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zysi [14]
3 years ago
14

Harper is working two summer jobs, making $19 per hour lifeguarding and making $8 per hour walking dogs. In a given week, she ca

n work at most 7 total hours and must earn a minimum of $80. If x x represents the number of hours lifeguarding and y y represents the number of hours walking dogs, write and solve a system of inequalities graphically and determine one possible solution.
Mathematics
1 answer:
ohaa [14]3 years ago
5 0

Answer:

We know that:

She makes $19 per hour of lifeguarding.

She makes $8 per hour walking dogs.

She can work at most 7 hours per week.

She must earn a minimum of $80 per week.

If x represents the number of hours lifeguarding and y represents the number of hours walking dogs, the inequalities will be:

x + y ≥ 7 hours.

(this says that she can work at most 7 hours per week)

x*$19 + y*$8 ≥ $80

(this says that she can earn a minimum of $80)

Then the system of inequalities is:

x + y ≥ 7 hours.

x*$19 + y*$8 ≥ $80

To graph these two we can write them as lines in standard form and simply graph both inequalities, the solution of the system will be the intersection between the solutions of each inequality.

Here we also should add the inequalities:

x ≥ 0

y ≥ 0

So we only look at the first quadrant.

The graph can be seen in the image below: (the dark blue is the solution region for the first inequality, the light blue one is the solution region for the second inequality)

 

One possible solution can be:

x = 4 and y = 1

or

x = 4 and y = 2

and there are a lot of other possible solutions.

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Leo and Maggie volunteer at the local bird sanctuary.
sattari [20]

Answer:2.4

Step-by-step explanation:

12 * 20% = 12 * 0.20 = 2.4 hours

It will not last the entire shift.

7 0
3 years ago
Colton and his children went into a movie theater and he bought $48.50 worth of bags of popcorn and candies. Each bag of popcorn
Inessa [10]

Answer:

5 bags of popcorn and 6 candies.

Step-by-step explanation:

(5 * $5.50) + ($3.5*6) = $48.5

4 0
3 years ago
<img src="https://tex.z-dn.net/?f=%5Cleft%28%5Csqrt%7B3%7D%2B4%5Cright%29%5Cleft%281%2B%5Csqrt%7B3%7D%5Cright%29" id="TexFormula
kirza4 [7]

Answer:

\huge\boxed{\sf 7 + 5\sqrt{3} }

Step-by-step explanation:

(\sqrt{3} +4)(1+\sqrt{3})\\\\= \sqrt{3}(1+\sqrt{3} )+4(1+\sqrt{3})\\\\= \sqrt{3} + (\sqrt{3} )^2 + 4 + 4\sqrt{3} \\\\= \sqrt{3} + 3+4+4\sqrt{3}  \\\\= 7 + \sqrt{3}  + 4\sqrt{3} \\\\Take \ \sqrt{3} \ common\\\\= 7 + \sqrt{3} (1+4)\\\\= 7 + \sqrt{3}(5)\\\\= 7 + 5\sqrt{3} \\\\\rule[225]{225}{2}

Hope this helped!

<h3>~AH1807</h3>
4 0
2 years ago
0.661 rounded to nearest hundretg
elena-s [515]
Since you are doing decimals, know that you are mirroring what you would do on the left side

Your decimal number: .661

The first 6, which is .6 is the tenths place

The second 6, which is .06 is the hundredths place

1 which is .001 is the thousands place

The farther you go left, the bigger the digit number value

So when rounding up, you look at the digit after the number you are rounding

So what is after the hundredths place? Its the thousandths place which is 1

Is 61 closer to 60 or 70? Since 1 is smaller than the halfway point which is 5, its closer to 60

Answer: .661 rounded to the nearest hundredths is .660 or just simply written as .66
8 0
3 years ago
Javier bought a microwave for $105.The cost was 30% off the original price.what was the price of the microwave before the sale
tatuchka [14]

Answer:

$ 150

Step-by-step explanation:

Given:

Cost price of a microwave = $105

Discount % = 30

Question asked:

what was the price of the microwave before sale = ?

Solution:

Let the price of the microwave before sale = x

Price before sale - 30 % discount = cost price of  microwave (by Javier)

x - 30\% of x = 105

x - \frac{30x}{100} = 105

\frac{70x}{100} = 105\\

Multiplying both side by 100

70x = 105 \times 100

70x = 10500

Dividing both side by 70

x = \frac{10500}{70} \\x = 150

x = price of the microwave before sale = $ 150

Thus, price of the microwave before the sale = $150

6 0
3 years ago
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