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kati45 [8]
2 years ago
5

Which expression is the as 400.902

Mathematics
1 answer:
siniylev [52]2 years ago
4 0

Answer:

4*100+.9*0.1+.002*.001

Step-by-step explanation:

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Given a rectangle with length of (2x+9)cm and width of (3x+1)cm.Two squares, each with sides x cm is removed from the rectangle.
il63 [147K]

Answer: The length is 13cm and the width is 7cm

Step-by-step explanation:

For a rectangle of length L and width W, the area is:

A = W*L

In this case we have:

L = (2*x + 9) cm

W=(3*x + 1) cm

Then the area of the rectangle is:

A = (2*x + 9)*(3*x + 1) cm^2

A = (6*x^2 + 2*x + 27*x + 9) cm^2

A = (6*x^2 + 29*x + 9) cm^2

now we remove two squares with sides of x cm

The area of each one of these squares is (x cm)*(x cm)  = x^2 cm^2

Then the area of the figure will be:

area = (6*x^2 + 29*x + 9) cm^2 - (2*x^2 ) cm^2

area = (4*x^2 + 29*x + 9) cm^2

Now we know that the area of this shape is 83 cm^2, then we need to solve:

83 cm^2 = (4*x^2 + 29*x + 9) cm^2

0 =  (4*x^2 + 29*x + 9) cm^2 - 83 cm^2

0 = (4*x^2 + 29*x - 74) cm^2

Then we need to solve:

0 = 4*x^2 + 29*x - 74

Here we can use Bhaskara's equation, the solutions of this equation are given by:

x = \frac{-29 \pm \sqrt{29^2 - 4*4*(-74)}  }{2*4} = \frac{-29 \pm 45}{8}

Then the two solutions are:

x = (-29 - 45)/8 = -9.25  (for how the length and width are defined, we can not have x as a negative number, then this solution can be discarded).

The other solution is:

x = (-29 + 45)/8 = 2

x = 2

Then the length and width of the rectangle are:

Length = (2*2 + 9)cm = 13 cm

Width = (3*2 + 1)cm = 7cm

4 0
2 years ago
Which inequality represents all the solutions of 10(3x + 2) > 7(2x − 4)?
Mrrafil [7]

Answer:

x>-3

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
The area of a circle is 615.44 in2. What is the diameter of the circle? Use 3.14 for π.
Shalnov [3]
615.44 = (3.14)(radius)^2 

<span>radius = square-root of (615.44/3.14) </span>

<span>diameter = radius x 2 </span>

<span>diameter = 28 inches 

3.14

</span>
6 0
3 years ago
Read 2 more answers
Is 6x and 4x+2 equivalent
Eduardwww [97]

Answer:

Is 6x and 4x+2 equivalent

? No!

Step-by-step explanation:

6x doesn't equal 4x+2

In order for them to be the same you would have to add the same terms example:

4x+2x would equal 6x

Extra explaining:

The only way for those term to be added would be if they had the same variable since only 4x has a variable the 2 cant be added. In math you CANNOT move your variables off of a number and add them back on after.

3 0
2 years ago
Product of 2 numbers increased by 9
tino4ka555 [31]
(X * y) + 9
Xy + 9
you can't reduce it further

~Zoe
4 0
3 years ago
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