All categories

2 years ago

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 ≤ - $\frac{7}{2}$

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

x > 1

Solution is

x ≤ - $\frac{7}{2}$ or x > 1

You might be interested in

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

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

= -2.1

4 0

2 years ago

Read 2 more answers

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.

bazaltina [42]

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:

it would be 10

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

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

Total units = 4 + 6 = 10

Perimeter = 40

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