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lukranit [14]
3 years ago
12

Adult and student tickets to the high school basketball game are sold each week. For every two adult tickets, seven student tick

ets are sold. How many total tickets were sold if 92 adult tickets were sold?
Mathematics
1 answer:
Gemiola [76]3 years ago
7 0

Answer:

414 tickets!

Step-by-step explanation:

If there were sold 92 adult tickets, and for every two of them, 7 student tickects are sold, we have the following:

92 / 2 = 46

Multiply by 7.

46 * 7 = 322 student tickets.

322 students tickets + 92 adult tickets = 414 tickets in total.

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1 (15 Points]. Prove the following statement: is divisible by 3 if only if it is a sum of three consecutive integers. be ddvisbk
Alinara [238K]

Answer:

<em>First.</em> Let us prove that the sum of three consecutive integers is divisible by 3.

Three consecutive integers can be written as k, k+1, k+2. Then, if we denote their sum as n:

n = k+(k+1)+(k+2) = 3k+3 = 3(k+1).

So, n can be written as 3 times another integer, thus n is divisible by 3.

<em>Second. </em>Let us prove that any number divisible by 3 can be written as the sum of three consecutive integers.

Assume that n is divisible by 3. The above proof suggest that we write it as

n=3(k+1)=3k+3=k + k + k +1+2 = k + (k+1) + (k+2).

As k, k+1, k+2 are three consecutive integers, we have completed our goal.

Step-by-step explanation:

4 0
2 years ago
A 2.2 kg ball strikes a wall with a velocity of 7.4 m/s to the left. The ball bounces off with a velocity of 6.2 m/s to the righ
Naya [18.7K]

Answer:

The constant force exerted on the ball by the wall is 119.68 N.

Step-by-step explanation:

Consider the provided information.

It is given that the mass of the ball is m = 2.2 kg

The initial velocity of the ball towards left is 7.4 m/s

So the momentum of the ball when it strikes is = 2.2\times 7.4=16.28

The final velocity of the ball is -6.2 m/s

So the momentum of the ball when it strikes back is = 2.2\times -6.2=-13.64

Thus change in moment is: 16.28-(-13.64)=29.92

The duration of force exerted on the ball t = 0.25 s

Therefore, the constant force exerted on the ball by the wall is:

\frac{29.92}{0.25}=119.68

Hence, the constant force exerted on the ball by the wall is 119.68 N.

6 0
3 years ago
Which of the following is not one of the 8th roots of unity?
Anika [276]

Answer:

1+i

Step-by-step explanation:

To find the 8th roots of unity, you have to find the trigonometric form of unity.

1.  Since z=1=1+0\cdot i, then

Rez=1,\\ \\Im z=0

and

|z|=\sqrt{1^2+0^2}=1,\\ \\\\\cos\varphi =\dfrac{Rez}{|z|}=\dfrac{1}{1}=1,\\ \\\sin\varphi =\dfrac{Imz}{|z|}=\dfrac{0}{1}=0.

This gives you \varphi=0.

Thus,

z=1\cdot(\cos 0+i\sin 0).

2. The 8th roots can be calculated using following formula:

\sqrt[8]{z}=\{\sqrt[8]{|z|} (\cos\dfrac{\varphi+2\pi k}{8}+i\sin \dfrac{\varphi+2\pi k}{8}), k=0,\ 1,\dots,7\}.

Now

at k=0,  z_0=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 0}{8}+i\sin \dfrac{0+2\pi \cdot 0}{8})=1\cdot (1+0\cdot i)=1;

at k=1,  z_1=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 1}{8}+i\sin \dfrac{0+2\pi \cdot 1}{8})=1\cdot (\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2})=\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2};

at k=2,  z_2=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 2}{8}+i\sin \dfrac{0+2\pi \cdot 2}{8})=1\cdot (0+1\cdot i)=i;

at k=3,  z_3=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 3}{8}+i\sin \dfrac{0+2\pi \cdot 3}{8})=1\cdot (-\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2})=-\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2};

at k=4,  z_4=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 4}{8}+i\sin \dfrac{0+2\pi \cdot 4}{8})=1\cdot (-1+0\cdot i)=-1;

at k=5,  z_5=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 5}{8}+i\sin \dfrac{0+2\pi \cdot 5}{8})=1\cdot (-\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2})=-\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2};

at k=6,  z_6=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 6}{8}+i\sin \dfrac{0+2\pi \cdot 6}{8})=1\cdot (0-1\cdot i)=-i;

at k=7,  z_7=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 7}{8}+i\sin \dfrac{0+2\pi \cdot 7}{8})=1\cdot (\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2})=\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2};

The 8th roots are

\{1,\ \dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2},\ i, -\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2},\ -1, -\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2},\ -i,\ \dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2}\}.

Option C is icncorrect.

5 0
3 years ago
Evaluate 2(5 + x2) + y if x = 3 and y = 2
photoshop1234 [79]

Answer:

26

Step-by-step explanation:

8 0
2 years ago
Write the linear equation in slope-intercept form​
dolphi86 [110]

The y intercept is 0, and the slope is 5x.

Equation: y = 5x +0.

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3 years ago
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