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2 years ago

Factor 3a^2+6ab-24b^2

Mathematics

1 answer:

Monica [59]2 years ago

7 0

(3a²+6ab-24²)= 3a(a+2b)x(4b)

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James is 8 years old. Last year, his father was 4 times as old as he was. In how many years' time will their combined age be 51?

Snowcat [4.5K]

Last year He was 7 years old.

His father is 4 times the age 7 x 4 = 28

Last year his dad was 28, so this year he is 29.

Combined age this year = 29 + 8 = 37

51 - 37 = 14 years

14/ 2 people = 7 years

8 + 7 = 15

29 + 7 = 36

15 + 36 = 51

It will take 7 years.

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2 years ago

Ab(-2 13)(0 3) CD (-5 0)(10 3) parallel lines identify please help

mojhsa [17]

Answer:

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Step-by-step explanation:

they intersect eachother

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2 years ago

Lisa has a certain amount of money. She spent 39 dollars and has 3/4th of the original amount left. How much money did she have

harina [27]

If $\frac { 3 }{ 4 }$ is left, that means $\frac { 1 }{ 4 }$ was spent. So $\frac { 1 }{ 4 }$ of the total amount is equal to 39.. Let's say x to the total amount. $\frac { 1 }{ 4 } \cdot x=39\\ x=4\cdot 39\\ x=156\\$

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2 years ago

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Mica is making a paste for an art project. He mixes 8 cups of water with glue. If he wants to make a double batch how many quart

dusya [7]

He needs one more quart. That is half of a gallon.

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1 year ago

When the effective interest rate is 9% per annum, what is the present value of a series of 50 annual payments that start at $100

ser-zykov [4K]

Answer:

$1,109.62

Step-by-step explanation:

Let's first compute the future value FV.

In order to see the rule of formation, let's see the value (in $) for the first few years

End of year 0

1,000

End of year 1(capital + interest + new deposit)

1,000*(1.09)+10

End of year 2 (capital + interest + new deposit)

(1,000*(1.09)+10)*1.09 +10 =

$\bf 1,000*(1.09)^2+10(1+1.09)$

End of year 3 (capital + interest + new deposit)

$\bf (1,000*(1.09)^2+10(1+1.09))(1.09)+10=\\1,000*(1.09)^3+10(1+1.09+1.09^2)$

and we can see that at the end of year 50, the future value is

$\bf FV=1,000*(1.09)^{50}+10(1+1.09+(1.09)^2+...+(1.09)^{49}$

The sum

$\bf 1+1.09+(1.09)^2+...+(1.09)^{49}$

is the sum of a geometric sequence with common ratio 1.09 and is equal to

$\bf \frac{(1.09)^{50}-1}{1.09-1}=815.08356$

and the future value is then

$\bf FV=1,000*(1.09)^{50}+10*815.08356=82,508.35564$

The present value PV is

$\bf PV=\frac{FV}{(1.09)^{50}}=\frac{82508.35564}{74.35572}=1,109.616829\approx \$1,109.62$

rounded to the nearest hundredth.

5 0

2 years ago