)}

<u>Part B</u>

The vertex will be a minimum because the coefficient of x^2 is positive.

The x-coordinate of the vertex is x=-\frac{-7}{2(4)}=\frac{7}{8}

Substituting this back into the function, we get f\left(\frac{7}{8} \right)=4\left(\frac{7}{8} \right)^2 -7\left(\frac{7}{8} \right)^2 -15=-\frac{289}{16}

So, the coordinates of the vertex are \boxed{\left(\frac{7}{8}, -\frac{289}{16} \right)}

<u>Part C</u>

Plot the vertex and the x-intercepts and draw a parabola that passes through these three points.

The graph is shown in the attached image.

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An horse gallops 200ft turns and trots 350ft turns again and travels 410ft
bija089 [108]

The area of the triangle formed by his path is 34971.98 ft sq to the nearest hundredth.

<h3>What is the Heron's formula?</h3>

The Heron's formula is given as;

√s(s-a)(s-b)(s-c)

where s is half the perimeter of the triangle

WE have been given that horse gallops 200ft, turns and trots 350ft, turns again and travels 410ft to return to the point he started from.

Perimeter of the triangle is given as = 200 + 350 + 410 = 960 ft

Semi perimeter =  960 ft/ 2 = 480 ft

Area =  √s(s-a)(s-b)(s-c)

Area =  √480 (480 -200)(480 -350)(480 -410)

Area =  √480 (280)(130)(70)

Area =  √480 (2548000)

Area = 34971.98

The area of the triangle formed by his path is 34971.98 ft sq to the nearest hundredth.

Learn more about the Heron's formula;

brainly.com/question/20934807

#SPJ1

The complete question is

A horse gallops 200ft, turns and trots 350ft, turns again and travels 410ft to return to the point he started from. What is the area of the triangle formed by his path? round to the nearest hundredth.

6 0
1 year ago
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