Paul and Karina both collect old Nintendo video games. Paul has 72 video games so far and is collecting four each month. Karina has 120 video games so far and is collecting two each month. After how many months will Paul and Karina have the same number of video games? How many video games will each have?

Answer:

[tex]y=\frac{48}{x}[/tex]

Step-by-step explanation:

When x = 3, y = 16

When x = 6, y = 8

We need to model the inverse variation.

Inverse Variation : When one value increase another value decrease. But product of both always constant.  

[tex]xy=k[/tex]

when x=3, y=16

k=48

When x=6, y=8

k=48

Model of the inverse variation:

[tex]y=\frac{48}{x}[/tex]

Hence, The model of inverse variation is

[tex]y=\frac{48}{x}[/tex]

Answer:

The inverse variation equation can be used to model this function is:

[tex]y=\frac{48}{x}[/tex]

Step-by-step explanation:

An inverse relationship between two variables implies that if the value of one variable increases the value of the other variable will decreases and vice-versa.

The inverse function describing the relationship between x and y is as follows:

[tex]y=\frac{a}{x}[/tex]

Here, a is a constant.

It is provided that when the value of x is 3 the value of y is 16.

Compute the value of a as follows:

[tex]y=\frac{a}{x}[/tex]

[tex]16=\frac{a}{3}\\\\[/tex]

[tex]a=48[/tex]

It is also provided that when the value of x is 6 the value of y is 8.

Compute the value of a as follows:

[tex]y=\frac{a}{x}[/tex]

[tex]8=\frac{a}{6}\\\\[/tex]

[tex]a=48[/tex]

The value of a is 48.

Then the inverse variation equation can be used to model this function is:

[tex]y=\frac{48}{x}[/tex]

Answer:

[tex]3i\sqrt{2}[/tex]

Step-by-step explanation:

If we have the expression [tex]\sqrt{-18}[/tex], we can divide -18 by 2.

[tex]\sqrt{2\cdot-9}[/tex]

The square root of 9 is 3, and since we’re finding the square root of a negative number, we append the “i” to the term: so 3i.

This goes outside the root, making the expression [tex]3i\sqrt{2}[/tex].

Hope this helped!

Answer:

22/15 in fraction 1 7/15

Step-by-step explanation:

Answer:

___________

Exact Form:

22 / 15

Decimal Form:

1.46 continuous

Mixed Number Form:

1 7/15

To write 9/5 as a fraction with a common denominator, multiply by 3/3

9/5 x 3/3 - 1/3

To write −1/3  as a fraction with a common denominator, multiply by 5/5.

9/5 x 3/3−1/3 x 5/5

Write each expression with a common denominator of 15, by multiplying each by a factor of 1

Multiply 9/5 and 3/3

9 x 3/5 x 3 - 1/3 x 5/5

Multiply 5 by 3

9 x 3/15 − 1/3 x 5/5

Multiply 1/3 and 5/5

9 x 3/15 − 5/3 x 5

Multiply 3 by 5

9 x 3/15 − 5/15

Then combine the numerator over the common denominator

9 x 3 - 5 / 15

then simplify the numerator

mutiply 9 by 3

27 - 5/15

subtract 5 from 27

22/15

Answer:

9:15 am

Step-by-step explanation:

Alarms sound at 7:15 am

Alarm frequencies are 40 min and 60 min

Since 40= 20*2 and 60= 20*3, the overlapping frequency is:

So next time both alarms sound at 7:15 am + 2 hours = 9:15 am

Answer:

Trust me its 9:15 am

Step-by-step explanation:

Answer: bus driver

Step-by-step explanation:

Given: Earning of bus driver =  1600 dollars per month

Earning of  manager  = 6800 dollars per month

Amount donated by bus driver = 1200 dollars

Amount donated by manager = 4500 dollars

Percentage of amount donated by bus driver = [tex]\dfrac{1200}{1600}\times100 \%=\dfrac{3}{4}\times100\%=75\%[/tex]

Percentage of amount donated by manager = [tex]\dfrac{4500}{6800}\times100 \%\approx66.18\%[/tex]

Clearly, 75> 66.18

So, bus driver donated  higher percentage of money.

