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drek231 [11]
3 years ago
14

How many factor pairs does 24 have? explain ​

Mathematics
2 answers:
Masja [62]3 years ago
8 0

Answer:

4 pairs

Step-by-step explanation:

Find the total number of factors of 24.

A factor is a positive whole number that can go into 24 without remainders.

The factors are:

1, goes in 24 times

2, goes in 12 times

3, goes in 8 times

4, goes in 6 times

There are also 6, 8, 12 and 24, but they are already found from the number of times the other numbers can go in.

The pairs are:

1 X 24

2 X 12

3 X 8

4 X 6

Therefore 24 has 4 factor pairs.

Harman [31]3 years ago
8 0
There are 4 pairs

The factor pairs of 24 are: 1 x 24, 2 x 12, 3 x 8, and 4 x 6.

1 times 24 = 24
2 times 12 = 24 <— (12+12)
3 times 8 = 24 <—- (8+8+8)
4 times 6 = 24 <—- (6+6+6+6)
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Is 1/7 greater than -5​
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Answer:

no

Step-by-step explanation:

1/7 is positive, -5 is negative. Negative is less than positive

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3 years ago
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A circle whose area is 4 has a radius of x find the area of a circle whose radius is 3x
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The first one is 1.12867 because you need to set it up like this.
4=3.14(x)squared
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The second one is done simply by multiplying it out.
A=3.14(3x)squared
A=3.14(9x[squared])
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3 years ago
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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}

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3 years ago
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Step-by-step explanation:

To find the total area, we will break the shape up into two different parts.

[] The rounded part is 39.25 in². Let us assume the rounded part is exactly half of a circle.

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