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Irina-Kira [14]
3 years ago
8

Simplify the expression using long division. (10x2 – 85x – 10) ÷ (x – 8)

Mathematics
1 answer:
Lelechka [254]3 years ago
8 0

Answer: 5 • (2x2 - 17x - 2)

 ———————————————————

        x - 8      

Step-by-step explanation:

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 

Step  2  :

           10x2 - 85x - 10

Simplify   ———————————————

                x - 8      

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  10x2 - 85x - 10  =   5 • (2x2 - 17x - 2)  

Trying to factor by splitting the middle term

3.2     Factoring  2x2 - 17x - 2  

The first term is,  2x2  its coefficient is  2 .

The middle term is,  -17x  its coefficient is  -17 .

The last term, "the constant", is  -2  

Step-1 : Multiply the coefficient of the first term by the constant   2 • -2 = -4  

Step-2 : Find two factors of  -4  whose sum equals the coefficient of the middle term, which is   -17 .

     -4    +    1    =    -3  

     -2    +    2    =    0  

     -1    +    4    =    3  

Observation : No two such factors can be found !!  

Conclusion : Trinomial can not be factored

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Elimination <br> 2x - 5y = 8 <br> x - 3y = -1
ruslelena [56]
X=29 and y=10

You would isolate one of the variables and then plug the expression into the other equation to find the value of one variable. Then you would plug this value into the other equation to determine the value of the remaining variable.

8 0
3 years ago
You are planning to make an open rectangular box from aa 4141​-in.-by-8181​-in. piece of cardboard by cutting congruent squares
marissa [1.9K]

Answer:

13058.83 cubic inches

Step-by-step explanation:

Given that a rectangular box is having dimensions as 41x81 inches.

Let x be the side of square cut from all the four corners.

The open box made would have height as x and length 41-2x with width 81-2x

Volume =

V(x) = x(41-2x)(81-2x)\\V(x) =x(3321-244x+4x^2)\\V(x) = 3321x-244x^2+4x^3\\V'(x) = 3321-488x+12x^2\\V"(x) = -488+24x\\

Equate first derivative to 0

We get applicable root as x = 8.642

Max volume = 13058.83 cubic inches

3 0
3 years ago
Work out<br> 5.2<br> % of <br> 628.55<br> km<br> Give your answer rounded to 2 DP.
Setler [38]
18.63 is your answer please give brainliest!
7 0
3 years ago
-4x - 6x = -20 =?<br><br> -3(2x - 3) = 33 = ?<br><br> 4x + 3x + 2x = 180 = ?
postnew [5]

Answer:

-4x-6x=-20=

x=2

-3(2x-3)=33=

x=-4

4x+3x+2x=180

x=20

Step-by-step explanation:

-4x-6x=-20                                

-4+(-6)=-10x

-10x=20 (divide both by 10)

x=-2 (divide by -1 to get positive)

x=2

-3(2x-3)=33

-6x+9=33

     -9 .  -9

-6x=24 (divide both by -6)

x=-4 (divide by -1 to make positive)

4x+3x+2x=180

(combine like terms)

9x=180 (divide both sides by 9)

x=20

5 0
3 years ago
Y = 3x2 − 18x − 19.
Crank

Answer:

  A) y = 3(x -3)^2 -46

  B) (3, -46)

  C) look at the y-coordinate of the vertex

Step-by-step explanation:

A) Factor the leading coefficient from the variable terms.

  y = 3(x^2 -6x) -19

Inside parentheses, add the square of half the x-coefficient. Outside, subtract the same value.

  y = 3(x^2 -6x +9) -19 -3(9)

  y = 3(x -3)^2 -46

__

B) Compared to the vertex form, ...

  y = a(x -h)^2 +k

we find a=3, (h, k) = (3, -46).

The vertex is (3, -46).

__

C) The vertex is an extreme value (as is any vertex). The sign of the leading coefficient tells you whether the parabola opens upward (+) or downward (-). This parabola opens upward, so the vertex is a minimum.

If the leading coefficient is positive, the y-coordinate of the vertex is a minimum. If the leading coefficient is negative, the y-coordinate of the vertex is a maximum.

3 0
3 years ago
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