Step-by-step explanation:
we see 2 confirmed points with whole integers as coordinates.
(-2, -1) and (1, 2)
the general equation for a line is
y = ax + b
a is the slope expressed as y/x ratio indicating how many units y changes , when x changes for a certain amount of units when going from one point to another.
so, when going from (-2, -1) to (1, 2)
x changes by +3 units (from -2 to 1)
y changes by +3 units (from -1 to 2)
so, the slope (a) is 3/3 = 1
b is the y-intercept (the y value when x=0, so, the point where the line crosses the y-axis).
our equation looks now like this
y = x + b
to get b we use the coordinates of one of the points as x and y. e.g. (1, 2) :
2 = 1 + b
b = 1
the full equation is
y = x + 1
-6- -2n=3n -(6+5)
combine like terms
-6 +2n = 3n -11
subtract 2n from each side
-6 = n-11
add 11 to each side
-6 +11 = n
5 =n
Answer:
What is the slope of a line perpendicular to the line whose equation is 2x+y=3?
Step-by-step explanation:
-1/2
Step-by-step explanation:
perpendicular slopes are the opposite reciprical
so you basically flip it and change the sign
I hope this helps :)
Answer:
3
Step-by-step explanation:
Set the denominator in
3
x
2
−
2
x
−
15
equal to
0
to find where the expression is undefined.
x
2
−
2
x
−
15
=
0
Solve for
x
.
Tap for more steps...
x
=
5
,
−
3
The domain is all values of
x
that make the expression defined.
Interval Notation:
(
−
∞
,
−
3
)
∪
(
−
3
,
5
)
∪
(
5
,
∞
)
Set-Builder Notation:
{
x
|
x
≠
−
3
,
5
}
Let's first deal with the angles towards the top of the diagram. You should immediately notice that angle H is opposite the right angle and therefore angle H has a value of 90 degrees.
Now that will mean that the sum of the angles that are listed as (8m - 18) and (5p + 2) will add up to 90. And since the angle (7m + 3) is opposite to the (5p + 2) angle, they're equal. Therefore (8m - 18) + (7m +3) = 90. Let's see what m is
(8m - 18) + (7m +3) = 90
8m - 18 + 7m + 3 = 90
15m - 15 = 90
15m = 105
m = 7
Since m = 7, you immediately know that (8m - 18) = 38, and (7m + 3) = 52.
And because of the opposite angles, you also know that (5p + 2) = 52, so p = 10, and (11t - 17) = 38, so t = 5
The line CE has been divided into 2 equal halves by point D, so
5a + 12 = 9a - 12
Solving for a, gets
5a + 12 = 9a - 12
12 = 4a - 12
24 = 4a
6 = a
So a = 6
The two angles off of point E are marked as congruent, so
48 = 21s + 6
42 = 21s
2 = s
So s = 2.
Now let's arrange the variables in numeric order.
s = 2
t = 5
a = 6
m = 7
p = 10
And upon doing so I see the word "stamp" as the answer to the riddle "What sits in a corner but travels around the world?"
