the difference of twenty-one and eight times a number n is thiry-five

    The question gives us two points,  (-1, -1) and (98, 87), from which we can find the slope and later the equation of the line.

Finding the Slope  

The slope of the line (m)   = (y₂ - y₁) ÷ (x₂ - x₁)  

                                            = (87 - (-1)) ÷ (98 - (-1))        

                                            =  (88) ÷ (99)    

                                            =   ⁸/₉  

Checking my answer visually:  

Finding the Equation

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line. Once we have that equation, we can graph it to see if it passes through the two points. If it does, then we calculated the slope correctly.

                               ⇒  y - (-1) = ⁸/₉ (x - (-1)              [using the point (-1, -1)]

                                      y + 1  = ⁸/₉ (x + 1)  

To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.  

Answer:

x=10

x=-4

Step-by-step explanation:

Quadratic Equation:  (x – 3)^2 = 4

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    (x-3)^2-(49)=0

Step 1:

valuate :  (x-3)²   =    x²-6x+9

Factoring x²-6x-40  

The first term is, x²its coefficient is  1 .

The middle term is,  -6x  its coefficient is  -6 .

The last term, "the constant", is  -40  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -40 = -40  

Step-2 : Find two factors of  -40  whose sum equals the coefficient of the middle term, which is   -6 .

     -40    +    1    =    -39  

     -20    +    2    =    -18  

     -10    +    4    =    -6    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  4

x²- 10x + 4x - 40

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-10)

             Add up the last 2 terms, pulling out common factors :

                   4 • (x-10)

Step-5 : Add up the four terms of step 4 :

                   (x+4)  •  (x-10)

            Which is the desired factorization

Equation at the end of step

1

:

 (x + 4) • (x - 10)  = 0  

STEP

2 :

Theory - Roots of a product

A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

Solve  :    x+4 = 0  

Subtract  4  from both sides of the equation :  

                     x = -4

Solving a Single Variable Equation:

Solve  :    x-10 = 0  

Add  10  to both sides of the equation :  

                     x = 10

Supplement : Solving Quadratic Equation Directly

Solving x²-6x-40  = 0   directly  

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

Find the Vertex of   y =x²-6x-40

For any parabola,Ax²+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   3.0000  

Plugging into the parabola formula   3.0000  for  x  we can calculate the  y -coordinate :  

 y = 1.0 * 3.00 * 3.00 - 6.0 * 3.00 - 40.0

or   y = -49.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x²-6x-40

Axis of Symmetry (dashed)  {x}={ 3.00}  

Vertex at  {x,y} = { 3.00,-49.00}  

x -Intercepts (Roots) :

Root 1 at  {x,y} = {-4.00, 0.00}  

Root 2 at  {x,y} = {10.00, 0.00}

Solve Quadratic Equation by Completing The Square

Solving   x²-6x-40 = 0 by Completing The Square .

Add  40  to both side of the equation :

  x2-6x = 40

Now the clever bit: Take the coefficient of  x , which is  6 , divide by two, giving  3 , and finally square it giving  9  

Add  9  to both sides of the equation :

 On the right hand side we have :

  40  +  9    or,  (40/1)+(9/1)  

 The common denominator of the two fractions is  1   Adding  (40/1)+(9/1)  gives  49/1  

 So adding to both sides we finally get :

  x2-6x+9 = 49

Adding  9  has completed the left hand side into a perfect square :

  x2-6x+9  =

  (x-3) • (x-3)  =

 (x-3)2

Things which are equal to the same thing are also equal to one another. Since

  x2-6x+9 = 49 and

  x2-6x+9 = (x-3)2

then, according to the law of transitivity,

  (x-3)2 = 49

We'll refer to this Equation as  Eq. #3.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-3)2   is

