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statuscvo [17]
3 years ago
14

Every integer is a divisor of itself. A proper divisor of an integer means a positive divisor other than the integer itself. For

example, the divisors of 8 are 1, 2,4, and 8, but the proper divisors of 8 are just 1,2, and 4.
What is the smallest positive integer whose proper divisors add up to more than the integer itself?
Mathematics
2 answers:
Kazeer [188]3 years ago
5 0
I believe it is 4 because it would be 2 and 2

algol [13]3 years ago
5 0
The correct answer is 4? :)
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Part 4: Identify the vertex, focus and directrix of each. Then sketch the graph.
Nezavi [6.7K]

Answer: 1) Vertex: (6, -2)    Focus: (6, -7/4)     Directrix: y = -9/4

              2) Vertex: (-2, -1)   Focus: (-7/4, -1)     Directrix: x = -9/4

<u>Step-by-step explanation:</u>

Rewrite the equation in vertex format y = a(x - h)² + k   or   x = a(y - k)² + h by completing the square. Divide the b-value by 2 and square it - add that value to both sides of the equation.

  • (h, k) is the vertex
  • p is the distance from the vertex to the focus
  • -p is the distance from the vertex to the directrix

    \bullet\quad a=\dfrac{1}{4p}

1) y = x² - 12x + 34

y-34=x^2-12x\\\\y-34+\bigg(\dfrac{-12}{2}\bigg)^2=x^2-12x+\bigg(\dfrac{-12}{2}\bigg)^2\\\\\\y-34+36=(x-6)^2\\\\y+2=(x-6)^2\\\\y=(x-6)^2-2\qquad \rightarrow \qquad a=1\quad (h,k)=(6,-2)\\

a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=\dfrac{1}{4}\\\\\\\text{Focus = Vertex + p}\\.\qquad \quad =\dfrac{-8}{4}+\dfrac{1}{4}\\\\.\qquad \quad =-\dfrac{7}{4}\quad \rightarrow \quad\text{Focus}=\bigg(6,-\dfrac{7}{4}\bigg)\\\\\\\text{Directrix: y= Vertex - p}\\.\qquad \qquad y=\dfrac{-8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad y=-\dfrac{9}{4}

*******************************************************************************************

2) x = y² + 2y - 1

x+1=y^2+2y\\\\x+1+\bigg(\dfrac{2}{2}\bigg)^2=y^2+2y+\bigg(\dfrac{2}{2}\bigg)^2\\\\\\x+1+1=(y+1)^2\\\\x+2=(y+1)^2\\\\x=(y+1)^2-2\qquad \rightarrow \qquad a=1\quad (h,k)=(-2,-1)\\

a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=\dfrac{1}{4}\\\\\\\text{Focus = Vertex + p}\\.\qquad \quad =\dfrac{-8}{4}+\dfrac{1}{4}\\\\.\qquad \quad =-\dfrac{7}{4}\quad \rightarrow \quad\text{Focus}=\bigg(-\dfrac{7}{4},-1\bigg)\\\\\\\text{Directrix: x= Vertex - p}\\.\qquad \qquad y=\dfrac{-8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad x=-\dfrac{9}{4}

4 0
3 years ago
What is x if 4x-79=3x-29
elena-14-01-66 [18.8K]
<em>4x-79=3x-29</em>

<em>Move the terms with "x" on the left, and the numbers on the right.</em>

<em>4x-3x=79-29</em>
<em>x=50</em>
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7 less than twice a number
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Answer:

2x-7

Step-by-step explanation:

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A student ran a distance of 2 1/2 miles each day for 9 days. The student ran a distance of 5 3/4 miles each day for the next 3 d
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39.75 miles

Step-by-step explanation:

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6+2x=5-7x WHAT DOES X EQUAL PLEASE ANSWER FAST
ycow [4]

Answer:

x= -1/9

Step-by-step explanation:

6+2x=5-7x

-2x. -2x

6=5-9x

-5. -5

1=-9x/-9

-1/9=x

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