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3 years ago

How would you convince a fellow student hat the number 0.57 is a rational number

1 answer:

4 0

Start by proving to them that the number 0.57 can be converted into a fraction . A whole number can't exactly be put in to a fraction. 0.57 can be converted to 14.25/25. This information means that 0.57 IS a rational number. Hope this convinced them!

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2/5 of the members of a school band are 6th graders. What percent of

faust18 [17]

Answer:

60%

Step-by-step explanation:

3/5 is 60%

7 0

2 years ago

Read 2 more answers

Which equations represent functions?

never [62]

Answer:

2x + 3y = 10, 3y = 18 (in both cases, for each input x, there is exactly one output y.

Step-by-step explanation:

3y = 10 - 2x, or y = (1/3)(10 - 2x) Yes, this is a function.

4x = 16 → x = 4 NOT a Function, because for x = 4 there are an infinite number of possible y -values

2x - 3 = 14 → 2x = 17 → x = 17/2 Not a function. See reason given above.

3y = 18 → y = 6 Function

2x = 14.6 → x = 7.3 Not a function. See reason given above

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3 years ago

Pls write down your reaction to the algebraic magic trick note I already did it I just need your reaction and pls no links also

valentinak56 [21]

Hdbbsnaknabdbdjrnwkqonf fnjfjkew

4 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

The total area of two square windows is 1,025 in.^2. each side of the larger window is 5 in. longer than the sides of the smalle

vampirchik [111]

The area of a square is expressed as:

Area = s^2

We are given the area of both windows. We will use this value for the calculations. We set s as the side of the larger window and a for the smaller window.

Total area = Area larger + area smaller
1025 = s^2 + a^2

Since it was said that the side of the larger window, s is 5 in longer than the side of the smaller window, a (s = 5+a) then:

<span>1025 = s^2 + a^2
</span>1025 = (5+a)^2 + a^2

simplifying we obtain,

a = 20 inches

8 0

2 years ago

Read 2 more answers