Please help me with this homework

Part a)

Given the expression

[tex]54m^3n\:+\:81m^4n^2[/tex]

Apply exponent rule:    [tex]a^{b+c}=a^ba^c[/tex]

[tex]54m^3n\:+\:81m^4n^2=54m^3n+81m^3mnn[/tex]     ∵ [tex]m^4n^2=m^3mnn[/tex]

Rewrite 81 as 3 · 27

Rewrite 54 as 2 · 27

                             [tex]=2\cdot \:27m^3n+3\cdot \:27m^3mnn[/tex]

Factor out the common term:   27m³n

                              [tex]=27m^3n\left(2+3mn\right)[/tex]      

Therefore,

[tex]54m^3n\:+\:81m^4n^2=54m^3n+81m^3mnn=27m^3n\left(2+3mn\right)[/tex]

Part B)

Given the expression

[tex]15x^2y^3z+25x^3y^2z+35x^2y^2z[/tex]

Apply exponent rule:    [tex]a^{b+c}=a^ba^c[/tex]

[tex]15x^2y^3z+25x^3y^2z+35x^2y^2z=15x^2y^2yz+25x^2xy^2z+35x^2y^2z[/tex]

Rewrite as

                                               [tex]=3\cdot \:5y^2x^2zy+5\cdot \:5y^2x^2zx+7\cdot \:5y^2x^2z[/tex]

Factor out common term 5y²x²z

                                                [tex]=5y^2x^2z\left(3y+5x+7\right)[/tex]

Therefore,

[tex]15x^2y^3z+25x^3y^2z+35x^2y^2z=5y^2x^2z\left(3y+5x+7\right)[/tex]

Answer:

i think it's 25.12.

Step-by-step explanation:

because you multiple 2x3.14×4

Answer:

24

Step-by-step explanation:

If there will be 8 for 30

and it's 90 it mean it's just has more 30's

30 + 30+ 30=90

Answer: 20

Step-by-step explanation:

To answer these types of questions, you have to think about what number minus 7 would equal 13. You can find out by simply adding 13+7. Then check your answer.

20-17=13 is accurate

Answer:

A.

Step-by-step explanation:

If you divide the numerator and the denominator by 10, you get 5 over 10.

Answer:

A. 50/100

Step-by-step explanation:

10 goes into 100, 10 times. With that information all you have to is multiply 5 by 10 and you get 50!

I hope this helps, and have a great day! :)

Answer:

Infinite

Step-by-step explanation:

A triangle that has all 60-degree angles is equilateral, which means that all side lengths are the same. However, there are infinite possibilities for the side lengths!

I hope this helped, please give brainliest if this is correct! Thank you!

Answer: The slope is -3

Answer:

(i) (x + 3) is a factor of p(x)= x⁴ + 4x³ + 4x² + 4x + 3 and the remaining factors are (x + 1) and ( x²  +  1).

(ii) (x + 1) is not a factor of p(x)= 2x⁴ - 5x² - 2 and the remainder is -5.

Step-by-step explanation:

(i) Given;

Polynomial, p(x)= x⁴ + 4x³ + 4x² + 4x + 3

Factor, = x + 3

            x = -3

if (x + 3) is a factor of the polynomial, then p(-3) = 0

p(-3) = (-3)⁴ + 4(-3)³ + 4(-3)² + 4(-3) + 3

        = 81 -108 + 36 - 12 + 3

        = 0

(x + 3) is a factor of the given polynomial and the remainder is 0.

