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

Class intervals in a grouped frequency distribution are given as 4−11, 12−19, 20−27, 28−35, 36−43. Write the next two class intervals.
i) what is the each class interval?
ii) write the class boundaries of all classes?
iii) what are the class marks of each class?​

Answers

Answer:

{44-55}{52- 59 } are the last two interval s

Step-by-step explanation:

To get the class boundaries deduct 0.5 from the first number and add 0.5 to the second number = 4-0.5 = 3.5 = 11.5 + 0.5 = 11.5 = 3.5 -11.5 as in the fish class boundary .same for all other boundaries

What is the area of the school crossing sign represented below?
15 inches 15 inches
15 inches
15 inches
help me plsss

Answers

C. 675 square inches

Sanjay surveyed 95 students at his school about their favorite class. Of the students surveyed, 19 said their favorite was Spanish. What is the experimental probability that the next student Sanjay talks to will pick Spanish?

Answers

Answer:

0.2 = 20% experimental probability that the next student Sanjay talks to will pick Spanish

Step-by-step explanation:

Probability:

A probability is the number of desired outcomes divided by the number of total outcomes.

It is called experimental when both these number of outcomes come from experiences, from a trial, as is the case in this exercise.

What is the experimental probability that the next student Sanjay talks to will pick Spanish?

19 out of 95. So

p = 19/95 = 0.2

0.2 = 20% experimental probability that the next student Sanjay talks to will pick Spanish

no the correct answer is gonna be 1/5

A salesman is paid $15.00 per hour for 7 hours plus $9.00 for each sale, x, she makes. She wants to earn more than $150.

Which inequality matches the situation?

Answers

Answer:

what are the options???

The periscope of a submarine is at sea level. The boat captain spots an airplane with
an elevation angle of 30°. The airplane is flying at an altitude of 2000 feet.

The straight line distance between the submarine and the airplane is...

Answers

Answer:

The airplane is 100.4 flying at an altitude of 30,000 feet. AB = 210,000 feet. At what angle is the plane descending (the angle of depression)?. Above is a picture of astronauts ...

7 pages·477 KB

The straight line distance between the submarine and the airplane is 4000 feet.

What is trigonometric ratio?

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let d represent the straight line distance between the submarine and the airplane. Hence:

sin(30) = 2000/d

d = 4000 feet

The straight line distance between the submarine and the airplane is 4000 feet.

Find out more on trigonometric ratio at: https://brainly.com/question/24349828

What is the absolute value of 8.15

Answers

Answer:

pretty sure its 8.15

Step-by-step explanation:

4x + 7y - 3x - y show work please

Answers

Answer:

Step-by-step explanation:

4x + 7y - 3x - y

Move like terms next to each other.

4x - 3x + 7y - y

Subtract them

4x-3x= 1x or x

7y-y = 6y

So we have:

x + 6y

the initial deposit into an account?
a. compound interest
b. simple interest
c. interest rate
d. principal

Answers

Answer:

B

Step-by-step explanation:

Simple interest is based on the principal amount of a loan or deposit.

Solve for x using
cross multiplication.
x 1 = 2x + 4 5
x = [?]

Answers

Answer:

x = -7

Step-by-step explanation:

Given:

[tex] \frac{x - 1}{4} = \frac{2x + 4){5} [/tex]

Required:

Find x using cross multiplication

Solution:

Cross multiply

(2x + 4)*4 = (x - 1)*5

8x + 16 = 5x - 5

Collect like terms

8x - 5x = -16 - 5

3x = -21

Divide both sides by 3

x = -21/3

x = -7

If a dozen dozen candies cost a half-a-dozen dimes a dozen, how much will a half-a-dozen dozen candies cost?

Answers

Answer:

74

Step-by-step explanation:

The cost of half-a-dozeon dozen candies for this case will be $3.6

How much a dozen consists of ?

A dozen of a thing means 12 of such thing is in consideration. If we say we have a dozen pencils, then twe mean we have 12 pencils.

For this case, it is given that:

Cost of a dozen dozen candies = half a dozen dimes a dozenCost of a half a dozen dozen candies = ? (to find)

A dozen contains 12 quantities.

A dozen dozen candies means 12 times 12 = 144 candies

half a dozen dimes dozen cost = (12/2) × 12 dimes = 72 dimes

That means:

144 candies cost 72 dimes.

