What is the remainder of (x3 - 6x2 -9x + 3) ÷ (x - 3)
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True or false An invalid statistical test measure may have questions that are misinterpreted.
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A sequence is defined recursively using the equation f(n + 1)=f(n) - 8. If f(1) = 100, what is f(6)?
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your work.
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2x + 4y
The x and y cannot be combined but the y can be added to the 3y. If you ever have a letter that had no number in from of it it just means it’s 1. No need to put it like 1y because some teachers count it wrong. So just keep it as the single letter. Hope this helps good luck!
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-5x=56/:(-5)
x=-56/5
x=-11 1/5
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Answer:
a = 7/2
Step-by-step explanation:
Step 1: Write equation
6a - (2a + 4) = 11 - 3(a - 2)
Step 2: Solve for a
- Distribute: 5a - 2a - 4 = 11 - 3a + 6
- Combine like terms: 3a - 4 = 17 - 3a
- Add 3a to both sides: 6a - 4 = 17
- Add 4 to both sides: 6a = 21
- Divide both sides by 6: a = 7/2
Final answer:
The variable 'a' in the given equation is 3. First, simplify both sides of the equation, then isolate 'a' by adding and subtracting the same terms on both sides. Finally, divide to find 'a'.
Explanation:
The first step to solve the equation 6a-(2a+4)=11-3(a-2) is simplifying both sides. On the left-hand side, distribute the negative sign into the parenthesis, resulting in 6a - 2a - 4. Simplifying this gives 4a - 4. On the right-hand side, distribute the negative 3 into the parenthesis, resulting in 11 - 3a + 6. Simplifying this gives -3a + 17.
So, the simplified equation is 4a - 4 = -3a + 17. To isolate the variable a on one side, add 3a to both sides to get 7a - 4 = 17. Then add 4 to both sides to get 7a = 21. Finally, divide both sides by 7 to get a = 3.
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a. What height was the ball originally thrown from?
b. When will the ball reach 130 feet?
c. Will the ball ever reach 250 feet? Explain.
d. When will the ball hit the ground?
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a. To find the height the ball was originally thrown from, we need to look at the equation h(t) = -16t² + 112t + 6. The initial height is represented by the constant term, which is 6. Therefore, the ball was originally thrown from a height of 6 feet.
b. To find when the ball will reach 130 feet, we need to set h(t) = 130 and solve for t. This gives us the equation -16t² + 112t + 6 = 130. Simplifying, we get -16t² + 112t - 124 = 0. Dividing by -4, we get 4t² - 28t + 31 = 0. Using the quadratic formula, we find that t ≈ 1.16 seconds or t ≈ 1.84 seconds. Therefore, the ball will reach a height of 130 feet after approximately 1.16 seconds or 1.84 seconds.
c. To determine if the ball will ever reach 250 feet, we need to look at the maximum height the ball will reach. The maximum height is given by the vertex of the parabolic equation h(t) = -16t² + 112t + 6. The t-coordinate of the vertex is given by -b/2a, where a = -16 and b = 112. Therefore, t = -112/(2*-16) = 3.5 seconds. Substituting t = 3.5 seconds into the equation, we get h(3.5) = -16(3.5)² + 112(3.5) + 6 ≈ 222. Therefore, the ball will not reach a height of 250 feet.
d. To find when the ball will hit the ground, we need to set h(t) = 0 and solve for t. This gives us the equation -16t² + 112t + 6 = 0. Dividing by 2, we get -8t² + 56t + 3 = 0. Using the quadratic formula, we find that t ≈ 0.07 seconds or t ≈ 7.93 seconds. Since the ball was thrown upwards, we can discard the negative solution. Therefore, the ball will hit the ground after approximately 7.93 seconds.
b. False