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2 years ago

If y varies inversely as x and y = 8 when x = 9, find x when y = 12.

Mathematics

1 answer:

myrzilka [38]2 years ago

5 0

Answer:

x = 6

Step-by-step explanation:

An inverse variation is

xy = k where k is the constant of variation

8*9 = k

72 = k

xy = k

Let y = 12

x*12 = 72

Divide each side by 12

12x/12 =72/12

x = 6

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Equation of the line contains the points (-3,2) and (5,-5)

makkiz [27]

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

$y = mx + b$

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

We have the following points through which the line passes:

$(x_ {1}, y_ {1}): (- 3,2)\\(x_ {2}, y_ {2}) :( 5, -5)$

So the slope is:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-5-2} {5 - (- 3)} = \frac {-7} {5 + 3} = - \frac {7} {8}$

Thus, the equation of the line is of the form:

$y = - \frac {7} {8} x + b$

We substitute one of the points and find "b":

$2 = - \frac {7} {8} (- 3) + b\\2 = \frac {21} {8} + b\\b = 2- \frac {21} {8}\\b = \frac {16-21} {8}\\b = - \frac {5} {8}$

Finally, the equation is:

$y = - \frac {7} {8} x- \frac {5} {8}$

Answer:

$y = - \frac {7} {8} x- \frac {5} {8}$

6 0

2 years ago

Mrs. Walters drove 360 miles on 25 gallons of gas. Mr. Walters drove 480 miles on 32 gallons of gas.

Temka [501]

Answer:

Mr.Walters car can go 15 miles on one gallon of gas.

Step-by-step explanation:

To find this, you first want to put it into a ratio.

480:32

Next, you want to divide.

480/32

After you divide, you get 15. That tells you that you get 15 miles off of one gallon of gas.

8 0

3 years ago

Read 2 more answers

A number plus itself, plus twice itself, plus 4 times itself is equal to -104

NARA [144]

The scenario will will be represented by: $x+x+2x+4x=-104$

The number will be -13

Step-by-step explanation:

We have to convert the given situation into the mathematical form

Let x be the number

Then

"a number plus itself"

x+x

"plus twice itself"

x+x+2x

"plus 4 times itself"

x+x+2x+4x

"is equal to -104"

$x+x+2x+4x=-104$

This can also be written as:

$x+x+2x+4x=-104\\8x=-104\\Dividing\ both\ sides\ by\ 8\\\frac{8x}{8}=\frac{-104}{8}\\x=-13$

Keywords: Linear Equation

Learn more about linear equation at:

#LearnwithBrainly

7 0

2 years ago

X2 + 2xy + y2 - m2<br> Factorise

Morgarella [4.7K]

Answer:

x^2 + 2xy + y^2 - m^2

= (x+y)^2-m^2

5 0

2 years ago

After a 25% discount, the sale price of a sweater that Amanda wants to purchase is $18. What was the original price? *

GalinKa [24]

Answer:

$72

Step-by-step explanation:

18/.25 will get you the original price

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2 years ago