  (x-3)2/2 =

 (x-3)1 =

  x-3

Now, applying the Square Root Principle to  Eq. #3.2.1  we get:

  x-3 = √ 49

Add  3  to both sides to obtain:

  x = 3 + √ 49

Since a square root has two values, one positive and the other negative

  x2 - 6x - 40 = 0

  has two solutions:

 x = 3 + √ 49

  or

 x = 3 - √ 49

Solve Quadratic Equation using the Quadratic Formula

3.3     Solving    x2-6x-40 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     1

                     B   =    -6

                     C   =  -40

Accordingly,  B2  -  4AC   =

                    36 - (-160) =

                    196

Applying the quadratic formula :

              6 ± √ 196

  x  =    —————

                   2

Can  √ 196 be simplified ?

Yes!   The prime factorization of  196   is

  2•2•7•7  

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 196   =  √ 2•2•7•7   =2•7•√ 1   =

               ±  14 • √ 1   =

               ±  14

So now we are looking at:

          x  =  ( 6 ± 14) / 2

Two real solutions:

x =(6+√196)/2=3+7= 10.000

or:

x =(6-√196)/2=3-7= -4.000

Two solutions were found :

x = 10

x= -4

Answer:

the answer is C

Step-by-step explanation:

yeah-ya.... right?

Step-by-step explanation:

After you find y when x is the following you apply points on graph to get a straight line.

Answer:

2 would be a':-8,-8 b': -8,4 c': 8,10 d': 8,-6

Answer:

256

Step-by-step explanation:

Answer:

20cm

Step-by-step explanation:

1. First find the area of the triangle

a = 1/2 × base × h

a = 1/2 × 10 × 11

a = 55cm²

2. Then times the area of the triangle by 8 to find the area of the rectangle

55 × 8 = 440cm²

3. Find the width of the rectangle:

The area of a rectangle is = l × w

22 × width = 440cm²

width = 440 ÷ 22

width = 20cm

Answer: Width = 20

Step-by-step explanation:

Give the area of triangle = x

So the area of rectangle = 8x

the area of triangle = (11 × 10) ÷ 2 = 55

So the area of rectangle = 8(55) = 440

The area of rectangle = W × L

So 440 = W × 22

W = 20

please give me a brainliest answer

Answer:

False

Step-by-step explanation:

a>b

Let c> 0 then ac>bc because we are multiplying by a positive number

if c<0  then ac < bc because we are multiplying by a negative number we have to flip the inequality symbol

Since we do not know the value of c, we have to go with false

Answer:

(2^2)3 = 2^6

(2^3)2 = 2^6

Step-by-step explanation:

There are various exponent rules. The problems that you were assigned must follow the power of a power rule:

(x^a)^b = x^a*b

Exponents must be multiplied according to this rule. Hope this helps.

Answer:

B

Step-by-step explanation:

it's triangle, all corners sums 180

11X+6=40+7X+2

X=9

Answer:

x = 12

Step-by-step explanation:

Answer:

B. 12w + 62 = 242 is the answer  Happy to Help :)

Step-by-step explanation:

Answer:

Travels 4.25 miles in thirty minutes

Step-by-step explanation:

In order to find the answer to this question you need to first find how many miles the boat travels in a hour and then divide it once more to find how many miles it traveled in half a hour.

[tex]17\div2[/tex]

[tex]`7\div2=8.5[/tex]

[tex]2=17[/tex]

[tex]1=8.5[/tex]

[tex]8.5\div2=4.25[/tex]

[tex]=4.25[/tex]

Hope this helps.

Answer:

x = 2

Step-by-step explanation:

12x - 4 = 4(2x + 1)

Distribution first

12x - 4 = 4(2x) + 4(1)

12x - 4 = 8x + 4

Isolate x to one side

12x - 4 - 8x = 8x - 8x + 4

12x - 8x - 4 = 4

4x - 4 = 4

4x - 4 + 4 = 4 + 4

4x = 8

4x/4 = 8/4

x = 2

We want to see if the given statement is true. (which is, by definition).

