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2 years ago

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Jenny and Hanan are collecting clothes for a clothing drive. Hanan collected 1/2 as many bags of clothes as Jenny did. If Jenny

collected 3/ 4 of a bag of clothes, what portion of a bag of clothes did Hanan collect?

1 answer:

Montano1993 [528]2 years ago

5 0

Answer:

Hanan collect $\frac{3}{8}$ of a bag of clothes

Step-by-step explanation:

Let

x ------> amount of clothing bag that Jenny collected

y ------> amount of clothing bag that Hanan collected

we know that

$y=\frac{1}{2}x$ -----> equation A

$x=\frac{3}{4}$ -----> equation B

Substitute equation B in equation A

$y=\frac{1}{2}(\frac{3}{4})$

$y=\frac{3}{8}$

therefore

Hanan collect $\frac{3}{8}$ of a bag of clothes

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2/6 + 1/3 =<br><br> _ / _ + _ / _ = _ / _ = _ / _

Thepotemich [5.8K]

Answer:

1/3 = 2/6

2/6 + 2/6 = 4/6 = 2/3

2/3 or 4/6 is your answer. You should probably go with 2/3 b/c that is the most simplified!

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Evaluate the integral of the quantity x divided by the quantity x to the fourth plus sixteen, dx . (2 points) one eighth times t

Anika [276]

Answer:

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c$

Step-by-step explanation:

Given

$\int\limits {\frac{x}{x^4 + 16}} \, dx$

Required

Solve

Let

$u = \frac{x^2}{4}$

Differentiate

$du = 2 * \frac{x^{2-1}}{4}\ dx$

$du = 2 * \frac{x}{4}\ dx$

$du = \frac{x}{2}\ dx$

Make dx the subject

$dx = \frac{2}{x}\ du$

The given integral becomes:

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{x}{x^4 + 16}} \, * \frac{2}{x}\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{1}{x^4 + 16}} \, * \frac{2}{1}\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du$

Recall that: $u = \frac{x^2}{4}$

Make $x^2$ the subject

$x^2= 4u$

Square both sides

$x^4= (4u)^2$

$x^4= 16u^2$

Substitute $16u^2$ for $x^4$ in $\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16u^2 + 16}} \,\ du$

Simplify

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16}* \frac{1}{8u^2 + 8}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{2}{16}\int\limits {\frac{1}{u^2 + 1}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du$

In standard integration

$\int\limits {\frac{1}{u^2 + 1}} \,\ du = arctan(u)$

So, the expression becomes:

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(u)$

Recall that: $u = \frac{x^2}{4}$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c$

4 0

2 years ago

The library is 0.96 mile away from Theo’s home. Write this distance as a fraction in simplest from.

Alexeev081 [22]

24/25 in fraction and simplest form. Hope this helps!

3 0

2 years ago

Please I need a quick reply

Rom4ik [11]

Answer:

B

Step-by-step explanation:

It sounds most likely to the right answer

¯\_(ツ)_/¯

4 0

2 years ago

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What is the area of the regular polygon?

BartSMP [9]

Answer:

You could use the polygon area formula OR here's an easier solution

We draw the lines DC and DE

Angle ADC = 120°

Triangle ADC is a 30 60 90 triangle

In such a triangle Line AE = hypotenuse * sq root (3) /2

Line AE = 3 * 0.8660254038 = 2.5980762114

Line DE = 1.5

Area of Triangle ADE = .5 * 1.5 * 2.5980762114 =

1.9485571586 square meters and entire area of Triangle

ABC = 6 * 1.9485571586

which equals 11.6913429513 square meters

Step-by-step explanation:

6 0

2 years ago