Dividing both quantities by 144 to get price of 1 candy:

144/144 = 1 candy's price = 72/144 dimes = 0.5 dimes = 0.05 dollars (1 dime = 0.1 dollars)

Half a dozen times dozen candies = 72 candies

1 candy costs 0.05 dollars

72 candies cost [tex]72 \times 0.05 = 3.6[/tex] dollars.

Thus, the cost of half-a-dozeon dozen candies for this case will be $3.6

Learn more about forming equations here:

https://brainly.com/question/11938672

Solve for x.
Enter the solutions from least to greatest.
(2x + 4)(3x − 2) = 0
lesser x =
greater x =

Answers

Answer:

lesser x = -2, greater x = 2/3

Step-by-step explanation:

(2x+4)= 0 ---> bring 4 to the other side

2x=-4 ----> divide by 2 on both sides

x= -4/2 = -2 ----> simplify

(3x-2)= 0 ----> bring the 2 to the other side

3x=2 ----> divide by three on both sides

x=2/3

hope this helps!

5(x + 2) = 5x + 10 is an example of the property?.​

Answers

Answer:

Distributive property

Step-by-step explanation:

During the Falcons game, Julio Jones ran a straight route 40 yards up the sideline before turning around and catching a pass from Matt Ryan. Defender, Malcolm Butler, who started 20 yards across the field from Jones, saw the play setup and ran horizontally toward the receiver. What was the distance the defender had to run to get to the spot where Jones caught the ball? (PLS DONT GIVE WEBSITE PLS JUST ANSWER)

Answers

Answer:

its 20 because he ran 20 from jones

50 POINTS!! URGENT !! PLS HELP

Answers

Answer:

Option C

Step-by-step explanation:

The two triangles will be similar if the ratio of their corresponding sides are proportional. Let's check this ,

1st side :-

= 8:3

2nd side :-

= 10 : 4 = 5:2

3rd side :-

= 6:5 .

Since the ratio of the sides of triangle are not same therefore that 2 triangles are not similar .

Option C is correct .

A nurse administers 25 milligrams of a drug to a patient. The amount of the drug, A, in milligrams, left in the patient after thours can be modeled by the function A(t) = 25e 0.354
How many hours will it take for the amount of the drug left in the patient to drop to 0.25 milligrams? Round your answer to the nearest tenth of an hour.
hours
Pls helppp

Answers

Answer:

heyy guyss how r u all I'm Aditya from. India I've changed my server to Ireland is this Ireland

Step-by-step explanation:

and plss guyss fo llo w me

How many, and what type of solutions, does 6x squared - 2x + 7 = 0 have

Answers

Answer:

the correct answer is 2 no real solurions hope this helps

what is 91,360 in expanded form

Answers

Answer:

Expanded Notation Form:

 91,360 =

 90,000  

+ 1,000  

+ 300  

+ 60  

+ 0  

Expanded Factors Form:

   91,360 =

 9 × 10,000  

+ 1 × 1,000  

+ 3 × 100  

+ 6 × 10  

+ 0 × 1  

Expanded Exponential Form:

 91,360 =

9 × 104

+ 1 × 103

+ 3 × 102

+ 6 × 101

+ 0 × 100

Word Form:

91,360 =

ninety-one thousand three hundred sixty

Hope this helps! mark me as brainliest if possible, you dont have too!

Step-by-step explanation:

A vehicle purchased for $29,800 depreciates at a constant rate of 4%. Determine the approximate value of
the vehicle 10 years after purchase. Round to the nearest whole dollar.

Answers

Answer:

$44104

Step-by-step explanation:

Given data

Cost = $29800

Rate= 4%

Time= 10years

Applying the formula below, we can find the cost after 10 years as

A=P(1+r)^t

A= 29800(1+0.04)^10

A=29800(1.04)^10

A=29800*1.480

A=$44104

Hence the new cost is $44104

Find the scale factor used to go from the actual picture to the scale drawing!

Answers

Answer:

1/3

Step-by-step explanation:

9:6

3:2

9/3 = 3

6/2 = 3

9 x (1/3) =  3

6 x (1/3) = 2

scale factor is 1/3

Graph this function.

F(x)= -1/3x + 8

I need help ASAP! The -1/3x is a fraction. Can anyone help?

Answers

Step-by-step explanation:

Rewrite the function as an equation.

[tex]y = - \frac{x}{3} + 8[/tex]

Rewrite in slope-intercept form.

