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Vlada [557]
3 years ago
13

A total of

Mathematics
1 answer:
LuckyWell [14K]3 years ago
4 0
If we make a an integer that represents the adults that bought tickets, and s the number of students, then we have the equations a+s=682, and a=68+s. 

Using the second equation, we find that s=a-68, so we plug this value of s into the first equation to get a+(a-68)=682. We simplify to find 2a=750. We divide by 2 to isolate the desired variable to get a=\boxed{375\text{ adult tickets were sold}}. 
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Determine the equation of g(x) that results from translating the function f(x)=x^2+9 upward 10 units.
Rus_ich [418]
The simple/ <span>common sense method:
</span>The typical lay out of a quadratic equation is ax^2+bx+c 
'c' represents where the line crosses the 'y' axis. 
The equation is only translated in the 'y' (upwards/downwards) direction, therefore only the 'c' component of the equation is going to change. 
A translation upwards of 10 units means that the line will cross the 'y' axis 10 places higher. 
9+10=19, 
therefore <u>c=19</u>. 
The new equation is: <u>y=x^2+19 </u>
<span>
<span>The most complicated/thorough method: 
</span></span>This is useful for when the graph is translated both along the 'y' axis and 'x' axis.
ax^2+bx+c 
a=1, b=0, c=9
Find the vertex (the highest of lowest point) of f(x). 
Use the -b/2a formula to find the 'x' coordinate of your vertex.. 
x= -0/2*1, your x coordinate is therefore 0. 
substitute your x coordinate into your equation to find your y coordinate.. 
y= 0^2+0+9
y=9. 
Your coordinates of your vertex f(x) are therefore <u>(0,9) </u>
The translation of upward 10 units means that the y coordinate of the vertex will increase by 10. The coordinates of the vertex g(x)  are therefore: 
<u>(0, 19) </u>
substitute your vertex's y coordinate into f(x) 
19=x^2+c
19=0+c
c=19
therefore <u>g(x)=x^2+19</u>

7 0
3 years ago
Read 2 more answers
Please help me with this geometry question !!!
Inessa05 [86]

Answer:

see explanation

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 90°

a point (x, y ) → (- y, x ), thus

P(1, - 1 ) → P'(1, 1 )

Q(3, - 2 ) → Q'(2, 3 )

R(3, - 4 ) → R'(4, 3 )

8 0
2 years ago
A local little league has a total of 85 players, of whom 40% are left-handed. How many left-handed players are there?
Mkey [24]

Answer:

34 players

Step-by-step explanation:

40.00%

=0.4

0.4*85

=34

3 0
2 years ago
The function f(x)=(25)x is shown on the coordinate plane.
andre [41]
It is a straight line


3 0
3 years ago
Read 2 more answers
Using the Kinetic Molecular Theory, explain Charles's Law of gases. Refer to specific points of the
liubo4ka [24]

Answer:

Kinetic theory explains why the volume of a container must expand when the temperature of the gas inside increases in order for the pressure to remain constant.

Step-by-step explanation:

Charles' law: for a fixed mass of gas at constant pressure the volume is directly proportional to the temperature.

Analysis of a gas when its temperature increases according to kinetic theory:

The temperature has increased therefore the molecules have more kinetic energy, so they move with a greater velocity.¹

If the container's dimensions do not change the molecules will travel across the container between the walls in less time (because they are moving faster and covering the same distance between the container walls). This will increase the rate of collisions, which would increase the pressure.²

But if the dimensions of the container increased then the molecules would cover a larger distance faster thereby maintaining a constant rate of collisions. This would maintain a constant pressure.

6 0
2 years ago
Read 2 more answers
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