Answer:

- 4

Step-by-step explanation:

The conjugate of - 2 + i is - 2 - i, thus

- 2 + i + (- 2) - i

= - 2 + i - 2 - i ← collect like terms

= - 4 ← in the form a + bi with b = 0

The sum of -2 + i and its complex conjugate is:

w = -4 + 0i

The complex conjugate of a number z = a + bi is:

z' = a - bi.

Then the complex conjugate of -2 + i is -2 - i.

The sum will give:

w = -2 + i + (-2 - i) = -4 + 0

Writing it in the wanted form we get:

w = -4 + 0i

If you want to learn more about complex numbers, you can read:

https://brainly.com/question/10662770

#SPJ2

Answer:

A

Step-by-step explanation:

Think of this always

Whole Numbers > integers > rational numbers > Real numbers

Not all real numbers are whole numbers. It could be and integer like 1.5 which is a real number but not a whole number. So A is lying.

Answer:

The Answer is A.

Step-by-step explanation:

All numbers are real numbers but not all real numbers are a whole. I can't give any further explanation but this is what we were taught when I was younger so it should be correct.

Answer:

SU = 36

Step-by-step explanation:

T is the mid point so the distance of ST and TU is the same. Since ST and TU are the same, 7x + 4 = 10x - 2.

Solve for x

7x + 4 = 10x - 2

7x - 10x = - 2 - 4

-3x = -6

x = 2.

Find SU

SU = ST + TU

= (7x + 4) + (10x - 2)

substitute the value for x into the equation (x=2)

[7(2) + 4] + [10(2) - 2] = 36

I hope this helps :)

Answer: (-7, 7)

Step-by-step explanation:

Answer:

[tex]\mathrm{Solution\:} = (- 7,7) = \mathrm{Last\:}\mathrm{Option\:}[/tex]

Step-by-step explanation:

In my point of view the easiest approach to solving this problem would be by determining the distance between the given points (the midpoint and the other given point) --- (1) and then going through all the answer choices and matching their distance to the midpoint --- (2). This may seem like a hard approach, but you can eliminate many of the answer choices.

The answer is the last choice, so let's prove it.

[tex]\mathrm{Distance\:between\:}\left(1,\:5\right)\mathrm{\:and\:}\left(9,\:3\right) = \sqrt{\left(9-1\right)^2+\left(3-5\right)^2} = 2\sqrt{17}[/tex]

[tex]\mathrm{Distance\:between\:}\left(1,\:5\right)\mathrm{\:and\:}\left(-7,\:7\right)=\sqrt{\left(-7-1\right)^2+\left(7-5\right)^2}=2\sqrt{17}[/tex]

[tex]2\sqrt{17} = 2\sqrt{17}[/tex]

As the distance between points (1,5) and (9,3) respectively (1,5) and (- 7,7) is the same, we proved that our answer is the last choice.

um you need to be more specific on the question bud

Answer: The prime factorization is 3*11*11.

Answer:

The answer is -2 5/14 if you're trying to solve for m

Step-by-step explanation:

first you get rid of the fractions by mutiplying both sides by 4.

4(4m-3/4)=(-9+4m/8)4

16m-3=-36+2m      then you put the varible terms on one side and the numbers on one side

14m=-33

then divide -33 by 14

which will give you the fraction -2 5/14 unless you want decimal form which would be around -2.36

Answer:

[tex]m=-\frac{33}{14}[/tex]

Step-by-step explanation:

[tex]4m-\frac{3}{4}=-9+\frac{4m}{8}[/tex]

[tex](4m-\frac{3}{4})8=(-9+\frac{4m}{8})8[/tex] multiply by 8 to get rid of the largest denominator

[tex]32m-\frac{24}{4}=-72+4m[/tex]

[tex]32m-6=-72+4m[/tex]

[tex]32m-4m=-72+6[/tex] Rearrange the equation and Collect like-terms

[tex]28m=-66[/tex]

[tex]m=-\frac{66}{28}[/tex] simplify

[tex]m=-\frac{33}{14}[/tex]

Answer:

10

Step-by-step explanation:

10. ................ ..........

