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puteri [66]
3 years ago
7

While testing a new pesticide, an agricultural scientist uses two functions to predict the yields of two same-sized potato farms

that have different soil conditions. The scientist's predicted yield, in tons, of the first farm can be represented by the following function, where x is the liters of pesticide he uses per acre of the farm. His predicted yield, in tons, of the second farm can be represented by the following function, where x is the liters of pesticide he uses per acre of the farm. If the scientist uses the same amount of pesticide on the two farms, select the function that accurately represents the predicted combined yield from both farms.
f(x)= -2.43x^2+10.37x+9 and g(x)= -3.43^2+13x+25


A. h(x)= -5.86x^2 + 23.37x + 34
B. h(x)= -5.86x^2 + 2.63x + 34
C. h(x)= -x^2 + 2.63x + 16
D. h(x)= x^2 + 2.63x - 16
Mathematics
1 answer:
Pepsi [2]3 years ago
4 0

Answer:

A. h(x)= -5.86x^2 + 23.37x + 34

Step-by-step explanation:

If the scientist uses the same amount of pesticide on the two farms then the x's of the functions are the same.

Then, the combined yield h(x) of the two farms is just the yield of the first farm plus the yield of the second farm:

h(x)=f(x)+g(x).

Now, since

f(x)= -2.43x^2+10.37x+9

and

g(x)= -3.43x^2+13x+25,

then

h(x)= (-2.43x^2+10.37x+9)+(-3.43x^2+13x+25)

we add the coefficients of the  corresponding terms to get:

h(x)= (-2.43x^2-3.43x^2)+(10.37x+13x)+(9+25)

\boxed {h(x)=-5.86 x^2 + 23.37 x + 34.}

Which is choice A.

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Answer: 24.24 miles

Step-by-step explanation:

We should note that 1000 metres = 1 kilometer.

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Since 1 meter = 1.094 yards

39000 meters = 39000 × 1.094 = 42666 yards

To find find the distance Imelda rode her bicycle to the nearest mile goes thus:

1 mi = 1760 yd

42666 yards will be converted to miles. This will be: 42666/1760 = 24.24 miles

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Answer:

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Step-by-step explanation:

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Answer:

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The area of the equilateral, isosceles and right angled triangle are 12.6mm², 9.61in² and 16.81yds² respectively.

<h3>What is the area of the equilateral, isosceles and right angle triangle?</h3>

Note that:

The area of an Equilateral triangle is expressed as A = ((√3)/4)a²

Where a is the dimension of the side.

The area of an Isosceles triangle is expressed as A = (ah)/2

Where a is the dimension of the base and h is the height.

The area of a Right angled triangle is expressed as A = (ab)/2

Where a and b is the dimension of the two sides other than the hypotenuse.

For the Equilateral triangle.

Given that;

  • a = 5.4mm
  • Area A = ?

A = ((√3)/4)(5.4mm)²

A = ((√3)/4)( 29.16mm² )

A = 12.6mm²

Area of the Equilateral triangle is 12.6mm²

For the Isosceles triangle.

Given that;

  • Base a = 3.4in
  • Slant height b = 5.9in
  • height h = ?
  • Area A = ?

The height h is the imaginary line drawn upward from the center of a.

First, we calculate the height using Pythagorean theorem

x² = y² + z²

Where x = b = 5.9in, y = a/2 = 3.4in/2 = 1.7in, and z = h

(5.9in)² = (1.7in)² + h²

34.81in² = 2.89in² + h²

h² = 34.81in² - 2.89in²

h² = 31.92in²

h = √31.92in²

h = 5.65in

Now, the area will be;

A = (ah)/2

A = (3.4in × 5.65in )/2

A = 19.21in²/2

A = 9.61in²

Area of the Isosceles triangle is 9.61in².

For the Right angled triangle

Given that;

  • a = 8.2yds
  • b = 4.1yds
  • c = 9.17yds
  • Area A = ?

A = (ab)/2

A = ( 8.2yds × 4.1yds)/2

A = ( 33.62yds²)/2

A = 16.81yds²

Area of the Right angled triangle is 16.81yds²

Therefore, the area of the equilateral, isosceles and right angled triangle are 12.6mm², 9.61in² and 16.81yds² respectively.

Learn more about Pythagorean theorem here: brainly.com/question/343682

#SPJ1

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