Pamela is 12 years younger than Jiri. The sum of their ages is 80. What is Jiri's age?<br> years old

X is inversely proportional to y, and x = 18 when y = 4. Write an equation relating the two

Alenkasestr [34]

Answer:

$xy=72$

Step-by-step explanation:

If x is inversely porportionaly to y, then for some constant k,

$x = \frac{k}{y}\\xy=k$

Since y is 4 when x = 18, k is equal to 4*18=72, so the equation is:

$xy=72$

8 0

3 years ago

Slope for y=5,520.619x - 1,091.393

Bad White [126]

Answer:

m = 5,520.619

Step-by-step explanation:

The given equation is :

y=5,520.619x-1,091.393 ....(1)

The general form of equation is given by :

y = mx +c ...(2)

Where

m is slope of line

c is y-intercept

Comparing equation (1) and (2), we get :

Slope, m = 5,520.619

Hence, the slope of the given line is 5,520.619.

3 0

3 years ago

A vehicle uses 1 7/8 gallons of gasoline to travel 56 1/4 miles. At this rate, how many miles can the vehicle travel per gallon

sweet [91]

Answer:

30 miles

Step-by-step explanation:

In this context, "per" means "divided by", so to find miles per gallon, divide miles by gallons:

(56 1/4 mi)/(1 7/8 gal) = 30 mi/gal

The vehicle can travel 30 miles per gallon of gas.

_____

My calculator divides mixed numbers directly, as many graphing calculators do. If you're working this out by hand, you can convert to improper fractions, then multiply the numerator by the inverse of the denominator.

(56 1/4)/(1 7/8) = (225/4)/(15/8)

= (225/4)·(8/15) = (225/15)·(8/4)

= 15·2 = 30

4 0

3 years ago

An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the ref

hichkok12 [17]

Answer:

P is exactly 3km east from the oil refinery.

Step-by-step explanation:

Let's d be the distance in km from the oil refinery to point P. So the horizontal distance from P to the storage is 3 - d and the vertical distance is 2. Hence the diagonal distance is:

$\sqrt{(3 - d)^2 + 2^2} = \sqrt{(3 - d)^2 + 4}$

So the cost of laying pipe under water with this distance is

$800000\sqrt{(3 - d)^2 + 4}$

And the cost of laying pipe over land from the refinery to point P is 400000d. Hence the total cost:

$800000\sqrt{(3 - d)^2 + 4} + 400000d$

We can find the minimum value of this by taking the 1st derivative and set it to 0

$800000\frac{2*0.5*(3-d)(-1)}{\sqrt{(3 - d)^2 + 4}} + 400000 = 0$

We can move the first term over to the right hand side and divide both sides by 400000

$1 = 2\frac{3 - d}{\sqrt{(3 - d)^2 + 4}}$

$\sqrt{(3 - d)^2 + 4} = 6 - 2d$

From here we can square up both sides

$(3 - d)^2 + 4 = (6 - 2d)^2$

$9 - 6d + d^2 + 4 = 36 - 24d + 4d^2$

$3d^2-18d+27 = 0$

$d^2 - 6d + 9 = 0$

$(d - 3)^2 = 0$

$d -3 = 0$

d = 3

So the cost of pipeline is minimum when P is exactly 3km east from the oil refinery.

3 0

3 years ago

In a certain Algebra 2 class of 29 students, 14 of them play basketball and 8 of them play baseball. There are 9 students who pl

EastWind [94]

Answer:

2/29

Step-by-step explanation:

If 9 play none, of the 29 students, 29-9 =20 play at least one. If 14 play basketball, then 20-14 = 6 play only baseball. Since 8 play baseball, there must be 8-6 = 2 who play both baseball and basketball.

Choosing at random, the probability is 2/29 that a student will be chosen who plays both sports.

8 0

4 years ago

Pamela is 12 years younger than Jiri. The sum of their ages is 80. What is Jiri's age? years old