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

Answers

Answer 1

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


Related Questions

I have the answer for this geometry question just how to I solve it. Quickest and correct and semi-long explanation gets brainliest and 100 points. HURRY PLEASE!!!

Answers

Answer:

75

Step-by-step explanation:

If the area of ABCD is equal to 45, then the perimeter of EFG is equal to x * 1.5 = 45. 45 / 1.5 = 30, so the perimeter of EFG is equal to 30. This means that each side is equal to 10.

The height of the equilateral triangle EFG creates two 30-60-90 triangles, each with a hypotenuse of 10 and a short side equal to 5. We know that the long side of the 30-60-90 triangle (here the height of EFG) is equal to √3 times the short side, or 5√3.

We then apply the formula for the area of a triangle, which is 1/2 * b * h. We get 1/2 * 10 * 5√3 = 5 * 5√3 = 25√3.

In general, the height of an equilateral triangle is equal to √3 / 2 times a side of the equilateral triangle. The area of an equilateral triangle is equal to 1/2 * √3s/ 2 * s = √3s2/4.

plz help I will give the brainlist David drew this diagram of a picture frame he is going to make. Each square represents 1 square inch. What is the area of the picture​ frame?

Answers

Answer:

32

Step-by-step explanation:

A sphere has a radius of 2 m. Calculate its surface area. Round to the nearest whole number
a
b.
50 sq.m
113 sq.m
C.
d.
212 sq.m
103 sq.m
Please select the best answer from the choices provided
A

Answers

Answer:

50 square meters should be your answer

Step-by-step explanation:

The formula of the Surface Area of a sphere is 4πr2 (4*r*squared)

if the radius of the sphere is 2 m, our formula will become 4π(2)[squared]

let us break this down into two pieces:

4π = 12.5663706144

2[squared] = 4

Then when we multiply our answers:

12.5663706144 * 4 = 50.2654824576

since it says to round it to the nearest whole number, we can round this to 50

I HOPE YOU HAVE A WONDERFUL DAY AND GET THIS CORRECT!!!

Please rate and heart if my answer helped you!!!!

C and D are mutually exclusive events. Find P(C or D).
P(C)= 3/7= P(D)= 4/7
P(C or D)

Answers

Answer:

[tex]P(C\ or\ D) = 1[/tex]

Step-by-step explanation:

Given

[tex]P(C) = \frac{3}{7}[/tex]

[tex]P(D) = \frac{4}{7}[/tex]

Required

[tex]P(C\ or\ D)[/tex]

Since the events are mutually exclusive, then:

[tex]P(C\ or\ D) = P(C) + P(D)[/tex]

So, we have:

[tex]P(C\ or\ D) = \frac{3}{7} + \frac{4}{7}[/tex]

Take LCM

[tex]P(C\ or\ D) = \frac{3+4}{7}[/tex]

[tex]P(C\ or\ D) = \frac{7}{7}[/tex]

[tex]P(C\ or\ D) = 1[/tex]

jackson spent 8.55 for 3 bags of chips.how many bags of chips can he got for $30

Answers

Answer:

10

Step-by-step explanation:

Select all of the solutions to the original equation X=4X equals -16 X equals minus 4X equals 16 X equals minus 8X equals minus 1X equals one X equals eight

Answers

Answer: i don´t know the answer sorry

Step-by-step explanation:

$1400 is placed in account with an animal interest-rate of 7.25% to the nearest 10th of a year how long will it take for the account value to reach 4600$

Answers

Answer : 17

Explanation

The variables x and y vary inversely, and x = 12 when y = 6. Use the inverse variation formula, k = xy, to
find y when x = 3.

Answers

Answer:

D=24

Step-by-step explanation:

y inversely as x

x=k/y

By cross multiplication

k=xy

k=12*6

k=72

finding y

72=3y

y=24

The value of y given the inverse proportional relationship between the variables is b24.

What is the inverse proportion?

When two variables vary inversely, as one of the variable increases, the other variable decreases.

