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miv72 [106K]
3 years ago
8

When two polynomials are subtracted the difference is -4x^2-7x+9. If one of the polynomials is x^2-4x+2, then determine the two

possible options for the other polynomial.
Mathematics
1 answer:
algol [13]3 years ago
7 0

Answer:

The two options are:

-3x² - 11x + 11 and 5x² + 3x - 7

Step-by-step explanation:

When two polynomials are subtracted the difference is

-4x² - 7x + 9

One of the polynomials is

x² - 4x + 2

To get the second polynomial, we an either add x² - 4x + 2 to -4x² - 7x + 9 or subtract -4x² - 7x + 9 from x² - 4x + 2

First Option:

(x² - 4x + 2) + (-4x² - 7x + 9)

= x² - 4x + 2 - 4x² - 7x + 9

= x² - 4x² - 4x - 7x + 2 + 9

= -3x² - 11x + 11

Secons Option:

(x² - 4x + 2) - (-4x² - 7x + 9)

= x² - 4x + 2 + 4x² + 7x - 9

= x² + 4x² - 4x + 7x + 2 - 9

= 5x² + 3x - 7

Therefore, the two options are:

-3x² - 11x + 11 and 5x² + 3x - 7

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3 0
3 years ago
Aiden gets paid 152.80 for 8 hours of washing cars at this rate how much will aiden make in half an hour
Luden [163]

Answer:

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Step-by-step explanation:

152.80/8=19.10-what he makes per hour

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3 0
3 years ago
Read 2 more answers
Find an equation of the line through (2,7) and parallel to y=3x-6 Y=
Sliva [168]

As we know the formula to calculate the line of equation is y - y1 = m (x - x1)

Where m is the slope. y1 is the first y co ordinate. x1 is the first x co ordinate.

Now we do know that the slope of parallel line is the same as the slope of the original line.

So parallel line slope is 3 so slope for our line is 3. Hence equation is y - 7 = 3 (x - 2) which becomes y = 3x + 1.


6 0
3 years ago
if the product of 4 and a number is decreased by 12, the result is twice the opposite of the number. Find the number. EXPLAIN PL
ELEN [110]
Answer:  The number is:  "2 " .
__________________________________________
Explanation:
__________________________________________
Write the expression; which is an equation, as follows:
__________________________________________
     " 4x <span>− 12 = 2(-x) " ;  in which "x" represents "the number for which we shall                                       solve" .
___________________________________________
Note:  

If the "number" = "x" ;  the "opposite of the number"  =  " -x " ;
</span>___________________________________________
Rewrite as:  " 4x <span>− 12 = -2x " ;
</span>_____________________________________________
     →  Add "12" ; & add "2x" ; to EACH SIDE of the equation:

                      4x − 12 + 12 + 2x = -2x + 12 + 2x ;

           to get:    6x  = 12  ;
____________________________________________________
 Now, divide each side of the equation by "6" ; 
     to isolate "x" on one side of the equation; & to solve for "x" ;
____________________________________________________
                         6x / 6  =  12 / 6 ;

                    to get:    x = 2 .
____________________________________________________
Answer:  The number is:  "2 " .
____________________________________________________
Let us check our answer, by plugging in "2" for "x" in our original equation:
_____________________________________________________
        →   " 4x − 12 = 2(-x) " ;

  Let us plug in "2" for "x" ; to see if the equation holds true; that is; if both side of the equation are equal; when "x = 2" ;

        →   " 4(2) − 12 = ?  2(-2) ?? 

        →    8 − 12 = ?  -4 ? ;
 
        →    -4 = ? -4 ??  Yes!
 __________________________________________________    
6 0
3 years ago
At 7:00 A.M., Alicia pours a cup of tea whose temperature is 200°F. The tea starts to cool to room temperature (72°F). At 7:02 A
alexgriva [62]

Answer: A) Option B

B) 22.3 minutes.

Step-by-step explanation:

The temperature decreases in an exponential decrease, this means that we can write the equation as:

T(x) = A*r^x + B

Where A is the difference between the initial temperature and the room temperature, B is the room temperature, and r is a positive number smaller than 1, that says "how fast" the temperature decreases (and x is the variable, in units of time)

We know that the initial temperature

A = 200° - 72° = 128°

B = 72°

T(x) = 128°r^x + 72°

The only option with those two values is option B.

T(x) =  128(0.989)^x + 72

We should check that when x = 2m, the temperature must be 197°

T(2m) = 128*(0.989)^2 + 72 = 197.2° (that we can round down to 197°)

So this equation is correct

Now we want to find the time such the temperature is 172°F

then:

172° = 128°(0.989)^x + 72°

100° = 128°(0.989)^x

100/128 = (0.989)^x

x = ln(100/128)/ln(0.989) = 22.3 minutes.

Let's check in our equation:

T(22.3) =  128°(0.989)^22.3 + 72 = 172°

8 0
3 years ago
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