Maths-
General
Easy
Question
Hugo is pumping regular gas into his truck. Write and solve an absolute value equation to represent how many gallons of gas will be pumped when the total is 
plus or minus
Hint:
|x| is known as the absolute value of x. It is the non-negative value of x irrespective of its sign. The value of absolute value of x is given by
We will construct an equation which models the situation with the help of the concept of absolute value.
The correct answer is: Combining the above the two equations, we get 9.8 ≤x ≤ 10.2
Step by step solution:
Given,
Let the quantity of gas pumped in the truck be x gallons
Price of the regular gas (per gallon)= $2.50
Error that is allowed in money spent on gas = $ 0.50
We form an equation in terms of price of the gas.
We can write the above prices as
2.5x ≤ 25+ 0.50
And
We can rewrite the above equations as
2.5x – 25 ≤ 0.50
And
We combine the above two cases to get the following equation.
Thus, the equation representing the given situation is
Now, we solve this equation.
Using the definition of absolute value,
We get two possibilities,
Simplifying, we get
Subtracting 25 both sides, we have
Dividing throughout by -2.5, we get
Dividing by 2.5 on both sides, we get
Combining the above the two equations, we get
And
We can rewrite the above equations as
And
We combine the above two cases to get the following equation.
Thus, the equation representing the given situation is
Now, we solve this equation.
Using the definition of absolute value,
We get two possibilities,
Simplifying, we get
Subtracting 25 both sides, we have
Dividing throughout by -2.5, we get
Dividing by 2.5 on both sides, we get
Combining the above the two equations, we get
A statement containing an absolute value is an absolute value equation. The variable of the equation is included in the absolute value.
¶To solve the constant absolute value equations. First, find 'x' values that make the expression inside the absolute value positive or negative. Now, Plot two lines for the positive and negative cases to meet at the expression's zero to graph absolute value functions.
¶For instance, 4 has an absolute value of 4, and so does 4, which also has an absolute value of 4. A number's distance from zero on the real number line can be thought of as its absolute value. Furthermore, the distance between any two real numbers equals their absolute difference.
Related Questions to study
Maths-
What property would you use first to solve 0.5x - 6 = 10 .
What property would you use first to solve 0.5x - 6 = 10 .
Maths-General
Maths-
Solve : 2/3(6x -15) + 5x = 26
Solve : 2/3(6x -15) + 5x = 26
Maths-General
Maths-
Ashton is hosting a banquet, he plans to spend 
, plus or minus 
, at a cost of per guest. Solve 
to find the maximum and minimum number of guests. If there can be up to 7 guests at each table, what is the minimum number of tables Ashton should reserve so that every guest has a seat?
Ashton is hosting a banquet, he plans to spend , plus or minus , at a cost of per guest. Solve to find the maximum and minimum number of guests. If there can be up to 7 guests at each table, what is the minimum number of tables Ashton should reserve so that every guest has a seat?
Maths-General
Maths-
A mason will lay rows of bricks to build a wall. The mason will spread 3/8 inch of mortar on top of all but the last row of bricks . The finished wall will be 1 1/8 inch less than 4 feet high.
A. The mason wants to lay the bricks , so that the shortest edge of each brick is vertical. How many rows of bricks are needed ? Show your work .
A mason will lay rows of bricks to build a wall. The mason will spread 3/8 inch of mortar on top of all but the last row of bricks . The finished wall will be 1 1/8 inch less than 4 feet high.
A. The mason wants to lay the bricks , so that the shortest edge of each brick is vertical. How many rows of bricks are needed ? Show your work .
Maths-General
Maths-
Factor the given radicand using the product property of square roots. 8√8
Factor the given radicand using the product property of square roots. 8√8
Maths-General
Maths-
Factor the given radicand using the product property of square roots. √200
Factor the given radicand using the product property of square roots. √200
Maths-General
Maths-
What is the solution of 1200 - 5(3X + 30) = 600?
What is the solution of 1200 - 5(3X + 30) = 600?