The equation that represents inverse proportion : x = k / y

where b = constant of proportionality

k = xy

k = 12 x 6 = 72

y = k / x

72 / 3 = 24

To learn more about inverse proportion, please check: https://brainly.com/question/27233899

A. Without using pencil and paper to actually find the products, how will the product of 3 x 10.6 compare to the product of 2.7 x 10.6? Explain your answer.

B. How will the product of 2.7 X 10.6 compare to the product of 3 X 10.6? Explain your answer.


how do i answer these i forgot all this-​

Answers

Answer:

Step-by-step explanation:

in A , because we are multiplying a number by the same number in each case, 10.6  we know, that the 3  as compared to the 2.7 , will make a bigger number 3*10.6  is greater than  2.7 * 10.6    ,  it's just a quick way to make sure our answer is good

in B,  as above, we know that 2.7*10.6 will be less than 3*10.6      see?

PLEASE HELP!!! ILL GIVE BRAINLIEST !! Which is the correct answer ?

Answers

Answer:

C. Alternate Interior angles.

Step-by-step explanation:

Alternate interior angles are inside parallel lines, and on opposite sides of the transversal line that crosses the parallel lines.

It's not A, because corresponding angles are in the same position on parallel lines. Angles 2 & 6 are corresponding angles. It's not B, because the two are not next to each other, forming a straight line. 6&7 are straight angles, and 5&6 are straight angles.

What is the period of f(x) = sin(x)?
Pi over 2
Pi
3 pi over 2
2 pi

Answers

Answer:

2pi

2pi radians are equal to 360 degrees. After this point, the function f(x) = sin(x) repeats its values again. Each cycle is 2pi radians long.

Step-by-step explanation:

Please help As Soon As Possible

Answers

Answer:

12, sorry if I'm wrong

Step-by-step explanation:

hope it helps

Answer:

Both are correct

Step-by-step explanation:

Tan = Opposite / Adjacent

Tan A = 3/4....... therefore she is correct

Tan C = 4/3........therefore she is also correct

Please mark as brainliest for further answers :)

PLEASE ANSWER ASAP FOR BRAINELST!!!!!!!!!!!!!!!!!!!!! :D
please show work if you can. thank you in advance! (NO LINKS OR YOU WILL BE REPORTED!!!!)

Answers

Answer:

C.

Step-by-step explanation:

Frosted:

6*6*6+10*10*6

This equals 816

Not frosted:

6*6+10*10

This equals 136

Subtract

816-136= 680 sq inches

Decide whether the integral is improper.
[infinity]
â« ln(x3) dx
0

Answers

Answer:

Yes, It is improper.

Step-by-step explanation:

Your answer is correct. The limits of integration are finite. The integrand is not continuous on [1, ∞). At least one of the limits of integration is not finite. The integrand is continuous on [1, ∞).

a) 2x – 7x +3y if x= 3, y= -4
b) y + 3xy if x= 7, y= 5
c) 5x3 + 2y2 if x= 2, y =3

Answers

a) 2(3) - 7(3) + 3(-4)
=6 - 21 + (-12)
=-27
b) (5) + 3(7)(5)
=5 + 105
=110
c) is 3 and 2 an exponent? if so
5(2)^3 + 2(3)^2
=40 + 36
=76

Deena works at a customer service call center. She fields an average of 5 calls per hour. Employees are encouraged to field more
than 200 calls per week Deena has already fielded 75 calls this week.
How many more hours, x, does Deena need to work this week to reach the weekly goal of fielded calls if she continutes to field an
average of 5 calls per hour? Select the inequality that includes the fewest number of hours Deena can work this week and still
reach the weekly goal.

Answers

1. She needs to field 240 calls, but has already done 96. => 240-96=144

2. She fields six calls per hour, and how many hours will it take. This is a hint for division. 144/6=24

3. Therefore, x, where x is the minimum number of hours Deena will need to answer 144 more calls, is at least 144.

4. Answer: c. x>24

Find the missing angle

Answers

Answer:

x+63=90(complementary angle)

x=90-63

x=27

X = 27 both sides need to equal 90 in a angle like this so 27+63=99

Find the slope and y-intercept from the following graph of a linear equation.

