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3 years ago

Which ratio is expressed as a unit rate?

Mathematics

2 answers:

Sergeeva-Olga [200]3 years ago

3 0

Answer:

1.45 per ounce

Step-by-step explanation:

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cluponka [151]3 years ago

3 0

Answer:

$1.45: per ounce

Step-by-step explanation:

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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

The first step in determining the solution to the system of equations, y = -x2 - 4x – 3 and y = 2x + 5, akyettically is to set t

riadik2000 [5.3K]

Answer:

Step-by-step explanation:

6 0

3 years ago

A circle has a radius of 30cm what is the area

Lana71 [14]

r = 30 cm

formula: A = πr²

A = πr²

A = π30²

A = 900π

if π = 3.14, then the answer is 2,826 cm

if π is not defined, the answer is 2,827.43 cm

3 0

3 years ago

Points A, B, and C are midpoints of the sides of right triangle DEF.

Radda [10]

Answer:

1) True 2) True 3) False 4) True

Step-by-step explanation:

In this question let's verify those options

1.Triangle A B C is inside triangle D E F. (true)

If A, B and C are midpoints of DEF then connecting those midpoints we have an interior triangle.

2. Point A is the midpoint of side F D, point B is the midpoint of side D E, point C is the midpoint of side F E. (true)

3. Angles D F E and A B C are right angles. (false)

These triangles are similar. And In this case, the right angles are:

$E\hat{D}F\cong A\hat{C}B=90^{\circ}\\\measuredangle D=\measuredangle C=90^{\circ}$

D and C are opposed to the larger side, and not F, and B

Because: $\measuredangle F\cong\measuredangle B \neq90^{\circ}$

4. The length of D E is 10 centimeters, the length of F D is 6 centimeters, and the length of F E is 8 centimeters. (true)

Let's test this by the Pythagorean Theorem. For DE is the hypotenuse and FD and FE is their legs.

$\overline{DE}=\sqrt{FD^{2}+FE^{2}}\\\overline{DE}=\sqrt{8^{2}+6^{2}}\\10= \sqrt{100}\\10=10$

8 0

3 years ago

Read 2 more answers

HELP ASAP PLEASE!!!! I’m really confused

8_murik_8 [283]

1. first option= 84
2. first option= (1+6)/7
3. last option= 0.40-m

6 0

3 years ago