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3 years ago

Determine the area of the figure on the coordinate grid. Round to the nearest hundredth if needed

Mathematics

1 answer:

Nutka1998 [239]3 years ago

8 0

Answer:

72 square units

Step-by-step explanation:

Consider the figure as the difference of a trapezoid and a rectangle.

Area of the trapezoid:

a = 3 - (-2) = 5 units
b = 9 - (-6) = 15 units
h = 5 - (-5) = 10 units
A = (a + b)h/2 = (5 + 15)(10)/2 = 100 square units

Area of the rectangle:

l = 5 - (-2) = 7 units
w = -1 - (-5) = 4 units
A = lw = 4*7 = 28 square units

Area of the figure:

100 - 28 = 72 square units

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Scott is reading two books at the same time to prepare for a report he is writing. So far, he has read 407 of the total number o

Hitman42 [59]

Answer:

The system of equations are

x+y=557

$\frac35x+\frac56 y=407$

The total pages in shorter book is 245

The total pages in longer book is 312

Step-by-step explanation:

Given that,

Scott has read 407 of the total number of 557 pages, which $\frac35$ of the shorter book and $\frac56$ of longer book.

Total number of pages of shorter book be x and longer book be y.

Then,

$\frac35$ page of the shorter book $=\frac35 x$

$\frac56$ pages of the longer book = $\frac56y$

So, he has read $=\frac35x+\frac 56y$

Total number of pages of both book is = x+y

According to the problem,

x+y=557.........(1)

$\frac35x+\frac56 y=407$ .......(2)

We can write equation (2) as

$\frac35x+\frac56 y=407$

$\Rightarrow \frac{18x+25y}{30}=407$

$\Rightarrow {18x+25y}=407\times 30$

$\Rightarrow {18x+25y}=12,210$ ......(3)

Now 18 times of equation (1) subtract from equation (3)

18x+25y=12210

18x+18y=10026

- - -

_______________

25y-18y=12,210-10,026

⇒7y=2,184

$\Rightarrow y=\frac{2184}{7}$

⇒y= 312

Plug y=312 in equation (1)

x+312=557

⇒x=557-312

⇒x=245

The total pages in shorter book is 245

The total pages in longer book is 312

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Step-by-step explanation:

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Answer:

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6(4+9)

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