A number multiplied by <span>13</span> only produces an irrational number if it is itself an irrational number.
Explanation:
Suppose there were some rational number which when multiplied by <span>13</span> generated an irrational number.
If the number is rational then, by definition, it can be expressed as <span>ab</span> for some pair of integers a and b.
<span><span>ab</span>×<span>13</span>=<span><span>a×1</span><span>b×3</span></span>=<span>a<span>3b</span></span></span>
Since a is an integer and
since if b is an integer then <span>3b</span> is also an integer,
then
by definition <span><span>a3</span>b</span> is a rational number, contrary to our supposition that some rational number <span>ab</span> when multiplied by <span>13</span> could generate an irrational number.
Answer:
see explanation
Step-by-step explanation:
Using the property of parallelograms
• The diagonals bisect each other, hence
DH = HF and GH = HE
x + 1 = 3y and 3x - 4 = 5y + 1 ⇒ 3x = 5y + 5
Solving the 2 equations simultaneously
x + 1 = 3y → (1)
3x = 5y + 5 → (2)
rearrange (1) expressing x in terms of y
x = 3y - 1 → (3)
substitute x = 3y - 1 in (2)
3(3y - 1) = 5y + 5
9y - 3 = 5y + 5 ( subtract 5y from both sides )
4y - 3 = 5 ( add 3 to both sides )
4y = 8 ( divide both sides by 4 )
y = 2
substitute y = 2 into (3)
x = (3 × 2) - 1 = 6 - 1 = 5
Hence x = 5, y = 2
Mom gave $ 320 to each girl
<u>Solution:</u>
Given that Lily and Elsa are both college students
Before mom gave them this months allowance lily had $750 and Elsa had &215
<em><u>So amount with Lily and Elsa already is:</u></em>
amount with Lily = $ 750
amount with Elsa = $ 215
After mom gave each girl an equal amount of money for this months allowance, lily had twice as much money as Elsa
Let "a" be the equal amount of money which mom gave to Lily and Elsa
<em><u>So now amount with Lily and Elsa after mom gave equal amount is:</u></em>
amount with Lily = amount with Lily already + a
amount with Lily = 750 + a
amount with Elsa = amount with Elsa already + a
amount with Elsa = 215 + a
<em><u>Now given that lily had twice as much money as Elsa</u></em>
Amount with lily = 2(amount with elsa)
750 + a = 2(215 + a)
750 + a = 430 + 2a
2a - a = 750 - 430
a = 320
Thus mom gave $ 320 to each girl
Answer:
it will be
=> 4854
Step-by-step explanation:
hope it's helpful for you xd
Answer:
D < 40.2 inches
Step-by-step explanation:
The maximum width of the TV must be 36 inches. Since TVs are approximately twice as wide as they are tall, the maximum height is 18 inches.
The diagonal of a TV can be determined as a function of its width (w) and height (h) as follows:
Therefore, the diagonal must be at most 40.2 inches.
Since the answer choices were not provided with the question, you should choose the biggest value that is under 40.2 inches.
