y varies inversely x and y =-4 when x =7 . find the constant of variation and use it to write the equation that relates the variables

Answers

Answer 1

When y varies inversely with x, we have the follow equation:

y = kx

k = constant of variation

To find k, plugin the values for y = -4 and x = 7 and then solve for k

y = kx
-4 = k7
-4 / 7 = k7/7
-4 / 7 = k
k = -4 / 7
Now that we found k, we write the equation that relates the variables like below
[tex]y = -\frac{4}{7}x[/tex]

Related Questions

A series contains 18 numbers and has a sum of 4,185. The last number of the series is 275. What is the first number?

Answers

The sum of arithmetic series is given by:
Sn=n/2(a1+an)
where:
n=number of terms
a1=first term
an=nth term
but
n=18, an=275, Sn=4185
plugging the values in the formula we get:
4185=18/2(a1+275)
simplifying this we get:
4185=9(a1+275)
dividing through by 9 we get:
465=a1+275
thus
a1=465-275
a1=190

Answer: first number is 190

Answer:

B on edge 190

Step-by-step explanation:

The exponential function represented by the table can be written in the form y=ab^x. Find the values for a and b.

Answers

If this function can be written in the form y = ab^x, then we see that when x is inputted as 0, y is outputted as 4. This means that
                                          4 = ab^0
                                          a = 4
The value of a is 4.
We see that when x = 1, y = 2 thus
                                           y = 4b^x
                                          2 = 4(b^1)
                                          b = 1/2
The answers are a = 4 and b = 1/2

The exponential function gotten from the table is given by y = 4(1/2)ˣ

Exponential function

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multipliers.

From the table, at point (0, 4):

4 = ab⁰a = 4

At point (3, 1/2):

y = abˣ1/2 = 4b³b = 1/2

The exponential function gotten from the table is given by y = 4(1/2)ˣ

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A certain country's postal service currently uses 6-digit zip codes in most areas. how many zip codes are possible if there are no restrictions on the digits used? how many would be possible if the first number could not be 0?

Answers

If any digit can be 0 to 9 with no restrictions, the number of possible zip codes is ...
10×10×10×10×10×10 = 10⁶ = 1,000,000.

Final answer:

For a 6-digit zip code with no restrictions, there would be 1,000,000 possible zip codes. If the first digit could not be a '0', the number of possible zip codes would decrease to 900,000.

Explanation:

We're dealing with a counting problem here. This problem involves basic principles of combinatorics.

Firstly, if there are no restrictions on the digits used, each of the six positions in the zip code can hold any digit from 0 to 9. There are 10 choices (from 0 to 9) for each of the 6 digits in the zip code which leads to 10^6 = 1,000,000 possible zip codes.

However, if the first number could not be 0, there are 9 possible choices for the first digit and 10 choices for each of the remaining 5 digits. Therefore, the number of possible zip codes would be 9 * 10^5 = 900,000.

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Which of the following sets shows all the numbers from the set {0, 0.5, 1, 2.5, 3} that make the inequality 2a + 3 ≥ 8 true?
{2.5, 3}
{1, 2.5, 3}
{0, 0.5, 1}
{0.5, 1}

Explain how you got your answer
PLEASE AND THANK YOU

Answers

It’s A because I used a calculator

Answer: A

Step-by-step explanation:

function is a line points (3,2), (5,8), and (8,y) what is y

Answers

y = mx + b

[tex](3;\ 2)\to x_1=3;\ y_1=2\\\\(5;\ 8)\to x_2=5;\ y_2=8\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\to m=\dfrac{8-2}{5-3}=\dfrac{6}{2}=3[/tex]

Therefore we have: y = 3x + b.

Put the coordinates of the point (3; 2) to the equation of the line:

[tex]2 = 3\cdot3+b\\2=9+b\ \ \ |-9\\b=-7[/tex]

Therefore we have: y = 3x - 7

Substitute the coordinates of the point (8; y) to the equation of the line:

[tex]y = 3\cdot8-7=24-7=17[/tex]

Answer: y = 17.

To test upper h 0 : mu equals 72 versus upper h 1 : mu less than 72, a simple random sample of size nequals20 is obtained from a population that is known to be normally distributed, and the sample standard deviation is found to be 6. complete parts (a) and (b) below.

