4x - 2y = 5
4x - 4x - 2y = -4x + 5
-2y = -4x + 5
-2 -2
y = 2x - 2¹/₂
y - y₁ = m(x - x₁)
y - 4 = 2(x - 3)
y - 4 = 2(x) - 2(3)
y - 4 = 2x - 6
+ 4 + 4
y = 2x - 2
Answer: a) x = 2 and -4 b) p = 4.12 and -2.4
Step-by-step explanation:
a) Using the completing the square me those to solve x²+2x = 8
firstly, we divide the equation by the coefficient of x² to give
x²+2x=8
Secondly, we need to get the constant of the equation x²+2x by adding the value gotten from dividing coefficient of x by 2 and squaring it i.e(2/2)² to give 1 as the constant
The equation becomes
x²+2x+1-1= 8
Note that 1 was subtracted just to ensure the question isn't altered
(x²+2x+1)-1 = 8
(x+1)(x+1)-1= 8
(x+1)(x+1)= 8+1
(x+1)² = 9
Squaring both sides of the equation
√(x+1)² = +/-√9
x+1 = +/-3
x = +3-1 = 2
x = -3-1 = -4
therefore x = 2 and -4
b) Using the same funny concept to solve the equation
7p² − 12p + 4 = 0
7p²-12p = -4
Dividing by coefficient of p²
p²-12/7p= -4/7
Completing the equation at the right hand side i.e p²-12/7p
We will add the square of half of the coefficient of p to both sides of the given equation (-12/7×1/2)² = (-12/14)²
= 144/196
p²-12/7p+144/196 = -4+144/196
(p-12/14)² = 640/196
Squaring both sides
√(p-12/14)² = +/-√640/196
p-12/14 = +/-3.26
p = +3.26+12/14 = 4.12
and p = -3.26+12/14 = -2.4
Answer:
The chart below shows Mrs. Thompson's grocery bill. What is the average amount Mrs. Thompson spent on groceries?
A. $58
B. $68
C. $78
D. $340
Answer:
x = 5.34
Step-by-step explanation:
The reference angle is 24 degrees. I'm sure you are aware from the square at the other base angle that is a right triangle. Right triangles have ratios by which we can determine missing side and angle measures. The sin of a reference angle has a ratio that is side opposite/hypotenuse. The cos of a reference angle has a ratio that is side adjacent/hypotenyse. The tan of a reference angle has a ratio that is side opposite/side adjacent.
We need to decide which of these fits our needs according to the angle and sides we are given and need to find. We have the reference angle as 24 degrees, we have the side adjacent to this angle as 12. We are looking for x, which is the side opposite the reference angle. Looking to what our definitions are for each ratio, the sides opposite and adjacent are defining the tan of the reference angle. Setting up the ratio then looks like this:
Multiply both sides by 12 to get
12 tan(24) = x
Do this on your calculator in DEGREE mode to get that
x = 5.342744224
Not sure what your teacher has you round to, but I usually have my students give me 2 decimal places