MATHEMATICS HIGH SCHOOL

A farmer uses a lever to move a large rock. The force required to move the rock varies inversely with the distance from the pivot to the point the force is applied. A force of 50 pounds applied to the lever 36 inches from the pivot point of the lever will move the rock. Which function models the relationship between f, the amount of force applied to the lever and d the distance of the applied force from the pivot point?

Answers

Answer 1

Answer:

Answer:f=1800/d Inverse proportion function. Provided f is in pounds & d is in inches.

Step-by-step explanation: the relationship between f & d is inverse proportion.

A constant k has to be derived from the relationship.

If f is inversely proportional to d then f=k(1/d)

K= f X d

= 50 X 36

=> constant K=1800.

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Select all sets that contain the number 0.484848.A. Integer
B. Irrational
C. Natural
D. Rational
E. Whole

Select all that apply

Answers

0.484848 . . . . .

A. Integer . . . no, it's not
B. Irrational . . . no, it's not
C. Natural. . . no, it's not
D. Rational . . . Yes ! It is !
E. Whole . . . no, it's not

Izzy is making cookies. The recipe for 1/4 cup of butter and 3/8 cup of sugar. How much sugar would Izzy use if she used 1 cup of butter? Write your answer as a mixed number

Answers

To solve this equation, we have to set up a proportion, because we want to keep the ratio of butter to sugar equal between the two recipes. Let x represent the amount of sugar that we are trying to find.

1/4 cup butter/3/8 cup sugar = 1 cup butter/ x cup sugar

To solve this proportion, we need to use cross products, or the multiplication of the numerator of one fraction by the denominator of the other, and setting them equal to one another. If done properly, the resulting equation is:

1/4x= 3/8

Finally, we just need to divide both sides by 1/4, which is the coefficient of x, as we are trying to get x alone. Your final answer is

x=1.5.

Therefore, this means that if Izzy uses 1 cup of butter, she would use 1 1/2 cups of sugar.

Translate to algebraic expression.Justin had $46 before spending n dollars on jeans. How much money remains?

Answers

Answer:

m = 46 - n

Good luck

Look at this sequence.95, 80, 65, 50,... Which function represents this sequence? A. a(n) = 110n - 15 B. a(n) = 15n + 80 C. a(n) = 95n - 15 D. a(n) = -15n + 95

Answers

Answer:

Hi,
answer A

Step-by-step explanation:

The sequence is an AP with first term equal 95 and common difference equal -15

$a_n=a_1+(-15)*(n-1)= 95+(-15)*(n-1)=95-15n+15\n\n\boxed{a_n=110-15n}\n$

Can someone please help me with this and explain in detail? Thank you so much!

Answers

9514 1404 393

Answer:

m = 1/4
b = 2
y = 1/4x +2

Step-by-step explanation:

The slope is the ratio of rise to run. The rise between the two points is 2 units; the run is 8 units, so the slope is ...

m = rise/run = 2/8 = 1/4

The y-intercept (b) is the y-value where the line crosses the y-axis. For this line, that is y = 2, so b = 2.

Putting these values of m and b into the equation y = mx +b gives ...

y = 1/4x +2

What are the factors of x2 – 100?

Answers

Answer:

(x - 10)(x + 10)

Step-by-step explanation:

x² - 100 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

x² - 100

= x² - 10²

= (x - 10)(x + 10)

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