Answers

We solve using equation [tex] \beta \sqrt{x} \sqrt[n]{x} \lim_{n \to \infty} a_n \alpha [/tex]⇔ ∈ ω. ㏒

2(3y-1)3(y-4)=13 please show step by step

Answers

[tex]2(3y-1)+3(y-4)=13\\\\2\cdot3y+2\cdot(-1)+3\cdot y+3\cdot(-4)=13\\\\6y-2+3y-12=13\\\\\underbrace{6y+3y}_{9y}\underbrace{-2-12}_{-14}=13\\\\9y-14=13\ \ \ |\text{add 14 to the both sides}\\\\9y=27\ \ \ |\text{divide both sides by 9}\\\\\boxed{y=3} [/tex]

Evaluate log416 -2 1/2 2

Answers

16 = 4²

So, by the definition of logarithms

[tex]\log_4{16}=2[/tex]

A real estate broker sold your house for $189,000. The broker's commission was 4.5 percent of the selling price. How much would you get for the house after the commission is paid?

Answers

First, we are going to find the commission of the broker. To do that we are going to multiply the selling price of your house by 4.5 percent:
[tex]189000*[/tex]4.5%=[tex]189000* \frac{4.5}{100}=8505 [/tex]

Next we are going to subtract the broker's commission ($8505) from the selling price of your house:
[tex]189000-8505=180495[/tex]

We can conclude that you will get $180,495 from your house after the commission is paid.

Which conversion requires multiplication? Use the metric table to help answer the question.

Answers

Any conversion that goes down to a smaller value

Ex: Kilometer to meter will be x1000
meter to centimenter is x100

BUT going up will be division
Meter to kilometer is /1000

Answer:

centimeters to kilometers

Step-by-step explanation:

At a college, 4/5 of the students take an English class. Of these students, 5/6 Composition. Which fraction of the students at the college take Composition?

Answers

If I’m doing it correctly it’s 2/3 but I haven’t done it in a while

Final answer:

The fraction of students who take Composition at the college is 2/3.

Explanation:

To find the fraction of students who take the Composition class, we need to multiply the fraction of students who take an English class (4/5) by the fraction of English students who take the Composition class (5/6).

Multiplying these fractions, we get (4/5) * (5/6) = 20/30 = 2/3.

Therefore, 2/3 of the students at the college take Composition.

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If 75 capsules of a drug cost $60, what would 40 capsules of the same drug cost?

Answers

75 capsules = $60

1 capsule = 60 ÷ 75 = $0.80

40 capsules = $0.80 x 40 = $32

Answer: $32

You’re getting riped of for that price

What is 3km 9hm 9dm +7km 7dam

Answers

3+9+9+7+7=36
Good night hope thid helps

using conversion

let km be the base unit

9 hm = 0.9km
9 dm = 0.0009 km
7 dam = 0.07km

adding all of the values

3 + 0.9 + 0.00009 + 7 + 0.07 = 10.97009

Coco's garden has 888 tomato plants, 444 pepper plants, 333 squash plants, and 666 pumpkin plants.
For every 777 plants in Coco's garden, there are 2_____ plants.

Answers

8 + 4 + 3 + 6 = 21There are 21 plants altogether.21 is 3 times 7.For every 21 plants there are 6 pumpkin plants, sofor every 7 plants, there are 2 pumpkin plants.

find the center and radius of the circle (x+8)^2+(y-2)^2=25

Answers

The circle equation is in the format: (x – h)^2 + (y – k)^2 = r^2
The center is at the point (h,k) and the radius is r

In the equation (x+8)^2+(y-2)^2=25,

Center = (-8, 2)
Radius = 5

Hope this helps. :)

The students at Porterville Elementary sold raffle tickets, each for the same price, for a fundraiser. The equation below shows how much money was raised with the tickets sold. $1,760 = $20t. What is the unit rate in the equation above?

Answers

The "unit rate" appears to be $20 per ticket.

Select whether the number is rational, irrational, or imaginary. 1/4

Answers

Hey there!

The correct answer should be rational.

Hope this helps!

The value of number 1 / 4 is a Rational number.

What is Rational number?

A number which can be written in the form of fraction p / q , where q is non zero, are called Rational numbers.

We have to given that;

The number is,

⇒ 1 / 4

Now, Number 1 / 4 is of the form p / q (fraction form).

Hence, We can say that;

The value of number 1 / 4 is a Rational number.

Thus, It is a Rational number.

