weight A weighs 50 pounds. weight B weighs 100 pounds. if A is placed 6 feet from the pivot, how far must B be placed from the pivot in order for the bar to achieve balance?

Two positive integers x and y

x - y = 4

x² + y = 68

x and y

Add the two equations together.

... (x - y) + (x² + y) = (4) + (68)

... x² + x = 72

Rearrange to standard form and factor.

... x² + x - 72 = 0

... (x + 9)(x - 8) = 0

Use the zero product rule to find the solutions. That rule says the product is zero when one or more factors is zero.

... x + 9 = 0 ⇒ x = -9

... x - 8 = 0 ⇒ x = 8 . . . . . . the positive solution

Then we can find y from

... 8 - y = 4

... y = 4 . . . . . . . add y-4 to the equation

The two positive integers are 8 and 4.

To solve for the two positive integers where their difference is 4 and the sum of the smaller and the square of the larger is 68, we set up a quadratic equation and solve for n to find that the integers are 4 and 8.

The problem given is a classic algebra question where we are asked to determine two positive integers based on their relationship to each other and an additional numeric condition. We know that the difference between these two numbers is 4, and when the smaller integer is added to the square of the larger, the result is 68.

Let's denote the smaller number as n and the larger number as n+4, since there is a difference of 4 between them. Now, according to the second condition given, we can set up the following equation: n + (n+4)2 = 68.

Expanding the squared term and combining like terms, we get a quadratic equation: n2 + 8n + 16 + n = 68. Simplifying, n2 + 9n + 16 = 68. Further simplification leads to n2 + 9n - 52 = 0. Factoring this quadratic equation, we find the integers that satisfy the equation: n = 4 and n = -13. Since we are looking for positive integers, the solution is n = 4 and n+4 = 8.

Therefore, the two positive integers are 4 and 8.

Bill Gates makes approximately $22,831.05 per minute, calculated by dividing his annual earnings of $12 billion by the number of minutes in a year (525,600).

To calculate how much Bill Gates makes per minute, we need to start by determining how much he makes per year. According to the question, Bill Gates makes approximately $12 billion a year. To find out how much that is per minute, we need to follow these steps:

Therefore, on average, Bill Gates makes $22,831.05 per minute.

Final answer:

To solve an algebraic equation, identify knowns, find suitable equations, simplify algebraically, substitute known values, solve for the unknown, and check if the answer is reasonable.

Explanation:

To solve an algebraic equation, follow these systematic steps:

Firstly, identify the knowns and make a list of what is given or can be inferred from the problem.

Then, find the appropriate equation or set of equations that contain the unknown you need to solve for.

Simplify the algebra by eliminating terms wherever possible. This might require algebraic rearrangement such as dividing terms or multiplying both sides of the equation to isolate the unknown.

Substitute the known values into the equation.

Solve for the unknown and make sure to include units where necessary.

Finally, always check your answer to see if it is reasonable and makes sense.

These steps should yield a solution that is both accurate and verifiable.

There are 10 integers from 1 to 700 that are divisible by 2, 5, and 7. This is calculated by finding the least common multiple (LCM) of the numbers, which is 70, and then determining how many multiples of 70 are within the given range.

The question asks to find out how many integers from 1 to 700 are divisible by 2, 5, and 7. An integer divisible by 2, 5, and 7 is also divisible by their least common multiple (LCM). The LCM of 2, 5, and 7 is 70 since 2 x 5 x 7 = 70. So, the task is to find the number of multiples of 70 between 1 and 700.

To find the number of multiples of 70 in that range, you can use the following steps:

Therefore, there are 10 integers from 1 to 700 that are divisible by 2, 5, and 7.

The quadratic equation defined by the table is f(x) = 2.35x^2 + 4.72x -1.55

A quadratic function is represented as:

f(x) = ax^2 + bx + c

Using the table of values, we have:

a(0)^2 + b(0) + c = -1.55

This gives

c = -1.55

Also, we have:

a(2)^2 + b(2) + c = 17.29

4a + 2b -1.55 = 17.29

This gives

4a + 2b = 18.84

Divide through by 2

2a + b = 9.42 --- (2)

Also, we have:

a(4)^2 + b(4) + c = 54.93

16a + 4b -1.55 = 54.93

This gives

16a + 4b = 56.48

Divide through by 4

4a + b = 14.12 ---- (3)

Subtract (2) from (3)

2a = 4.7

Divide by 2

a = 2.35

Substitute a = 2.35 in 4a + b = 14.12

4*2.35 + b = 14.12

Evaluate

b = 4.72

Substitute values for a, b and c in f(x) = ax^2 + bx + c

f(x) = 2.35x^2 + 4.72x -1.55

Hence, the quadratic equation defined by the table is f(x) = 2.35x^2 + 4.72x -1.55

Read more about quadratic equation at:

https://brainly.com/question/1214333

#SPJ6

We know that we are solving for y.

