Answer:
1.Equation ----- 8x=12
2. x=1.5
3. cost of a single song is $1.5
4.$12 gift card will download 8 songs
Step-by-step explanation:
The amount of money the gift card holds is $12
Number of songs bought= 8 songs
Let the cost of a single song to be =$x
The cost of 8 songs will be =$x × 8=$ 8x
So the 8 songs will all cost $12
This means; $ 8x = $12
Equation------ 8x=12
Finding cost of a single song
8x=12------------------divide by 8 both sides
x=12/8------------------simplify
x=3/2 = $ 1.5
Checking for solution
if a single song costs $1.5 , who many songs can a gift card with $12 download?
Here we divide $12 by $1.5 = $12/$1.5= 8 songs------------correct number of songs as mentioned in the question.
to get the slope of any line, all we need is two points off of it, so let's get the slope and thus its equation, hmmmm let's see points (-2,-3) and the origin are the obvious ones =)
![\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{0}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{0-(-3)}{0-(-2)}\implies \cfrac{0+3}{0+2}\implies \cfrac{3}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-3)=\cfrac{3}{2}[x-(-2)]\implies y+3=\cfrac{3}{2}(x+2) \\\\\\ y+3=\cfrac{3}{2}x+3\implies y=\cfrac{3}{2}x](https://tex.z-dn.net/?f=%5Cbf%20%28%5Cstackrel%7Bx_1%7D%7B-2%7D~%2C~%5Cstackrel%7By_1%7D%7B-3%7D%29%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B0%7D~%2C~%5Cstackrel%7By_2%7D%7B0%7D%29%20%5C%5C%5C%5C%5C%5C%20slope%20%3D%20m%5Cimplies%20%5Ccfrac%7B%5Cstackrel%7Brise%7D%7B%20y_2-%20y_1%7D%7D%7B%5Cstackrel%7Brun%7D%7B%20x_2-%20x_1%7D%7D%5Cimplies%20%5Ccfrac%7B0-%28-3%29%7D%7B0-%28-2%29%7D%5Cimplies%20%5Ccfrac%7B0%2B3%7D%7B0%2B2%7D%5Cimplies%20%5Ccfrac%7B3%7D%7B2%7D%20%5C%5C%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7B%7Cc%7Cll%7D%20%5Ccline%7B1-1%7D%20%5Ctextit%7Bpoint-slope%20form%7D%5C%5C%20%5Ccline%7B1-1%7D%20%5C%5C%20y-y_1%3Dm%28x-x_1%29%20%5C%5C%5C%5C%20%5Ccline%7B1-1%7D%20%5Cend%7Barray%7D%5Cimplies%20y-%28-3%29%3D%5Ccfrac%7B3%7D%7B2%7D%5Bx-%28-2%29%5D%5Cimplies%20y%2B3%3D%5Ccfrac%7B3%7D%7B2%7D%28x%2B2%29%20%5C%5C%5C%5C%5C%5C%20y%2B3%3D%5Ccfrac%7B3%7D%7B2%7Dx%2B3%5Cimplies%20y%3D%5Ccfrac%7B3%7D%7B2%7Dx)
If z = a-bi, the complex conjugate of z is a + bi.
So the imaginary part is "b"
"b" is opposite of -b, so correct answer is c)
Answer:
x = 0 .
-20/19 (see below).
Step-by-step explanation:
√(x + 1) + √5x = √(7x + 1)
Squaring both sides:
x + 1 + 5x + 2√(x + 1)√5x = 7x + 1
2√(x + 1)√5x = 7x +1 - 1 - x - 5x = x
Squaring both sides:
4(x + 1)(5x) = x^2
20x^2 + 20x - x^2 = 0
19x^2 + 20x) = 0
x(19x + 20) = 0
x = 0, -20/19.
If we substitute x = 0 into the original equation we get
√(0 + 1) + √5*0 = √(7*0 + 1)
1 = 1 so this is a true solution.
-20/19 :- √(-20/19 + 1) is not real so unless we allow complex square root this is extraneous.
