MATHEMATICS COLLEGE

GCF of 48, 36, and 16. (this is all I need thx) :)

Answers

Answer 1
Answer:

Answer:

4

Step-by-step explanation:

16=2^4

48=2^4·3

36=2²·3²

GCF=2^2

=4

hope this helps :)

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Adam bought 12 bagels. It cost him $30. How much does each bagel cost

Answers

Answer:

$2.50

Step-by-step explanation:

$30 divided by 12 = 2.5

Each bagel is $2.5

(1) -3x-4y+11z from-9y+6z-3x
(2) 3x⁴-4x³+7x-2 from 9-7x⁴+6x³-2x²-11x​

Answers

Answer:

1) 5y + 5z

2) 10x⁴ - 10x³ + 2x² + 18x - 11

Step-by-step explanation:

Given the subtraction of the following polynomial expressions:

(1) -3x - 4y + 11z from -9y + 6z - 3x

In order to make it easier for us to perform the required mathematical operations, we must first rearrange the terms in the subtrahend by alphabetical order.

-3x - 4y + 11z  

-3x - 9y + 6z  ⇒ This is the subtrahend.

Now, we can finally perform the subtraction on both trinomials:

\displaystyle\mathsf{\left \ \quad\:\:\:\:{-3x - 4y + 11z} \atop -\quad{\underline{-3x - 9y + 6z\:\:\underline}} \right.}

In the subtrahend, the coefficients of x and y are both negative. Thus, performing the subtraction operations on these coefficients transforms their sign into positive.  

\displaystyle\mathsf{\left \ \quad\:\:\:\:{-3x - 4y + 11z} \atop -\quad{\underline{-3x - 9y + 6z\:\:\underline}}\right.} \n\qquad\sf {\qquad\:\:\:0x\:+\:5y\:+5z

The difference is: 5y + 5z.

(2) 3x⁴- 4x³ + 7x - 2 from 9 - 7x⁴ + 6x³- 2x² - 11x​

Similar to the how we arranged the given trinomials in Question 1, we must rearrange the given polynomials in descending degree of terms before subtracting like terms.

3x⁴- 4x³ + 7x - 2           ⇒  Already in descending order (degree).

9 - 7x⁴ + 6x³- 2x² - 11x​   ⇒  -7x⁴ + 6x³- 2x² - 11x​ + 9

In subtracting polynomials, we can only subtract like terms, which are terms that have the same variables and exponents.  

\displaystyle\mathsf{\left \ \quad\:\:{3x^4\:-4x^3\:+\:0x^2\:+\:7x\:-\:2} \atop -\quad{\underline{-7x^4\:+6x^3\:-2x^2\:-11x\:+\:9 \:\:\underline}}\right.}  

In the minuend, I added the "0x²" to make it less-confusing for us to perform the subtraction operations.  

The same rules apply in terms of coefficients with negative signs in the subtrahend, such as: -7x⁴, - 2x², and - 11x​ ⇒  their coefficients turn into positive when performing subtraction.  

\displaystyle\mathsf{\left \ \quad\:\:{3x^4\:-4x^3\:+\:0x^2\:+\:7x\:-\:2} \atop -\quad{\underline{-7x^4\:+6x^3\:-2x^2\:-11x\:+\:9 \:\:\underline}}\right.} \n\qquad\sf {\qquad\:\:10x^4-10x^3+2x^2+18x\:-11  

Therefore, the difference is: 10x⁴ - 10x³ + 2x² + 18x - 11.

Solve for X
x+3 1/3=8 1/2

Answers

Answer:x= 31/6

Step-by-step explanation:

Solve for  

x

by simplifying both sides of the equation, then isolating the variable.

The perimeter of a rectangle is 52 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 120 square feet. I need to find the solution set for this.

Answers

Answer:

2x+2y=52

x*y=120

Step-by-step explanation:

Final answer:

The possible lengths of a side of the rectangle are 22, 21, 20, 19, 18, 17, 16 feet.

Explanation:

To find the possible lengths of a side of the rectangle, let's use the formula for the perimeter of a rectangle, which is 2(length + width). We can set up an equation using the given information:

2(length + width) = 52

Dividing both sides by 2, we get:

length + width = 26

Now, to find the possible lengths, we need to consider the area. The formula for the area of a rectangle is length x width. We are given that the area is not to exceed 120 square feet, so we can set up the inequality:

length x width <= 120

Using the relationship length + width = 26, we can substitute length = 26 - width into the inequality:

(26 - width) x width <= 120

Simplifying the inequality, we get:

-width^2 + 26width - 120 <= 0

Now, we can solve this quadratic inequality to find the range of possible widths. Once we have the widths, we can substitute them back into the equation length + width = 26 to find the corresponding lengths.

By solving the quadratic inequality, we find that the possible widths are 4 <= width <= 10. Substituting these widths back into the equation length + width = 26, we get the corresponding lengths:

If width = 4, then length = 22

If width = 5, then length = 21

If width = 6, then length = 20

If width = 7, then length = 19

If width = 8, then length = 18

If width = 9, then length = 17

If width = 10, then length = 16

The possible lengths of a side of the rectangle are {22, 21, 20, 19, 18, 17, 16} feet.

Learn more about rectangle side lengths here:

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The owner of a small machine shop has just lost one of his largest customers. The solution to his problem,he says, is to fire three machinists to balance his workforce with his current level of business. The owner says that it is a simple problem with a simple solution. The three machinists disagree. Why

Answers

Answer:

It may look simple to the owner because he is not the one losing a job. For the three machinists it represents a major event with major consequences

Determine which statements about the relationship are true. Choose two options. g is the dependent variable. u is the dependent variable. g is the independent variable. u is the independent variable. The two variables cannot be labeled as independent or dependent without a table of values.

Answers

In this context, g is the independent variable and u is the dependent variable.

Explanation:

A variable is classified as the independent variable if its value is being controlled or manipulated. Conversely, a variable is classified as the dependent variable if its value is being observed or measured. In this context, based on the given statements, it is clear that g is the independent variable and u is the dependent variable.

Therefore, the correct options are: g is the independent variable and u is the dependent variable.

Answer:

1) g is the dependent variable.(A)

2) u is the independent variable.(D)

Step-by-step explanation:
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