Answer:
x = 8, and y = 12
Step-by-step explanation:
There are 2 variables, so you need 2 equations to form a system of equations in two variables.
The upper left triangle has all angle measures given: 100, 2x + y, 5x + y. We know that the sum of the measures of the angles of a triangle is 180.
First equation:
100 + 2x + y + 5x + y = 180
Simplify:
7x + 2y = 80 (First equation)
Now we see that the upper and lower sides are parallel, so alternate interior angles are congruent. The angles measuring 2x + y and 5x - y are alternate interior angles and are congruent.
Second equation:
2x + y = 5x - y
Simplify:
3x - 2y = 0 (Second equation)
Now we use the first equation and the second equation as a system of simultaneous equations to solve for x and y.
7x + 2y = 80
3x - 2y = 0
Solve the second equation for 2x.
3x = 2y
Now replace 2y in the first equation with 3x.
7x + 3x = 80
10x = 80
x = 8
Replace x with 8 in the second equation.
3(8) - 2x = 0
24 = 2x
x = 12
Answer: x = 8, and y = 12
Answer:
h = b - 11.50
Step-by-step explanation:
Sharron(h) has 11.50 less than Rita(b)
h = b - 11.50
The answer should be 6 units. -1 > 0 > 1 > 2 > 3 > 4 > 5 : 6 units
Answer:
The line represents a direct variation function.
Step-by-step explanation:
This line would cross the point (0, 0) making it a direct variation function.
We know the line would cross (0, 0) because the slope of the line is 2/3 (change in y over change in x, so 4-2 over 6-3 which simplifies to 2/3). From the point (3, 2), we can use the slope to calculate backwards to the origin.
