To solve the inequality 1/2w - 1 < -4w + 7, you can follow these steps:
1. Simplify each side of the inequality:
- Add 4w to both sides: 1/2w + 4w - 1 < 7
- Combine like terms: 9/2w - 1 < 7
2. Add 1 to both sides: 9/2w < 8
- Now the inequality is: 9/2w < 8
3. Multiply both sides by 2/9 to isolate w:
(2/9) * (9/2w) < (2/9) * 8
- The inequality becomes: w < 16/9
So, the solution to the inequality 1/2w - 1 < -4w + 7 is w < 16/9.
Solve the inequality of w
1/2w-1<-4w+7
Simplify as much as possible
5 answers
A model rocket is launched with an initial upward velocity of 195ft/s. The rocket’s height h in feet after t seconds is given by the following
h=195t-16t^2
Find all the values of t for which the rocket height is 87feet
h=195t-16t^2
Find all the values of t for which the rocket height is 87feet
To find the values of t for which the rocket's height is 87 feet, you can set the equation h = 87 and solve for t.
87 = 195t - 16t^2
Rewriting the equation in standard form:
16t^2 - 195t + 87 = 0
To solve this quadratic equation, you can either factor it or use the quadratic formula. In this case, factoring may not be straightforward, so let's use the quadratic formula.
The quadratic formula is given by:
t = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 16, b = -195, and c = 87. Plugging these values into the quadratic formula, we get:
t = (195 ± √((-195)^2 - 4 * 16 * 87)) / (2 * 16)
Simplifying under the square root:
t = (195 ± √(38025 - 55776)) / 32
t = (195 ± √(-17751)) / 32
Since √(-17751) is an imaginary number, there are no real solutions for t. Therefore, there are no values of t for which the rocket's height is exactly 87 feet.
87 = 195t - 16t^2
Rewriting the equation in standard form:
16t^2 - 195t + 87 = 0
To solve this quadratic equation, you can either factor it or use the quadratic formula. In this case, factoring may not be straightforward, so let's use the quadratic formula.
The quadratic formula is given by:
t = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 16, b = -195, and c = 87. Plugging these values into the quadratic formula, we get:
t = (195 ± √((-195)^2 - 4 * 16 * 87)) / (2 * 16)
Simplifying under the square root:
t = (195 ± √(38025 - 55776)) / 32
t = (195 ± √(-17751)) / 32
Since √(-17751) is an imaginary number, there are no real solutions for t. Therefore, there are no values of t for which the rocket's height is exactly 87 feet.
Multiply
(5u-x+7)(3u-x)
(5u-x+7)(3u-x)
To multiply (5u - x + 7)(3u - x), you can use the distributive property and combine like terms. Here's how:
First, distribute the 3u - x to each term in the first parenthesis:
(5u - x + 7)(3u - x) = (5u)(3u) + (5u)(-x) + (5u)(7) + (-x)(3u) + (-x)(-x) + (-x)(7)
Simplifying each term:
= 15u^2 - 5ux + 35u - 3ux + x^2 - 7x
Now, combine like terms:
= 15u^2 - 8ux + 35u + x^2 - 7x
So, the product of (5u - x + 7)(3u - x) is 15u^2 - 8ux + 35u + x^2 - 7x.
First, distribute the 3u - x to each term in the first parenthesis:
(5u - x + 7)(3u - x) = (5u)(3u) + (5u)(-x) + (5u)(7) + (-x)(3u) + (-x)(-x) + (-x)(7)
Simplifying each term:
= 15u^2 - 5ux + 35u - 3ux + x^2 - 7x
Now, combine like terms:
= 15u^2 - 8ux + 35u + x^2 - 7x
So, the product of (5u - x + 7)(3u - x) is 15u^2 - 8ux + 35u + x^2 - 7x.