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3 years ago

Suppose that a diamond weighs 0.0182 carat.What is that number in expanded form

Mathematics

1 answer:

kvv77 [185]3 years ago

7 0

0.0182=(0 x 1)+ (0/10) + (1/100) + (8/1000) + (2/10000).

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How do you write 19,830 in scientific notation? _____× 10^_____

pshichka [43]

Answer:

1.983(10⁴)

Step-by-step explanation:

Since we need to have ones and decimals as proper scientific notation, we have 1.983. Since we need the value of 19830, we need to move the decimal place 4 places to the right, so our exponent is 4.

*I double checked my work this time.

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3 years ago

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Solve the following

Pepsi [2]

Answer

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Will mark brainliest! Questions are in the picture!

alexdok [17]

Answer:

52.9 inches .

Step-by-step explanation:

Given that the triangular indentation has an area of 100 in.² and the base and height of this traingle are represented by expressions 3x and x+3 respectively . We need to find out the perimeter to the nearest tenth.

As we know that the area of triangle is ,

$\rm\longrightarrow Area_{\triangle}=\dfrac{1}{2}(base)(height)$

Substituting the respective values,

$\rm\longrightarrow 100\ =\dfrac{1}{2}(x+3)(3x)\\\\\rm\longrightarrow 2(100) = 3x(x+3)\\\\\rm\longrightarrow200 = 3x^2+9x\\\\\rm\longrightarrow 3x^2+9x-200=0$

On using the Quadratic formula , we have;

$\rm\longrightarrow x =\dfrac{-9\pm\sqrt{9^2-4(3)(-200)}}{2(3)} \\\\\rm\longrightarrow x =\dfrac{-9\pm \sqrt{81+1200}}{6}\\\\\rm\longrightarrow x =\dfrac{-9\pm \sqrt{1281}}{6}$

On simplifying above , we will get ,

$\rm\longrightarrow x = 6.802,-9.802$

Since sides can't be negative, therefore,

$\rm\longrightarrow\underline{\underline{ x =6.802}}$

Therefore ,

$\rm\longrightarrow Base = 3x =3(6.802)in = 20.406\ in\\$
$\rm\longrightarrow Height = x +3=6.802+3=9.802\ in$

Next let's find out the hypotenuse using Pythagoras theorem, as ;

$\rm\longrightarrow h=\sqrt{ b^2+p^2}\\$

$\rm\longrightarrow h =\sqrt{ (20.406)^2+(9.802)^2}\\$

$\rm\longrightarrow h =\sqrt{416.40+96.07}\\$

$\rm\longrightarrow h = 22.63\ in$

Now we may find perimeter as ,

$\rm\longrightarrow P = p + b + h \\$

$\rm\longrightarrow P = (22.63 + 9.802 + 20.406)in.$

$\\\rm\longrightarrow P = 52.89 \ in.\\$

$\rm\longrightarrow \underline{\underline{ Perimeter = 52.9\ in .}}$

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3 years ago

How to find the area of irregular figures

Cloud [144]

Instead, break down the shape into rectangles. Next, calculate the area of both rectangles and add them together. The area of the first rectangle is 72 square centimeters and the area of the second rectangle is 50 square centimeters. Together there are 72 + 50 = 122 square centimeters.

That is how u find a irregular figure..hope this help u

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3 years ago

If triangle ABC is rotated 90 degrees counterclockwise about point P to form triangle DEF, then line AB will have the same lengt

notsponge [240]

Answer:

Step-by-step explanation:

This is because these are the corresponding sides of the triangle, as in ABC and DEF.

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3 years ago

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