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7 days ago

5

The area of ABED is 49 square units. Given AGequals9 units and ACequals10 units, what fraction of the area of ACIG is represent

ed by the shaded region?

1 answer:

Svet_ta [4.3K]7 days ago

5 0

Answer:

The shaped region accounts for 7/18 of the area of ACIG.

Step-by-step explanation:

Refer to the attached diagram for further clarity on the problem.

Step 1

Determine the length of one side of square ABED.

We know that

AB=BE=ED=AD

The area of a square can be calculated as

$A=b^{2}$

where b is the side length.

We have

$A=49\ units^2$

So we substitute

$49=b^{2}$

$b=7\ units$

Thus,

$AB=BE=ED=AD=7\ units$

Step 2

Calculate the area of ACIG.

The area of rectangle ACIG is determined by

$A=(AC)(AG)$

Substituting the given values yields

$A=(9)(10)=90\ units^2$

Step 3

Determine the area of the shaded rectangle DEHG.

The area of rectangle DEHG is given by

$A=(DE)(DG)$

We find $DE=7\ units$

$DG=AG-AD=9-7=2\ units$

and substitute $A=(7)(2)=14\ units^2$

Step 4

Calculate the area of shaded rectangle BCFE.

The area of rectangle BCFE equals

$A=(EF)(CF)$

We see that

$EF=AC-AB=10-7=3\ units$

$CF=BE=7\ units$

and substitute

$A=(3)(7)=21\ units^2$

Step 5

Add the areas of the shaded regions together.

$14+21=35\ units^2$

Step 6

Divide the area of the shaded region by the area of ACIG.

$\frac{35}{90}$

Simplify this fraction by dividing both the numerator and denominator by 5.

$\frac{7}{18}$

Hence, the shaped region represents 7/18 of the area of ACIG.

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For this scenario, we can define:
$d = v * t
$
Where,
d represents distance
v signifies speed
t indicates time
Rearranging to find time gives us:
$t = d / v
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The total driving duration is half an hour:
$t = d / v1 + d / v2

1.5 = d / 30 + d / 20$
Rearranging for d results in:
$1.5 * 30 * 20 = 20d + 30d

1.5 * 30 * 20 = 50d

d = (1.5 * 30 * 20) / (50)

d = 18 miles$
Conclusion:
she lives 18 miles from the store

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0.5r

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If Jerry completed his journey in half the duration that Macy did, it implies Macy's time was twice as lengthy. Assuming Jerry’s speed is r, Macy’s speed would therefore be 0.5r, indicating she travels at half Jerry's pace and takes twice as long to cover the distance.

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The population p of a small community on the outskirts of a city grows rapidly over a 20-year period: t05101520p1002004509502000

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Answer:

After five years beyond the initial 20-year stretch, the population of this small community will be 4268.

Step-by-step explanation:

t | 0 | 5 | 10 | 15 | 20

p | 100 | 200 | 450 | 950 | 2000

The representation of the exponential function is:

p = aeᵏᵗ

where a and k represent constants.

Taking the natural logarithm on both sides:

In p = In aeᵏᵗ

In p = In a + In eᵏᵗ

In p = In a + kt

In p = kt + In a.

We can apply linear regression to model the relationship between In p and t, thereby determining the values of k and In a.

t | 0 | 5 | 10 | 15 | 20

p | 100 | 200 | 450 | 950 | 2000

In p | 4.605 | 5.298 | 6.109 | 6.856 | 7.601

In p = kt + In a.

y = mx + b

Here m corresponds to k and b is In a

By conducting a linear regression on the transformed linear relationship among In p and t and creating a graph of the variables, we derive the regression equation:

y = 0.151x + 4.584

The first image illustrates the equations needed for estimating the parameters of linear regression.

The second image displays the regression calculations alongside the graph of In p versus t.

By comparing

y = 0.151x + 4.584

to

In p = kt + In a.

y = In p

k = 0.151

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Thus, the exponential relationship between p and t is formulated as:

p = 97.905 e⁰•¹⁵¹ᵗ

In order to forecast the population for 5 years ahead from the 20-year mark, we need to find p at t=25 years.

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p(t=25) = 97.905 e³•⁷⁷⁵ = 4268.41, which rounds down to 4268.

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