Answer:
Option (B)
Step-by-step explanation:
There are two lines on the graph representing the system of equations.
First line passes through two points (-3, 1) and (-2, 3).
Slope of the line =
=
m = 2
Equation of the line passing through (x', y') and slope = m is,
y - y' = m(x - x')
Equation of the line passing through (-3, 1) and slope = 2 will be,
y - 1 = 2(x + 3)
y = 2x + 7 ----------(1)
Second line passes through (0, 1) and (-1, 4) and y-intercept 'b' of the line is 1.
Let the equation of this line is,
y = mx + b
Slope 'm' =
=
= -3
Here 'b' = 1
Therefore, equation of the line will be,
y = -3x + 1 ---------(2)
From equation (1) and (2),
2x + 7 = -3x + 1
5x = -6
x =
x =
From equation (1),
y = 2x + 7
y =
=
=
=
Therefore, exact solution of the system of equations is .
Option (B) will be the answer.
Answer:
Ok. So, I can't see the image. Buttttt, depending on how many cubic feet she wants. If she wanted 5.5 cubic feet of soil, she would buy 10 bags of soil. Each showing 1/2 of a cubic foot. Use your fingers to help saying, " Half, One, One and a half, two, two and a half...." So on and so forth.
Step-by-step explanation:
Answer:
2x+3y+32
Step-by-step explanation:
The correct answer is: [B]: " (2, 5) ".
__________________________________________
Given:
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-5x + y = -5 ;
-4x + 2y = 2 .
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Consider the first equation:
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-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".
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y - 5x + 5x = -5 + 5x
y = -5 + 5x ; ↔ y = 5x - 5 ;
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Now, take our second equation:
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-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] " .
___________________________________________________________
Answer:
$892.50
Step-by-step explanation:
The amount of interest earned is given by ...
I = Prt
Filling in the given values, we have ...
$178.50 = P·0.04·5
Dividing by 0.20 gives ...
$178.50/0.20 = P = $892.50
The principal amount in Kelly's account is $892.50.