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mr Goodwill [35]
3 years ago
11

How to find the smallest integer k such that 60k is a perfect square

Mathematics
1 answer:
suter [353]3 years ago
6 0

9514 1404 393

Answer:

  k = 15

Step-by-step explanation:

Look for the missing factors that make all of the factors of 60k be squares.

  60 = 2² × 3 × 5

The factors 3 and 5 each have an odd exponent (1), so those two factors must be part of k.

  60k = 2² × 3 × 5 × k

is a perfect square when ...

  3 × 5 = k = 15

For k = 15, 60k = 900 = 30²

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The stem and leaf plot shows the number of items in each of the 12 collections in a museum.
Ivahew [28]

Answer:

2

Step-by-step explanation:

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8 0
3 years ago
Which of these intervals has an average rate of change that is less than 1/4
RideAnS [48]

Answer:

Interval [b,c] and interval [c,d]

Step-by-step explanation:

a(-5,0)

b(-1,2)

c(4,3)

d(11,4)

The average rate of change is the the total rise over the total run.

The Rise means the vertical increase and the Run means horizontal incease.

For interval [a,b]

rate of change is \dfrac{2-0}{-1-(-5)}=\dfrac{2}{4}=\dfrac{1}{2}

For [b,c]

\frac{3-2}{4-(-1)}=\frac{1}{5}

For [c,d]

\dfrac{4-3}{11-4}=\dfrac{1}{7}

8 0
2 years ago
What is the value of f(4) + f(7)
tatyana61 [14]
Is there more to this problem? By saying f(4), you'd be inputting a 4 for every variable x. There is not enough info here to answer the question.
7 0
3 years ago
14.What is the solution of the system?
Archy [21]

Answer:

14.  x=-2.5,  y = -7

15.  x=28  y = -20

Step-by-step explanation:

14.  Let's solve this system by elimination.  Multiply the first equation by -1.

-1*(4x-y)= -1*(- 3)

-4x +y = 3

Then add this to the second equation.

-4x+y = 3

6x-y= - 8

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

2x   = -5


Divide each side by 2

x = -2.5

We still need to find y

-4x+y =3

-4(-2.5) + y =3

10 +y =3

Subtract 10 from each side.

y = 3-10

y = -7


15.I will again use elimination to solve this system, because using substitution will give me fractions which are harder to work with.   I will elimiate the y variable.  Multiply the first equation by 11

11( 5x+6y)= 11*20

55x+66y = 220

Multiply the second equation by -6

-6(9x+11y)=32*(-6)

-54x-66y = -192


Add the modified equations together.

55x+66y = 220

-54x-66y = -192

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

x = 28

We still need to solve for y

5x+6y = 20

5*28 + 6y =20

140 + 6y = 20

Subtract 140 from each side

6y = -120

Divide by 6

y = -20

3 0
2 years ago
What is the LCM of 8 and 10
iragen [17]
40


8x5=40
10x4=40

Hope this helps
3 0
2 years ago
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