The remaining factors can be obtained as follows;

               x³  +  x² + x + 1

            --------------------------------

x + 3 √x⁴ + 4x³ + 4x² + 4x + 3

        - ( x⁴  + 3x³)

          --------------------------------

                    x³ +  4x² + 4x + 3

                   -(x³  + 3x²)

          ----------------------------------

                            x² + 4x + 3

                          -(x²  + 3x)

         ---------------------------------------

                                     x + 3

                                   -(x + 3)

           ---------------------------------------

                                          0

 Further divide x³  +  x² + x + 1  by x + 1

                      x²  +  1

                    ---------------------

        x + 1 √x³  +  x² + x + 1

                 -(x³  +  x²)

                  ------------------------

                                   x +  1  

                                 -( x  + 1)

                             -----------------

                                      0              

Thus, the factors of  x⁴ + 4x³ + 4x² + 4x + 3 = (x + 3)(x + 1)( x²  +  1)

(ii) Given;

Polynomial, p(x)= 2x⁴ - 5x² - 2

Factor, = x + 1

            x = -1

if (x + 1) is a factor of the polynomial, then p(-1) = 0

p(-1) = 2(-1)⁴  - 5(-1)² - 2

       = 2 - 5 - 2

       = -5

Thus, (x + 1) is not a factor of the given polynomial and the remainder is -5.

Answer:

π(12x^3y^5z)^2

Step-by-step explanation:

I doubt your teacher would want you to evaluate the whole thing but if they do leave a comment

Answer:

The total number of students in the school is 750. You can use algebraic equation to calculate the number of the students. Let x be the total number of students in the school. Hope this helps.

Answer:

Step-by-step explanation:

What is the least common denominator of 1/3 and 1 2?

The denominator of the largest piece that covers both fractions is the least common denominator (LCD) of the two fractions. So, the least common denominator of 12 and 13 is 6 .

Answer:

Ok so I think it might be multiplying or dividing

Step-by-step explanation:

My answer for multiplying is 6,732

My answer for dividing is 46.33333

Answer:

Step-by-step explanation:

There are 561 people.

When you divide by 12 you get 46 complete tables of 12

There are 9 people left over.

You can't round down. You must round up. These 9 people  get a table all to themselves.

So you need 47 tables.

Answer:

"The expression will always equal m" is true about the quotient of [tex]\frac{m}{n}[/tex] ÷ [tex]\frac{1}{n}[/tex]

Step-by-step explanation:

Let us solve the question

∵ The expression is [tex]\frac{m}{n}[/tex] ÷ [tex]\frac{1}{n}[/tex]

→ In the division of fractions, we change the division to multiplication

   and reciprocal the fraction after the division sign

∵ The reciprocal of  [tex]\frac{1}{n}[/tex] is [tex]\frac{n}{1}[/tex]

∴  [tex]\frac{m}{n}[/tex] ÷ [tex]\frac{1}{n}[/tex] =  [tex]\frac{m}{n}[/tex] × [tex]\frac{n}{1}[/tex]

→ In the multiplication of fractions, we can simplify the terms in

    the numerators by the terms in the denominators

∵ There is n in the numerator and denominator

∴ Cancel n up and down

∴  [tex]\frac{m}{n}[/tex] × [tex]\frac{n}{1}[/tex] = [tex]\frac{m}{1}[/tex]

∴  [tex]\frac{m}{n}[/tex] × [tex]\frac{n}{1}[/tex] = m

∴  [tex]\frac{m}{n}[/tex] ÷ [tex]\frac{1}{n}[/tex] = m

∴ The quotient is m

∴ The expression will always equal m

Answer:

0

Step-by-step explanation:

The y-intercept of y = -3x is zero.

Answer:

0

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

y = -3x

Step 2: Break Function

Identify Parts

Slope m = -3

y-intercept b = 0

*We assume that if the variable isn't there, it is 0 or being multiplied by 0.

Answer:

Answer is<

Step-by-step explanation:

the square root of 54 is 7.34<7.4

Answer:

6 minutes

Step-by-step explanation:

Given

Leo = 36 sec / rev

Stan = 40 sec/rev

Required

Determine the time (in minutes) they'll meet again

We start by getting the multiples of 36 and 40 uptil we get a common multiple.

Leo: 36 = 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, .....

Stan: 40 = 40, 80, 120, 160, 200, 240, 280, 320, 360....

From above, the common multiple is:

Common Multiple = 360

This means that they'll meet at 360 seconds

Convert to minutes

360 sec = 360/60 mins

360 Seca = 6 mins

Hence,it will take them 6 minutes to meet again at the starting point

Given:

The point is (6,2).

