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2 years ago

Find the area of the polygon.

Mathematics

1 answer:

kotegsom [21]2 years ago

6 0

Answer:

$(30 \times 30) + ( \frac{1}{2} \times (30 + 15) \times 30 \\ 900 + 675 \\ 1575$

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Outside a home, there is a 10-key keypad with the letters A, B, C, D, E, F, G, H, I, and J that can be used to open the garage i

Assoli18 [71]

Answer:

3,628,800 (aka "10!")

Step-by-step explanation:

The first letter in the code can be 10 possible letters.

Since every letter can only be used once, the second letter can only be 9 possible letters.

E.G.: If the first letter is A, the second letter is B-J.

The third letter would be 8 possible letters, than the fourth would be 7, etc.

In math form, figuring out the possible combinations would be written out as so:

10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

An easier way to write this out would be using "10!", which stands for "10 Factorial"

The result of the above equals 3,628,800.

4 0

3 years ago

Write the equation -4x^2+9y^2+32x+36y-64=0 in standard form. Please show me each step of the process!

IgorC [24]

Hey there, hope I can help!

$-4x^2+9y^2+32x+36y-64=0$

$\mathrm{Add\:}64\mathrm{\:to\:both\:sides} \ \textgreater \ 9y^2+32x+36y-4x^2=64$

$\mathrm{Factor\:out\:coefficient\:of\:square\:terms} \ \textgreater \ -4\left(x^2-8x\right)+9\left(y^2+4y\right)=64$

$\mathrm{Divide\:by\:coefficient\:of\:square\:terms:\:}4$
$-\left(x^2-8x\right)+\frac{9}{4}\left(y^2+4y\right)=16$

$\mathrm{Divide\:by\:coefficient\:of\:square\:terms:\:}9$
$-\frac{1}{9}\left(x^2-8x\right)+\frac{1}{4}\left(y^2+4y\right)=\frac{16}{9}$

$\mathrm{Convert}\:x\:\mathrm{to\:square\:form}$
$-\frac{1}{9}\left(x^2-8x+16\right)+\frac{1}{4}\left(y^2+4y\right)=\frac{16}{9}-\frac{1}{9}\left(16\right)$

$\mathrm{Convert\:to\:square\:form}$
$-\frac{1}{9}\left(x-4\right)^2+\frac{1}{4}\left(y^2+4y\right)=\frac{16}{9}-\frac{1}{9}\left(16\right)$

$\mathrm{Convert}\:y\:\mathrm{to\:square\:form}$
$-\frac{1}{9}\left(x-4\right)^2+\frac{1}{4}\left(y^2+4y+4\right)=\frac{16}{9}-\frac{1}{9}\left(16\right)+\frac{1}{4}\left(4\right)$

$\mathrm{Convert\:to\:square\:form}$
$-\frac{1}{9}\left(x-4\right)^2+\frac{1}{4}\left(y+2\right)^2=\frac{16}{9}-\frac{1}{9}\left(16\right)+\frac{1}{4}\left(4\right)$

$\mathrm{Refine\:}\frac{16}{9}-\frac{1}{9}\left(16\right)+\frac{1}{4}\left(4\right) \ \textgreater \ -\frac{1}{9}\left(x-4\right)^2+\frac{1}{4}\left(y+2\right)^2=1$

$Refine\;once\;more\;-\frac{\left(x-4\right)^2}{9}+\frac{\left(y+2\right)^2}{4}=1$

For me I used
$\frac{\left(y-k\right)^2}{a^2}-\frac{\left(x-h\right)^2}{b^2}= 1$
$As\;\mathrm{it\;\:is\:the\:standard\:equation\:for\:an\:up-down\:facing\:hyperbola}$

I know yours is an equation which is why I did not go any further because this is the standard form you are looking for. I would rewrite mine to get my hyperbola standard form. However the one I have provided is the form you need where mine would be.
$\frac{\left(y-\left(-2\right)\right)^2}{2^2}-\frac{\left(x-4\right)^2}{3^2}=1$

Hope this helps!

4 0

3 years ago

You are at the edge of a cliff

gavmur [86]

Answer:

tell the teacher u ar at home

7 0

2 years ago

Figures A and B at right are similar. Assuming that figure A is the original figure, find the scale factor and find the lengths

AnnZ [28]

The scale factor is: 1/5.

The missing sides of figure B are: 2.4, 3.6, and 4.

<h3>How to find Scale Factor?</h3>

Scale factor = dimension of new figure / dimension of original figure

The polygons given are shown in the diagram attached below.

Figure A is the original figure

Figure B is the new figure.

x, y, and z has been used to mark the missing sides of figure B.

One dimension of original figure = 15

Corresponding dimension of the new figure = 3

Scale factor = new/original = 3/15

Scale factor = 1/5

To find the missing sides of figure B, multiply each corresponding side lengths of Figure A by the scale factor:

x = 12 × 1/5 = 2.4

y = 18 × 1/5 = 3.6

z = 20 × 1/5 = 4

In summary:

The scale factor is: 1/5.

The missing sides of figure B are: 2.4, 3.6, and 4.

Learn more about scale factor on:

brainly.com/question/2826496

3 0

2 years ago

A boogie board that has a regular price of $6. If the sales tax on the boogie board is 7%, what is the total cost of the board?

zavuch27 [327]

Answer:

6.42$

Step-by-step explanation:

6.00 divided by 100 equals 0.6 multiplied by 7 equals 0.42 so the sales tax is 0.42 cents and the total is 6.42$

7 0

3 years ago