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Luba_88 [7]
1 year ago
7

Point G is on line segment FH. Given FG=5x+2,GH=3x-1, and FG=9, determine the numerical length of FG

Mathematics
1 answer:
stealth61 [152]1 year ago
8 0

Given:

FG=5x+2

GH=3x-1

FG=9

Let us draw the line segment as follows,

Equating the length of FG, we get,

\begin{gathered} 5x+2=9 \\ 5x=9-2 \\ 5x=7 \\ x=\frac{7}{5} \end{gathered}

Substitute the value of x in the given value of GH,

\begin{gathered} GH=3x-1 \\ =3(\frac{7}{5})-1 \\ =\frac{21}{5}-1 \\ =\frac{16}{5} \\ =3.2 \end{gathered}

And the total length FH is,

\begin{gathered} FH=FG+GH \\ =9+3.2 \\ =12.2 \end{gathered}

Hence, the lengths are,

\begin{gathered} FG=9 \\ GH=3.2 \\ FH=12.2 \end{gathered}

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Ainat [17]

Answer:

(i) The area of the rabbit cage when the width is 5.2 m is 81.5 m²

(ii) The area of the rabbit cage if Wilson has 40 meters of wire mesh is 75 m²

Step-by-step explanation:

(i) The given relation of the area, A to the width P of the rabbit cage is A = 3·p²

The graph of the function between the values of 0 and 6 inclusive is found as follows;

A,              3·p²

0,               0

1,                1

2,               12

3,               27

4,               48

5,               75

6,               108

Please find attached the graph of A to 3·p²

From the graph, we have when the the width, p, of the rabbit cage = 5.2, the area, A ≈ 81.5 m²

The area of the rabbit cage when the width is 5.2 m = 81.5 m²

(ii) Also from the graph given that the total wire mess with Wilson = 40 meters, we have;

The formula for the perimeter of the cage = The formula for the perimeter of a rectangle = 2×length + 2×width

The formula for the perimeter of the cage = 2×3×p + 2× p = 8·p

Where the total length of the wire mesh available = 40 meters for the cage

The 40 meters of wire mesh will be used round the perimeter of the cage

∴ 40 m. = 8·p

p = 40/8 = 5 m.

At p = 5 m. the area is given as A = 75 m².

Therefore, the area of the rabbit cage if Wilson has 40 meters of wire mesh = 75 m².

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3 years ago
David’s statement shows a previous balance of $5834.53, a payment of $150, and new transactions totaling $325. His APR is 20.4%.
DaniilM [7]
Finance charge
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New balance
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3 years ago
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(The slope is always the coefficient of the independent variable, in this case x . The slope is therefore 2.)
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