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2 years ago

9

Perform the indicated operation. 3m-6/4m+12*m^2+5m+6/m^2-4

1 answer:

Troyanec [42]2 years ago

5 0

Answer:

$\frac{3}{4}$

Step-by-step explanation:

The given expression is:

$\frac{3m-6}{4m+12} \cdot \frac{m^2+5m+6}{m^2-4}$

We factor to get:

$\frac{3(m-2)}{4(m+3)} \cdot \frac{(m+2)(m+3)}{(m-2)(m+2)}$

Cancel out the common factors to get:

$\frac{3(m-2)}{4(m+3)} \cdot \frac{(m+3)}{(m-2)}$

We cancel further to get:

$\frac{3(m-2)}{4(m+3)} \cdot\frac{(m+3)}{(m-2)}=\frac{3}{4}$

The correct chice is B.

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Kim got a prize point for every four raffle tickets she sold. She sold 362 raffle tickets. How many prize points did she get?

Diano4ka-milaya [45]

Answer:90 1/2

Step-by-step explanation:

She sold 362 tickets

She gets prize point for every 4 tickets

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2 years ago

An online video game club charges $10 to join and $8 per month after that. Which equation can you solve to find out how long you

Arlecino [84]

You have to add 10 last.
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3 years ago

Compute the surface area of the portion of the sphere with center the origin and radius 4 that lies inside the cylinder x^2+y^2=

Tom [10]

Answer:

16π

Step-by-step explanation:

Given that:

The sphere of the radius = $x^2 + y^2 +z^2 = 4^2$

$z^2 = 16 -x^2 -y^2$

$z = \sqrt{16-x^2-y^2}$

The partial derivatives of $Z_x = \dfrac{-2x}{2 \sqrt{16-x^2 -y^2}}$

$Z_x = \dfrac{-x}{\sqrt{16-x^2 -y^2}}$

Similarly;

$Z_y = \dfrac{-y}{\sqrt{16-x^2 -y^2}}$

∴

$dS = \sqrt{1 + Z_x^2 +Z_y^2} \ \ . dA$

$=\sqrt{1 + \dfrac{x^2}{16-x^2-y^2} + \dfrac{y^2}{16-x^2-y^2} }\ \ .dA$

$=\sqrt{ \dfrac{16}{16-x^2-y^2} }\ \ .dA$

$=\dfrac{4}{\sqrt{ 16-x^2-y^2} }\ \ .dA$

Now; the region R = x² + y² = 12

Let;

x = rcosθ = x; x varies from 0 to 2π

y = rsinθ = y; y varies from 0 to $\sqrt{12}$

dA = rdrdθ

∴

The surface area $S = \int \limits _R \int \ dS$

$= \int \limits _R\int \ \dfrac{4}{\sqrt{ 16-x^2 -y^2} } \ dA$

$= \int \limits^{2 \pi}_{0} } \int^{\sqrt{12}}_{0} \dfrac{4}{\sqrt{16-r^2}} \ \ rdrd \theta$

$= 2 \pi \int^{\sqrt{12}}_{0} \ \dfrac{4r}{\sqrt{16-r^2}}\ dr$

$= 2 \pi \times 4 \Bigg [ \dfrac{\sqrt{16-r^2}}{\dfrac{1}{2}(-2)} \Bigg]^{\sqrt{12}}_{0}$

$= 8\pi ( - \sqrt{4} + \sqrt{16})$

= 8π ( -2 + 4)

= 8π(2)

= 16π

4 0

2 years ago

Plz answer 9, 10, 11, 12, 13, 15, 16, 17, 18 and 19

Licemer1 [7]

9.
$\frac{2}{3}$

10.
$\frac{3}{16}$

11.
$\frac{14}{5}$

12.
$\frac{3}{8}$

13.
$\frac{3}{5}$

15.
$\frac{1}{9}$

16.
$15$

17.
$\frac{6}{7}$

18.
$\frac{1}{20}$

19.
$\frac{36}{49}$

7 0

2 years ago

Alicia hiked 334 miles for 8 Saturdays in a row. Then she hiked 514 miles for the next 4 Saturdays. What is the total distance A

Sholpan [36]

Answer: 5242 miles.

Step-by-step explanation:

334 times 8 plus 514 times 4 equals 5242.

8 0

3 years ago