Step-by-step explanation:
when a line intersects with 2 (or more) parallel lines. then, of course, the intersection angle is the same with every of the intersected lines. otherwise they would not be parallel.
so,
7x - 10 = 60
7x = 70
x = 10
Answer:
B. 455
Step-by-step explanation:
The order in which the toppings are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.

In this question:
3 toppings from a set of 15. So

455 3-topping sundaes can be made.
Answer:
5
Step-by-step explanation:
See the attached image below for the drawing.
Point G = midpoint of segment DE
Point H = midpoint of segment FD
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Add up the x coordinates of points D and E, then divide by 2. So you should get (x1+x2)/2 = (0+2)/2 = 2/2 = 1. This is the x coordinate of point G.
Repeat for the y coordinates of D and E. So we have (y1+y2)/2 = (7+0)/2 = 7/2 = 3.5
Therefore point G is located at (x,y) = (1, 3.5)
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These steps will be repeated to find the midpoint H
Add up the x coordinates of F and D, then divide by 2. So, (x1+x2)/2 = (6+0)/2 = 6/2 = 3
Do the same for the y coordinates: (y1+y2)/2 = (7+0)/2 = 7/2 = 3.5
Point H is located at (3, 3.5)
Answer:
(14, -9)
Step-by-step explanation:
So you can solve this using substitution. When you're solving a systems of equations, you're looking for when (x, y) is the same for both equations, or in other words where the two linear equations intersect. Because of this we can solve for x or y in one equation and substitute it into the other equation, since the x and y in one equation should equal the x and y in the other equation.
Original equation:
x + 2y = -4
Subtract 2y from both sides
x = -2y - 4
Original equation:
2x + 3y = 1
Substitute -2y -4 as x
2(-2y - 4) + 3y = 1
Distribute the 2
-4y - 8 + 3y = 1
Combine like terms
-y - 8 = 1
Add 8 to both sides
-y = 9
Multiply both sides by -1
y = -9
So now that you know what y is, you can plug it into either equation to solve for x:
x + 2y = -4
Plug in -9 as y
x + 2(-9) = -4
Multiply
x - 18 = -4
Add 18 to both sides
x = 14
So this gives you the solution (14, -9)