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Ne4ueva [31]
1 year ago
9

I need to know how to do this problem and graph it on a graph like this one below…Problem: Makayla earns $7 per hour at the bage

l shop and $12 per hour mowing lawns. Makayla needs to earn at least $120 per week, but must work less than 30 hours per week. Write and graph the system of linear inequalities that describes this situation. Graph:

Mathematics
1 answer:
kirza4 [7]1 year ago
3 0

Given that:

- Makayla earns $7 per hour at the bagel shop and $12 per hour mowing lawns.

- She needs to earn at least $120 per week, but must work less than 30 hours per week.

Let be "x" the number of hours Makayla works in the bagel shop, and "y" the number of hours she works in the mowing lawns.

Using the information given, you can set up the following System of Linear Inequalities:

\begin{cases}7x+12y\ge120 \\ x+y

The first inequality means that she needs to earn at least $120 per week, and the second inequality means that she needs to work less than 30 hours per week.

You can rewrite each equation by solving for "y":

- For the first inequality:

\begin{gathered} 12y\ge-7x+120 \\  \\ y\ge-\frac{7}{12}+\frac{120}{12} \\  \\ y\ge-\frac{7}{12}x+10 \end{gathered}

- And for the second inequality:

y

Notice that the boundary line of the first inequality is:

y=-\frac{7}{12}x+10

It is written in Slope-Intercept Form:

y=mx+b

Where "m" is the slope and "b" is the y-intercept.

Notice that, for the first line:

\begin{gathered} m_1=-\frac{7}{12} \\  \\ b_1=10 \end{gathered}

The slope indicates that the lines move 12 units to the right and 7 units down.

Since the symbol of the inequality is:

\ge

The line is solid and the shaded region is above the line.

The boundary line of the second inequality is:

y=-x+30

Notice that:

\begin{gathered} m_2=-1 \\ b_2=30 \end{gathered}

Since the symbol is "Less than", the line is dashed and the shaded region must be below the line.

Now you can graph the System of Linear Inequalities.

Hence, the answer is:

- System of Linear Inequalities:

\begin{cases}7x+12y\ge120 \\ x+y

- Graph:

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The first trophy is 6 inches wide while the second trophy is 11 inches wide.
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HURRY WILL NAME BRAINLIEST Which pairs of rational numbers are equivalent? Select all that apply.
sleet_krkn [62]

Answer:

Which ever choice is 283% works.

2 5/6= 2.83= 283%

Step-by-step explanation:

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Please help me with 1,2,3,4 and show me how you get it the answers
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Answer:

Step-by-step explanation:

Use the formula of distance between the two points (x_1,y_1) and (x_2,y_2),

Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

1. Distance between A(3, 4) and B(8, 12),

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2. Distance between C(-2, 10) and D(3, -2),

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3. Distance between X(20, 4) and Y(17, 0),

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3 years ago
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Iteru [2.4K]

Answer:

Gross monthly income:$1,125

Monthly Federal income tax (11.6%): $130.50

Monthly Social security (FICA) (6.2%): $69.75

Monthly Medicare (1.45%): $16.3125

Monthly State Tax (4%): $45

Monthly Local Tax (0.1%): $1.125

Total Monthly deductions $262.6875

Trey’s NMI $862.3125

Explanation:

Calculation for What is his monthly taxes

First step is to calculate the Gross monthly income

Using this formula

Gross monthly income=Annual salary/Numbers of months in a year

Let plug in the formula

Gross monthly income=$13,500/12 months

Gross monthly income=$1,125

Therefore the Gross monthly income is :$1,125

Monthly Federal income tax (11.6%): $130.50

($1,125*11.6%)

Monthly Social security (FICA) (6.2%): $69.75

($1,125*6.2%)

Monthly Medicare (1.45%): $16.3125

($1,125*1.45%)

Monthly State Tax (4%): $45

($1,125*4%)

Monthly Local Tax (0.1%): $1.125

($1,125*0.1%)

Total Monthly deductions $262.6875

($130.50+$69.75+$16.3125+$45+$1.125)

Trey’s NMI $862.3125

Trey’s NMI=Gross monthly income-Total Monthly deductions

Trey’s NMI=$1,125-$262.6875

Trey’s NMI=$862.3125

Therefore his monthly taxes are:

Gross monthly income:$1,125

Monthly Federal income tax (11.6%): $130.50

Monthly Social security (FICA) (6.2%): $69.75

Monthly Medicare (1.45%): $16.3125

Monthly State Tax (4%): $45

Monthly Local Tax (0.1%): $1.125

Total Monthly deductions $262.6875

Trey’s NMI $862.3125

Step-by-step explanation:

7 0
3 years ago
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