All categories

3 years ago

One ordered pair (a,b) satisfies the two equations ab^4 = 384 and a^2 b^5 = 4608. What is the value of a in this ordered pair?

Mathematics

1 answer:

Alekssandra [29.7K]3 years ago

5 0

Answer: a = 3∛2

<u>Step-by-step explanation:</u>

ab⁴ = 384 --> a = 384/b⁴

Substitute a = 384/b⁴ into the second equation to solve for "b".

a²b⁵ = 4608

$\bigg(\dfrac{384}{b^4}\bigg)^2\cdot b^5=4608\\\\\\\dfrac{147,456b^5}{b^8}=4608\\\\\\\dfrac{147,456}{b^3}=4608\\\\\\\dfrac{147,456}{4608}=b^3\\\\\\32=b^3\\\\\\\sqrt[3]{32} =b\\\\\\2\sqrt[3]{4} =b$

Substitute b = 2∛4 into the first equation to solve for "a".

ab⁴ = 384

a(2∛4)⁴ = 384

a = 384/(2∛4)⁴

a = 24/4∛4

= 6/∛4

= 6(∛2)/2

= 3∛2

You might be interested in

which polynomial correctly combines the like terms and expresses the given polynomial in standard form? 8mn5-2m6+5m2n4-m3n3+n6-4

Lelechka [254]

Answer:

The answer would be 7mn^5 - 2m^6 + 14m^2n^4 - 5m^3n^3 + n^6

Step-by-step explanation:

In order to find that answer, start by grouping all of the terms by their variable values. Ones that are the same should be combined.

8mn^5 - mn^5 = 7mn^5

2m^6 - 4m^6 = -2m^6

5m^2n^4 + 9m^2n^4 = 14m^2n^4

-m^3n^3 - 4m^3n^3 = -5m^3n^3

n^6 = n^6

Now we simply combine them all to get

7mn^5 - 2m^6 + 14m^2n^4 - 5m^3n^3 + n^6

6 0

3 years ago

What is 32 rounded to the nearest hundred

Anni [7]

It would be 100 since it it the closest 100

7 0

3 years ago

2(3 + 4x) = 8x + 6<br> How Many solutions?

Mrrafil [7]

Answer:

Infinite number of solutions

Step-by-step explanation:

$2(3 + 4x) = 8x + 6\\6 + 8x = 8x+6\\8x-8x=6-6\\0=0$

For any value of x, both equations are equal to each other because both sides are identical

4 0

2 years ago

Read 2 more answers

For problem number four on the paper I’m confused I don’t know how to do the table with decimals can someone please explain how

Lostsunrise [7]

Answer:

$7.00

Step-by-step explanation:

$2.10 \div 6 = 0.35$

4a) 1 oz of coffee is equal to 0.35c, which is consistent with everything in the table.

4b)Knowing this, if we have 20 oz of coffee, and we multiply it by 0.35, we will get how much it costs for this cup.

20*0.35 = 7.00

Hope this makes sense and feel free to ask questions!

6 0

2 years ago

Sarah would like to make a 6 lb nut mixture that is 60% peanuts and 40% almonds. She has several pounds of a mixture that is 80%

weeeeeb [17]

Answer: a. The system that models this situation is,

x + y = 6 , 8 x + 5 y = 36.

b. Solution is x = 2lb and y = 4lb

where x is the quantity of 80% of peanuts mixture mix with y quantity of 50% of peanuts mixture for making 60% of peanuts mixture.

Step-by-step explanation:

Let x quantity of 80% of peanuts mixture mix with y quantity of 50% of peanuts mixture for making 60% of peanuts mixture.

Then According to the question,

x + y = 6 --------- (1)

And, 80 % of x + 50 % of y = 60 % of 6

⇒ 0.8 x + 0.5 y = 3.6

⇒ 8 x + 5 y = 36 --------- (2)

Where equation 1) and equation 2) are the required equation which models the given situation.

Now, 8 × equation 1)

We get, 8 x + 8 y = 48 ----------(3)

equation (3) - equation (2)

we get, 3 y = 12

⇒ y = 4

By putting the value of y in equation (2)

we get, x = 2

Thus, he mixed 2 lb of mixture 80/20 and 4 lb of mixture 50/50 for making 6 lb of 50/50 mixture.

4 0

2 years ago