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Reika [66]
2 years ago
12

Pleasee helppp insert two arithnetic means between -5 and 1

Mathematics
1 answer:
Salsk061 [2.6K]2 years ago
3 0

Answer:

a₂ = -3

a₃  = -1

Step-by-step explanation:

We have to  insert two arithmetic means between -5 and 1

Let a₁ and b₂ be the two arithmetic means between -5 and 1

-5, a₂, a₃, 1

Here,

  • a₄ = 1
  • a₁ = -5

We know that the nth term of an Arithmetic sequence

aₙ = a₁ + (n-1)d

a₄ = -5 + (4-1)d

1 = -5 + 3d    

1  + 5 = 3d

3d = 6

Dividing both sides by 2

d = 2

Also

a₂ = a₁ + (2-1)d

a₂ = -5 + d

a₂ = -5 + 2          ∵ d = 2

a₂  = -3

a₃ = a₁ + (3-1)d

a₃  = -5 + 2d

a₃  = -5 + 2(2)   ∵ d = 2

a₃  = -5 + 4

a₃  = -1

Thus,

a₂ = -3

a₃  = -1

Thus, the sequence becomes:

-5, -3, -3, 1

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Which equation is true when x = 5? A 8x = 80 B x + 4 = 9 C 10 ÷ x = 5 D x − 6= 1
Pie

Answer:

B

Step-by-step explanation:

A. 8 * x = 80

8 * 5 = 40. 40 is not 80, so it doesn't work.

B. x + 4 = 9

5 + 4 = 9. This works.

C. 10 ÷ x = 5

10 ÷ 5 = 2. 5 is not 2, so it doesn't work.

D. x - 6 = 1

5 - 6 = -1. 1 is not -1, so it doesn't work.

5 0
2 years ago
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Vlad [161]
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2 years ago
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:

<u>According to the Figure Given:</u>

Total Horizontal Distance = 14 in

Length = 6 in

<u>To Find :</u>

The Area of the composite figure

<u>Solution:</u>

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!

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Match the equal dominoes then write the true number sentences
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Determine the slope of the line passing through the given points (1,2) and (2,-1)
alex41 [277]
I hope this helps you



slope=y2-y1/x2-x1



slope=2-(-1)/1-2


slope=3/-1


slope= -3
3 0
3 years ago
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