Answer:
Take a look at my notes. I hope this helps.
Answer:
5.5 inches
Step-by-step explanation:
Answer:
360,360
Step-by-step explanation:
So we only have 5 spots, but 15 bands to fill those spots.
For the first spot, we can choose from any of the 15 bands, so we have 15 choices.
For the second spot, we can choose from the 14 remaining bands (because we already chose one for the first spot), so we have 14 choices.
For the third spot, by similar reasoning as above, we have 13 choices; for the fourth spot, 12 choices; and for the last spot, we have 11 choices.
We realize that for each of the 15 possible bands in the first spot, we still have 14 possible bands for the second spot, and so on. Thus, we know to multiply instead of add.
Our answer is: 15 * 14 * 13 * 12 * 11 = 360,360
Answer:
(3,1) because x is 3 and y is 1.
Step-by-step explanation:
x+2y=5
3x+5y=14
Multiply first equation by 3:
3x+6y=15
3x+5y=14
Subtract 3x:
1y=1
Therefore, y = 1
Plug it back into 1st equation:
x+2(1)=5
x+2=5
Therefore, x = 3
Judging from your answers, it looks like (3,1) because x is 3 and y is 1.
I hope this helped!
If points f and g are symmetric with respect to the line y=x, then the line connecting f and g is perpendicular to y=x, and f and g are equidistant from y=x.
This problem could be solved graphically by graphing y=x and (8,-1). With a ruler, measure the perpendicular distance from y=x of (8,-1), and then plot point g that distance from y=x in the opposite direction. Read the coordinates of point g from the graph.
Alternatively, calculate the distance from y=x of (8,-1). As before, this distance is perpendicular to y=x and is measured along the line y= -x + b, where b is the vertical intercept of this line. What is b? y = -x + b must be satisfied by (8,-1): -1 = -8 + b, or b = 7. Then the line thru (8,-1) perpendicular to y=x is y = -x + 7. Where does this line intersect y = x?
y = x = y = -x + 7, or 2x = 7, or x = 3.5. Since y=x, the point of intersection of y=x and y= -x + 7 is (3.5, 3.5).
Use the distance formula to determine the distance between (3.5, 3.5) and (8, -1). This produces the answer to this question.
