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noname [10]
3 years ago
6

-3 is a solution to 4x + 2 < -6

Mathematics
1 answer:
adelina 88 [10]3 years ago
3 0

Answer:

-3 is a solution

Step-by-step explanation:

4x+2 < -6

subtract 2 from each side

4x < -8

divide by 2

x < -2

-3 is a solution


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A triangle has one side length of 12 inches and another of 8 inches. Describe all possible lengths of the third side. Show and e
katrin [286]

Answer:

The third side must be smaller than 20 inches and greater than 4 inches

4

Step-by-step explanation:

Let a, b and c be the lengths of triangle's sides. Then

a+b>c\\ \\a+c>b\\ \\b+c>a

Use this rule in your case. So, if a=12 and b=8, then

12+8>c\\ \\12+c>8\\ \\8+c>12

Hence, you get

c-4\\ \\c>4

From these inequalities, you can state that

4

So, c must be smaller than 20 inches and greater than 4 inches.

5 0
3 years ago
Read 2 more answers
Please help! Thank you!
KIM [24]
The correct answer is:  [B]:  " (2, 5) ".
__________________________________________
Given:
__________________________________________
  -5x + y = -5 ;
  -4x + 2y = 2 .
___________________________________________
  Consider the first equation:
___________________________
-5x + y = -5 ;  ↔ y + (-5x) = -5 ;

↔ y - 5x = -5 ;  Add "5x" to each side of the equation; to isolate "y" on one side of the equation; and to solve in terms of "y".
_____________________________________________
   y - 5x + 5x = -5 + 5x  

   y = -5 + 5x ;  ↔ y = 5x - 5 ;
____________________________________________
 Now, take our second equation:
______________________________
     -4x + 2y = 2 ; and plug in "(5x - 5)" for "y" ;  and solve for "x" :
_____________________________________________________
         -4x + 2(5x - 5) = 2 ; 
______________________________________________________
Note, 2(5x - 5) = 2(5x) - 2(5)  = 10x - 10 ;
__________________________________________
So:   -4x + 10x - 10 = 2 ;

On the left-hand side of the equation, combine the "like terms" ;

-4x +10x = 6x ;  and rewrite:

6x - 10 = 2  ;

Now, add "10" to each side of the equation:

6x - 10 + 10 = 2 + 10 ;

to get:

           6x = 12 ;  Now, divide EACH side of the equation by "6" ; to isolate "x" on one side of the equation; and to solve for "x" ; 

           6x/6 = 12 / 6 ;
 
                 x = 2 ;
_________________________________
Now, take our first given equation; and plug our solved value for "x" ; which is "2" ; and solve for "y" ;
_____________________________________
-5x + y = -5  ;

-5(2) + y = -5 ;

-10 + y = -5 ;  ↔
                              y - 10 = -5  ;

Add "10" to each side of the equation; to isolate "y" on one side of the equation; and to solve for "y" ;
     
         y - 10 + 10 = -5 + 10 ;

                   y = 5 .
_____________________________
So, we have, x = 2 ; and y = 5 .
____________________________
Now, let us check our work by plugging in "2" for "x" and "5" for "y" in BOTH the original first and second equations:
______________________________
first equation: 

-5x + y = -5 ;

-5(2) + 5 =? -5?

-10 + 5 =? -5 ? YES!
______________________
second equation:

-4x + 2y = 2 ;

-4(2) + 2(5) =? 2 ?

-8 + 10 =? 2 ?  Yes!
_______________________________________________________
So, the answer is: 
___________________________________________________________
          x = 2 , y = 5 ; or, "(2, 5)" ;  which is: "Answer choice: [B] " .
___________________________________________________________



3 0
3 years ago
A set of buttons sells for $2.75 and costs $0.55 to make. Twenty percent of the profit (the difference between the purchase pric
Rufina [12.5K]

Answer: b

Step-by-step explanation: I am 95% sure

6 0
2 years ago
Find the missing terms in each arithmetic sequence <br> 1,__,__,-17<br> 2,__,__,20
Galina-37 [17]

Answer:

-5,-11

8,14

Step-by-step explanation:

Let 's say r the commun difference

1)

1,1+r,1+2r,1+3r=-17

1+3r=-17

3r=-18

r=-6

Sequence is 1,-5,-11,-17

2)

2,2+r,2+2r,2+3r=20

2+3r=20

3r=18

r=6

Sequence is 2,8,14,20

4 0
2 years ago
The sales tax for an item was $24.50 and it cost $350 before tax. Find the sales tax rate.
Karo-lina-s [1.5K]
Find the number that when multiplied with 350 will give you 24.5. This number happens to be .07 or in terms of sales tax, 7%.
3 0
3 years ago
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