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3 years ago

6

Use the equation 135⋅42=5,670 and what you know about fractions, decimals, and place value to explain how to place the decimal p

oint when you compute (1.35)⋅(4.2).

1 answer:

Jobisdone [24]3 years ago

7 0

7x + 4 = 9

7x + 4 = 19

2x = 19 - 4

7x = 15

x= 15 – 7

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Regular hexagon ABCDEF has vertices at A(4, 4!3), B(8, 4!3), C(10, 2!3), D(8, 0), E(4, 0) and F(2, 2!3).

marissa [1.9K]

Since the given hexagon is a regular hexagon all it's sides will be of equal length. Now, we know that the Area of any regular hexagon is given by:

$A=\frac{3\sqrt{3}}{2} a^2$

Where $A$ is the area of the regular hexagon

$a$ is the side length of the regular hexagon

Also, it's Perimeter is given by:

$P=6a$

Thus, all that we need to do is to find the side length of any one of the sides and to do that let us have a look at at the data of vertices points given and find out which points are definitely adjacent to each other and are also easy to calculate.

A quick search will yield that D(8, 0) and E(4, 0) are definitely adjacent to each other.

Please check the attached file here for a better understanding of the diagram of the original regular hexagon. Points D and E indeed are adjacent to each other.

Let us now find the distance between the points D and E using the distance formula which is as:

$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

Where $d$ is the distance.

$(x_1,y_1)$ and $(x_2,y_2)$ are the coordinates of points D and E respectively. (please note that interchanging the values of the coordinates will not alter the distance $d$ )

Applying the above formula we get:

$d=\sqrt{(8-4)^2+(0-0)^2} =\sqrt{4^2}=4$

$\therefore d=4$

We know that this distance is the side length of the given regular hexagon.

$\therefore d=a=4$

Now, if the sides of the given regular polygon are reduced by 40%, then the new length of the sides will be:

$a_{small}=4-\frac{40}{100}\times 4=2.4$

Thus, the area of the smaller hexagon will be:

$A_{small}=\frac{3\sqrt{3}}{2} a_{small}^2=\frac{3\sqrt{3}}{2} (2.4)^2\approx14.96$ unit squared

and the new smaller perimeter will be:

$P_{small}=6a_{small}=6\times 2.4=14.4$ unit

Which are the required answers.

5 0

3 years ago

Help me with hanger math...

andrew11 [14]

The answer is 3 First you subtract 2 from 17 and then you divide 15 by 5 to get the answer of 3

6 0

2 years ago

It is January 17th 2021

alekssr [168]

Yes is is, is your area still there?

6 0

3 years ago

Hey I really need help on this question please

Dmitry_Shevchenko [17]

A circle’s standard form of an equation is:
(x-h)^2 + (y-k)^2 = radius^2

Plug in h and k immediately because that is something you automatically know. H and k are derived from the center of the circle. The center of the circle is (h,k). Don’t get tripped up though, your center of a circle has negative coordinates. When you have two negatives, they become positive.

So now you have:
(x+4)^2 + (y-2)^2 = radius^2

So figure out what the radius is. Use the distance formula to find out. You have a change of 5 from -4 to 1 in x. You have a change of 2 from 2 to 4 in y. Distance formula has the distance as the square root of x distance squared and y distance squared. That would mean that the distance/radius is equal to the square root of (25 + 4). 5 squared is 25 while 2 squared is 4.

The radius of the circle is equal to the square root of (29). However, looking back at the circle equation the radius should be squared for the equation. Square root of 29 squared gets you 29.

Plug that in and you get:
(x+4)^2 + (y-2)^2 = 29

5 0

2 years ago

Plzzzzzzzzzzzzzzz<br><br>evaluate 4x(4+(2^6x2^-3))

Scilla [17]

11. Factoring and solving equations - A. Factor- 1. Factor 3x2 + 6x if possible. Look for monomial (single-term) factors first; 3 is a factor of both 3x2 and 6x and so is x . Factor them out to get 3x2 + 6x = 3(x2 + 2x1 = 3x(x+ 2) . 2. Factor x2 + x - 6 if possible. Here we have no common monomial factors. To get the x2 term we'll have the form (x +-)(x +-) . Since (x+A)(x+B) = x2 + (A+B)x + AB , we need two numbers A and B whose sum is 1 and whose product is -6 . Integer possibilities that will give a product of -6 are -6 and 1, 6 and -1, -3 and 2, 3 and -2. The only pair whose sum is 1 is (3 and -2) , so the factorization is x2 + x - 6 = (x+3)(x-2) . 3. Factor 4x2 - 3x - 10 if possible. Because of the 4x2 term the factored form wli be either (4x+A)(x +B) or (2x+A)(2x+B) . Because of the -10 the integer possibilities for the pair A, B are 10 and -1 , -10 and 1 , 5 and -2 . -5 and 2 , plus each of these in reversed order. Check the various possibilities by trial and error. It may help to write out the expansions (4x + A)(x+ B) = 4x2 + (4B+A)x + A8 1 trying to get -3 here (2x+A)(2x+B) = 4x2 + (2B+ 2A)x + AB Trial and error gives the factorization 4x2 - 3x - 10 - (4x+5)(x- 2) . 4. Difference of two squares. Since (A + B)(A - B) = - B~ , any expression of the form A' - B' can be factored. Note that A and B might be anything at all. Examples: 9x2 - 16 = (3x1' - 4' = (3x +4)(3x - 4) x2 - 29 = x2 - (my)* = (x+ JTy)(x- my)

8 0

3 years ago