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2 years ago

Vertex of parabola (x-7)^2+5

Mathematics

2 answers:

gulaghasi [49]2 years ago

6 0

(7,5) use Desmos calculator to find the vertex of these problems

UNO [17]2 years ago

4 0

Answer:

(7,5)

Step-by-step explanation:

You can use the desmos website for math problems like this.

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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

1 year ago

What is 12.3 -(-9.6) =12.3 + 9.6 simplified?

BlackZzzverrR [31]

Answer:

Step-by-step explanation:

12.3 + 9.6 = 21.9

4 0

3 years ago

Which expression can be used to convert AU$22 in the US dollars

miv72 [106K]

0.71 x 22 is the expression that works, because 1 AUD = 0.71USD.

5 0

3 years ago

Parabolas y=−2x^2 and y=2x^2 +k intersect at points A and B that are in the third and the fourth quadrants respectively. Find k

OverLord2011 [107]

Answer:

-25

Step-by-step explanation:

(1) y = -2x²

(2) y = 2x² + k Subtract (1) from (2)

0 = 4x² + k Subtract 4x² from each side

k = -4x²

The parabolas are symmetrical about the y-axis.

Segment AB = 5, so x = +2.5 and x = +2.5.

k = -4(±2.5)² = -4 × 6.25 = -25

8 0

2 years ago

The volume of a ball is 562.5 pi cubic inches. What is the diameter of the ball?

Angelina_Jolie [31]

Big brain math 1+1=2+22=24+26

5 0

2 years ago

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