To find the slope of a line given two points, use: (y2 - y1) / (x2 - x1)
A. (7-3) / (-1-5) = (4/-6) or -2/3
B. The slope of a line parallel to another line will be the same, so -2/3
C. The slope of a line perpendicular to another line will be the reciprocal and the sign will also change. Because the slope was -2/3, the slope of the perpendicular changes to 3/2 (positive)
<span><em>12 pennies, 3 nickles, and 2 dimes</em>
p = number of pennies
n = number of nickles
d = number of dimes
p(1) + n(5) + d(10) = 47
that is, the number of pennies x 1 cent + number nickles x 5 cents
+ number of dimes x ten cents equals 47 cents
p = 4n
p + n + d = 17
Substituting 4n for p in the above
4n + n + d = 17
5n + d = 17
Subtract 5n from each side
d = 17 - 5n
We will now substitute 4n for p and ( 17-5n ) for d in
the equation
p(1) + n(5) + d(10) = 47
4n(1) +n(5) + (17-5n)(10) = 47
9n + 170 - 50n = 47
-41n + 170 = 47
Subtract 170 from each side
-41n = 47 - 170
-41n = -123
Divide each side by -41
n = 3
Since p = 4n
p = 4(3)
p = 12
Since p + n + d = 17
12 + 3 + d = 17
15 + d = 17
d = 2
So we have 12 pennies, 3 nickles and 2 dimes
12 + 3(5) + 2(10) ?= 47
12 + 15 + 20 ?= 47</span>
The answer is 14 because
4 divided by 2 is 2 multipled by 5 = 10 that exponet on the base of 2 equals four and 4+10=14
Solve the following system using elimination:
{x - 2 y = -23 | (equation 1)
{x - y = 7 | (equation 2)
Subtract equation 1 from equation 2:
{x - 2 y = -23 | (equation 1)
{0 x+y = 30 | (equation 2)
Add 2 × (equation 2) to equation 1:
{x+0 y = 37 | (equation 1)
{0 x+y = 30 | (equation 2)
Collect results:
Answer: {x = 37 , y = 30
Answer:
7.5 ounces
Step-by-step explanation:
