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noname [10]
4 years ago
15

Veronica teaches French in groups of four students. She rents a room for $200 per month. She charges $45 per hour per student. V

eronica teaches seven groups of students, and her net earnings per month are $6,100. If each student learns French for the same number of hours, write an equation that can be used to calculate the number of hours each student learns French in a month.
Mathematics
1 answer:
alexandr402 [8]4 years ago
4 0
<span>of the task , we know that :
</span>
profit netto = $ 6100
<span>influenza students = 7
</span>hourly rate for one lesson of the French language  = $45

<span>we do not know about
</span>
profit brutto = ?    <span>denoted as x

</span><span>the amount collected lessons
for one student = ?    denoted as y

x = $6100 + $200
</span>y =  \frac{x}{45*7}
<span>
</span>\left \{ {{x=6300} \atop {y= \frac{6300}{315} =2}} \right.
<span>
2 away

</span>y =  \frac{6100 + 200}{45 * 7}  = 2<span>
</span>
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Answer:

Here's what I get.

Step-by-step explanation:

1. Rotate 180° about origin

The formula for rotation of a point (x,y) by an angle θ about the origin is  

x' = xcosθ  -  ysinθ

y' = ycosθ + xsinθ

If θ = 180°, sinθ = 0 and cosθ = -1, and the formula becomes

x' =   -x

y' =  -y

The rule is then (x, y) ⟶ (-x, -y).

H: (-3, -5) ⟶ (3, 5)

J: (-5, -3) ⟶ (5, 3)

Q: (0, -1) ⟶ (0, 1)  

The vertices of H'J'Q' are (3, 5), (5, 3), and (0, 1).

2. Rotation 90° counterclockwise about origin

cos90°  = 0 and sin90° = 1

x' = xcos90°  -  ysin90° = -y

y' = ycos90° + xsin90° =  x

The rule is then (x, y) ⟶ (-y, x).

B: (4, 5) ⟶ (-5, 4)

L: (5, 0) ⟶ (0, 5)

S: (2, 2) ⟶ (-2, 2)  

The vertices of B'L'S' are (-5, 4), (0, 5), and (-2, 2).

3. Rotation 90° clockwise about origin

cos(-90°) = 0 and sin(-90°) = -1

x' = xcos(-90°)  -  ysin(-90°) =  y

y' = ycos(-90°) + xsin(-90°) =  -x

The rule is then (x, y) ⟶ (y, -x).

F: (1, -5) ⟶ (-5, -1)

H: (-2, -3) ⟶ (-3, 2)

U: (-4, -5) ⟶ (-5, 4)  

The vertices of F'H'U' are (-5, -1), (-3, -2), and (-5, 4).

4. Rotate 180° about origin

The rule is (x, y) ⟶ (-x, -y).

J: (1, -1) ⟶ (-1, 1)

V: (2, 0) ⟶ (-2, 0)

Y: (5, -3) ⟶ (-5, 3)

R: (4, -3) ⟶ (-4, 3)  

The vertices of J'V'Y'R' are (-1, 1), (-2, 0), (-5, 3), and (-4, 3).

The figures below show your shapes before and after the rotations.

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