Answers

The y intercept is -2

Find the mean for the scores: 3.850; 5,300: 8,540; 4.300; 5,360. ​

Answers

Answer:5470

Step-by-step explanation:The mean is the average of the data collected in the graph.Step one add everthing together which is 3,850+ 5,300+ 8,540+ 4,300+5,360=27,350, Step two divide 27,350 with the total amount of numbers that's in the graph which is 5 if you divide those two number together you will get on average 5,470.

The area of a rectangle is given by the tri nominal y^2+4y-45. If the Length of the rectangle is y+9, what is the width of the rectangle

Answers

Answer:

width = y - 5

Step-by-step explanation:

area = y^2 + 4y - 45

(y + 9)(y - 5)

Distributive property 3x(x - 1)
how do u do this?step by step

Answers

I can’t do this step by step but the answer is 3x^2 -3x

HELP NEEDED ASAP WILL GIVE BRAINLIEST.NO TROLLS

Answers

Answer:

what t f do u need?

Step-by-step explanation:

Answer:

WHATS THE QUESTION

Step-by-step explanation:

$? Kim spent 41/100 ​

Answers

Answer:

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used

Step-by-step explanation:

Answer:

$0.27

Step-by-step explanation:

In total, Kim has .68 cents to spend.

She spend .41 cents.

0.68-0.41=0.27

Therefore, Kim has a total of .27 cents left over.

Please help, brainliest for correct answer

Answers

Answer:

800

Step-by-step explanation:

3/4*3.14*(14/2)^3 = 807.77

Answer:

1435.99 rounded.

Step-by-step explanation:

Remark

Just as a note, you would be better off using 22/7 for pi

Formula

V = 4/3 * pi * r^3

Givens

Pi = 3.14

d = 14 units

Solution

r = d / 2

r = 14/2

r = 7

Volume = 4/3 * 3.14 * 7^3

Volume = 1.3333 * 3.14 * 7^3

Volume = 1.3333 * 3.14 * 343

Volume = 1435.99 rounded to the nearest 1/100 th.

A 14
B 8
C 11
D 20
I'm pose to simplify it ​

Answers

try photo math it shows you the answer
Hopes this helps:

Answer: 11

1. Simplify 3^2 to 9.
9 + 1 • 2


2. Simplify 1 • 2 to 2.
9 + 2


3. Simplify.
11


Ben ate 3/8 of a pizza. The remaining fraction of the pizza is ____​

Answers

Answer:

fnndmd

Step-by-step explanation:

cnbbzbznznzxjjdjdjdkkxkxnxndnxnxnxnnxnxjxjxnxkxkxkkxmxmzmzmzmxmxmbald mfmd

how do you do stuff like 20 x 0.4?? i forgot ​

Answers

Answer: the answer is 8.0

Step-by-step explanation: what i do is 20*4 which is 80 and i just add the decimals back in hoped this helped :))

A food truck at the fair had 24 pies to sell. Each pie was cut into pieces and each piece was cut into 1/8 of a pie. How many pieces of pie did the food truck have to sell?

Answers

Answer:

192

Step-by-step explanation:

Find the exAct length of a line segment whose endpoints are (4,-5) and (6,-2).

Answers

Answer:

Square root of 13

Step-by-step explanation:

distance between two points = under root (x2-x1)^2 + (y2-y1)^2

here, (x1,y1)=(4,-5) & (x2,y2)=(6,-2)

Substitute values and finally you can get it..

No scams. Show your work. write answer as a percent and round the nearest whole number if needed.​

Answers

Answer:

Step-by-step explanation:

we will find the area of the inner circle and then the area of the outer circle and see what the ratio is between those 2

area of a circle = [tex]\pi[/tex][tex]r^{2}[/tex]  (where r is the radius, NOT the diameter, easy to confuse)

the radius of the inner circle is 2.5. which  is half of the diameter of 5

inner circle = [tex]\pi[/tex]*(2.5)^2

inner circle =  19.6349...

outer circle = [tex]\pi[/tex]*(10^2)

outer circle = 314.1592...

the ratio is    19.6349... /  314.1592...  = 0.0625

0.0625 = 6.25%

= 6% ( rounded to nearest whole number )

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