I am a 3-digit number. If you switch my first and last digits, I decrease by 297. Also, mymiddle digit is 6 less than my first digit, which is 2 less than 2 times my last digit. What
number am I?

Answers

Answer 1
Answer:

Answer:

  • 865

Step-by-step explanation:

Let the 3-digit number is abc = 100a + 10b + c.

We have:

  • 100a + 10b + c - 100c - 10b - a = 297
  • b = a - 6
  • a = 2c - 2

Simplify the first equation:

  • 99a - 99c = 297
  • a - c = 3
  • a = c + 3

Solve for c by substitution:

  • 2c - 2 = c + 3
  • 2c - c = 3 + 2
  • c = 5

Find a:

  • a = 3 + 5 = 8

Find b:

  • b = 8 - 2 = 6

The number is:

  • 865

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A rectangle with an area of 12 square units, what are the demensions?

Answers

Answer:

area= base(length)*height(width)

possible dimensions

4 *3, 3*4

6*2, 2*6

12*1, 1*12

(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.

Packer Concrete Company pours concrete slabs for single-family dwellings. Wolff Construction Company, which operates outside Packer’s normal sales territory, asks Packer to pour 40 slabs for Wolff’s new development of homes. Packer has the capacity to build 300 slabs and is presently working on 250 of them. Wolff is willing to pay only $2,750 per slab. Packer estimates the cost of a typical job to include unit-level materials, $1,200; unit-level labor, $600; and an allocated portion of facility-level overhead, $1,000.Required:
a. Calculate the contribution to profit from the special order.

Answers

Answer:

The contribution to profit from the special order us $38,000.

Step-by-step explanation:

Consider the provided information.

We need to calculate the contribution on to profit from the special order.

Wolff Construction Company, which operates outside Packer’s normal sales territory, asks Packer to pour 40 slabs for Wolff’s new development of homes. Packer has the capacity to build 300 slabs and is presently working on 250 of them. Wolff is willing to pay only $2,750 per slab.

Sale = 40 × $2,750 = $110,000

To find the profit subtract the materials and labor cost from sale amount.

     Particulars                                              Amount

Sale (40 × $2,750)                                     $110,000

Less: Variable expense

Unit level materials (40× $1,200)              $48,000

Unit level labor(40× $600)                        $24,000

Contribution margin                                   $38,000

The overhead cost will not be considered while determine the contribution to profit from accepting the order of 40 slab.

Hence, the contribution to profit from the special order us $38,000.

Evaluate −b2−2bx2−x when x=−2.

Answers

An expression is defined as a set of numbers, variables, and mathematical operations. The value of −b²−2bx²−x when the value of x=-2 is −b²−8b + 4.

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The value of the expression −b²−2bx²−x will be,

−b² − 2bx² − x

= − b² − 2b(-2)² − (-2)

= − b² − 8b + 4

Hence, the value of −b²−2bx²−x when the value of x=-2 is −b²−8b + 4.

Learn more about Expression:

brainly.com/question/13947055

#SPJ2

The answer...... is 6x+2

A rental company rents big-screen televisions for $22 down plus $4 a day. If the final bill is $46, how many days did you rent the television for? *

Answers

Answer:  6 days

Step-by-step explanation:

take 22 off of the final price 46-22=24

now divid 24 by 4

and u have 6

Freida drove 18 miles in 24 minutes. At this rate, how many miles did she drive in 6 minutes?

Answers

Answer:

4.5

Step-by-step explanation: you divide 24 by what you do  to get 6 which is 4 then you use 4 to divide 18 which is 4.5 or 4 and a half. Have A Great Day!