Can someone help :(!

Mathematics

1 answer:

Andru [333]3 years ago

5 0

Answer:

1/(t+4)²

Step-by-step explanation:

$\dfrac{t+3}{t+4}\div(t^2+7t+12)=\dfrac{t+3}{t+4}\cdot\dfrac{1}{(t+3)(t+4)}=\dfrac{(t+3)}{(t+3)(t+4)^2}\\\\=\boxed{\dfrac{1}{(t+4)^2}}$

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Find the reciprocal of 19/13

mariarad [96]

Answer:

13/19

Step-by-step explanation:

To find the reciprocal, flip the number.

The reciprocal of 19/13 is 13/19

7 0

3 years ago

Read 2 more answers

Raymond has 120 books on his bookshelf that he has not read. He plans on reading 3 books per week until there are only 24 books

Oksi-84 [34.3K]

Answer: The correct option is (A) $120-3w=24;~32.$

Step-by-step explanation: Given that Raymond has 120 books on his bookshelf that he has not read. He plans on reading 3 books per week until there are only 24 books that he still needs to read.

We are to find the equation that can be used to determine the number of weeks it will take Raymond to have only 24 books left.

Also, we are to find the number of weeks.

The number of weeks it will take Raymond to have only 24 books left is represented by 'w'.

We have

number of books read by Raymond is 1 week = 3.

So, number of books read by Raymond is w weeks = 3w.

Since, there are total 120 books on his bookshelf, so the number of books left to read after w weeks will be

$120-3w.$

According to the given information, we get

$120-3w=24\\\\\Rightarrow 3w=120-24\\\\\Rightarrow 3w=96\\\\\Rightarrow w=32.$

thus, the required equation is $120-3w=24$ and number of weeks is 32.

Option (A) is correct.

8 0

3 years ago

Establish the identity.<br> (2 cos 0-6 sin 0)² + (6 cos 0+2 sin 0)2 = 40

kogti [31]

Rewriting the left-hand side as follows,

$(2\cos\theta-6\sin \theta)^2 +(6\cos \theta+2\sin \theta)^2\\\\=4\cos^2 \theta-24\cos \theta \sin \theta+36 \sin^2 \theta+36 \cos^2 \theta+24 \cos \theta \sin \theta+4 \sin^2 \theta\\\\=40\cos^2 \theta+40 \sin^2 \theta\\\\=40(\cos^2 \theta+\sin^2 \theta)\\\\=40$