Which term is the constant in this expression (3x ^ 2 - 5x + 2) ?
7 answers
The constant in the expression 3x^2 - 5x + 2 is 2.
When solving the equation for x: (x / 2 + 4 = 11) what inverse operation would you use first?
To solve the equation (x / 2 + 4 = 11), you would use the inverse operation of addition first.
Jimmy goes to the farmer's market to get some pears. The particular type of pears he likes costs $2.35 per pound. If he can
only spend $10 or less, how many pounds can he buy? The inequality would be [
] pounds of pears.
]. Jimmy could buy
only spend $10 or less, how many pounds can he buy? The inequality would be [
] pounds of pears.
]. Jimmy could buy
The inequality to represent the situation would be:
2.35x ≤ 10
where x represents the number of pounds of pears Jimmy can buy.
To find the number of pounds Jimmy can buy, we need to solve this inequality by isolating x. We divide both sides of the inequality by 2.35:
x ≤ 10 / 2.35
Simplifying this:
x ≤ 4.26
So Jimmy can buy a maximum of 4.26 pounds of pears. However, since he can only buy whole pounds, the maximum number of pounds he can buy would be 4 pounds.
2.35x ≤ 10
where x represents the number of pounds of pears Jimmy can buy.
To find the number of pounds Jimmy can buy, we need to solve this inequality by isolating x. We divide both sides of the inequality by 2.35:
x ≤ 10 / 2.35
Simplifying this:
x ≤ 4.26
So Jimmy can buy a maximum of 4.26 pounds of pears. However, since he can only buy whole pounds, the maximum number of pounds he can buy would be 4 pounds.
The length of a rectangle is four meters less than twice its width. If the area of the rectangle is 96 m², what is the length and the width? An expression for the length of the rectangle in terms of the width would be: area of a rectangle is: The formula for the Using trial and error, if the area is 96 m², then the length and width are:
Let's denote the width of the rectangle as "w" meters.
According to the problem, the length is four meters less than twice the width. So, the expression for the length in terms of the width would be:
Length = 2w - 4
The formula for the area of a rectangle is length multiplied by width:
Area = Length × Width
Since the area is given as 96 m², we can set up the equation:
96 = (2w - 4) × w
To solve this equation, let's distribute and rearrange:
96 = 2w^2 - 4w
2w^2 - 4w - 96 = 0
Now, we can solve this quadratic equation either by factoring, completing the square, or using the quadratic formula. By factoring, we get:
2(w - 8)(w + 6) = 0
This gives us two possible solutions for w:
w - 8 = 0 or w + 6 = 0
If w - 8 = 0, then w = 8
If w + 6 = 0, then w = -6
Since the width cannot be negative, we disregard the solution w = -6.
Therefore, the width of the rectangle is 8 meters.
Now we can substitute this value of w back into our expression for the length:
Length = 2w - 4 = 2(8) - 4 = 16 - 4 = 12
So, the length of the rectangle is 12 meters and the width is 8 meters.
According to the problem, the length is four meters less than twice the width. So, the expression for the length in terms of the width would be:
Length = 2w - 4
The formula for the area of a rectangle is length multiplied by width:
Area = Length × Width
Since the area is given as 96 m², we can set up the equation:
96 = (2w - 4) × w
To solve this equation, let's distribute and rearrange:
96 = 2w^2 - 4w
2w^2 - 4w - 96 = 0
Now, we can solve this quadratic equation either by factoring, completing the square, or using the quadratic formula. By factoring, we get:
2(w - 8)(w + 6) = 0
This gives us two possible solutions for w:
w - 8 = 0 or w + 6 = 0
If w - 8 = 0, then w = 8
If w + 6 = 0, then w = -6
Since the width cannot be negative, we disregard the solution w = -6.
Therefore, the width of the rectangle is 8 meters.
Now we can substitute this value of w back into our expression for the length:
Length = 2w - 4 = 2(8) - 4 = 16 - 4 = 12
So, the length of the rectangle is 12 meters and the width is 8 meters.
1 answer