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1 year ago

A 6 inch by 10 inch rectangle is dilated by afactor of 3. What is the area of the dilatedrectangle?

Mathematics

1 answer:

qaws [65]1 year ago

5 0

Given;

There are given that the 6 inches by 10-inch rectangle.

Explanation:

dilated by a factor of three means that the two dimensions needed for the area are multiplied by 3.

So,

The width of the rectangular is:

$width=6\times3=18$

And,

The length of the rectangular is:

$10\times3=30$

Then,

The area of dilated rectangular is:

$\begin{gathered} Area\text{ of dilated rectanular=}width\times\text{length} \\ =18\times30 \\ =540inch^2 \end{gathered}$

Final answer:

Hence, the area of the dilated rectangle is 540 inch^2.

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Use the unit circle to evaluate these expressions:

sergeinik [125]

Answer:

a) We can remove the complete rotations around the unitary circle like this, because we know that one complete revolution is equivalent to $2\pi$ :

$17 \pi/4 - 2\pi = \frac{9\pi}{4} -2\pi = \pi/4$

For this case we know that $sin (\pi/4) = \frac{\sqrt{2}}{2}$

So then $sin(\frac{17 \pi}{4}) = \frac{\sqrt{2}}{2}$

b) We can remove the complete rotations around the unitary circle like this, because we know that one complete revolution is equivalent to $2\pi$ :

$19 \pi/6 - 2\pi = \frac{7\pi}{6}$

For this case we know that $cos (\pi/6) = \frac{\sqrt{3}}{2}$

And we know that $\frac{7\pi}{6}$ is on the III quadrant since is equivalent to 210 degrees. And on the III quadrant the cosine is negative. So then $cos(\frac{19 \pi}{6}) = -\frac{\sqrt{3}}{2}$

c) For this case that any factor of $\pi$ the sin function is equal to 0.

So from definition of tan we have this:

$tan (450\pi) = \frac{sin(450 \pi)}{cos(450 \pi)}= \frac{0}{cos(450\pi)}= 0$

Step-by-step explanation:

a. sin (17pi / 4 )

We can remove the complete rotations around the unitary circle like this, because we know that one complete revolution is equivalent to $2\pi$ :

$17 \pi/4 - 2\pi = \frac{9\pi}{4} -2\pi = \pi/4$

For this case we know that $sin (\pi/4) = \frac{\sqrt{2}}{2}$

So then $sin(\frac{17 \pi}{4}) = \frac{\sqrt{2}}{2}$

b. cos (19pi / 6 )

We can remove the complete rotations around the unitary circle like this, because we know that one complete revolution is equivalent to $2\pi$ :

$19 \pi/6 - 2\pi = \frac{7\pi}{6}$

For this case we know that $cos (\pi/6) = \frac{\sqrt{3}}{2}$

And we know that $\frac{7\pi}{6}$ is on the III quadrant since is equivalent to 210 degrees. And on the III quadrant the cosine is negative. So then $cos(\frac{19 \pi}{6}) = -\frac{\sqrt{3}}{2}$

c. tan(450pi)

For this case that any factor of $\pi$ the sin function is equal to 0.

So from definition of tan we have this:

$tan (450\pi) = \frac{sin(450 \pi)}{cos(450 \pi)}= \frac{0}{cos(450\pi)}= 0$

4 0

3 years ago

If the length of an arc is 12 inches and the radius of the circle is 10 inches, what is the measure of the arc?

a_sh-v [17]

I guess what you are asking is what is the measure of the central angle?

arc length = radius * central angle (in radians)

central angle (in radians) = arc length / radius

central angle (in radians) = 12 / 10

central angle (in radians) = 1.2 radians = 68.7549 degrees

3 0

3 years ago

A customer calls and has questions about the bill for their first month's subscription. They want to know why the monthly rate i

HACTEHA [7]

Answer:

The subscription began about 10 days before the 15th of the month.

Step-by-step explanation:

The correct option is:

The subscription began about 10 days before the 15th of the month.

The reason for being charged $60 instead of $45 which is the monthly rate is that they started the subscription prior the the cycle date of the bill period. Due to the change in the cycle date, the customer is getting a prorated charge for the days that had service prior to the date of the bill and current cycle starting

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3 years ago

At 6AM the temperatures was -

Gennadij [26K]

Answer: 12.25

Step-by-step explanation:

-4.05+16.3

Hope this helped! :) let me know if I can help with anything else!

8 0

3 years ago

Together, Dien and Jane can eat 2/3 of a pizza in 4 seconds. How long would it take each of them to eat the whole pizza alone if

Nezavi [6.7K]

Answer:

Dien - 15 seconds, Jane - 10 seconds

Step-by-step explanation:

Together:

2/3 of pizza ⇒ 4 seconds
Full pizza ⇒ 4 ÷ 2/3 = 6 seconds

Dien needs x seconds to eat pizza

Jane needs x - 5 seconds to eat pizza

In one second, Dien can eat 1/x, Jane can eat 1/(x - 5), together 1/6 of a pizza

1/x + 1/(x - 5) = 1/6
x(x - 5) = 6(x + x - 5)
x² - 5x - 12x + 30 = 0
x² - 17x + 30 = 0
(x - 15)(x - 2) = 0
x = 15 (x = 2 is discounted as not realistic)

Dien can eat a pizza in 15 seconds, Jane can eat a pizza in 10 seconds

5 0

3 years ago