Paralell means has same slope
y=mx+b
m=slope
given
y=3/4x-9
sloe is 3/4
y=3/4x+b
find b
given point (-8,-18)
sub
x=-8 and y=-18
-18=3/4(-8)+b
-18=-6+b
add 6
-12=b
y=3/4x-12 is equation
Answer:
- adult tickets: $13
- student tickets $7
Step-by-step explanation:
The given equations are ...
4a +5s = 87
2a +2s = 40
We observe that the coefficient of 'a' in the first equation is 2 times that in the second equation. We can multiply the second equation by -2 and add it to the first to eliminate 'a' terms.
(4a +5s) -2(2a +2s) = (87) -2(40)
4a +5s -4a -4s = 87 -80 . . . . . . . . . eliminate parentheses
s = 7 . . . . . . . . . . . . . . . . . .simplify
2a +2(7) = 40 . . . substitute for s in the second equation
2a = 26 . . . . . . subtract 14
a = 13 . . . . . . . divide by 2
Adult tickets cost $13; student tickets cost $7.
<span>There are several ways to do this problem. One of them is to realize that there's only 14 possible calendars for any year (a year may start on any of 7 days, and a year may be either a leap year, or a non-leap year. So 7*2 = 14 possible calendars for any year). And since there's only 14 different possibilities, it's quite easy to perform an exhaustive search to prove that any year has between 1 and 3 Friday the 13ths.
Let's first deal with non-leap years. Initially, I'll determine what day of the week the 13th falls for each month for a year that starts on Sunday.
Jan - Friday
Feb - Monday
Mar - Monday
Apr - Thursday
May - Saturday
Jun - Tuesday
Jul - Thursday
Aug - Sunday
Sep - Wednesday
Oct - Friday
Nov - Monday
Dec - Wednesday
Now let's count how many times for each weekday, the 13th falls there.
Sunday - 1
Monday - 3
Tuesday - 1
Wednesday - 2
Thursday - 2
Friday - 2
Saturday - 1
The key thing to notice is that there is that the number of times the 13th falls upon a weekday is always in the range of 1 to 3 days. And if the non-leap year were to start on any other day of the week, the numbers would simply rotate to the next days. The above list is generated for a year where January 1st falls on a Sunday. If instead it were to fall on a Monday, then the value above for Sunday would be the value for Monday. The value above for Monday would be the value for Tuesday, etc.
So we've handled all possible non-leap years. Let's do that again for a leap year starting on a Sunday. We get:
Jan - Friday
Feb - Monday
Mar - Tuesday
Apr - Friday
May - Sunday
Jun - Wednesday
Jul - Friday
Aug - Monday
Sep - Thursday
Oct - Saturday
Nov - Tuesday
Dec - Thursday
And the weekday totals are:
Sunday - 1
Monday - 2
Tuesday - 2
Wednesday - 1
Thursday - 2
Friday - 3
Saturday - 1
And once again, for every weekday, the total is between 1 and 3. And the same argument applies for every leap year.
And since we've covered both leap and non-leap years. Then we've demonstrated that for every possible year, Friday the 13th will happen at least once, and no more than 3 times.</span>
Answer:
a. 29.3 units²
Step-by-step explanation:
The area of a circle is A = πr².
The area of each triangle is A = ½bh.
The vertex angle of each triangle is 360/5 = 72°. If we cut the triangle in half, we can use trig to write:
sin 36° = (½b) / r
b = 2r sin 36°
And:
cos 36° = h / r
h = r cos 36°
Substituting, we get the area of each triangle is:
A = r² sin 36° cos 36°
A = ½ r² sin 72°
The radius of the circle is 8. So the area of the circle minus the area of the 5 triangles is:
A = π (8)² − 5 (½) (8)² (sin 72°)
A ≈ 48.9 units²
Three fifths of the area is shaded, so:
⅗ A ≈ 29.3
Answer:
Given is that Lance rotates the figure 180° and Celina rotates the figure 90°
Now, when the figure is rotated 180 degrees, it will be turned around the origin in a way that the new place of the image will lie in a straight line in accordance to the original position. So, the second image is Lance's image.
When a figure is rotated 90 degrees counterclockwise, this means the figure will turn to the left and the point of the figure will be downwards. So, the first image is Celina's image.