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asambeis [7]
2 years ago
10

Please help me out with this!!

Mathematics
1 answer:
galina1969 [7]2 years ago
7 0

Answer:

see explanation

Step-by-step explanation:

Given

x + \frac{1}{2} ≤ - 3 or x - 3 > - 2

Solve the left and right inequalities separately, that is

x + \frac{1}{2} ≤ - 3 ( isolate x by subtracting \frac{1}{2} from both sides )

x ≤ - 3 - \frac{1}{2}, that is

x ≤ - \frac{6}{2} - \frac{1}{2}, thus

x ≤ - \frac{7}{2}

OR

x - 3 > - 2 ( isolate x by adding 3 to both sides )

x > 1

Solution is

x ≤ - \frac{7}{2} or x > 1

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Notah lives in Minnesota. He records the lowest temperature each day for one week. What is the mean of the temperatures? -7.3°F,
natita [175]

Answer:

-2.1

Step-by-step explanation:

-7.3 - 11.2 - 1.7 + 0 + 0 +2.2 + 3.3

--------------------------------------------------

                            7

= -2.1

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The measure of two sides of a triangle are given. If the perimeter is 11x^2 - 29x + 10, find the measure of the third side. ​
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Answer:

I would say use photomath if you cant find your answer.

Step-by-step explanation:

5 0
3 years ago
I need help! if you answer wrong for points I will report you! but hurry this is timed!
anyanavicka [17]

Answer:

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Step-by-step explanation:


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The perimeter of a rectangle is 40 feet. The ratio of the width to the length is 2:3 find the length and the width
ziro4ka [17]

Width : Length

2 : 3

Perimeter = 2* width + 2*length

Ratio becomes:

Width : Length

4 : 6

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Answer: Width is 8 ft and Length is 12 ft.

5 0
2 years ago
Prove A-(BnC) = (A-B)U(A-C), explain with an example​
NikAS [45]

Answer:

Prove set equality by showing that for any element x, x \in (A \backslash (B \cap C)) if and only if x \in ((A \backslash B) \cup (A \backslash C)).

Example:

A = \lbrace 0,\, 1,\, 2,\, 3 \rbrace.

B = \lbrace0,\, 1 \rbrace.

C = \lbrace0,\, 2 \rbrace.

\begin{aligned} & A \backslash (B \cap C) \\ =\; & \lbrace 0,\, 1,\, 2,\, 3 \rbrace \backslash \lbrace 0 \rbrace \\ =\; & \lbrace 1,\, 2,\, 3 \rbrace \end{aligned}.

\begin{aligned}& (A \backslash B) \cup (A \backslash C) \\ =\; & \lbrace 2,\, 3\rbrace \cup \lbrace 1,\, 3 \rbrace \\ =\; & \lbrace 1,\, 2,\, 3 \rbrace\end{aligned}.

Step-by-step explanation:

Proof for [x \in (A \backslash (B \cap C))] \implies [x \in ((A \backslash B) \cup (A \backslash C))] for any element x:

Assume that x \in (A \backslash (B \cap C)). Thus, x \in A and x \not \in (B \cap C).

Since x \not \in (B \cap C), either x \not \in B or x \not \in C (or both.)

  • If x \not \in B, then combined with x \in A, x \in (A \backslash B).
  • Similarly, if x \not \in C, then combined with x \in A, x \in (A \backslash C).

Thus, either x \in (A \backslash B) or x \in (A \backslash C) (or both.)

Therefore, x \in ((A \backslash B) \cup (A \backslash C)) as required.

Proof for [x \in ((A \backslash B) \cup (A \backslash C))] \implies [x \in (A \backslash (B \cap C))]:

Assume that x \in ((A \backslash B) \cup (A \backslash C)). Thus, either x \in (A \backslash B) or x \in (A \backslash C) (or both.)

  • If x \in (A \backslash B), then x \in A and x \not \in B. Notice that (x \not \in B) \implies (x \not \in (B \cap C)) since the contrapositive of that statement, (x \in (B \cap C)) \implies (x \in B), is true. Therefore, x \not \in (B \cap C) and thus x \in A \backslash (B \cap C).
  • Otherwise, if x \in A \backslash C, then x \in A and x \not \in C. Similarly, x \not \in C \! implies x \not \in (B \cap C). Therefore, x \in A \backslash (B \cap C).

Either way, x \in A \backslash (B \cap C).

Therefore, x \in ((A \backslash B) \cup (A \backslash C)) implies x \in A \backslash (B \cap C), as required.

8 0
2 years ago
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