Answer:
Step-by-step explanation:
<h3>AP given</h3>
<h3>To find</h3>
<h3>Solution</h3>
Common difference
<u>Difference of first two</u>
- d = (a -b) - (a + b) = -2b
<u>Difference of second two</u>
<u>Difference of last two</u>
<u>Now comparing d:</u>
- -2b = ab - (a - b)
- ab - a = - 3b
- a(1 - b) = 3b
- a = 3b/(1 - b)
and
- a/b - ab = -2b
- a(1/b - b) = -2b
- a = 2b²/(b² - 1)
<u>Eliminating a:</u>
- 2b²/(b² - 1) = 3b/(1 - b)
- 2b/(b+1) = -3
- 2b = -3b - 3
- 5b = - 3
- b = -3/5
<u>Finding a:</u>
- a = 3b/(1 - b) =
- 3*(-3/5) *1/(1 - (-3/5)) =
- -9/5*5/8 =
- -9/8
<u>So the first term is:</u>
- a + b = -3/5 - 9/8 = -24/40 - 45/40 = - 69/40
<u>Common difference:</u>
<u>The 6th term:</u>
- a₆ = a₁ + 5d =
- -69/40 + 5*6/5 =
- -69/40 + 240/40 =
- 171/40 = 4 11/40
Answer:
y = (-5/2)x + 27
Step-by-step explanation:
Use the point slope formula y = mx + b.
Replace m with -5/2, x with -8 and y with 7:
7 = (-5/2)(8) + b. Find the y-intercept, b:
7 = -20 = b, or b = 27
The equation of this line is y = (-5/2)x + 27.
It is C bc it is on the opposite side and on the outside
Answer:
A dress originally costs $120
Step-by-step explanation:
To find the original cost of the dress, we will follow the steps below;
let x represent the original cost of the dress
75% of x = $90
× x = $90
= $90
MULTIPLY both-side of the equation by 100
× 100 = $90×100
At the right-hand side of the equation, 100 will cancel out 100, leaving us with just 75x
75x = $9000
DIVIDE both-side of the equation by 75
75x/75 = $9000/75
At the left-hand side of the equation 75 will cancel-out 75 leaving us with just x
x= $9000/75
x = $120
A dress originally costs $120