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3 years ago

Using prime factorization what is the GCF 3y 2 squared, 24y 3 cubed

Mathematics

1 answer:

WINSTONCH [101]3 years ago

8 0

Answer:

$3y^2$

Step-by-step explanation:

Given:

To find the GCF of $3y^2\ and\ 24y^3$ using prime factorization.

Writing each in prime factors:

3 = 1 $\times$ <u>3</u>

24 = 1 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ <u>3</u>

Now, GCF of 3 and 24 is 3

$y^2=1\times y\times y$

$y^3=1\times y\times y\times y$

GCF of $y^2$ and $y^3$ is $y\times y=y^2$ .

Therefore, the overall GCF of the two terms is $3y^2$

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Toby's Tiny Toys have fixed expenses of $53,900 for the production of their tiny toys. Toby's has a variable expense of $12.50 a

ipn [44]

The total cost of the factory will be the sum of its variable costs and it's fixed costs. The factory has fixed costs of $53,900 and variable costs of $12.50 per unit produced. Let $x$ be the number of toy's produced by this Toby's Tiny Toys, then the total variable costs will be $12.50x$ . From this information we can gather that the cost function for this factory is,

$C(x)=53\,900+12.50x.$

On the other hand, if we let $x$ be the number of toys sold, we can gather that at the selling price of 16.50, the revenue function will be ,

$R(x)=16.50x.$

Toby's Tiny Toys will reach their break even point when the total costs are equal to the total revenue. At this break even point ,we have that

$R(x)=C(x)\\\implies 16.50x=12.50x+53\,900\\\implies 16.50x-12.50x=53\,900\\\implies 4x=53\,900\\\implies x=\frac{53\,900}{4} \\\implies x=134\,750.$

The company has to sell 134 750 units to break even.

6 0

4 years ago

The football coach bought enough sports mix to make 60 L of a sports drink.

Katena32 [7]

The answer to this is 253.2 cups

5 0

3 years ago

The area of a rectangle is 20 cm². The height is 4 cm longer than thrice the width.

Ludmilka [50]

Answer:

width = 2 cm

Step-by-step explanation:

are of rectangle is equal to length times width

x is the width, then length is 3x + 4

so x(3x + 4) = 20

3x^2 + 4x = 20

3x^2 + 4x - 20 = 0

The formula to solve a quadratic equation of the form ax^2 + bx + c = 0 is equal to x = [-b +/-√(b^2 - 4ac)]/2a

so a = 3

b = 4

c = -20

substitute in the formula

x = [-4 +/-√(4^2 - 4(3)(-20))]/2(3)

x = [-4 +/- √(16 + 240)]/6

x = [-4 +/- 16]/6

x1 = (-4 + 16)/6 = 2

x2 = (-4 - 16)/6 = -20/6

since the width can't be a negative number, x2 is not the right answer

so x = 2

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3 years ago

Which situations can be represented by isometric transformations? Check all that apply. A photo is projected from a computer int

Romashka-Z-Leto [24]

Answer:

The correct options are;

A circular game piece is moved three squares forward

The flag on a mailbox is turned up

Step-by-step explanation:

An isometric transformation also known as isometry, is the rigid motion transformation or movement that preserves the shape, angles, and distances between of a pre-image (object) and the final image.

Rotation, reflection, translation (parallel motion), glide deflection (transformation involving translation and reflection) such as snow footprints are forms of isometric transformation.

6 0

4 years ago

Read 2 more answers

At the beginning of 2009 Marilyn invested $5000 in a savings account account pays 4% interest per year at the end of the year at

solong [7]

Answer:

$5200

Step-by-step explanation:

Given :

Amount invested, Principal, P = $5000

Interest rate, r = 4% = 4/100 = 0.04

Amount in account at the end of the year, A

period, t = 1 year

Using the relation :

A = P(1 + rt)

A = $5000(1 + 0.04*1)

A = $5000(1 + 0.04)

A = $5000 * 1.04

Amount in account at year end = $5200

8 0

3 years ago