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pentagon [3]
3 years ago
13

The area of Tracy's backyard is 1 1/3 acres she plants a garden that take up 1/3 of the backyard what area in acres of the garde

n
Mathematics
1 answer:
attashe74 [19]3 years ago
3 0

Answer:

\frac{4}{9}\ acres

Step-by-step explanation:

step 1

we know that

The area of Tracy's backyard is 1\frac{1}{3}\ acres

Convert to an improper fraction

1\frac{1}{3}=\frac{3*1+1}{3}=\frac{4}{3}\ acres

step 2

To find the area of the garden, multiply the area of the backyard by 1/3

so

\frac{4}{3}(\frac{1}{3})=\frac{4}{9}\ acres

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Answer:

8/32=0.25

Step-by-step explanation:

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Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.
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5 0
1 year ago
You are constructing a cardboard box from a piece of cardboard with the dimensions 2 m by 4 m. You then cut equal-size squares f
postnew [5]

Answer:

Dimensions:

l =3,15 m

w=1,15 m

x= 0,42 m   (height)

V(max) = 1,52 m³

Step-by-step explanation:

The cardboard is L = 4 m   and   W = 2 m

Let call x the length of the square to cut in each corner, then, volume of open box is:

For the side L       is  L - 2*x               l =  4 - 2*x

For the side W      is  W - 2*x             w=  2 - 2*x

The height              is  x

Volume of the open box, as function of x is:

V(x) = ( 4 -2x) * ( 2 - 2x) *x    ⇒  V(x) = ( 8 - 8x -4x + 4x²) *x

V(x) = ( 8 -12x + 4x² )*x     V(x) = 8x - 12x² + 4x³

V(x) = 8x - 12x² + 4x³

Taking derivatives on both sides of the equation

V´(x) = 8 - 24x + 12x²

V´(x) = 0       8  - 24x + 12x² = 0     reordering    12x² - 24x + 8  = 0

or    3x² - 6x + 2 = 0

A second degree equation. Solving for x

x₁,₂  = ( 6 ± √36 - 24 ) /6

x₁,₂  = ( 6 ± 3.46) /6

x₁  =  6 + 3,46 /6     x₁  = 1.58  we dismiss such solution because 1,58 * 2 = 3,15 and is bigger than 2 one of the side of the cardboard

x₂  =( 6 - 3,46 ) / 6

x₂  = 0,42 m

Dimensions of the open box

l  = 4 - 2*x     l  = 4 - 0,85      l  =  3,15 m

w = 2 -2*x    w  = 2 - 0,85     w = 1,15 m

x = 0,42 m

V(max) =3,15*1,15*0,42

V(max) = 1,52 m³

8 0
3 years ago
F(x) ≥ -(x+4)^2<br>axis of symmetry: <br>vertex:
BlackZzzverrR [31]

Answer:

so the vertex is (-4, 0) and the axis of symmetry is x=-4

Step-by-step explanation:

f(x) ≥ -(x+4)^2

f(x) ≥ -(x- -4)^2

this is in the form

f(x)> a(x-h)^2 +k

where (h,k) is the vertex and h is the axis of symmetry

so the vertex is (-4, 0) and the axis of symmetry is x=-4

6 0
2 years ago
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