We define two inverse matrixes A and B as two matrixes that when multiplied are equal to a matrix with only ones in the diagonal.

This matrix with only ones in the diagonal (and zeros every else) is called the identity matrix.

Then the statement:

"If matrix A and B are inverses of each other, then A times B=I,where I is the identity matrix"

Is true by definition of inverse matrixes.

If you want to learn more, you can read:

https://brainly.com/question/4017205

Answer:

what is the question?

210 people were asked.

Answer:

390

Step-by-step explanation:

5 or more, means round up.

So 385 ( 5 or above ) - round to the nearest tenths place...

= 390

Answer:

390

Step-by-step explanation:

The number in the tenth place is 80 so you look on the right, the number is 5. If the number is 5 or above, that means you go up. SO it's 390

Answer:

9.  A: 3:00 A.M.

10. C: 6.535 kg

11. D: Php 1,600.00

12. D: 217,500

13. A: P450.00

14. A: 7  

15. D: 5.48 x 10^4

4 - x = 10

-x = 10 - 4

-x = 6

x = -6

Answer:

x = -6

Step-by-step explanation:

[tex]4-x = 10\\\\4 = 10 + x\\\\4-10 = x\\\\x = -6[/tex]

Feel free to mark this as brainliest! :D

The time it will a take them for both ricardo and his father to finish the painting if they work together is;

t = 2.4 hours

Time for ricardo to paint the set of kitchen cabinets = 6 hours

Time for Ricardo's father to finish painting = 4 hours

This means that ricardo in 1 hour paints 1/6 of the cabinets

His father in 1 hour paints 1/4 of the cabinets

If they work together, in one hour, they would have painted;

1/6 + 1/4 = 5/12 of the cabinet

then 12/12 will be done in; ((12/12) × 1)/(5/12)

⇒ 1 × 12/5

⇒ 2.4 hours

Read more at; https://brainly.com/question/8317268

The correct answer is:  " 2 hours and 24 minutes ";

or; write as:  " 2.4 hours " .

____

Step-by-step explanation:

[tex]\frac{x}{4} + \frac{x}{6} = 1[/tex]  ;  → { " 1 (one) whole job." }.

       We want to solve for "x" ; the total time, in "hours", that will take them if they work together.
        What is the LCD (least common denominator of "4" and "6" ?
→  Note that "4 * 6 = 24" ;  so, "24" would work, but let's see if we can find the LCD —a number less then "24" ;

4:  2, 4,  12, 16, 20, 24,

6: 1, 2, 3, 6, 12

⇒  We see that "12" is the LCD.
_____
So, " [tex]\frac{x}{4} = \frac{?}{12}[/tex] " ;  to solve for "?" ;

 →  4 * (what value?) = 12 ?
   →   12 ÷ 4 = (that value) ; ⇒   =  " 3 " .
 _____
So:  [tex]\frac{x}{4} = \frac{(x*3)}{(4*3)} = \frac{3x}{12}[/tex] ;
_____
 Now:  " [tex]\frac{x}{6} = \frac{?}{12}[/tex] " ; to solve for "?" ;

→  6 * (what value?) = 12 ?
   →   12 ÷ 6 = (that value) ;  ⇒   =  " 2 " .

 _____

So:  " [tex]\frac{x}{6} = \frac{(x*2)}{(6*2)} = \frac{2x}{12}[/tex] ;

Now:  →  [tex]\frac{x}{4} + \frac{x}{6} = 1[/tex] ;

Substitute our converted values:
         →   [tex]\frac{3x}{12} + \frac{2x}{12}=1[/tex] ;

Then simplify the "left-hand side" of the equation:
_____
        →   [tex]\frac{3x}{12} + \frac{2x}{12} = \frac{(3x+2x)}{12}[/tex]  = [tex]\frac{5x}{12}[/tex]  ;

