Samantha correctly solved the equation x2 -4x= 4 by completing the square. Which equation is part of her solution?

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

Which is not equivalent to 3/5

Valentin [98]

Answer: d.

15/24 is not an equivalent fraction of 3/5.

8 0

3 years ago

Show me a step by step work and solve the problem

AveGali [126]

What’s the question?

6 0

3 years ago

What is the ratio for sin B?

Y_Kistochka [10]

Answer: 22.6°

Approximately: 23°

Step-by-step explanation:

Sin B = Opp/Hyp

Sin B = 5/13

Sin B = 0.3846

Inverse of Sin B

B = 22.6°

Approximately: 23°

3 0

3 years ago

A bakery was about to sell fresh baguettes, and people formed a line outside to wait. While waiting for the bread to bake, every

Vikentia [17]

Answer:

The number of people standing in the original line is 22 people

Step-by-step explanation:

The information given are;

The number of baguettes that was shared by the people on the line = 85

The number of baguettes each person received = 1 each

Therefore;

The number of people that were finally on the line = 85

Let the number of people in the original line = X

Then each space between two people in X was filled by 1 new person of the first set of people who joined the line

Therefore;

The number of the first set of people who joined the line = The number of spaces between two count of people in X

Which gives;

The number of people who joined the line = X - 1

The new total number of people on the line = X + X - 1 = 2·X - 1

As time passed, a second set of people joined the line such that each space between the people waiting was filled with a new person (from the second set) who joined the line

Therefore, the number of people in the second set = Number of people waiting - 1

Which gives;

The number of people in the second set = 2·X - 1 - 1 = 2·X - 2

The total number of people on the line becomes 2·X - 1 + 2·X - 2 = 4·X - 3

The 85 baguettes is then able to go round (each) among the total number of people on the line

Therefore;

The total number of people on the line = The number of baguettes sheared

4·X - 3 = 85

4·X = 85 + 3 = 88

X = 88/4 = 22

Therefore;

The number of people standing in the original line = 22.

8 0

3 years ago