[tex]y = - \frac{1}{3} x + 8[/tex]

Use the slope-intercept form to find the  slope  and  y-intercept.

Slope : - 1/3

y-intercept: (0,8)

Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.

Graph the line using the slope and the y-intercept, or the points.


The graph of a linear function
is shown on the grid.
What is the rate of change of y with respect to x for this function?
Record your answer in the space below.

Answers

Rate of change is Y= -.5x +5
If the slope (-.5) needed to be a decimal it would be -1/2
The y value is 5

Enter a value of b that will make the expression factorable.
x2^ + bx – 40

Answers

B would be 6
X^2+6x-40
(x-4)(x+10)

What is the product of (t – 4) (t? + 2t - 6)?

Answers

Answer:

Step-by-step explanation:

(t - 4) (t + 2t - 6)

= t2 + 2t2 - 6t - 4t - 6t + 24

= Solving like terms

= 3t2 - 16t + 24

PLEASE HELP!!! i’m mid test
Question 16
Round to the nearest tenth, if necessary.
Find the distance between (4, 16) and (12, 27).

Answers

the answer should be 13.6 in decimal form

Answer:

[tex]\sqrt{185}[/tex] or 14 (13.6)

Step-by-step explanation:

Compute the distances between

[tex]\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

The distances between ↑ are

[tex]\sqrt{\left(12-4\right)^2+\left(27-16\right)^2}[/tex]

Simplify

[tex]\sqrt{185}[/tex] or 14

hope this helps

~R3V0

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following results. T
oday 5 Years Ago Mean 82 88 Variance 112.5 54 Sample Size 45 36
The standard deviation of the difference between the means of the two populations is
A) 12.9
B) 9.3
C) 4
D) 2

Answers

Answer: D) 2

Step-by-step explanation:

The standard deviation of the difference between the means of the two populations is given by:-

[tex]S.E.=\sqrt{\dfrac{\sigma^2_1}{n_1}+\dfrac{\sigma^2_2}{n_2}}}[/tex]

where [tex]n_1[/tex]= sample size of population 1

[tex]n_2[/tex]= sample size of population 2

[tex]\sigma^2_1[/tex]= variance of population 1

[tex]\sigma^2_2[/tex]= variance of population 2

As per given,

[tex]S.E.=\sqrt{\dfrac{112.5}{45}+\dfrac{54}{36}}}\\\\=\sqrt{4}\\=2[/tex]

Hence, the correct option is D) 2.

HELP TIMED URGENT PLS

Answers

Answer:

3 cm!

Step-by-step explanation:

Volume= length times width times height

90/3=30

30/10=3!

How do I solve this?​

Answers

9514 1404 393

Answer:

  b=-9

  intersection point (3, -3)

Step-by-step explanation:

There are a couple of ways to do this. The method that does not involve calculus is to set the two equations equal and find 'b' such that there is exactly one solution.

  x^2 -4x = y = 2x +b

In standard form, this is ...

  x^2 -6x -b = 0 . . . . . . . we call this the "combined quadratic"

This will have one solution when the discriminant is zero. You may recall that the discriminant of quadratic ax^2 +bx +c is d = (b^2-4ac). We want ...

  d = (-6)^2 -4(1)(-b) = 0

  36 +4b = 0 . . . . . simplify

  b = -36/4 = -9 . . . solve for b

Then the linear equation is ...

  y = 2x -9

__

If the discriminant is zero, the solution to the "combined quadratic" is ...

  x = -b/(2a) . . . . . . . . with a, b, c from the quadratic form (not y-intercept)

  x = -(-6)/(2(1)) = 3

And the point of intersection of the line and the parabola is ...

  y = 2(3) -9 = -3   ⇒   (x, y) = (3, -3)

__

The graph is attached.

A box of 15 cookies cost nine dollars what is the cost for one cookie

Answers

Answer:

9:15 = 0.6

answer : 0,6

.............

Let f(x) = 9 – x g(x) = 3 – x. Find (f – g)(x)

Answers

Answer:

Step-by-step explanation:

Remark

This would be easier to understand if it was written like f(x) - g(x). You might see what the question really is.

Equation

(f - g)x = f(x) - g(x)

Solution

(f - g)x = 9 - x - (3 - x)                       remove the brackets

(f - g)x = 9 - x - 3 + x

(f - g)x = 6

Are these triangles similar? If yes, write a similarity statement.

Answers

Yes because they both have the same degrees, but one is slightly rotated
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