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3 years ago

Consider the function represented by 9x+3y= 12 with x as the independent variable. How can this function be written using

Mathematics

1 answer:

kozerog [31]3 years ago

8 0

Answer:

f(x) = - 3x + 4

Step-by-step explanation:

Given

9x + 3y = 12

We require to rearrange expressing y in terms of x

Subtract 9x from both sides

3y = - 9x + 12 ( divide all terms by 3 )

y = - 3x + 4

Expressed in functional notation by replacing y by f(x), that is

f(x) = - 3x + 4

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Find the area of the composite figure.

Roman55 [17]

Answer:

The Area of the composite figure would be 76.26 in^2

Step-by-step explanation:

According to the Figure Given:

Total Horizontal Distance = 14 in

Length = 6 in

To Find :

The Area of the composite figure

Solution:

Firstly we need to find the area of Rectangular part.

So We know that,

$\boxed{ \rm \: Area \: of \: Rectangle = Length×Breadth}$

Here, Length is 6 in but the breadth is unknown.

To Find out the breadth, we’ll use this formula:

$\boxed{\rm \: Breadth = total \: distance - Radius}$

According to the Figure, we can see one side of a rectangle and radius of the circle are common, hence,

$\longrightarrow\rm \: Length \: of \: the \: circle = Radius$

Since Length = 6 in ;

$\longrightarrow \rm \: 6 \: in = radius$

Hence Radius is 6 in.

So Substitute the value of Total distance and Radius:

Total Horizontal Distance= 14
Radius = 6

$\longrightarrow\rm \: Breadth = 14-6$

$\longrightarrow\rm \: Breadth = 8 \: in$

Hence, the Breadth is 8 in.

Then, Substitute the values of Length and Breadth in the formula of Rectangle :

Length = 6
Breadth = 8

$\longrightarrow\rm \: Area \: of \: Rectangle = 6 \times 8$

$\longrightarrow \rm \: Area \: of \: Rectangle = 48 \: in {}^{2}$

Then, We need to find the area of Quarter circle :

We know that,

$\boxed{\rm Area_{(Quarter \; Circle) } = \cfrac{\pi{r} {}^{2} }{4}}$

Now Substitute their values:

r = radius = 6
π = 3.14

$\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times 6 {}^{2} }{4}$

Solve it.

$\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times 36}{4}$

$\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times \cancel{{36} } \: ^{9} }{ \cancel4}$

$\longrightarrow\rm Area_{(Quarter \; Circle)} =3.14 \times 9$

$\longrightarrow\rm Area_{(Quarter \; Circle) } = 28.26 \: {in}^{2}$

Now we can Find out the total Area of composite figure:

We know that,

$\boxed{ \rm \: Area_{(Composite Figure)} =Area_{(rectangle)}+ Area_{ (Quarter Circle)}}$

So Substitute their values:

$\rm Area_{(rectangle)}$ = 48
$\rm Area_{(Quarter Circle)}$ = 28.26

$\longrightarrow \rm \: Area_{(Composite Figure)} =48 + 28 .26$

Solve it.

$\longrightarrow \rm \: Area_{(Composite Figure)} =\boxed{\tt 76.26 \:\rm in {}^{2}}$

Hence, the area of the composite figure would be 76.26 in² or 76.26 sq. in.

$\rule{225pt}{2pt}$

I hope this helps!

3 0

2 years ago

Help please I’m almost done also I’ll mark brainliest

tatuchka [14]

Answer:

this is a ratio of 4 inches:5 feet.

if one side becomes 30 feet, means that other one is also multiplied by 6.

4 * 6 = 24 or A

pls mark as brainliest

Step-by-step explanation:

4 0

3 years ago

If a trader gained 15% by selling an article for naira 560.00 what is the cost price of the article?

Flauer [41]

Answer:

Mxmxmdsmmwsllsm

Step-by-step explanation:

Xld dlxlxzlzmsspsp

8 0

3 years ago

What is the equation of the line perpendicular to y= 2/3x+1 that passes through the point (12, 6)?

charle [14.2K]

Answer:

y=(-3/2)x+24

Step-by-step explanation:

a perpendicular line should have the negative reciprocal of the line that it is perpendicular to.

negative reciprocal of 2/3 is -3/2

out line should look something like this

y=(-3/2)x+b

then we use the given point to find b

6=(-3/2)12+b

6=-18+b

b=24

6 0

4 years ago

Ryan purchased a kayak on sale for 130$ before tax. The regular price was 200$ before tax. What percent represents the change is

Norma-Jean [14]

Answer:

Step-by-step explanation:

7 0

3 years ago