Simplify the expression:z2-z(z+3)+3z

Answers

Answer 1

Answer: $z^2-z(z+3)+3z=z^2-z\cdot z-z\cdot3+3z=z^2-z^2-3z+3z=0$

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What is the period of the graph of the equation y=3cos2x

Answers

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Use division to find all the whole number ratios equivalent to 168 : 56

Answers

$168|2\n.\ 84|2\n.\ 42|2\n.\ 21|3\n.\ \ 7|7\n.\ \ 1|\n\n56|2\n28|2\n14|2\n.\ 7|7\n.\ 1|$

$168:56=(2\cdot2\cdot2\cdot3\cdot7)/(2\cdot2\cdot2\cdot7)\n\n=(2\cdot2\cdot3\cdot7)/(2\cdot2\cdot7)=\boxed{(84)/(28)}\n\n=(2\cdot2\cdot2\cdot3)/(2\cdot2\cdot2)=\boxed{(24)/(8)}\n\n=(2\cdot3\cdot7)/(2\cdot7)=\boxed{(42)/(14)}\n\n=(2\cdot3)/(2)=\boxed{(6)/(2)}\n\n=\boxed{(3)/(1)}\n\n=(2\cdot2\cdot3)/(2\cdot2)=\boxed{(12)/(4)}\n\n=(3\cdot7)/(7)=\boxed{(21)/(7)}$

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28° + x-4°+2x=180°

Answers

Answer:

x = 52

Step-by-step explanation:

28 + x - 4 + 2x = 180

Simplify the left side

3x + 24 = 180

Subtract 24 from each side

3x = 156

Divide each side by 3

x = 52

Brian bought beverages for his coworkers. One day he bought 3 lemonades and 4 iced teas for $12.00. The next day he bought 5 lemonades and 2 iced teas for $11.50. Find the cost of 1 lemonade and 1 iced tea, to the nearest cent.

Answers

Let's take lemonade's price as 'x' and iced tea's price as 'y'.

$\left \{ {{3x+4y=12} \atop {5x+2y=11.5}} \right. \n \left \{ {{x=4-y} \atop {5(4-y)+2y=11.5}} \right. \n \left \{ {{x=4-y} \atop {20-3y=11.5}} \right. \n \left \{ {{x=4-y} \atop {y=2.83}} \right. \n \left \{ {{x=1.17} \atop {y=2.83}} \right.$

Price of lemonade is $2.83, iced tea's $1.17.

Make x the subject 6x+a=5(x+t)