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Explanation:
The equation d = 65t means that the rate is r = 65. So Malcolm's family travels at an average rate of 65 mph. Note this is the slope of the line.
The graph has a slope of 50 because each time we go up 50, we move to the right 1. Ie, slope = rise/run = 50/1 = 50. You could use the slope formula to get the same result.
Since the graph has a slope of 50, this means Theo's family is going at an average speed of 50 mph.
Subtract the two speeds to get 65-50 = 15 mph
The system of linear equations 3x + 7y = 22 and 12x + 28y = 88 actually represents the same line, indicating that there are infinite solutions. Any pair of (x, y) that satisfies one equation will satisfy the other.
To solve the system of linear equations 3x + 7y = 22 and 12x + 28y = 88, let's use substitution or elimination method. Here, the elimination method works best since the equations are multiples of each other. Divide the second equation by 4, you get 3x + 7y = 22, which is exactly the same equation as the first equation.
This means both equations represent the same line, so there are infinite solutions. Any x, y that satisfy one equation will satisfy the other. Therefore, the system is dependent.
Example of such solutions (x, y) can be obtained by isolating y in the first equation:
7y = 22 - 3x
y = (22 - 3x) / 7 or y = 9 + 3x
#SPJ12
The given system of equations has infinitely many solutions.
To solve for x and y in the given system of equations:
3x + 7y = 22
12x + 28y = 88
Multiply the first equation by 4 to eliminate the y variable:
12x + 28y = 88
12x + 28y = 88
Subtract the second equation from the first equation:
12x + 28y - 12x - 28y = 88 - 88
0 = 0
Since both variables have been eliminated, the equations are dependent and have infinitely many solutions. The solution is any pair of (x, y) values that satisfies the original equations.
#SPJ12
The true statement about an exterior angle of a triangle is C; It forms a linear pair with one of the interiior angles of the triangle .
An exterior angle of a triangle is equal to the sum of the opposite interior angles.
We know that the exterior angles are out of the triangle at all times and it adds up to make 180 with anyone of the inside angle of the triangle.
The pair also rests on the same straight line and that makes a pairs.
Therefore we can say that it is formed by a linear pair with one of the interior angles of the triangle.
So, the correct answer would be C.
Learn more about exterior angles;
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Answer:
D
Step-by-step explanation:
The exterior angles are out of the triangle at all times and it adds up to make 180 with anyone of the inside angle of the triangle.
The pair also rests on the same flat/straight line and that makes a pair.
Therefore we can say that it is formed by a linear pair/group with one of the interior/inside angles of the triangle.
So, the correct answer would be D.
Answer:
9
Step-by-step explanation:
|6|+|-3|=9