Answer:
m = 2, n = - 3
Step-by-step explanation:
Given the 2 equations
2m + 3n = - 5 → (1)
5m + 3n = 1 → (2)
Subtract (2) from (1) term by term to eliminate n
2m - 5m = - 5 - 1
- 3m = - 6 ( divide both sides by - 3 )
m = 2
Substitute m = 2 into either of the 2 equations and solve for n
Substituting into (1)
2(2) + 3n = - 5
4 + 3n = - 5 ( subtract 4 from both sides )
3n = - 9 ( divide both sides by 3 )
n = - 3
Answer: Angle ABC = 60, angle CBD = 120 and angle GFH = 60
Step-by-step explanation: Line ABD is parallel to line EFG. Line line CFH is a straight line that cuts across both parallel lines. Therefore, angle FBD and angle HFG are corresponding angles. That means angle FBD equals 3x. Also 3x plus 6X equals 180. That is,
3x + 6x = 180 {Sum of angles on a straight line equals 180}
9x = 180
Divide both sides of the equation by 9
x = 20.
That means angle 6x measures 6(20) and that is 120 degrees.
Also angle 3x measures 3(20) and that is 60 degrees.
Angle ABC + Angle CBD = 180 {Sum of angles on a straight line equals 180}
Angle ABC + 120 = 180
Angle ABC = 180 - 120
Angle ABC = 60
Also angle CBD equals 6x, and x = 20. Therefore angle CBD = 6 x 20
Angle CBD = 120.
And then, angle GFH = 3x, and x equals 20. Hence angle GFH = 60.
Therefore angle ABC = 60, angle CBD = 120 and angle GFH = 60.
Answer:
Range is 6 and mode is 2
Step-by-step explanation:
Range is the greatest number of the set (7) subtracted by the smallest number of the set(1).
Mode is the most repeated number of the set(2).
<em>Hope this was helpful:)</em>
To solve this problem, we first need to find each of their hourly rates. We can do this by dividing the boxes by the number of hours. Using this method, we get that Jack wraps 14 boxes per hour and Walter wraps 12 boxes per hour. So, since the question has them working together, the rate is the sum of each of their individual rates per hour. Since we know that they work for t hours, we can multiply their combined rate by t (since in a job problem, job = time * rate). And, on the other end of the equal sign, since we know that they wrapped 65 presents, we put 65 there. The equation becomes:
(14+12)t = 65
Which simplifies to
26t = 65
