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3 years ago

Fill in the Blank:

Mathematics

1 answer:

arsen [322]3 years ago

6 0

Answer:

The exponent of the second term (b) starts with 0 (b0 = 1) and then increases by one in each following term until it is equal to the exponent of the binomial (5).

Step-by-step explanation:

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What type of number is -100

Harlamova29_29 [7]

Answer:

The number -100 is a rational number and an integer

3 0

3 years ago

Cole has a rectangular garden with an area of 16.02 square meters. What is the width, in meters, of the garden?

exis [7]

Answer:

3.56m

Step-by-step explanation:Parameters given:

Area of the rectangular garden = 16.02m^2

Length of the rectangular garden = 4.5m

The Area of a rectangle can be calculated for using the formula below

Area (square meters) = length (meters) × width (meters)

Therefore, 16.02m^2 = 4.5m × width

Width = 16.02m^2 / 4.5m

Width = 3.56m

Therefore the width in meters of the garden is 3.56m

See the attachment below for an illustrative diagram

A = area

l = length

w = width

8 0

3 years ago

Read 2 more answers

How to prove this???

swat32

$\cos^3 2A + 3 \cos 2A \\
\Rightarrow \cos 2A (\cos^2 2A + 3) \\
\Rightarrow (\cos^2 A - \sin^2 A) (\cos^2 2A + 3) \\
\Rightarrow (\cos^2 A - \sin^2 A) (1 - \sin^2 2A + 3) \\
\Rightarrow (\cos^2 A - \sin^2 A) (4 - \sin^2 2A) \\
\Rightarrow (\cos^2 A - \sin^2 A) (4 - (2\sin A \cos A)(2\sin A \cos A)) \\
\Rightarrow (\cos^2 A - \sin^2 A) (4 - 4\sin^2 A \cos^2 A) \\ 
\Rightarrow 4(\cos^2 A - \sin^2 A) (1 - \sin^2 A \cos^2 A) 
$

go to right side now

$4( \cos^6 A - \sin^6 A)\\
\Rightarrow 4( \cos^3 A - \sin^3 A)(\cos^3 A + \sin^3 A)$

use $x^3 - y^3 = (x-y)(x^2 + xy + y^2)$ and $x^3 + y^3 = x^2 - xy + y^2$

$4( \cos^6 A - \sin^6 A)\\ \Rightarrow 4( \cos^3 A - \sin^3 A)(\cos^3 A + \sin^3 A) \\
\Rightarrow 4(\cos A - \sin A)(\cos^2 A + \cos A \sin A + \sin^2 A) \\
~\quad \quad\cdot ( \cos A + \sin A)(\cos^2 A - \cos A \sin A + \cos^2 A)$

so $\sin^2 A + \cos^2 A = 1$

$4( \cos^6 A - \sin^6 A)\\ \Rightarrow 4(\cos A - \sin A)(\cos^2 A + \cos A \sin A + \sin^2 A) \\ ~\quad \quad\cdot ( \cos A + \sin A)(\cos^2 A - \cos A \sin A + \cos^2 A) \\ \Rightarrow 4(\cos^2 A - \sin^2 A)(1 + \cos A \sin A )(1- \cos A \sin A ) \\ \Rightarrow 4(\cos^2 A - \sin^2 A)(1 - \cos^2 A \sin^2 A )\\ \Rightarrow 4(\cos^2 A - \sin^2 A)(1 - \sin^2 A \cos^2 A ) \\
 \Rightarrow Left hand side$

4 0

3 years ago

The ratio of the measures of the sides of a triangle is 8: 15: 17, and its perimeter is 480 in.. Find the measure of the shortes

lubasha [3.4K]

Answer:

Step-by-step explanation:

The ratio of the measure of sides of a triangle are 8:15:17

The perimeter is 480

8x + 15x + 17x= 480

40x= 480

x = 480/40

x = 12

Therefore the measure of the shortest side of the triangle can be calculated as follows

8×12

= 96

6 0

3 years ago

Twelve times the sum of three and a number is equal to five times the sum of eight more then twice the number

Andreas93 [3]

The equation is 12(3+x)=5(2x+8)

4 0

3 years ago