Maths-General
Maths-
A company manufactures cell phone cases. the length of a certain case must be with in of as shown. All cases with lengths outside of this range are removed from the inventory How could you use an absolute value inequality to represent the lengths of all the cases that should be removed ? Explain.
A company manufactures cell phone cases. the length of a certain case must be with in of as shown. All cases with lengths outside of this range are removed from the inventory How could you use an absolute value inequality to represent the lengths of all the cases that should be removed ? Explain.
Maths-General
Maths-
"Anna bought 8 tetras and 2 rainbow fish for her aquarium. The rainbow fish cost $6 more than the tetras. She paid a total of $37. Which of the following are true ? Select all that apply ;
A. The cost of 4 tetras is the same as the cost of a rainbow fish.
B. One rainbow fish plus 5 tetras Cost $21.
C. An equation to find the cost r, in dollars of a rainbow fish is 8r + 2(r + 6) = 37
D. Reducing the number of rainbow fish by 1 would result in a total cost of $28.50
E. An equation to find the cost t, in dollars , of a tetra is 8t + 2t + 6 = 37
Let's talk about the cost equation.
A company must determine the cost of producing and selling one of its products to create a cost equation. It must also calculate the overhead costs of production. Typically, the cost equation is the cost of manufacturing and selling one item multiplied by the number of items sold and added to the company's overhead costs.
For example, a company with $300,000 in overhead costs that manufacture and sells products that cost the company $5 each has a cost equation of 300,000 + $5. (5 x number of products sold).
"Anna bought 8 tetras and 2 rainbow fish for her aquarium. The rainbow fish cost $6 more than the tetras. She paid a total of $37. Which of the following are true ? Select all that apply ;
A. The cost of 4 tetras is the same as the cost of a rainbow fish.
B. One rainbow fish plus 5 tetras Cost $21.
C. An equation to find the cost r, in dollars of a rainbow fish is 8r + 2(r + 6) = 37
D. Reducing the number of rainbow fish by 1 would result in a total cost of $28.50
E. An equation to find the cost t, in dollars , of a tetra is 8t + 2t + 6 = 37
Maths-General
Let's talk about the cost equation.
A company must determine the cost of producing and selling one of its products to create a cost equation. It must also calculate the overhead costs of production. Typically, the cost equation is the cost of manufacturing and selling one item multiplied by the number of items sold and added to the company's overhead costs.
For example, a company with $300,000 in overhead costs that manufacture and sells products that cost the company $5 each has a cost equation of 300,000 + $5. (5 x number of products sold).
Maths-
Factor the given radicand using the product property of square roots. √11x5
Factor the given radicand using the product property of square roots. √11x5
Maths-General
Maths-
Solve each absolute value inequality. Graph the solution
Solve each absolute value inequality. Graph the solution
Maths-General
Maths-
A Scientist makes an acid solution by adding drops of acid to 1.2 L of water . The final volume the acid solution is 1.202 L, Assuming the volume of each drop is 0.05 mL, how many drops were added to the water ? About what percent of the solution is acid ? Round to the nearest hundredth of a percent .
A Scientist makes an acid solution by adding drops of acid to 1.2 L of water . The final volume the acid solution is 1.202 L, Assuming the volume of each drop is 0.05 mL, how many drops were added to the water ? About what percent of the solution is acid ? Round to the nearest hundredth of a percent .
Maths-General
Maths-
Factor the given radicand using the product property of square roots. √40x4
Factor the given radicand using the product property of square roots. √40x4
Maths-General
Maths-
Yuson used her calculator to solve the equation 4x/5 - 8 = 3 , she entered the following on her screen and got an incorrect answer. How could she use parentheses to find the correct answer ? Explain. What is the correct answer ?
Yuson used her calculator to solve the equation 4x/5 - 8 = 3 , she entered the following on her screen and got an incorrect answer. How could she use parentheses to find the correct answer ? Explain. What is the correct answer ?
Maths-General
Maths-
Solve each absolute value inequality. Graph the solution
Solve each absolute value inequality. Graph the solution
Maths-General