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this is not a question i just need someone to make sure i did #16 right. Thanks;)

Answers

I think the length of pool in inches is actually 12*12=144 because there are 12 inches in a foot.
Also, the scale factor would be 144/16 = 9.

1 foot = 12 inches
so length of pool = 12 inches x 12 feet = 144 inches

144 /16 = 9
so the scale factor would be 1:9
which means the blueprint is 9 times smaller than the real pool

change -115 degrees to radian measure in terms of pi

Answers

-23\pi/36 or -115\pi/180.

In order to find this, you need to take the degrees [ in this case -115 ] and multiply that by \pi/180. Then simplify that result if possible.

Hope this helps!

Answer:

-23/36 pi

Step-by-step explanation:

(-115 x pi) / 180

hey can you please help me posted picture of question

Answers

The points in the graph that will intersecr in the x axis would be 0. It has no points since it just involves a y axis line and ita pointa do not pass in the x axis. So the best and most correct answer is B. 0.

The nature of roots can help us to determine the answer to this question and discriminant can be used to determine the nature of the roots.

Discriminant = b² - 4ac

b = coefficient of x term = -9
a = coefficient of squared term = 4
c = constant term = 9

So, Discriminant = 81 - 4(4)(9) = -63

Since, the discriminant is negative, the equation will have complex zeros.This means its graph will not cross x-axis at any point.

So, the answer to this question is zero, option B

the quotient of a number and 9 is equal to the same number decreased by 40. what is the number

Answers

Quotient is the result of dividing two numbers.

x= the unknown number

The equation is x divided by 9 equals x minus 40.

x/9= x - 40
multiply both sides by 9

(9)(x/9)= (9)(x - 40)
x= 9x - 360

subtract 9x from both sides
-8x= -360

divide both sides by -8
x= 45

ANSWER: The number is 45.

Hops this helps! :)

Help me please!! I wanna make my mother proud>3

Find the product.

4(−12)(−3)
A) −144
B) −96
C) 144
D) 72

Answers

I believe it's C.

Hope this helps!

a) learn to use your calculator

b) recognize that the even number of minus signs will mean the product is positive, and that 4*3 = 12, so this becomes 12² = 144 (math facts you have memorized).

The appropriate choice is ...
C) 144

what is the best estimate for the total weight of these cold meat 1 7/8 lb of Bologna 1 and 1/2 pounds of ham and 7/8 lb of roast beef

Answers

well, it seems to be just a sum of all quantities, now let's firstly convert the mixed fractions to "improper"and then add them up,

[tex]\bf \stackrel{mixed}{1\frac{7}{8}}\implies \cfrac{1\cdot 8+7}{8}\implies \stackrel{improper}{\cfrac{15}{8}} \\\\\\ \stackrel{mixed}{1\frac{1}{2}}\implies \cfrac{1\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{3}{2}}\\\\ -------------------------------\\\\ \cfrac{15}{8}+\cfrac{3}{2}+\cfrac{7}{8}\quad \stackrel{LCD~8}{\implies }\quad \cfrac{15+12+7}{8}\implies \cfrac{34}{8}\implies \stackrel{simplified}{\cfrac{17}{4}}\implies 4\frac{1}{4}[/tex]

What is the slope of the line y = 3?

Answers

The slope of a line y = any constant real number is 0.

This is because the equation y = a number represents a straight horizontal line on a graph.

PLZ HELP NOOOOW!!

Sarah ran around a track 1 1/2 times. The track in 3/4 of a mile long.

How many miles did Sarah run?

Answers

Hey there! The answer is 1 1/8 mile.

To find the amount of miles Sarah ran, we need to multipy the length of the track by the times she run that distance.
[tex]1 \frac{1}{2} \times \frac{3}{4} = \frac{3}{2} \times \frac{3}{4} = \frac{9}{8} = 1 \frac{1}{8} [/tex]

Rembember: multiplying a fraction means you have to multiply the numerator by the numerator (of the other fraction) and the denominator by the denominator (of the other fraction)

The answer is 1 1/8 mile.
~ Hope this helps you!

Which ordered pair is the best estimate for the solution of the system of equations? y=−12x+4y=12x−3 (7, 1) (7, 0) (7, 0.5) (7.5, 0.5)

Answers

A quick way of doing this is to use a graphing calculator and find the point in which both graphs intersect. Another way of doing this is to substitute. Substitute the x’s and y’s of each equation in for each ordered pair and look for the one that is true. Though what’s confusing me is that, the solution is (0.3,0.5).