Answer:

p<5

Step-by-step explanation:

-3(p+1)<-18

-3p-3<-18

+3 +3

-3p<-15

-3p/3<-15/-3

p<5

Answer:

[tex]LS = 63[/tex]

Step-by-step explanation:

Given

[tex]LS = 14x - 21[/tex]

[tex]LH = 15[/tex]

[tex]HS = 8x[/tex]

Required

Determine the length of LS

Since H is between L and S, then

[tex]LS = LH + HS[/tex]

Substitute 14x - 21 for LS, 15 for LH and 8x for HS

[tex]14x - 21 = 15 + 8x[/tex]

Collect Like Terms

[tex]14x - 8x = 21 + 15[/tex]

[tex]6x = 36[/tex]

Divide both sides by 6

[tex]x = 6[/tex]

Substitute 6 for x in [tex]LS = 14x - 21[/tex]

[tex]LS = 14(6) - 21[/tex]

[tex]LS = 84 - 21[/tex]

[tex]LS = 63[/tex]

Hence, the length of LS is 63 units

Answer:  D.gallons

Step-by-step explanation:

Kilogram is a unit of mass

Now, Pounds, Tons and Ounces are also units of mass.

But Gallons is a unit of volume, where 1 gal = 3.785 L

Then you never can represent an amount of mass using units for volume, which means that gallons is incommensurabe with kilograms.

the correct option is D

Answer:

3.02

Step-by-step explanation:

quarters are .25

dimes are .10

nickels are .05

pennies are .01

9 * .25 + 4 * .10 + 7 *.05 + 2 *.01

2.25+0.4+0.35+0.02

3.02

Answer:

25.15 in

Step-by-step explanation:

let's say that x = wide

so x+5.89=length

the perimeter is = 2(width +length)

P=2(x+x+5.89)

108.39=2(2x+5.89)

2x+5.89=54.195

2x=48.305

x=24.1525 in

which is 24.15 in

Answer:

see explanation

Step-by-step explanation:

Using the method of completing the square.

Given

f(x) = x² + 4x - 6

add/subtract ( half the coefficient of the x- term )² to x² + 4x

f(x) = x² + 2(2)x 6 + 4 - 4 - 6

      = (x + 2)² - 10

with m = 2 and n = - 10

To solve the equation let f(x) = 0 , that is

(x + 2)² - 10 = 0 ( add 10 to both sides )

(x + 2)² = 10 ( take the square root of both sides )

x + 2 = ± [tex]\sqrt{10}[/tex] ( subtract 2 from both sides )

x = - 2 ± [tex]\sqrt{10}[/tex]

The positive solution is

x = - 2+ [tex]\sqrt{10}[/tex] ≈ 1.16 ( to 2 dec. places )

Answer:

The distance between L and Y is 15

Answer:

            About 20

           {19 exactly}

Step-by-step explanation:

Evaluate means find approximate value without exact calculation (usually done with great numbers or with fractions)

-8 is approximately -(2+5) so the sum is about 0

34-14 = 30-10 = 20

20 + 0 = 0

The exact calculation would be:

34 -8 - 14 + 2 + 5 = 34 - 14 - 8 + 7 = 20 - 1 = 19

Answer:

#1 N=2

#2 X= -3

#3 V=1, 1 1/2

Answer:

Hey mate!

Using Unitary Method, we get :

2 people -> 5 hours

1 person -> 5/2 = 2.5 hours

3 people -> 2.5 hours * 3 peoples

-> 7.5 hours

-> 7.5 * 60 = 450 mins.

