1. nolan purchased a shirt at store a. he paid $17.50 for the shirt. scott purchased the same shirt at store b for $20.95. how much money did nolan save by purchasing the shirt at store a instead of at store b? show your work and don't forget the ! sandy is making hair bows to sell at a craft show. each hair bow requires 2/3 yard of ribbon. sandy has 30 yards of ribbon and she wants to find the number of bows that she can make. she does the following problem incorrectly. explain her error and redo the problem showing the correct answer. show your wrok step by step and don't forget the 30 ∙2/3 = 30/1 ∙ 2/3 = 60/3 = 20 bows last week, ethan bought 9 1/2 gallons of gas at $2.50 per gallon. this week, he bought 7 3/10 gallons of gas at $2.60 per gallon. what was his total cost? show you work step by step and don't forget the ( calculator is allowed but write down the numbers that you enter into your calculator). need answers asap pl and you :

1. Nolan saved $3.45

2. She can make 45 bows

3.  The total cost for gas was $42.73

Step-by-step explanation:

1.  $20.95 - 17.50 = $3.45

Nolan saved $3.45

2. You need to divide not multiply

30 ÷ 2/3

copy dot flip

30 * 3/2

90/2

45

She can make 45 bows

3.   9 /12 = 9.5 as a decimal  7 3/10 = 7.3 as a decimal

 9.5 * 2.50 = $23.75 for gas last week

 7.3 * 2.60 = $18.98  for gas this week

add   23.75 + 18.98 = $42.73

Option B. -1.5x-3.5y=-31.5

Solution:

Equation of the lane passing through A and B: -7x+3y=-21.5

If we isolate y, and express the equation in the slope-intercept form y=mx+b, the coefficient of the variable "x" is the slope of this line:

Adding 7x both sides of the equation:

-7x+3y+7x=-21.5+7x

3y=7x-21.5

Dividing both sides of the equation by 3:

(3/3)y=(7/3)x-21.5/3

y=(7/3)x-21.5/3

The slope of this line is m1=7/3 (coefficient of variable x)

This line is perpendicular to the central line PQ, then the product of their slopes must be equal to -1.

Slope of AB: m1=7/3

Slope of PQ: m2

m1 m2 = -1

Replacing m1=7/3

(7/3) m2 = -1

Solving for m2: Multiplying both sides of the equation by 3/4:

(3/7)(7/3) m2 = (3/7)(-1)

m2 = - 3/7

According with the graph we know that the line PQ passes through the point P=(7,6)=(xp, yp)→xp=7, yp=6

Then, using the point-slope equation:

y-y1=m(x-x1); y1=yp=6, m=m2=-3/7, x1=xp=7

Replacing the values:

y-6=(-3/7)(x-7)

Multiplying both sides of the equation by 7:

7(y-6)=7(-3/7)(x-7)

7y-42=(-3)(x-7)

7y-42=-3x+21

Subtracting 7y and 21 both sides of the equation:

7y-42-7y-21=-3x+21-7y-21

-63=-3x-7y

-3x-7y=-63

Dividing all the terms by 2:

-(3/2)x-(7/2)y=-63/2

-1.5x-3.5y=-31.5