This is a step by step procedure to get the value of y.

First: Move all terms to the left side and set equal to zero.

Second: Then set each factor equal to zero.

The application is:

Given: py+7=6y+q 

-6y -7 -6y -7 = 0

(p-6)y = q-7

divide both sides by p-6
y=(q-7)/(p-6)

Answer is y = (q – 7) / (p – 6) 

The solution of expression for y as,

⇒ y = (q - 7) / (p - 6)

We have to given that,

An expression is,

⇒ py + 7 = 6y + q

Now, We can simplify the expression for y as,

⇒ py + 7 = 6y + q

Subtract 6y both side,

⇒ py - 6y + 7 = 6y + q - 6y

Subtract 7 both side,

⇒ py - 6y = q - 7

⇒ y (p - 6) = (q - 7)

Divide both side by (p - 6);

⇒ y = (q - 7) / (p - 6)

Therefore, The solution of expression for y as,

⇒ y = (q - 7) / (p - 6)

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ6

Answer:

The three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.

Step-by-step explanation:

It is given that the length of a table is 6 feet. On a scale drawing, the length is 2 inches.

The scale for drawing is

[tex]Scale=\frac{\text{Length in drawing}}{\text{Actual length}}=\text{Length in drawing}:\text{Actual length}[/tex]

First possible scale for the drawing is

2 inch : 6 feet

It can be written as

1 inch : 3 feet

We know that 1 feet = 12 in

1 inch : 36 inch

We know that 1 feet = 30.48 cm

1 inch : 91.44 cm

Therefore the three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.

The three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.

Here, we have,

It is given that the length of a table is 6 feet. On a scale drawing, the length is 2 inches.

The scale for drawing is

scale = length in drawn/actual length

scale = length in drawn : actual length

First possible scale for the drawing is

2 inch : 6 feet

It can be written as

1 inch : 3 feet

We know that 1 feet = 12 in

1 inch : 36 inch

We know that 1 feet = 30.48 cm

1 inch : 91.44 cm

Therefore the three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.

To learn more on ratio click:

brainly.com/question/13419413

#SPJ6

Answer:

2300

Step-by-step explanation:

The correlation coefficient of the given data pairs is most likely closest to 0.8694.

The correlation coefficient measures the strength and direction of the relationship between two variables. To find the correlation coefficient, you can use the formula:

r = [n(Σxy) - (Σx)(Σy)] / sqrt{[n(Σx^2) - (Σx)^2][n(Σy^2) - (Σy)^2]}

Using this formula, you can calculate the correlation coefficient for the given data pairs. The closest value to the correlation coefficient will be 0.8694, option d.

The answer closest to the correlation coefficient of the data is 0.835.

To find the correlation coefficient of the given data pairs, we can use the formula:

r = (Σxy - (Σx)(Σy)/n) / sqrt((Σx^2 - (Σx)^2/n)(Σy^2 - (Σy)^2/n))

where Σ represents the sum, n is the number of data pairs, x is the average temperature, y is the electricity cost, and xy is the product of x and y.

To calculate the correlation coefficient, we first need to find the sums and products of the data pairs:

Σx = 65 + 59 + 71 + 78 + 82 + 85 + 88 + 91 + 84 + 79 + 63 + 59 = 924
Σy = 147 + 141 + 176 + 189 + 183 + 211 + 231 + 227 + 198 + 188 + 152 + 126 = 2259
Σxy = (65*147) + (59*141) + (71*176) + (78*189) + (82*183) + (85*211) + (88*231) + (91*227) + (84*198) + (79*188) + (63*152) + (59*126) = 219907

Using these values, we can calculate the correlation coefficient:

r = (219907 - (924*2259)/12) / sqrt((Σx^2 - (Σx)^2/12)(Σy^2 - (Σy)^2/12))

Calculating the remaining sums:

Σx^2 = (65^2) + (59^2) + (71^2) + (78^2) + (82^2) + (85^2) + (88^2) + (91^2) + (84^2) + (79^2) + (63^2) + (59^2) = 73482
Σy^2 = (147^2) + (141^2) + (176^2) + (189^2) + (183^2) + (211^2) + (231^2) + (227^2) + (198^2) + (188^2) + (152^2) + (126^2) = 827259

Plugging in the values:

r = (219907 - (924*2259)/12) / sqrt((73482 - (924^2)/12)(827259 - (2259^2)/12))

After performing the calculations, the correlation coefficient is approximately 0.835.

Therefore, the answer closest to the correlation coefficient of the data is 0.835.

1 foot = 12 inches

 divide 69 by 12

69/12 = 5.75 feet