Answer:

3 people can plow a field in 450 minutes.

Step-by-step explanation:

This is a rate/ratio problem, so we have to make sure it's fully simplified.

First, you already know the ratio is 2 people can plow a field in 5 hours, so 2:5.

But that's not the unit rate.

To find the unit rate, you find how much an individual by itself can do their work, and divide numerator by denominator.

In this case, you do 5/2: which is 2.5.

It take's 2.5 hours for one person. Now you multiply by 3 people to get the ratio; since you already found the rate.

2.5x3 is 7.5, and that's in hours. 1 hour is 60 minutes, to find 7 hours, you do 60x7 and get 420 minutes. You add 30 minutes from the remaining half hour.

that results in 450 minutes.

3 people can plow a field in 450 minutes.

Answer:

The code is 571113

Step-by-step explanation:

The problem requires that we find the prime factors of 5005

1. 5005 is a multiple of 5 since it ends with a number 5

5 is one of the numbers

Dividing 5005/5 = 1001

the next prime number after 5 is 7

so 1001/7= 143

7 is one of the numbers

the next prime number after 7 is 11

so 143/11= 13

13 is one of the numbers

In all the prime factorization of 5005 is found as follows

5,7 11,13

Combining these numbers gives the 6 digit code

571113

Domain: (-∞,∞)

Range: (3,∞)

x-intercepts: none

y-intercepts: (0,7)

Interval positive: (3,∞)

Interval negative: none

Interval increasing: (7,∞)

Interval decreasing: (-∞,7)

I'm not sure what the average rate of change over is though.

Answer:

7 times greater

Step-by-step explanation:

This is because 84 divided by 12 is 7, so i guess that is your answer.

hope this helps

Answer:

The value of f(0) is Option (A) : - 2

Step-by-step explanation:

Hey, there!

As it is a Right angled triangle, taking reference angle as angle B.

hypotenuse (h)= AB

perpendicular (p)= 12

base (b)= 24.

Now, let's look which ratio can be used here as p and b are given. Let's use tan ratio here.( as tan = p/b)

[tex] \tan(theta) = \frac{p}{b} [/tex]

[tex]tan(theta) = \frac{12}{24} [/tex]

[tex] \tan(theta) = \frac{1}{2} [/tex]

or, tan theta = (0.5)

Shifting tan to right side making it inverse.

or, theta = tan inverse (0.5)

Therefore, theta = 26.56° or 27° { by rounding off 26.56° we get 27°}.

Hope it helps......

Answer:

Casy

Step by step explanation:

You divide the miles by their time

It took Jessica 6 minutes and .03 seconds to finish a mile

It took Casy 5 minutes and 54 seconds to finish a mile

Casy is .09 Seconds quicker than Jessica

Answer:

-4, 4

Step-by-step explanation:

it seems the most reasonable answer since the dot is not super close to the 6, 6 and it isnt close enough to be 1, 5 or 5, 1 so the answer must be -4, 4

Answer:

141  5/7

Step-by-step explanation:

8c + 10b ÷ 7a

Let c = 7, b = 12, and a = 5

8*7 + 10*12 ÷ 7*5

Multiply and divide from left to right

56+120 ÷7*5

56+ 600/7

Get a common denominator

392/7 + 600/7

992/7

Change from an improper fraction to a mixed number

141  5/7

Answer:

    416                    3

=  --------    or   59 ----

       7                     7

Step-by-step explanation:

8c + 10b ÷ 7a

if c = 7, b = 12, and a = 5

plug in values:

= 8(7) + 10(12) ÷ 7(5)

= 56 + 120 / 35

= 56 + 24/7 ---- convert into factions

  56 * 7      24

=  --------  + ------

        7         7

sine the denominator are equal, combine the fraction

    56 * 7 + 24

=  -----------------

             7

    416                    3

=  --------    or   59 ----

       7                     7