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3 years ago

12 1/2 as a fraction in the simplest form

Mathematics

1 answer:

djverab [1.8K]3 years ago

8 0

12 = 12/1 = 24/2, 24/2+1/2=25/2 so 25/2, and it's in simplest form because 2 can't go into 25

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Factor completely: 4a^2+b^2−c^2+4ab

Lapatulllka [165]

Answer:

$4a^{2} + b^{2} - c^{2} + 4ab$ $= (2a + b -c) (2a + b+c)$

Step-by-step explanation:

Here, the given expression is $4a^{2} + b^{2} - c^{2} + 4ab$

or, the given expression can be written as

$(4a^{2} + b^{2} + 4ab ) - c^{2}$

Now, by ALGEBRAIC IDENTITY: $(x+y)^{2} = x^{2} + y^{2} + 2xy$

So, similarly here, $(2a +b){2} = 4a^{2} + b^{2} + 4ab$

Hence, on simplification, the expression

$(4a^{2} + b^{2} + 4ab ) - c^{2} = (2a + b)^{2} - c^{2}$

Now, by ALGEBRAIC IDENTITY: $(x +y)(x-y) = x^{2} - y^{2}$

So, similarly $(2a + b)^{2} - c^{2}$ $= (2a + b -c) (2a + b+c)$

Hence, the given expression is factorized as:

$4a^{2} + b^{2} - c^{2} + 4ab$ $= (2a + b -c) (2a + b+c)$

7 0

3 years ago

What’s the answer pls help

IrinaVladis [17]

Answer:

Step-by-step explanation:

y=mx+b

m(slope)=rise/run=1

b(y intercept)=2

y=x+2

6 0

3 years ago

-243=-9(10+x) This is a 2 step equation plz help Ill give u 10<br> pts

Sliva [168]

Im pretty sure

The answer is x=17

6 0

4 years ago

Read 2 more answers

The population of a certain country in 1997 was 288 million people. In addition, the population of the country was growing at a

Crazy boy [7]

Answer:

a) In the year 1998 with 3 days, 2 hours, 44 minutes and 18.1006141 seconds

b) In the year 1998 with 19 days, 18 hours, 5 minutes and 35.10875472 seconds

Step-by-step explanation:

a) To know the time when the population will be 305 million people, we need to isolate the variable t in the equation, $P(t)=288(1.009)^{t-1997}$

So we isolate t with the property of logarithms that allow us go down the exponent, applying in both sides of the equation

For this subsection the value of P is equal to 305 million people

$Ln(305)=Ln[(288)(1.009)]^{t-1997}$

$Ln(305)=(t-1997)*Ln[(288)(1.009)]$

Now, we can isolate the value of t

$\frac{Ln(305)}{Ln[(288)(1.009)]} =t-1997$

$\frac{Ln(305)}{Ln[(288)(1.009)]}-1997 =t$

$t=1998.008531776402$

So to know the exact date we multiply the number after the point, that is 0.008531776402 for the number of days that have 1 year, equal to 365 days

0.008531776402*365= 3.114098387 days

then the number after the point, that is 0.114098387 will be multiply for the number of hours that have 1 day

0.114098387*24= 2.738361282 hours

then the number after the point, that is 0.738361282 will be multiply for the number of minutes that have 1 hour

0.738361282*60= 44.3016769 minutes

Finally, the number after the point, that is 0.3016769 will be multiply for the number of seconds that have 1 minute

0.3016769*60= 18.1006141 seconds

And we obtain that the time, when the population of the country is 305 million people, is in the year 1998 with 3 days, 2 hours, 44 minutes and 25.152 seconds

b) For calculate the time when the population is 395 million people, we do the same process we did in the subsection a)

$Ln(395)=Ln[(288)(1.009)]^{t-1997}$

$Ln(395)=(t-1997)*Ln[(288)(1.009)]$

Now, we can isolate the value of t

$\frac{Ln(395)}{Ln[(288)(1.009)]} =t-1997$

$\frac{Ln(395)}{Ln[(288)(1.009)]}-1997 =t$

$t=1998.05412021527$

0.05412021527*365= 19.75387857 days

0.75387857 *24= 18.09308577 hours

0.09308577*60= 5.585145912 minutes

0.585145912*60= 35.10875472 seconds

And we obtain that the time, when the population of the country is 395 million people, is in the year 1998 with 19 days, 18 hours, 5 minutes and 35.10875472 seconds

8 0

3 years ago

Tyler adds vitamin drops to the water the rabbits on the farm drink. Three drops of vitamins are added to every 4 pints. If the

AlladinOne [14]

The answer to this is 9 drops
How i got this is there are 3 4 pints in a 12 pint water container so 3x3=9
I hope I helped!

6 0

3 years ago