To find:

The image of given point after rotation of 270 degrees.

Solution:

Let the given point be P(6,2).

Rotation of 270 degrees means the figure is rotated 270 degrees counterclockwise about the origin. So, the rule of rotation is

[tex](x,y)\to (y,-x)[/tex]

Using this rule, we get

[tex]P(6,2)\to P'(2,-6)[/tex]

Therefore, the image of given point is (2,-6).

Answer:

32 cubes

Step-by-step explanation:

I would first determine the volume in inches of the rectangular prism.

V = 1/3 x 2/3 x 2/3 = 4/27 cubic inches.

Then I would calculate the volume of the cube with 1/6 inch sides

V = 1/6 x 1/6 x 1/6 = 1/216 cubic inches.

Then I would divide the V of the large prism by the V of the small cube

(4/27) / (1/216) = (4/27) * (216/1) = 32 cubes

Answer:

4

0

−

1

0

0

5

+

2

5

Step-by-step explanation:

Brainliest?

Answer:

2% of 65

2/100*65

13/10

1 3/10

your answer is

22.5

good luck :)

Answer:

3,131,313

Step-by-step explanation:

Let X represent the number of cases with diabetes in 1973.

An increase of 396% in diabetes cases in 1973 would be;

12.4 million = 396/100 × X

12.4 million = 396X/100

Cross multiply

12.4 million × 100 = 396X

X = [(12.4 million × 100) / 396]

X = 3,131,313

Therefore, the number of diabetes cases in 1973 is 3,131,313 cases

Given:

The expression is:

[tex]\sqrt[3]{\dfrac{-512}{729}}[/tex]

To find:

The value of the given expression.

Solution:

We have,

[tex]\sqrt[3]{\dfrac{-512}{729}}[/tex]

It can be rewritten as

[tex]=\sqrt[3]{\dfrac{(-8)\times (-8) \times (-8)}{9\times 9\times 9}}[/tex]

[tex]=\sqrt[3]{\dfrac{(-8)^3}{9^3}}[/tex]        [tex][\because a^ma^n=a^{m+n}][/tex]

[tex]=\sqrt[3]{\left(\dfrac{-8}{9}\right)^3}[/tex]        [tex][\because \dfrac{a^m}{b^m}=\left(\dfrac{a}{b}\right)^m][/tex]

[tex]=\dfrac{-8}{9}[/tex]        [tex][\because \sqrt[n]{x^n}=x][/tex]

The value of given expression is [tex]\dfrac{-8}{9}[/tex].

Therefore, the correct option is b.

Answer:

A and B and C

Step-by-step explanation:

Answer:

i think its B and C

Step-by-step explanation:

Answer:

The expression : 12x + 2.50y

Total cost = $103.5

Step-by-step explanation:

The number of people that went to the movie = x

Number of people that bought drinks = y

Total cost = 12x + 2.50y

Eight people went to a movie and three of them purchased a drink

Total cost = 12 × 8 + 2.50 × 3

Total cost = 96 + 7.5

Total cost = $103.5

Answer:

8 wrong and 15 right if every question is the same points

Step-by-step explanation:

3.26/5 is 0.652

15/23 is 0.652 ish rounded

So I assume 8 wrong

Answer:

12 pairs

Step-by-step explanation:

Represent Brown with B and Black with A

So:

[tex]A + B = 20[/tex] --- Pairs sold

[tex]30B + 35A = 640[/tex] --- Amount

Required

Solve for B (the brown pairs)

Make A the subject in the first equation

[tex]A = 20 - B[/tex]

Substitute 20 - B for A in the second

[tex]30B + 35(20-B) = 640[/tex]

Open bracket

[tex]30B + 700 - 35B = 640[/tex]

Collect Like Terms

[tex]30B - 35B = 640 -700[/tex]

[tex]-5B = -60[/tex]

Divide both sides by -5

[tex]B = \frac{-60}{-5}[/tex]

[tex]B =12[/tex]