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elixir [45]
2 years ago
12

If y varies inversely with x, and y = -3 when x = 18, find x when y = -2

Mathematics
1 answer:
Ira Lisetskai [31]2 years ago
8 0

Answer:

The correct answer would be 12, which isn't one of your options.

Step-by-step explanation:

When finding direct variation, you start with the base equation.

y = kx

Now we can use the initial values of x and y to find k.

-3 = k(18)

-1/6 = k

Now with the value of k, we can model the equation.

y = -1/6x

And we can find the new x by using our new value of y.

-2 = -1/6x

12 = x

You might be interested in
Distance between (-6, -2) and (0,-1)
s344n2d4d5 [400]

Hey there! I'm happy to help!

To find the distance between two points, you square the difference of the x-values and square the difference of the y-values, add them, and then you square root it!

First, we'll add our two x-values.

-6-0= -6

We square it, which means to multiply it by itself.

-6(-6)=36        (If you multiply an even number of negative numbers, your answer is positive. Since we have two negative numbers, we get positive 36)

Now, we do the same with the y-values.

-2-(-1)=-1           (two negatives make it a plus, as in minus minus 1 is plus one.)

We square it.

-1(-1)=1              

Now, we add these x and y value differences.

36+1=37

Now, we find the square root using a calculator.

√37≈6.08

Have a wonderful day!

5 0
3 years ago
An individual is planning a trip to a baseball game for 16 people. Of the people planning to go to the baseball game, 8 can go o
Sedaia [141]

Answer: There are 4 people who only go to the game on Saturday.

Step-by-step explanation:

Let the number of people go on Saturday be n(A).

Let the number of people go on Sunday be n(B).

Since we have given that

n(A) = 8

n(B) = 12

n(A∪B)  = 16

According to rules, we get that

n(A)+n(B)-n(A\cap B)=n(A\cup B)\\\\8+12-n(A\cap B)=16\\\\20-n(A\cap B)=16\\\\n(A\cap B)=20-16=4

So, n(only go on Saturday) = n(only A) = n(A) - n(A∩B) = 8-4 = 4

Hence, there are 4 people who only go to the game on Saturday.

4 0
3 years ago
Find the product.<br><br> (-3ab2)3<br><br> -27 a3b6<br> -9 a3b5<br> -23 a2b2<br> 27 ab
7nadin3 [17]

Answer:

a) -27 a³ b⁶

Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given ( -3 ab² )³

By using  (ab )ⁿ = aⁿ bⁿ      

   ( -3 ab² )³ = (-3)³ a³ (b²)³

Again , using formula   (a^{m} )^{n} = a^{mn}

                    =   -27 a³ b⁶

6 0
2 years ago
PLEASE HELP! 100 POINTS!
BartSMP [9]

Answer:

Mrs. Etercsid

Step-by-step explanation:

One thing we can do is just multiply the averages by the percents in each class and compare from there.

To get from percentages to decimals, we can divide by 100.

For Mr. Tats:

Homework: 25 % -> 0.25

Participation: 10% -> 0.1

Test: 40% -> 0.4

Final: 0.25 -> 0.25

For Mrs. Etercsid:

Homework: 15% -> 0.15

Participation: 10% -> 0.1

Test: 60% -> 0.6

Final: 15% -> 0.15

We can then multiply the averages by the decimals for each teacher and add them up.

Mr. Tats:

0.25 * 81 + 0.1 * 57 + 0.4 * 93 + 0.25 * 87 = 84.9

Mrs. Etercsid:

0.15 * 81 + 0.1 * 57 + 0.6 * 93 + 0.15 * 87 = 86.7

You would get the higher grade with Mrs. Etercsid

7 0
2 years ago
An open box with a square base is to have a volume of 18 ft^3.
kotegsom [21]

Answer:

2.29 ft of side length and 1.14 height

Step-by-step explanation:

a) Volume V = x2h, where x is side of square base and h is hite.

Then surface area S = x2 + 4xh because box is open.

b) From V = x2h = 6 we have h = 6/x2.

Substitude in formula for surface area: S = x2 + 4x·6/x2, S = x2 + 24/x.

We get S as function of one variable x. To get minimum we have to find derivative S' = 2x - 24/x2 = 0, from here 2x3 - 24 = 0, x3 = 12, x = (12)1/3 ≅ 2.29 ft.

Then h = 6/(12)2/3 = (12)1/3/2 ≅ 1.14 ft.

To prove that we have minimum let get second derivative: S'' = 2 + 48/x3, S''(121/3) = 2 + 48/12 = 6 > 0.

And because by second derivative test we have minimum: Smin = (12)2/3 + 4(12)1/3(12)1/3/2 = 3(12)2/3 ≅ 15.72 ft2

5 0
2 years ago
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