Simplifying
5x + 2 = 3x + -4
Reorder the terms:
2 + 5x = 3x + -4
Reorder the terms:
2 + 5x = -4 + 3x
Solving
2 + 5x = -4 + 3x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3x' to each side of the equation.
2 + 5x + -3x = -4 + 3x + -3x
Combine like terms: 5x + -3x = 2x
2 + 2x = -4 + 3x + -3x
Combine like terms: 3x + -3x = 0
2 + 2x = -4 + 0
2 + 2x = -4
Add '-2' to each side of the equation.
2 + -2 + 2x = -4 + -2
Combine like terms: 2 + -2 = 0
0 + 2x = -4 + -2
2x = -4 + -2
Combine like terms: -4 + -2 = -6
2x = -6
Divide each side by '2'.
x = -3
Simplifying
x = -3
Answer:
17.6
Step-by-step explanation:
Formula= sumfx÷sumf
sumfx= 63×0+34×0+27×1+13×2=53
sumfx=0+0+1+2=3
53÷3= 17.6
final answer =17.6
Answer:B half of the circumference
Step-by-step explanation:
Let's write the general form of the sine curve:
, where,
- A is the amplitude. Also, if A is negative, curve reflects about x axis
- B is the compression/stretching factor. It changes the period when it is a value other than 1.
- C is the phase shift. It translates curve left or right. Negative value shifts right and positive value shifts left.
- D is the vertical shift. It translates curve up or down. Negative value shifts down and positive value shifts up.
Let's check the 4 choices.
A.
Since this curve's A is -2, its amplitude is 2 and range is from -2 to 2. BUT since D value is -3, it shifts vertically 3 units down making the range from -1 to -5. Clearly choice A is not true.
B.
This graph is the graph of 
shifted 3 units DOWN since D is negative. This choice isn't true.
C.
Because of the - (minus) sign in front of the function, the function is reflected about x-axis, but amplitude doesn't change. Since A value is 2, amplitude is 2. This is true.
D.
Period depends on the B value. Here, B value is 1, so period is normal as the parent function of a sine curve, which is 
, NOT 
. So this is not correct.
ANSWER: C is true
Answer: (5,5)
Step by step explanation:
We have the two equations
-7x + y = -30 and y = 2x - 5
one of the equations "define" y therefore we can plug the value of y into the other equation and solve for x
-7x + y = -30
plug in y = 2x - 5
-7x + 2x - 5 = -30
combine like terms
-5x - 5 = -30
add 5 to both sides
-5x = -25
divide both sides by -5
-5x/-5 = x and -25/-5 = 5
we're left with x = 5
we now plug in the value of x into one of the equations and solve for y
2x - 5 = y
x = 5
2(5) - 5 = y
multiply 2 and 5
10 - 5 = y
subtract
y = 5
the solution is (5,5)
