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3 years ago

if f(x) and g(x) are a quadratic function but (f + g)(x) produce the graph below, which statement must be true

Mathematics

1 answer:

ArbitrLikvidat [17]3 years ago

7 0

The leading coefficients are opposites.

For instance
f(x) = 2x^2 + 5x + 6
g(x) = -2x^2 + 8x - 3
here the leading coefficients 2 and -2 are opposites

Adding function f(x) and g(x) gets us
f(x) + g(x) = (2x^2+5x+6) + (-2x^2+8x-3)
f(x) + g(x) = (2x^2-2x^2) + (5x+8x) + (6-3)
f(x) + g(x) = 0x^2 + 13x + 3
f(x) + g(x) = 13x + 3

The two quadratics add up to a linear equation

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jenna's rectangular garden borders a wall. she buys 80 ft of fencing. what are the dimensions of the garden that will maximize i

FrozenT [24]

Answer:

The dimensions are x =20 and y=20 of the garden that will maximize its area is 400

Step-by-step explanation:

Step 1:-

let 'x' be the length and the 'y' be the width of the rectangle

given Jenna's buys 80ft of fencing of rectangle so the perimeter of the rectangle is 2(x +y) = 80

x + y =40

y = 40 -x

now the area of the rectangle A = length X width

A = x y

substitute 'y' value in above A = x (40 - x)

A = 40 x - x^2 .....(1)

Step :2

now differentiating equation (1) with respective to 'x'

$\frac{dA}{dx} = 40 -2x$ ........(2)

Find the dimensions

$\frac{dA}{dx} = 0$

40 - 2x =0

40 = 2x

x = 20

and y = 40 - x = 40 -20 =20

The dimensions are x =20 and y=20

length = 20 and breadth = 20

Step 3:-

we have to find maximum area

Again differentiating equation (2) with respective to 'x' we get

$\frac{d^2A}{dx^2} = -2$

Now the maximum area A = x y at x =20 and y=20

A = 20 X 20 = 400

Conclusion:-

The dimensions are x =20 and y=20 of the garden that will maximize its area is 400

verification:-

The perimeter = 2(x +y) =80

2(20 +20) =80

2(40) =80

80 =80

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3 years ago

What’s in a equation or Leniar function y axis 1 and negative 7 and x axis negative 3 and 1

Elodia [21]

A linear function is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. For example, a common equation,

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and

as variables and

and

as constants. It is linear: the exponent of the

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3 years ago

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Klio2033 [76]

Answer:

Rah&fyjftyhh

Step-by-step explanation:

for TY hfhef

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2 years ago

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Explain how to compare two lengths that are measured in different sized units

nalin [4]

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3 years ago

Can someone please give me the answers to this? ... please ...

Gelneren [198K]

Step-by-step explanation:

the midpoint between 2 points (x1, y1) and (x2, y2) is simply ((x1+x2)/2, (y1+y2)/2).

so,

(9, 7) to (4, -3)

midpoint is ((9+4)/2, (7+ -3)/2) = (13/2, 4/2) = (6.5, 2)

(-7, -5) to (2, 1)

midpoint is ((-7+2)/2, (-5+1)/2) = (-5/2, -4/2) = (-2.5, -2)

now we have the midpoint and need the second point.

(4, 2) over (3, 4) to (x, y)

3 = (4 + x)/2

6 = 4 + x

x = 2

4 = (2 + y)/2

8 = 2 + y

y = 6

(-2, 1) over (-3, 2) to (x, y)

-3 = (-2 + x)/2

-6 = -2 + x

x = -4

2 = (1 + y)/2

4 = 1 + y

y = 3

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2 years ago