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UNO [17]
3 years ago
14

Two consecutive integers have a sum of 75. Find the integers.

Mathematics
1 answer:
Pie3 years ago
7 0

Answer:

37 and 38

Step-by-step explanation:

let the consecutive integers be x-1 and x

If their sum is 75

x-1+x = 75

2x - 1 = 75

2x = 75+1

2x = 76

x = 76/2

x = 38

First integer = x - 1

First integer = 38-1 = 37

Second integer is 38

Hence the integers are 37 and 38

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Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unknown
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Answer:

The other endpoint is (-33, 17)

Step-by-step explanation:

The rule of the mid-point of a segment whose endpoints are

(x_{1}, y_{1}) and (x_{2}, y_{2}) is

  • (x_{M},y_{M})  = (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})

In our question

∵ The coordinates of the endpoints of a segment are (-15, 13) and (x, y)

∴ x_{1} = -15 and x_{2} = x

∴ y_{1} = 13 and y_{2} = y

∵ The coordinates of the mid-point of this segment are (-24, 15)

∴ x_{M} = -24 and y_{M} = 15

→ Use the rule of the mid-point to find x and y

∵ -24=\frac{-15+x}{2}

→ Multiply both sides by 2

∴ -48 = -15 + x

→ Add 15 to both sides

∴ -33 = x

∵ 15=\frac{13+y}{2}

→ Multiply both sides by 2

∴ 30 = 13 + y

→ Subtract 13 from both sides

∴ 17 = y

∴ The other endpoint is (-33, 17)

5 0
4 years ago
Solve graphically the inequality \[ x ≥ 2 \]
Xelga [282]

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2) Select a point situated in any of the two regions obtained and test the inequality. If the point selected is a solution, then all the region is the solution set. If the selected point is not a solution, then the other (second) region represents the solution set.

3) Test: In this example, let us for example select the point with coordinates (3 , 2) which is in the region to the right of the line x = 2. If you substitute x in the inequality \( x ≥ 2 \) by 3 it becomes \( 3 ≥ 2 \) which is a true statement and therefore (3 , 2) is a solution. Hence, we can conclude that the region to the right of the vertical line x = 2 is a solution set including the line itself which is shown as a solid line because of the inequality symbol \( ≥ \) contains the \( = \) symbol. The solution set is represented by the blue hash region in the graph below including the line x = 2.

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