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2 years ago

What is the prime factorization of 140 using exponents

Mathematics

1 answer:

Scorpion4ik [409]2 years ago

8 0

2^2 x 5 x 7 =140

^ is used to represent exponent

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A marine aquarium has a small tank and a large tank, each containing only red and blue fish. In each tank, the ratio of red fish

Anna007 [38]

Answer:

Ratio of blue fish in the small tank to the red fish in large tank is 10 : 6279

Step-by-step explanation:

Let the number of red fish and blue fish in the large tank are x and y respectively.

Similarly ratio of red fish and blue fish in the small tank are x' and y' respectively.

Since in each tank ratio of the red fish to blue fish is 333 : 444

That means x : y = 333 : 444

Or $\frac{x}{y}=\frac{333}{444}$

⇒ $\frac{x}{y}=\frac{3}{4}$

⇒ y = $\frac{4x}{3}$ --------(1)

Similarly x' : y' = 333 : 444

⇒ $\frac{x'}{y'}=\frac{333}{444}$

⇒ $\frac{x'}{y'}=\frac{3}{4}$

⇒ x' = $\frac{3y'}{4}$ ------(2)

Ratio of the fish in large tank to the fish in small tank is 464646 : 555

So (x + y) : (x' + y') = 464646 : 555

$\frac{x+y}{x'+y'}=\frac{464646}{555}$

Now we replace the values of x and y' from equation (1) and equation (2)

$\frac{(x+\frac{4x}{3})}{(\frac{3y'}{4}+y')}=\frac{464646}{555}$

$\frac{\frac{7x}{3}}{\frac{7y'}{4}}=\frac{464646}{555}$

$\frac{4}{3}\times \frac{x}{y'}=\frac{464646}{555}$

$\frac{x}{y'}=\frac{3}{4}\times \frac{464646}{555}$

$\frac{x}{y'}=\frac{232323}{370}$

$\frac{y'}{x}=\frac{370}{232323}$

$\frac{y'}{x}=\frac{10}{6279}$

Therefore, ratio of blue fish in the small tank to the red fish in large tank is 10 : 6279

4 0

2 years ago

Find the error 3(x+2) + 3x = 36 3x + 6 + 3x = 36 6x + 6 = 36 6x = 42 x = 7

rusak2 [61]

Answer: 6x=42

Explanation: After the step 6x+6=36, it’ll equal 6x=30 because when you subtract the 6 on both sides, it’ll equal 30, revealing it’s actually 6x=30, with the conclusion of x=5.

3 0

2 years ago

!!! I NEED HELP ASAP!!! Please can you help me fill in this chart for 45-45-90 and 30-60-90 triangles I know how to do the first

Marina86 [1]

Answer:

u add 45 + 45 +90 that’s 180 and all triangles equal 180

Step-by-step explanation:

8 0

2 years ago

A rectangular garden 200 square feet in area is to be fenced o against rabbits. Find thedimensions that will require the least a

Rudiy27

Answer:

20 ft by 10ft

Step-by-step explanation:

Area of the garden =200 square feet

Let the dimensions of the garden be x and y

Area, xy=200

$x=\frac{200}{y}$

Since one side is already protected by a barn,

Perimeter of the garden=2x+y

$P(y)=\frac{2X200}{y}+y$

$P(y)=\frac{400}{y}+y$

$P(y)=\frac{400+y^2}{y}$

The minimum point of P(y) is the point where its derivative equals zero.

$P^{1}(y)=\frac{y^2-400}{y^2}$

$\frac{y^2-400}{y^2}=0$

$y^2-400=0$

$y^2=400$

y=20feet

Recall:

xy=200

20x=200

x=10feet

The dimensions of the garden that will require minimum fencing is 20 ft by 10ft

8 0

2 years ago

PLease help me(: !!!!!!!!!!!!!!!!!!!!

marin [14]

Answer:

should be 65

Step-by-step explanation:

if not then hmu

4 0

2 years ago