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2 years ago

Solve the system of equations by the addition method. 1 - 3x = -5y - 8 6x 3y = -5

1 answer:

3 0

$-3x = -5y -8~~~....(i) \\\\6x -3y = -5 ~~......(ii)\\\\\text{Multiply equation (i) by 2 and do (i) + (ii):}\\\\2 \cdot (-3x) + 6x -3y = 2(-5y-8) + (-5)\\\\\implies -6x +6x -3y = -10y -16 -5 \\\\\implies -3y = -10y -21\\\\\implies -3y +10y =-21\\\\\implies 7y = -21 \\\\\implies y = -\dfrac{21} 7 = -3\\\\\text{Substitute}~y =-3~ \text{in equation (ii):} \\\\6x - 3(-3) = -5\\\\\implies 6x +9 = -5\\\\\implies 6x = -5 -9 = -14\\\\\implies x = -\dfrac{14}6 = - \dfrac{7}3\\$

$\text{Hence}~ (x,y) = \left(-\dfrac 73, -3 \right)$

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A novel is 11/16 inch thick. If there are two shelves, each 99 inches wide, how many novels will be able to fit on the two shelv

34kurt

First let's just combine the shelves to make it easier. 99 + 99 = 198.

We can simply divide 198 by 11/16 to get the answer. First let's convert 11/16 to a decimal.

11 divided by 16 is 0.6875

So 198 divided by 0.6875 is 288.

288 novels can fit on both the shelves.

8 0

3 years ago

Cassie received a 20%-off coupon and a $10-off coupon from a department store. She visits the department store during a tax-free

UNO [17]

Answer:

B. The original purchase total must be at most to $44 before the discounts are applied.

Step-by-step explanation:

Solve the inequality by adding $10, then dividing by 0.8.

0.8x -$10 ≤ $25.20

0.8x ≤ $35.20 . . . . . . . . add $10

x ≤ $35.20/0.8 . . . . . . . divide by 0.8

x ≤ $44 . . . . . . . . . the before-discount purchase must be at most $44

4 0

3 years ago

Talia works 6 hours per day on Fridays and Saturdays each week. She earns $8.20 per hour

Simora [160]

Question 1

Talia works 6 hours on Friday and 6 hours on Saturday. Total Work = 6+6 = 12 hours.

Hourly Rate = 8.20 dollars per hour.

Gross Pay = (Total Work) x (Hourly Rate) = 12 x 8.20 = 98.40 dollars.

Hence, option D is correct i.e. 98.40 dollars.

Question 2

Mikey worked 8 hours on Wednesday, 6 hours on Thursday and 7 hours on Friday.

Total Work = 8+6+7 = 21 hours.

Gross Pay = 187.95 dollars.

Hourly Rate = (Gross pay)/(Total work) = (187.95)/21 = 8.95 dollars per hour.

Hence, option A is correct i.e. 8.95 dollars per hour.

Question 3

Nina's Hourly Rate for first 40 hours = 12.25 dollars per hour.

Overtime rate for after first 40 hours = 1.5 x 12.25 = 18.375 dollars per hour.

Total work = 46 hours.

Gross Pay = (Hourly rate)x(first 40 hours) + (Overtime rate)x(Excess time after first 40 hours)

Gross pay = (12.25 x 40) + (18.375 x 6)

Gross pay = 490 + 110.25

Gross pay = 600.25 dollars.

Hence, option A is correct i.e. 600.25 dollars.

Question 4

Tip amount = 15 dollars.

Meal cost = 75 dollars.

Tip percentage = (Tip amount / Meal cost) x 100

Tip percentage = (15 / 75) x 100 = 20%

Hence, option B is correct i.e. 20%

Question 5

Weekly Salary = 844 dollars.

Commision Rate = 4% = 0.04

Last week Sales = 3250 dollars.

Last week commission on sales = 0.04 x 3250 = 130 dollars.

Gross pay = Weekly Salary + Commission amount.

Gross pay = 844 + 130 = 974 dollars.

Hence, option C is correct i.e. 974.00 dollars.

5 0

2 years ago

Two trains leave a town at the same time heading in opposite directions. One train is traveling 12 mph faster than the

klemol [59]

Answer:

I'm going to paint you a picture in words of what this looks like on paper. We have a train leaving from a point on your paper heading straight west. We have another train leaving from the same point on your paper heading straight east. This is the "opposite directions" that your problem gives you.

Now let's make a table:

distance = rate * time

Train 1

Train 2

We will fill in this table from the info in the problem then refer back to our drawing. It says that one train is traveling 12 mph faster than the other train. We don't know how fast "the other train" is going, so let's call that rate r. If the first train is travelin 12 mph faster, that rate is r + 12. Let's put that into the table

distance = rate * time

Train 1 r

Train 2 (r + 12)

Then it says "after 2 hours", so the time for both trains is 2 hours:

distance = rate * time

Train 1 r * 2

Train 2 (r + 12) * 2

Since distance = rate * time, the distance (or length of the arrow pointing straight west) for Train 1 is 2r. The distance (or length of the arrow pointing straight east) for Train 2 is 2(r + 12) which is 2r + 24. The distance between them (which is also the length of the whole entire arrow) is 232. Thus:

2r + 2r + 24 = 232 and

4r = 208 so

r = 52

This means that Train 1 is traveling 52 mph and Train 2 is traveling 12 miles per hour faster than that at 64 mph

Step-by-step explanation:

3 0

3 years ago

Find the measure of of angle yvx

GarryVolchara [31]

Step-by-step explanation:

angle XUV+angle XVY+angle YVZ+angle ZVW=180°

43+angle XVY+52°+36°=180°

angle XVY=180-131

angle XVY=49°

6 0

2 years ago

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