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3 years ago

What is the value of 1/2+1/3

Mathematics

1 answer:

RideAnS [48]3 years ago

4 0

Answer:

5/6

Step-by-step explanation:

1/2=3/6

1/3=2/6

______

5/6

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Solve the following equation for x: 5x + 3y = 15.

Vladimir [108]

Answer:

Step-by-step explanation:

5x + 3y = 15

5x = -3y +15

x = -3/5y +3

7 0

3 years ago

Read 2 more answers

If a substance decays at a rate of 25% every 10 years, how long will it take 512 grams of the substance to decay to 121.5 grams

Juliette [100K]

Answer:

It will take 50 years to decay from 512 grams to 121.5 grams.

Step-by-step explanation:

The decay formula :

$N=N_0e^{-\lambda t}$

where

N= amount of substance after t time

N₀= initial of substance

t= time.

A substance decays at a rate 25% every 10 years.

So, remaining amount of the substance is = (100%-25%)= 75%

$\frac{N}{N_0}=\frac{75\%}{100\%}=\frac{75}{100}=\frac34$ , t= 10

$N=N_0e^{-\lambda t}$

$\Rightarrow \frac {N}{N_0}=e^{-\lambda t}$

$\Rightarrow \frac34 =e^{-\lambda .10}$

Taking ln both sides

$\Rightarrow ln|\frac34| =ln|e^{-\lambda .10}|$

$\Rightarrow ln|\frac34|=-10\lambda$

$\Rightarrow \lambda=\frac{ ln|\frac34|}{-10}$

Now , N₀= 512 grams, N= 121.5 grams, t=?

$N=N_0e^{-\lambda t}$

$\therefore 121.5=512e^{-\frac{ln|\frac34|}{-10}.t}$

$\Rightarrow 121.5=512e^{\frac{ln|\frac34|}{10}.t}$

$\Rightarrow \frac{121.5}{512}=e^{\frac{ln|\frac34|}{10}.t}$

Taking ln both sides

$\Rightarrow ln|\frac{121.5}{512}|=ln|e^{\frac{ln|\frac34|}{10}.t}|$

$\Rightarrow ln|\frac{121.5}{512}|={\frac{ln|\frac34|}{10}.t}$

$\Rightarrow t=\frac{ln|\frac{121.5}{512}|}{\frac{ln|\frac34|}{10}}$

$\Rightarrow t=\frac{10.ln|\frac{121.5}{512}|}{{ln|\frac34|}}$

⇒t=50 years

It will take 50 years to decay from 512 grams to 121.5 grams.

8 0

3 years ago

Please help. This question is on geometric sequences

Lyrx [107]

Answer:

13.89 to 2 dec places.

Step-by-step explanation:

a7 / a5 = r^2 where r is the common ratio.

So 3/5 = r^2

r^2 = 0.6

r = +√0.6

r = 0.7746.

The first term is a5 / r^4

= 5 / (0.7746)^4

= 13.89.

4 0

3 years ago

What are the next three terms in the sequence 4, -1, -6, -11, ...?

Fynjy0 [20]

Answer:

In summary, "the next three terms" are {-16, -21, -26}

Step-by-step explanation:

Note that the common difference separating the terms of 4, -1, -6, -11, ... is -5. Each new term is found by combining the previous term with -5.

Thus, the applicable formula is a(n) = 4-5(n-1).

We should test this. Take the term -6 and determine whether or not this formula correctly predicts the next term: -11:

a(4) = 4-5(4-1) = 4 - 5(3) = 4 - 15 = -11 (yes).

We have the first four terms and need the 5th, 6th and 7th terms.

The fifth term, a(5), is 4-5(5-1) = 4-20 = -16

The sixth term is a(6) = 4-5(6-1) = -21

The seventh term is a(7) = 4 -5(6) = -26

In summary, "the next three terms" are {-16, -21, -26}

8 0

3 years ago

Find the slope of the line passing through the points (7,-8)<br> and<br> (1, -1).

natita [175]

Answer:

5= - 7/6

Hope this helps

6 0

3 years ago

Read 2 more answers