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Ipatiy [6.2K]
3 years ago
6

Please help me answer this question. I do not understand how to do it.

Mathematics
1 answer:
ad-work [718]3 years ago
3 0
See attachment file below.

Hope it helped!

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What is --- <br> 8x + 2y = 30<br> 7x + 2y = 24
kolezko [41]

Answer:

x = 6 y = -9

Step-by-step explanation:

8x +2y = 30

-7x + 2y =24

x= 6

8(6)

48 + 2y =30

-48. -48

2y = -18

÷2. ÷2

y = -9

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Let A = { x ∈ R : x 2 − 5 x + 4 ≤ 0 } , B = (3 , 5), and C = (3 , 4]. Show that A ∩ B = C . (Recall, you must show two separate
kolbaska11 [484]

Answer:

You can proceed as follows:

Step-by-step explanation:

First solve the quadratic inequality x^{2}-5x+4\leq 0. To do that, factorize, then we have that (x-4)(x-1)\leq 0. This implies that

x-1\leq 0\, \text{and}\, x-4\geq 0

or

x-1 \geq 0\, \text{and}\, x-4\leq 0

In the first case the solution is the empty set \emptyset. In the second case the solution is the interval 1\leq x \leq 4. Now we have that

A=[1,4]

B=(3,5)

C=(3,4].

To show that A\cap B\subseteq C consider x\in A\cap B. Then 1\leq x \leq 4\, \text{and}\, 1, this implies that 3, then x\in C. Now, to show that C\subseteq A\cap B consider x\in C, then 3, then 1\leq x \leq 4\, \text{and}\, 3, then x\in [1,4] \, \text{and}\, x\in (3,5), this implies that x\in A\cap B.

Observe the image below.

7 0
4 years ago
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