The number of plums varies directly with the square of the number of apples. When there are 12 plums, there are 2 apples. How many apples are there when there are 75 plums?

Q: When building a house, the number of days required to build varies inversely with the number of…

A: Given One house was built in 21 days by 19 workers.How many days would it take to build a similar…

Q: The sum of two nonnegative numbers is 20. Find the numbers if the product of one number and the…

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Q: The square of a number exceeds twice the number, itself, by 60. What is the number?

A: The square of a number exceeds twice the number itself by 60.

Q: The weight of a great white shark varies directly as the cube of its length. A great white shark…

A: According to question ,weight of shark ∝ length of shark3i.eW∝L3W=KL3where K is constant .

Q: The length of a rectangular box is 8 inches longer than twice the width (x). The height is 9 inches.…

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Q: Susan is 5 years older than her sister Lucy. The sum of the square of Lucy's age and twice the age…

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Q: Find an equation of variation where y varies jointly as x and the square of z, and where y = 105…

A: y varies jointly as x and the square of z, and where y=105 when x=55 and z=7

Q: The sum of the squares of two consecutive even integers is 1252. Find the integers.

A: Given: The sum of the squares of two consecutive even integers is 1252. To find the integers.…

Q: If 4 pounds of sugar cost $2, the cost of 1 pound of sugar is $ and the cost of 10 pounds of sugar…

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Q: 3 times a number is 10 less than the square of that number. Find the negative solution.

A: find the negative solution

Q: The square of a number decreased by 1o is a mare than H times the number What is Hhe number. (6…

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Q: the square of a number increased by 16 is the same as 10 times the number. find the number a.8 b.4…

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Q: translate into equation If the side of the square is increased by 2 feet, the area is increased by…

A: To translate into equation: If the side of the square is increased by 2 feet, the area is increased…

Q: the square of the product of a and b. translate into symbolsb

A: Given variables are a and b.

Q: The length of a rectangular plot of land is 3 times the width. If the perimeter is 2000 feet, find…

A: Given,

Q: The square of the tens digit of a two-digit number is 7 less than the sum of the digits. If the…

A: Assume unit digit of number is x and tens digit is y, then use the condition given in the question

Q: Four times the square of a number decreased by 6 is equal to seven times the number increased by 9.…

A:

Q: The sum of a positive number and twice its square is 11.88. What is the number.

A: Given, let us take a positive number be

Q: in a standard television set the screen height is .75 times the screen width. If a television set…

A: Let width be x. Therefore, Height= 0.75x Given, Diagonal= 31 inches

Q: The length of a picture frame is 7 inches more than width.  For what values of x is the perimeter of…

A: The perimeter of a rectangle is given by P=2(l+b)  where l is the length of the rectangle and  b is…

Q: The pair of numbers whose difference is 18 and whose product is as small as possible is

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Q: The difference of two positive numbers is 2 and the difference of their squares is 44. Find the…

A: Let x and y are those two positive numbers and x>y.So, x-y=2 and x^2-y^2=44

Q: The Square of a number is ya more than the numbec itself, what is the number?

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Q: The profit for Cocoa Board cocoa beans is given by Π(x) = −15x2 + 180x −405 thousand dollars, where…

A:

Q: The illumination provided by a car's headlight varies inversely as the square of the distance from…

A: Let, Illumination of the car's headlight = IDistance from headlight = rAccording to question - I α…

Q: The square of a number added to 25 equals 10 times the number. What isthe number? Choose the…

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Q: The number of math homework questions Jared can complete on any given night varies directly as the…

A: let  m=number of math question s=number of hours of sleep p=number of pages…

Q: If the difference between the squares of two consecutive integers is 15, findthe larger integer.

A:

Q: Eli wants to walk to his friend, Ryland's house. If each unit on the grid represents 1 block, how…

A: From the graph we see that: Rylands house is at (-17, -3) and Eli's house is at (-5, -12)

Q: The variable y varies directly with the square of x. If y = 100 when x = -5, then the equation…

A:

Q: The difference of the square of a number and 24 is equal to 5 times that number. Finc the negative…

A: let us consider the number is x then according to given condition the difference of x2 and 25 will…

Q: The difference of the square of a number and 12 is equal to 4 times that number. Find the positive…

A: Suppose that number is x . Form the equation of one variable according to given in the question.

Q: Thrice the sum of two numbers is 30 and the sum of their squares is 52. Find the product of the…

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Q: The square of a number is equal to six tim number plus 18. What is the number?

A: ` 1.The square of a number is equal to six times the number plus 18.

Q: A varies directly as the square of r, and A = 2464 when r= 28.

A: Given A = 2464 when r= 28.

Q: If the square of the number is added to 3 times the number, the number is 108. Find the number.

A: We have to find the number if square of the number is added to 3 times the number then number is…

Q: The square of a negative number is 18 more than 3 times the negative number. Find the number.

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Q: A horse and a saddle cost $5000. If the horse cost 4 times as much as thesaddle, what was the cost…

A:

Q: The value of y varies jointly with x and the square of z, and y=12 when x=3 and z=4. What is the…

A:

Q: A square raised-bed garden takes up 57.8 square feet of Ricardo’s back yard. Which of the following…

A: This is a problem related to mensuration. Here area of the raised bed garden is given.  Based on the…

Q: The variable z varies jointly as the square root of x and the cube root of y. If z=31.2 when x=36…

A: The given joint variation can be formulated as follows.

Q: find two consecutive even integers if the sum of their squares is 164

A:

Q: If 64 is added to the difference between the square of a number and 16 times the number, the result…

A:

Q: The square of a number equals nine times that number. Find the number.

A: Assume number be x

Q: The length of a rectangular plot of land is 3 times the width. If the perimeter is 2000 feet, find…

A: our objective is to find the dimensions

Q: When x = 3 and y = 5, by how much does the value of 3x2 - 2y exceed the value of 2x2 - %3D Зу ?

A: Given:  To determine how much doesthe value 3x2-2y exceed the value of 2x2-3y whwn x=3and y=5

Q: In a certain family, 11 times the number of children is greater by 12 than twice the square of the…

A:

Q: A horse and a saddle cost 5000 dollars. If the horse cost 4 times as much as the saddle, what was…

A: Let the cost of saddle = $ x The cost of horse = $ 4x

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.