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stepladder [879]
3 years ago
14

Solve, using linear combination. 3x + y = 4. 2x + y = 5. A.. . . (–1, 7). . . B.. . . (–3, 12). . . C.. (0, 4). . . D.. . . (–3,

13).
Mathematics
2 answers:
Nady [450]3 years ago
8 0
3x + y = 4....multiply by -1
2x + y = 5
--------------
-3x - y = -4 (result of multiplying by -1)
2x + y = 5
--------------add
-x = 1
x = -1

2x + y = 5
2(-1) + y = 5
-2 + y = 5
y = 5 + 2
y = 7

solution is (-1,7)
Kisachek [45]3 years ago
5 0
3x + y = 4
2x + y = 5
-3x - y = -4 
2x + y = 5
-x = 1
x = -1
2x + y = 5
2(-1) + y = 5
-2 + y = 5
y = 5 + 2
y = 7

solution is (-1,7) hope this helps 
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Pablo borrowed $50,000 to start a business. Three years later, he repaid the $50,000 along with an interest of $9,375. What was
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Answer:

The annual interest rate is 6.25%

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P = $50,000

I = $9,375

t = 3 years

r = ?

The formula for simple interest is given by

I=Prt\\\\\text{Substituting the known values, we get}\\\\9375=50000(r)\cdot3\\\\r=\frac{9375}{50000\cdot3}\\\\r=0.0625\\\\r=6.25\%

Therefore, the annual interest rate is 6.25%

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0.004 of all math majors at a certain university double major in music. Express this decimal as a percent.
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3 years ago
Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour. She also does yard work for $12 per hour. Li
Fittoniya [83]

Answer:

(a)

r\geq  5

r+y\leq 15

8r+12y\geq 120

y\geq 0

(c)Maximum number of hours Lia can work at the restaurant and still meet her earnings goal = 15 hours

(d)Maximum Earning = $160

Step-by-step explanation:

Let r be the number of hours worked at the restaurant.

Let y be the number of hours of yard work,

Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour.

r\geq  5

Since she does yard work, y\geq 0

Lia’s parents allow her to work a maximum of 15 hours per week overall.

r+y\leq 15

Lia’s goal is to earn at least $120 per week.

The restaurant, r pays $8 per hour

Yard work, y pays $12 per hour.

Therefore:

8r+12y\geq 120

The system of inequalities that represent this problem is therefore:

r\geq  5

r+y\leq 15

8r+12y\geq 120

y\geq 0

(b)The graph of the inequality is attached below

(c)When the graph is plotted, the vertices of the feasible region are:

  • (5,10)
  • (5, 6.7)
  • (15,0)

Where the first term is for the number of hours worked in the restaurant.

The maximum value of r possible is 15 from the three points.

Therefore, she can work at the restaurant for 15 hours and still meet her earning goal.

(d)Maximum Amount Lia can earn in 1 Week

  • At (5,10), Earning=(5X8)+(10X12)=40+120=$160
  • At (5, 6.7), Earning=(5X8)+(6.7X12)=40+80.4=$120.4
  • At (15,0) Earning=(15X8)+(0X12)=$120

Since she has to work at least 5 hours at the restaurant, the maximum amount possible is $160.

8 0
3 years ago
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