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madam [21]
3 years ago
6

Describe how you would factor x^2 + 10x - 24. Be specific.

Mathematics
1 answer:
harkovskaia [24]3 years ago
3 0

Answer:

if u have more doubts feel free to ask :)

Step-by-step explanation:

x² + 10x -24  

x² + 12x - 2x - 24          

x(x + 12) -2(x + 12)

(x + 12) (x - 2)

Factors of 24 : ±1 , ±2 , ±3 , ±4 , ±6 , ±8 , ±12,  ±24. Combination of +12 and -2 gives "10" the middle term also " 24"

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The function H(t) = −16t2 + 80t + 112 shows the height H(t), in feet, of a cannon ball after t seconds. A second cannon ball mov
IRINA_888 [86]
The functions are H(t)= -16t^{2}+80t+112 and g(t)=5.2t+20,

are both functions which give the heights of cannonballs thrown from 2 different cannons.

A.
H(3)= -16(3)^{2}+80(3)+112=208
H(4)= -16(4)^{2}+80(4)+112=176
H(5)= -16(5)^{2}+80(5)+112=112
H(6)= -16(6)^{2}+80(6)+112=16

g(3)=5.2(3)+20=31.6
g(4)=5.2(4)+20=40.8
g(5)=5.2(5)+20=46
g(6)=5.2(6)+20=51.2

up to the 5th second, the ball from H is higher than the one from g, 
then from the 6th second the ball from H is lower than the ball from g,

this means that the solution of H(t)=g(t), is between the 5th and 6th seconds.

B. The solution of part A means that during the 3rd, until it falls, the ball from H is falling to the ground, but it is still higher than the ball g which is rising, until a point between the 5th and 6 th seconds, where the balls are at the same height for just one instant, then the ball H continues falling, while g rises up for a few more second.

4 0
3 years ago
The cost of 300 metres optic fibre is $200 what will be the cost if 1 metre of optic fibre.
Elden [556K]

The answer is:  " $0.67 / metre " ;  
                        or, write as:  " [ \frac{2}{3} dollar] per metre."
____________________

<u>Step-by-step explanation</u>:

This is a unit rate problem:
   Find the cost in dollars per [single unit—in this case: "metre(s)", "<em>m</em>" ;
_________________
 \frac{200 dollars}{300m} = \frac{? dollars}{1m} ;  Solve for the "?" <u>amount of dollars</u>.
_________________
Method 1)  "Cross-factor multiply" :
<u>Note</u>:  <u>Given</u><u>:</u> " \frac{a}{b} = \frac{c}{d} ;  [b\neq 0;  d\neq 0] " ;

 then:   ⟷  " ad = bc " ;
_________________

So:  " \frac{200 dollars}{300m} = \frac{? dollars}{1m} " ;

  then:   ⟷  " (200*1) = (300* ?) ;

     → "  (200) = (300  * ?)" ;

     ↔ " (300 * ?) = 200 " ;  

Let "x" refer to the "?" ; the "<u>unknown value</u>" (<u>in dollars</u>);

                for which we are trying to solve.

⇒ " 300x = 200 " ;  Solve for "x" ;
     → Divide each side of the equation by: "300" ;

       to isolate "x" on the "left-hand side" of the equation; & to              solve  for "x" ;
   ⇒  300x/ 300 = 200/300 ;

    To get:  " x = \frac{2}{3} dollars" ;  

= $0.666666666... ;

round to: $0.67 .

{since: " 1 dollar = $1.00 = 100 cents" ;
and since: "\frac{2}{3} " ;

= ["2 ÷ 3" = 0.666666...." ] ;  

⇒  round to:  "0.67 " ;  

and write as:
__________

⇒  $0.67 / metre ;   or, write as:
    " [ \frac{2}{3} dollar] per metre."
_________

Method 2)  <u>Note</u>:
\frac{200 dollars}{300m} = \frac{? dollars}{1m} ;

⇔   = "  \frac{200}{300}  \frac{dollars}{metre} " ;
      {<u>Note</u>:  "[200÷300]" can be simplified by "canceling out" the two (2) zeros in both the numerator and the denominator.}.

   = " \frac{2 dollars}{3m} ";
_________

  =  i.e. " \frac{\frac{2}{3} dollars}{metre} " or;  \frac{0.67 dollars} {m} ;  or:  <u>$0.67 / metre</u> .

         ⇒  {since:  " \frac{2}{3} of 1 dollar" = " \frac{2}{3} dollars of 100 cents" ;
        ⇒  {since:  "1 dollar = 100 cents"} ;

           ⇒ {and: " \frac{2}{3} " = 0.6666666666666... " } ;  

 → round to:  "0.67 " ; and thus: $0.67 / metre.
_________
Note that using either of these 2 (two) methods result in the same answer.
               Hope this is helpful!  Best wishes to you within your academic pursuits!
             _________________

7 0
3 years ago
Solve for x<br> Y= x-v/b
andrey2020 [161]

Answer:

x=y+v/b

Step-by-step explanation:

So first you have y=x-v/b. You want to isolate x, so subtract x from both sides. You'll get -x+y=-v/b. Next, you're going to want to subtract y to further isolate x now that it's on the left side. Now you'll have -x=-y-v/b. But you don't want x to be negative, so you can divide both sides by -1 to make x positive. Now you'll have x=y+v/b.

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Answer:

B

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

7 0
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