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2 years ago

Factorise (x+1)^2 + 4(x+1)

Mathematics

1 answer:

mafiozo [28]2 years ago

6 0

Answer:

(x + 1)(x + 5)

Step-by-step explanation:

Given

(x + 1)² + 4(x + 1) ← factor out (x + 1) from each term

= (x + 1)(x + 1 + 4)

= (x + 1)x + 5)

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What is the length of side BC of the triangle?

miv72 [106K]

x+8 = 2x-1

x+9 = 2x

9=x

BC = 3x-3 = 3(9)-3 = 27-3 = 24

BC = 24

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2 years ago

A circus tent is cylindrical up to a height of 7 m and is in the shape of a cone over it, the diameter of the cylindrical part i

yan [13]

$\bold{\huge{\underline{ Solution }}}$

<h3>Given :- </h3>

• The circus tent is composed of cylinder and a cone.

• The height and diameter of the cylindrical part are 7m and 10m

• The total height of the circus tent 19m

• The cost of making the tent at a cost of 35 m² cloth.

<h3>Let's Begin :- </h3>

Here, we have ,

Cylinder and cone
The height and diameter of the cylinder are 7m and 10m
Therefore , radius = 5 m

We know that, 

Curved Surface area of the cylinder

$\sf{ = 2{\pi}rh}$

Subsitute the required values,

$\sf{ = 2{\times}3.14{\times}5{\times}7}$

$\sf{ = 6.28 {\times}5{\times}7}$

$\sf{ = 6.28 {\times}35}$

$\bold{ = 219.8m^{2}}$

Thus, The area of the cylinder is 219.8m² .

•We have to find the area of the cone.

•Here, Base of cone = diameter of the cylinder.

•The height of the cone will be

= Height of the tent - Height of cylinder

$\sf{ = 19 - 7 }$

$\bold{ = 12 m }$

We know that, 

Area of cone

$\bold{ = {\pi}rl }$

Here, l is the slant height.

Slant height of the cone

$\sf{ = \sqrt{ h^{2} + r^{2}} }$

$\sf{ = \sqrt{ (12)^{2} + (5)^{2}} }$

$\sf{ = \sqrt{ 144 + 25}}$

$\sf{ = \sqrt{ 169}}$

$\sf{ = \sqrt{ 13{\times} 13 }}$

$\bold{ = 13 m }$

Thus, The slant height of the cone is 13 m

Subsitute the required values in the above formula

$\sf{ = 3.14 {\times} 5 {\times} 13}$

$\sf{ = 3.14 {\times} 65}$

$\bold{ = 204.1 m^{2}}$

Thus, The area of the cone is 204.1 m² .

<h3>Therefore ,</h3>

The total area of the circus tent

$\sf{ = 204.1 + 219.8}$

$\bold{ = 423.9m^{2} \: or \: 424 m^{2}}$

We have to find the total cost of making the tent.
The cost for 1 m² = 35

Therefore,

The total cost for making the circus tent

$\sf{ = 424 {\times} 35}$

$\bold{ = 14840}$

Hence, The total cost for making the tent is 14840 .

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2 years ago

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12. 100 = 10 = 1 13. 10 x 100 The unknown is

ELEN [110]

You’re mom shejwjsjxjsksidjkwkw

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2 years ago

A 15-m2 wooded area has the following: 30 ferns, 150 grass plants, and 6 oak trees. What is the population density per m2 of eac

swat32

Answer:

See the procedure

Step-by-step explanation:

we know that

To find the population density per m² of each of the above species, divide the amount of each species by the total area

Ferns

$\frac{30}{15}=2\frac{ferns}{m^{2}}$

Grass plants

$\frac{150}{15}=10\frac{grass\ plants}{m^{2}}$

Oaks Trees

$\frac{6}{15}=0.4\frac{oaks\ trees}{m^{2}}$

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3 years ago

What is the recursive formula for this arithmetic sequence 6, -24, 96, -384

Artemon [7]

Answer:

Option A. $a_{1} =6$ $a_{n}= a_{n-1}(-4)$

Step-by-step explanation:

The given sequence in the question is 6,-24,96,-384.......n

and we have to give the recursive formula for this arithmetic sequence.

We can re write the sequence to make it more simpler

6,6(-4),(-24)(-4),(96)(-4).......n terms

Now we can say $a_{1} = 6$

and $a_{n}= a_{n-1}(-4)$

Therefore the recursive formula of the sequence is $a_{1} = 6$

$a_{n}= a_{n-1}(-4)$

7 0

3 years ago