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2 years ago

Find the prime factors of 60 by dividing by prime numbers.

Mathematics

1 answer:

Mars2501 [29]2 years ago

7 0

Let's start with the smallest prime number 2

60/2 = 30

Divide that result over 2

30/2 = 15

We can't divide this by 2 because 15/2 = 7.5 isn't a whole number

Let's move onto 3

15/3 = 5

The result is a prime number, so we stop.

The values we divided as denominators were: {2, 2, 3}

We add the result 5 to the set to completely list all of the prime factors of 60

The prime factorization would be

which is the same as saying

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Solve this polynomial expression please.

Sedbober [7]

-9x^3 +54x^2 -30x +12

5 0

2 years ago

4. A horizontal ellipse, centered at the origin has a major axis of 10 units and minor axis of 8 units. Write the

s2008m [1.1K]

Answer:

$\frac{x^2}{25} +\frac{y^2}{16} =1$

Step-by-step explanation:

For ellipses, the length of the major axis is represents as:

Major axis = $2a$

where $a$ is called the semi-major axis.

In this case since the major axis is equal to 10 units:

$10=2a$

solving for the semi-major axis $a$ :

$a=10/2\\a=5$

and also the minor axis of an ellipse is represented as:

Minor axis = $2b$

where $b$ is called the semi-minor axis.

Since the minor axis has a length of 8 units:

$8=2b$

solving for b:

$b=8/2\\b=4$

Now we can use the equation for an ellipse centered at the origin (0,0):

$\frac{x^2}{a^2} +\frac{y^2}{b^2} =1$

and substituting the values for $a$ and $b$ :

$\frac{x^2}{5^2} +\frac{y^2}{4^2} =1$

and finall we simplify the expression to get the equation of the ellipse:

$\frac{x^2}{25} +\frac{y^2}{16} =1$

5 0

2 years ago

Help its lateee and i suck at this

s2008m [1.1K]

Answer:

1. Identify the problem: Packaging boxes use too much material and create waste

2. What are the equations for the volume and surface area of a cube and rectangular prism?

Volume of a cube: Vcube = L x L x L = L3

Surface area of a cube: SAcube = 6 x (L x L) = 6L2

Volume of a rectangular prism: VRP = L x W x H = LWH

Surface area of a rectangular prism: SARP = 2 x (L x W) + 2 x (L x H) + 2 x (W x H) = 2(LW + LH + WH)

3. What is the difference in surface area of the packages below? (Note that they have the same volume.)

SAcube = 6L2

= 6 (20 cm)2

= 2,400 cm2

SARP = 2(LW + LH + WH) = 2 (20cm x 10cm + 20cm x 40cm + 10cm x 40cm) = 2,800 cm2

SARP – SAcube = 2,800 cm2

– 2,400cm2

= 400 cm

Step-by-step explanation:

everything in bold is the answer

Can I please get the Brainlist

3 0

2 years ago

Algebra 2 question need help.

MrMuchimi

Answer: Choice C

h(x) = -x^4 + 2x^3 + 3x^2 + 4x + 5

===========================================

Explanation:

When reflecting the function f(x) over the y axis, we replace every x with -x and simplify like so

f(x) = -x^4 - 2x^3 + 3x^2 - 4x + 5

f(-x) = -(-x)^4 - 2(-x)^3 + 3(-x)^2 - 4(-x) + 5

f(-x) = -x^4 + 2x^3 + 3x^2 + 4x + 5

h(x) = -x^4 + 2x^3 + 3x^2 + 4x + 5

Note the sign changes that occur for the terms that have odd exponents (the terms -2x^3 and -4x become +2x^3 and +4x); while the even exponent terms keep the same sign.

The reason why we replace every x with -x is because of the examples mentioned below

-----------

Examples:

The point (1,2) moves to (-1,2) after a y axis reflection

Similarly, (-5,7) moves to (5,7) after a y axis reflection.

As you can see, the y coordinate stays the same but the x coordinate flips in sign from negative to positive or vice versa. This is the direct reason for the replacement of every x with -x.

4 0

2 years ago

Factor: 24x^3−81<br><br> x^3 is x to the third power

MArishka [77]

Hi again!

24x³ - 81

= 3(2x -3)(4x²+6x+9)

I hope that helps!

Please Brainliest answer :)

8 0

3 years ago

Find the prime factors of 60 by dividing by prime numbers.​

Find the prime factors of 60 by dividing by prime numbers.