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maria [59]
3 years ago
6

HELP! Which triangles are congruent?

Mathematics
1 answer:
kati45 [8]3 years ago
8 0

9514 1404 393

Answer:

  4.  A, B, C, and D

Step-by-step explanation:

Each right triangle has a short leg of 3 units and a long leg of 4 units. They are all congruent by the SAS congruence postulate.

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What is the minimum value of C = 7x + 8y, given the constraints: 2x + y ≥ 8, x + y ≥ 6, x ≥ 0, y ≥ 0. A. 32 B. 42 C. 46 D. 64
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Answer: The minimum value of C is 46.

Step-by-step explanation:

Since, Here, We have to find out Min C = 7x+8y

Given the constraints are 2x+y\geq 8 -------(1)

x+y \geq 6   ------------- (2)

x \geq 0, y \geq 0  -------- (3)

Since, For equation 1) x-intercept, (4, 0) and y-intercept (0,8)

And, 2\times 0+0\geq 8⇒0\geq 8 ( false)

Therefore the area of line 1) does not contain the origin.

For equation 2) x-intercept, (6, 0) and y-intercept (0,6)

And, 0+0\geq 6⇒0\geq 6 ( false)

Therefore the area of line 2) does not contain the origin.

Thus after plotting the constraints 1) 2) and 3) we get Open Shaded feasible region AEB ( Shown in below graph)

At A≡(0,8) , C= 64

At E≡(2,4),  C= 46

At B≡(6,0),  C= 42

Thus at B, C is minimum, And its minimum value = 42


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