Answer:
Step-by-step explanation:
This problem can be readily solved if we are familiar with the point-slope form of straight lines:
y-y0=m(x-x0) ...................................(1)
where
m=slope of line
(x0,y0) is a point through which the line passes.
We know that the line passes through A(3,-6), B(1,2)
All options have a slope of -4, so that should not be a problem. In fact, if we check the slope=(yb-ya)/(xb-xa), we do find that the slope m=-4.
So we can check which line passes through which point:
a. y+6=-4(x-3)
Rearrange to the form of equation (1) above,
y-(-6)=-4(x-3) means that line passes through A(3,-6) => ok
b. y-1=-4(x-2) means line passes through (2,1), which is neither A nor B
****** this equation is not the line passing through A & B *****
c. y=-4x+6 subtract 2 from both sides (to make the y-coordinate 2)
y-2 = -4x+4, rearrange
y-2 = -4(x-1)
which means that it passes through B(1,2), so ok
d. y-2=-4(x-1)
this is the same as the previous equation, so it passes through B(1,2),
this equation is ok.
Answer: the equation y-1=-4(x-2) does NOT pass through both A and B.
Answer:
20n
Step-by-step explanation:
One pretzel has 20 calories. Write an algebraic expression for the total number of calories in n pretzels.
1 pretzel = 20 calories
n pretzel = x
Cross Multiply
x × 1 pretzel = n pretzel × 20 calories
x = n pretzel × 20 calories/1 pretzel
x = 20 n
Therefore, an algebraic expression for the total number of calories in n pretzels = 20n
Answer:
- -32x² +8x -8
- See below about the process
Step-by-step explanation:
The simplified expression is ...
3x(x -12x) +3x² -2(x -2)²
= 3x(-11x) +3x² -2(x² -4x +4) . . . . . simplify contents of parentheses
= -33x² +3x² -2x² +8x -8 . . . . . . . .eliminate parentheses
= (-33 +3 -2)x² +8x -8 . . . . . . . . . . group the coefficients of like terms
= -32x² +8x -8
Answer:
x = - 5, x = - 11
Step-by-step explanation:
Given
y = 
The denominator cannot be zero as this would make y undefined.
Equating the denominator to zero and solving gives the values that x cannot be, that is
(x + 5)(x + 11) = 0
Equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
x + 11 = 0 ⇒ x = - 11
Thus
x = - 11 and x = - 5 are excluded values.
