336 divided by 2 is 168.
so just change it up.
the two numbers can be 166+170
Let's say that y is the unknown
180=2x+3+5x+1+y
180=7x+4+y
180-7x-4=y
176-7x=y=third angle
-2<em>x</em> + 6<em>y</em> = -38
3<em>x</em> - 4<em>y</em> = 32
To solve by elimination, multiply the top equation by 3 and the bottom equation by 2.
3(-2<em>x</em> + 6<em>y</em> = -38) --> -6<em>x</em> + 18<em>y</em> = -114
2(3<em>x</em> - 4<em>y</em> = 32) --> 6<em>x</em> - 8<em>y</em> = 64
Add the equations.
-6<em>x </em>+ 18<em>y</em> = -114
6<em>x</em> - 8<em>y</em> = 64
+_____________
0 + 10<em>y</em> = -50
10<em>y</em> = -50
<em>y</em> = -5
Substitute -5 for y into one of the original equations to find x.
3<em>x</em> - 4<em>y</em> = 32
3<em>x</em> - 4(-5) = 32
3<em>x</em> + 20 = 32
3<em>x</em> = 12
<em>x</em> = 4
Check work by plugging the <em>x</em>- and <em>y</em>-values into both of the original equations.
-2<em>x</em> + 6<em>y</em> = -38
-2(4) + 6(-5) = -38
-8 - 30 = 38
38 = 38
3<em>x</em> - 4<em>y</em> = 32
3(4) - 4(-5) = 32
12 + 20 = 32
32 = 32
Answer:
<em>x</em> = 4 and <em>y</em> = -5; (4, -5).
Answer:
meters.
Step-by-step explanation:
We have been given Mr. Mole left his burrow and started digging his way down at a constant rate.
We are also given a table of data as:
Time (minutes) Altitude (meters)
6 -20.4
9 -27.6
12 -34.8
First of all, we will find Mr. Mole's digging rate using slope formula and given information as:
, where,
represents difference of two y-coordinates,
represents difference of two corresponding x-coordinates of y-coordinates.
Let 
be 
and 
be 
.
Now, we will use slope-intercept form of equation to find altitude of Mr. Mole's burrow.
, where,
m = Slope,
b = The initial value or the y-intercept.
Upon substituting and coordinates of point , we will get:
Since in our given case y-intercept represents the altitude of Mr. Mole's burrow, therefore, the altitude of Mr. Mole's burrow is meters.
Answer:
Step-by-step explanation:
Represent the width by W. Then, "The length of a rectangular field is 7 m less than 4 times the width" expressed symbolically is
L = 4W - 7 (dimensions in meters)
Recall that the perimeter formula in this case is P = 2L + 2W, and recognize that the perimeter value is 136 m. After substituting 4W - 7 for L, we get:
136 m = 2(4W - 7) + 2W, or
136 = 8W - 14 + 2W, or
150 = 10W These three equations are equivalent mathematical statements.
150 = 10W reduces to W = 15 (meters).
Part A: the independent variable is W, the width of the field.
Part B: The mathematical statement is 136 m = 2(4W - 7) + 2W, which after algebraic manipulation becomes 150 = 10W.
Part C: The above equation can be solved for W: W = 15 meters. This is the value of the independent variable.