Now, rewrite the simplified equation; and bring down the "1" :
_____

        →   [tex]\frac{5x}{12} = 1[/tex]   ;

Now, solve for "x" ; as follows:
_____
 ⇒   5x  =  ( 1 * 12 )  ;

  →   5x  =  12  ;

Now, divide Each Side of the equation by "5" ;

to isolate "x" on one side of the equation; & to solve for "x" (in hours):
 _____
  →   5x / 5  =  12 / 5  ;

_____
to get:   x =  (12/5) hours.
_____
Now:  We have (12/5) of 1 hour ;     24/10

Note the exact conversion:  " 60 min. = 1 hr." :

So, 12/5 of 60 minutes;

=  " [tex]\frac{12}{5}[/tex] * [tex]}\frac{60}{1}[/tex] "  (minutes) ;
____
The "5" cancels to a "1" ;  and the "60" cancels to a "12" :

  {since:  "60 ÷ 5 = 12" ;  & since:  "5 ÷ 5 = 1 " .}.

→ And we can rewrite as:
    " [tex]\frac{12}{1} * \frac{12}{1}[/tex] "  (minutes) =  "12 * 12" minutes =  144 minutes.
⇒  " 144 minutes" equals:  How many hours?  " 144 ÷ 60  =  2.4  hours " ;

or; more specifically:

⇒ We have "2 hours and _(some) minutes".

→ that is;  " 2 hours plus 0.4 hour(s) " .

⇒  [tex]\frac{(0.4) hr}{1}*\frac{(60)min}{1 hr} = [(0.4)*(60)] minutes[/tex] ;

                              =  24 minutes.

____

Alternate method:
____
(12/5 hours) = (12 ÷ 5) hours =   " 2.4 hours " ;  (and continue if desired).
____

So:  The correct answer is:  " 2 hours and 24 minutes ";

                                       or; write as:  " 2.4 hours " .

____
Hope this is helpful to you!  Best of luck!

____

Answer:

The first 3 student spend $8 per person

Step-by-step explanation:

1. $24=3x (divide both sides by 3)

2. $8=x

Hopefully I understood the question correctly

Step-by-step explanation:

a:

-2

b:

(-12m^5 * n^3) / (6m^5 * n^3)

c:

I don't what the two methods is,so I have no idea

Answer:

66.5

Step-by-step explanation:

Answer:

6x^6..........................

Step-by-step explanation:

start with g and next times by 7 means multiply by 7 and add 3 to the result

7g+3

Answer:p=-1 and q=1

Step-by-step explanation:

Answer:

p=3, q=5

Step-by-step explanation:

f(x) = x³-x²+px+q

factor: x+1 = 0   x = -1

(-1)³ - (-1)² + p*(-1) + q = 0

-2 - p + q = 0

p = q-2

(x-1) is factor of f(x) - 8, root x = 1 : f(x) = x³-x²+(q-2)x+q-8

(1)³ - (1)² + (q-2)(1) + q - 8 = 0

q - 2 + q - 8 = 0

2q = 10     q = 5

p = q-2 = 3

check: x³-x²+3x+5 = (x+1)(x²-2x+5)

x³-x²+3x+5 = (x²+3)(x-1) + 8

Answer: 3 to the third power

Step-by-step explanation: 3x3x3=27

                                             5x5=25          27 is bigger that 25

hope this helped!

Answer:

Step-by-step explanation:

Let H be the number of harcover, and S the number of softcover books.

We know that:

H+S=36

and $8*(H) + $2*(S) = $144

Rearrange the first: H = 36 - S

Use this definition of H in the second equestion:

$8*(H) + $2*(S) = $144

$8*(36-S) + $2*(S) = $144

$288 - 8S + 2S = $144

-6S = -144

S = 24

This means H = 36 - S is:

H = 36 - 24

H = 12

"You" purchased 24 softcover and 12 hardcover books.

Check the results: 24*2 + 12*8 = 48 + 96 = $144 It

works.