the restriction placed 0n the equation 3 sqrt4x-9 = 5/6 can be written in the form x greater than equal to a/b.
To find the restriction on the equation, let's solve it step by step:
Starting with the equation: 3√(4x) - 9 = 5/6
First, isolate the term involving the square root:
3√(4x) = 5/6 + 9
Simplify the right side:
3√(4x) = 5/6 + 54/6
3√(4x) = 59/6
Next, cube both sides to eliminate the square root:
(3√(4x))^3 = (59/6)^3
27(4x) = 59^3 / 6^3
Multiply and simplify the right side:
27(4x) = 205379 / 216
Now, divide both sides by 27 to solve for x:
4x = 205379 / 216 / 27
Simplify the right side:
4x = 205379 / 7776
Finally, divide both sides by 4 to isolate x:
x = 205379 / (4 * 7776)
x = 205379 / 31104
Therefore, the restriction on the equation can be written as x ≥ 205379 / 31104.
the restriction placed 0n the equation 3 sqrt4x-9 = 5/6 can be written in the form x greater than equal to a/b.
the value of a is Answer
the value of b is Answer
To find the values of a and b, let's simplify the equation:
3√(4x) - 9 = 5/6
Add 9 to both sides:
3√(4x) = 5/6 + 9
Combine the fractions on the right side:
3√(4x) = 5/6 + 54/6
3√(4x) = 59/6
Cube both sides to eliminate the square root:
(3√(4x))^3 = (59/6)^3
27(4x) = (59/6)^3
Simplify the right side:
27(4x) = 205379/216
Divide both sides by 27 to solve for x:
4x = 205379/216 / 27
Simplify the right side:
4x = 205379/7776
Divide both sides by 4 to isolate x:
x = 205379 / (4 * 7776)
The value of a is 205379, and the value of b is 7776.
Therefore, the restriction on the equation can be written as x ≥ 205379/7776.
write a function in standard form for the parabola that has the following characteristics:
- an axis of symmetry at x = -2
- an x-intercept at 4
- a y-intercept at (0, -96)
Select one:
a. y = 3x^2 + 12x - 96
b. y = 3x^2 -12x - 96
c. y = -3x^2 + 36x - 96
d. y = 3(x+8)(x+4)
To find the equation in standard form for the given parabola, we will use the information provided.
- Axis of symmetry at x = -2 implies that the parabola is in the form (x - h)^2 = 4p(y - k), where (h, k) is the vertex of the parabola.
Using the axis of symmetry, we know that the vertex is (-2, k). We can substitute this into our equation to get (x + 2)^2 = 4p(y - k).
- An x-intercept at 4 means that the parabola passes through the point (4, 0). Substituting this point into the equation, we get (4 + 2)^2 = 4p(0 - k).
- A y-intercept at (0, -96) gives us (0 + 2)^2 = 4p(-96 - k).
Now we have two equations:
6^2 = 4p(-k) -> equation 1
2^2 = 4p(-96 - k) -> equation 2
Simplifying equation 1:
36 = -4pk
Simplifying equation 2:
4 = -384p - 4pk
Simplifying equation 1 gives us: -pk = -9
Thus, k = 9/p.
Substituting the value of k in equation 2 gives us:
4 = -384p - 4p(9/p)
4 = -384p - 36
384p = -40
p = -40/384
p = -5/48
Now that we have the value of p, we can substitute it into equation 1 to find k:
-(-5/48)k = -9
5/48 * k = -9
k = -432/5
Substituting the values of p and k into the equation (x + 2)^2 = 4p(y - k) gives us:
(x + 2)^2 = 4(-5/48)(y + 432/5)
Multiplying through by 48:
48(x + 2)^2 = -20(y + 432/5)
Simplifying further:
48(x + 2)^2 + 20(y + 432/5) = 0
Converting to standard form by expanding the equation gives us:
48x^2 + 192x + 192 + 20y + 864 = 0
48x^2 + 192x + 20y + 1056 = 0
Therefore, the equation in standard form for the given parabola is:
48x^2 + 192x + 20y + 1056 = 0.
Therefore, none of the given options (a, b, c, d) matches the equation for the parabola with the given characteristics.
Lloyd used the quadratic formula to determine the zeros of the function f(x) = 5x^2 + 6x + 1. After Lloyd substitutes into the Quadratic formula and starts to simplify he ends up with an expression that looks like: x = Q+_ sqrt R/S
Q = Answer
R = Answer
S = Answer
the largest zero, expressed as a decimal rounded to the nearest tenth, is Answer
Let's use the quadratic formula to find the zeros of the function f(x) = 5x^2 + 6x + 1:
The quadratic formula is given by:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
For the function f(x) = 5x^2 + 6x + 1, we have:
a = 5
b = 6
c = 1
Plugging these values into the quadratic formula:
x = (-6 ± sqrt(6^2 - 4*5*1)) / (2*5)
Simplifying:
x = (-6 ± sqrt(36 - 20)) / 10
x = (-6 ± sqrt(16)) / 10
x = (-6 ± 4) / 10
Simplifying further, we have two possible solutions:
x = (-6 + 4) / 10 = -2/10 = -1/5
x = (-6 - 4) / 10 = -10/10 = -1
Therefore, the two zeros of the function f(x) = 5x^2 + 6x + 1 are x = -1/5 and x = -1.
To determine the largest zero, we can compare them. The larger zero is -1.
So, the largest zero, expressed as a decimal rounded to the nearest tenth, is -1.
7 is a prime number Premise or Conclusion Answer
7 is only divisible by 1 and 7 Premise or Conclusion Answer
a prime number is only divisible by 1 and itself Premise or Conclusion Answer
Madelyn cannot eat the pasta salad Premise or Conclusion Answer
the salad contains gluten Premise or Conclusion Answer
Madelyn is allergic to gluten Premise or Conclusion Answer
when Deakan goes outside for a long walk after supper he sleeps well that night Premise or Conclusion Answer
Deakan needs a good sleep tonight Premise or Conclusion Answer
Deakan Should go out for a long walk after eating supper Premise or Conclusion Answer
Premise: 7 is a prime number - Premise
Premise: 7 is only divisible by 1 and 7 - Premise
Premise: A prime number is only divisible by 1 and itself - Premise
Premise: The salad contains gluten - Premise
Premise: Madelyn is allergic to gluten - Premise
Conclusion: Madelyn cannot eat the pasta salad - Conclusion
Premise: When Deakan goes outside for a long walk after supper, he sleeps well that night - Premise
Premise: Deakan needs a good sleep tonight - Premise
Conclusion: Deakan should go out for a long walk after eating supper - Conclusion
ABCDEFGHI is a regular polygon.
the sum of all of the interior angles in polygon to the nearest degree is Answer