ANSWER

[tex](7,0.5)[/tex]

EXPLANATION

We want to solve the system;

[tex]y = - \frac{1}{2} x + 4...(1)[/tex]
and

[tex]y = \frac{1}{2} x - 3...(2)[/tex]

Add equations (1) and (2) to get,

[tex]y + y = 4 + - 3[/tex]

This implies that,

[tex]2y = 1[/tex]

[tex]y = \frac{1}{2} [/tex]

or

[tex]y = 0.5[/tex]

We put y=½ into equation (2) to get,

[tex] \frac{1}{2} = \frac{1}{2} x - 3[/tex]
Multiply through by 2 to get,

[tex]1 = x - 6[/tex]
This implies that,

[tex]x = 1 + 6 = 7[/tex]

Therefore the best estimate for the system of equations is
[tex]
(7,0.5)[/tex]
The correct answer is C

Diana uses 30 grams of coffee beans to make 48 fluid ounces of coffee. How many grams of coffee beans foes Diana uses when company comes?

Answers

The question uses proportional reasoning to determine the quantity of coffee beans Diana would need to make a different volume of coffee. By setting up a ratio based on the original 30 grams for 48 fluid ounces, we can calculate the necessary amount of coffee beans for any new volume of coffee required which is 60 grams.

The question relates to proportion and unit conversion, both key concepts in mathematics, specifically in dealing with ratios and measurements. Diana uses 30 grams of coffee beans to make 48 fluid ounces of coffee. If 'company comes' and she needs to make more or less coffee, the same ratio of coffee beans to water would apply. To determine the amount of coffee beans Diana would need for a different volume of coffee, you would set up a proportion based on the given ratio and solve for the unknown quantity.

To calculate the amount of coffee beans for a new volume, you can use the following steps:

Determine the new volume of coffee in fluid ounces.

Set up a ratio comparing 30 grams of coffee beans to 48 fluid ounces.

Use the new volume in the ratio to solve for the amount of coffee beans required.

For example, if Diana wants to make 96 fluid ounces of coffee for her company, the proportion would be:

30 grams / 48 fluid ounces = X grams / 96 fluid ounces

Solving this gives us X = (30 grams * 96 fluid ounces) / 48 fluid ounces = 60 grams. Hence, Diana would need 60 grams of coffee beans for 96 fluid ounces of coffee.

It costs $0.05 to send a text message and $0.10 to send a picture on your cell phone. You spend $4 and send five more text messages than pictures. How many text messages, x, and pictures, y, did you send?

Answers

The first thing we must do for this case is to define variables:
x: text messages
Y: pictures
We write the system of equations:
0.05x + 0.10y = 4
x = y + 5
Solving the system we have:
x = 30
y = 25
Answer:
you send:
30 text messages
25 pictures

Final answer:

This is a problem of system of linear equations. We form two equations from the conditions given in the problem, and solve the system of equations to find the number of text messages and pictures sent.

Explanation:

This is a problem of system of linear equations. Here are two conditions mentioned: The total cost and difference of number of text messages and pictures.

Let's denote the number of text messages as x and pictures as y as per your question.

From the cost, we have the equation: $0.05x + $0.10y = $4.

From the difference of the number of sent messages and pictures, we have: x = y + 5.

Now we can substitute x from the second equation into the first one, get the value for y, and calculate the value for x after. Here you have step-by-step solution for your problem.

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Mr. Sanchez bought 2 magazine for 9.95 each and 1 book for 14.95 if the sales tax is 6% what is the total cost of Mr. Sanchez purchases

Answers

rst you have to find the price of everything together

2 magazines for 9.95 each and a book for 14.95

9.95 + 9.95 + 14.95 = 34.85

Next you convert the percent to a decimal

6% = 0.06

Now you put a one in the ones place

1.06

Multiply this by the cost of everything

34.85 * 1.06 = 36.94

The answer is $36.94

Hope this helps!

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if a horse weighs 500kg and a spider 1g how many spiders weigh the same as one horse??

Answers

Hello!

First you have to put the horses weight into grams

There are 1000 kilograms in a gram

Multiply the horse weight by 1000 to get its weight in grams

500 * 1000 = 500000g

Divide the weight of the horse by the weight of the spider

500000 / 1 = 500000

The answer is 500,000 spiders

Hope this helps!

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