A 23­inch piece of string is to be cut into two pieces so that the length of the longer piece is three more than four times the shorter piece. If x represents the length of the shorter piece, find the lengths of both pieces.

Q: A 5­foot piece of string is cut into two pieces. If one piece isx feet long, express the other…

A: Since a 5-foot string is cut into two pieces, therefore, the sum of the length of these two pieces…

Q: "The length of the unknown side has to be greater than ___ and less than ____" The answer is numbers

A: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.…

Q: A drinking straw of length 21cm is cut into 3 pieces. The length of the first piece is x cm. The…

A: A drinking straw of length 21cm is cut into 3 pieces. The length of the first piece is =(x) cm. The…

Q: Find three positive numbers whose sum is 36 and such that the sum of their squares is as small as…

A: Solution is given below:

Q: The product of the current ages of Vanessa children is 360. If her oldest child is twice as old as…

A: Suppose, Vanessa has 2 children, whose ages are 2x, x such that: x < 2x  Given: x•2x = 360  So,…

Q: Find the number N such that fifteen less than twice the number is three fourths of the number.

A:

Q: Find a positive number for which the sum of its reciprocal and four times its square is the least.

A: Let x be a number. According to question

Q: A 30-foot piece of siding is cut into three pieces so that the second piece is four times as long as…

A:

Q: A 48­foot­long piece of cable wire is to be cut into three pieces so that the second piece is five…

A: A 48­foot­long piece of cable wire is to be cut into three pieces,the second piece is five times…

Q: A financial advisor has invested $5,000 in two accounts. If one account contains x dollars, express…

A: To express the amount in the second account in terms of x, the amount invested in the first account.

Q: Find the smaller of two consecutive integers such that twice the smaller exceeds the larger by 10.

A: We can solve the problem by taking the smaller one as x and the larger one as x+1.

Q: A train travelsa distance of 300 km at constant speed.If the speed of the trainis increased by 5km…

A:

Q: The price of a dress is reduced by 20% when the dress still does not sell the price was reduced by…

A:

Q: The length of a rectangle is 5 feet more than the width. If x represents the width, in feet, the…

A:

Q: A 18-foot piece of siding is cut into three pieces so that the second piece is three times as long…

A:

Q: Find two consecutive integers such that three times the larger is the same as 47 more than the…

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Q: The area of a triangle is equal to the length of the base times the height divide by 2 .if the area…

A:

Q: A 12­foot board is to be divided into two pieces so that one piece is twice as long as the other. If…

A: Given: A 12 foot board is to be divided into two pieces so that one piece is twice as long as the…

Q: A rectangle's length , x, is 2 meters greater than its width.  If the perimeter of the rectangle is…

A: Let the legth of the rectangle is x  And widht is y then according to the question x=2+y Or y=x-2

Q: Find three consecutive odd integers such that the sum of the first and second is 59 less than three…

A: Let the three consecutive odd integers be n-2, n and n+2.

Q: Find three consecutive positive odd integers such that the square of the first is 9 more than 6…

A: Given : The square of the first is 9 more than 6 times the sum of the second and third

Q: Find the length x. 2.5 x, 4,

A: Solution: The objective is to find the length of x

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: Find a number such that 10 less than two thirds the number is one fourth the number.

A:

Q: Assume that the number of hours Katie spent practicing soccer isrepresented by x. Michael practiced…

A:

Q: Suppose that you have entered an 87-mile biathlon that consists of a run and a bicycle race. During…

A: Distance is equal to speed times the time taken. So, to calculate the distance of the run, first we…

Q: Find a positive number for which the sum of its reciprocal and four times its square is the smallest…

A: 1. Let x be the positive number then according to question - S=1x+4x2 and we need to minimize this…

Q: Patrick gets paid three dollars less than four times what Kevin getspaid. If the number of dollars…

A: Number of dollars kevin gets paid = x Patrick gets paid three dollars less than four times what…

Q: A 42​-inch board is to be cut into three pieces so that the second piece is twice as long as the…

A: Given that length of first piece = x Length of second piece = 2x Length of third piece = 3x

Q: A triangle with area 45 square inches has a height that is two less than four times the base. Find…

A:

Q: A 48-foot piece of siding is cut into three pieces so that the second piece is three times as long…

A: Here we have to use the concept of linear equation.

Q: A 21­foot beam is to be cut into three pieces so that the second and the third piece are each 3…

A:

Q: A 24-inch board is to be cut into three pieces so that the second piece is twice as long as the…

A: The length of the board is 24-inch. It is given that the board is cut into three pieces. Let x, y…

Q: Find the two consecutive positive integers such that the square of the first is decreased by 17…

A:

Q: When a whole number, x is subtracted from 20, the result is less than 15.

A: x is subtracted from 20 means 20-x This is less then 15 means 20 - x < 15 20 - 15 < x Then  5…

Q: a two digit number is four times the and three times the prsuc t of its digits ,find the number

A: Given, a two digit number is four times the sum and three times the product of its digit. We have to…

Q: Find the length of BE 3x +47- 10 C x+27 x+26-

A:

Q: The circumference of the circle and the perimeter of the rectangle are equal such that the length of…

A: The circumference of the circle and the perimeter of the rectangle are equal such that the length of…

Q: A rectangle has a breadth of x cm and a length which is ten times longer than the breadth. If the…

A: Given,            A rectangle has a breadth of x cm and a length which is ten times longer than the…

Q: A 24​-inch board is to be cut into three pieces so that the second piece is 3 times as long as the…

A:

Q: Jess is twice as old as Dan , and Dan is four times as old as Jun . Express each of their ages in…

A:

Q: if kim can do a certain job in 5 hours, then at the end of  h hours she will have completed 5/h of…

A: Consider that the Kim can do a work in 5 hours. Then, the rate of doing job is 15 of the job. Thus,…

Q: Find two consecutive whole numbers that √39 lies between. and 10 x 5 ?

A: Given 39 We have to find two consecutive whole numbers that 39 lies between

Q: A 10­foot board is cut into two pieces. If one piece is x feet long, express the other length in…

A: The total length of the board is given by L = 10 ft The length of the one piece after cutting is x…

Q: An 18­ foot board is cut into two pieces. If one piece is x feet, express the length of the other…

A: (18-x) feet

Q: A rectangle has a length that is three feet more than twice it’s width. What would the perimeter of…

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Q: The length of the rectangle exceeds its breadth by 3 cm. If the length and breadth are each…

A:

Q: The perimeter of a rectangular fence is to be at least 132 feet and no more than 192 feet. If the…

A:

Q: Find two consecutive whole numbers that √22 lies between. and X Ś ?

A:

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.