So, givens: total lesson cost of $260, total lessons taken are 6, and the first lesson costs 1.5 (or 3/2) as much as the additional lessons.
First thing to do is to figure out how many additional lessons are in that, which are 5.
Then you can make a 1 variable equation with the information you have. I’m using x as my variable.
260= 3/2x + 5x
Combine like terms.
260 = 13/2x
Divide both sides by 13/2 (treat it as a fraction, and if your calculator cannot make fractions, then decimal might help for this. 13/2=6.5)
X=40
Short AnswerThere are two numbers
x1 = -0.25 + 0.9682i <<<<
answer 1x2 = - 0.25 - 0.9582i <<<<
answer 2 I take it there are two such numbers.
Let one number = x
Let one number = y
x + y = -0.5
y = - 0.5 - x (1)
xy = 1 (2)
Put equation 1 into equation 2
xy = 1
x(-0.5 - x) = 1
-0.5x - x^2 = 1 Subtract 1 from both sides.
-0.5x - x^2 - 1 = 0 Order these by powers
-x^2 - 0.5x -1 = 0 Multiply though by - 1
x^2 + 0.5x + 1 = 0 Use the quadratic formula to solve this.

a = 1
b = 0.5
c = 1

x = [-0.5 +/- sqrt(0.25 - 4)] / 2
x = [-0.5 +/- sqrt(-3.75)] / 2
x = [-0.25 +/- 0.9682i
x1 = -0.25 + 0.9682 i
x2 = -0.25 - 0.9682 i
These two are conjugates. They will add as x1 + x2 = -0.25 - 0.25 = - 0.50.
The complex parts cancel out. Getting them to multiply to 1 will be a little more difficult. I'll do that under the check.
Check(-0.25 - 0.9682i)(-0.25 + 0.9682i)
Use FOIL
F:-0.25 * -0.25 = 0.0625
O: -0.25*0.9682i
I: +0.25*0.9682i
L: -0.9682i*0.9682i = - 0.9375 i^2 = 0.9375
NoticeThe two middle terms (labled "O" and "I" ) cancel out. They are of opposite signs.
The final result is 0.9375 and 0.0625 add up to 1
We are asked to give the exact value of <span>cos(arcsin(one fourth)). In this case, we shift first the setting to degrees since this involves angles. we determine first arc sin of one fourth equal to 14.48 degrees. then we take the cos of 14.48 degrees equal to 0.9682. Answer is 0.9682.</span>
Answer:
3 3/10
Step-by-step explanation:
Step 1: Convert 2 4/5 to improper
2 4/5 = 14/5
Step 2: Rewrite
14/5 + 1/2
Step 3: Find common denominator
14/5(2/2) + 1/2(5/5)
28/10 + 5/10
Step 4: Add
33/10
Step 5: Simplify
3 3/10
Answer:
Step-by-step explanation:
2x - 3y = 9
-3y = -2x + 9

Parallel lines have same slope.So,
Slope m = 2/3
(4 , -1)
Equation: y - y1 = m(x - x1)
![y-[-1]=\frac{2}{3}(x - 4)\\\\y+1=\frac{2}{3}*x - \frac{2}{3}*4\\\\y+1=\frac{2}{3}x-\frac{8}{3}\\\\y=\frac{2}{3}x-\frac{8}{3}-1\\\\y=\frac{2}{3}x-\frac{8}{3}-\frac{3}{3}\\\\y=\frac{2}{3}x-\frac{11}{3}](https://tex.z-dn.net/?f=y-%5B-1%5D%3D%5Cfrac%7B2%7D%7B3%7D%28x%20-%204%29%5C%5C%5C%5Cy%2B1%3D%5Cfrac%7B2%7D%7B3%7D%2Ax%20-%20%5Cfrac%7B2%7D%7B3%7D%2A4%5C%5C%5C%5Cy%2B1%3D%5Cfrac%7B2%7D%7B3%7Dx-%5Cfrac%7B8%7D%7B3%7D%5C%5C%5C%5Cy%3D%5Cfrac%7B2%7D%7B3%7Dx-%5Cfrac%7B8%7D%7B3%7D-1%5C%5C%5C%5Cy%3D%5Cfrac%7B2%7D%7B3%7Dx-%5Cfrac%7B8%7D%7B3%7D-%5Cfrac%7B3%7D%7B3%7D%5C%5C%5C%5Cy%3D%5Cfrac%7B2%7D%7B3%7Dx-%5Cfrac%7B11%7D%7B3%7D)
b = -11/3