Ask question

Ask question

All categories

3 years ago

13

What does interior angle A of the polygon in the figure equal?

2 answers:

astra-53 [7]3 years ago

7 0

Answer:

The correct option is C.

Step-by-step explanation:

The sum of interior angles of any polygon is defined as

$S=(n-2)\times 180^{\circ}$

Where n is number of vertices of polygon.

From the given figure it is noticed that the number of vertices is 6. So, the sum of interior angles is

$S=(6-2)\times 180^{\circ}=720^{\circ}$

One exterior angle of 130 degree is given in the figure. So, the interior angle on that vertex is

$360-130=230$

Now, add all the interior angles.

$S=50+100+120+A+110+230$

$S=A+610$

Since the sum of interior angles is 720, therefore

$720=A+610$

Subtract 610 from both sides.

$720-610=A+610-610$

$A=110$

Therefore option C is correct.

JulsSmile [24]3 years ago

3 0

C.110 hopefully that's the right answer

You might be interested in

Need help. I can’t fail this!! 7

vodka [1.7K]

Answer:

Third one? I'm not sure though.

Step-by-step explanation:

3 0

3 years ago

The machine bottled 8,000 bottles in 4 hours. if the rate of the machine were doubled, how long would it take the machine to bot

valina [46]

It would take 20 hours since 8,000 times 5 is 40,000 so 4 times 5 is 20.

Logic.

4 0

3 years ago

A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

3 0

3 years ago

I got a 12 discount on a pair of jeans and a 25% discount on a t-shirt the original price of the jeans was $100 and thatof the T

Tcecarenko [31]

Answer:

$125.50

but I'm not sure

Step-by-step explanation:

100÷100=1

1×12=12

100-12=88

jeans with discount = $88

50÷100=0.5

0.5×25=12.50

5000-1250=3750

t-shirt with discount = $37.50

3750+8800=12550

6 0

2 years ago

Read 2 more answers

What is the answer to ten sevens subtracting two sevens

eduard

That would be 8/7 or 1 1/7. Hope this helps! :)

5 0

3 years ago

Read 2 more answers