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
To find the sum of all the interior angles in a regular polygon, we can use the formula:
Sum of interior angles = (n - 2) * 180 degrees
Where n represents the number of sides (or vertices) of the polygon.
Since the given polygon is represented by the letters A, B, C, D, E, F, and G, we count 7 vertices. Therefore, n = 7.
Substituting n = 7 into the formula:
Sum of interior angles = (7 - 2) * 180 degrees
Sum of interior angles = 5 * 180 degrees
Sum of interior angles = 900 degrees
Thus, the sum of all the interior angles in the given polygon, to the nearest degree, is 900 degrees.
triangle RST has R = 110 degree, t = 115 cm and r = 180 cm. the size of T is:
select one:
a. 34 degree
b. 37 degree
c. 60 degree
d. 55 degree
To find the size of angle T in triangle RST, we can use the Law of Sines:
sin(R)/r = sin(T)/t
Plugging in the given values:
sin(110°)/180 = sin(T)/115
Simplifying:
0.9397/180 = sin(T)/115
Cross multiplying:
0.9397 * 115 = sin(T) * 180
107.9575 = sin(T) * 180
Divide both sides by 180:
0.5998 = sin(T)
Take the inverse sine of both sides:
T = sin^(-1)(0.5998)
Using a calculator, we find:
T ≈ 36.9°
Therefore, the size of angle T in triangle RST is approximately 36.9 degrees.
The closest option to this value is:
a. 34 degrees
Nara uses fishing line for making crafts. four types of fishing line are available at an outdoor store.
Line Length(yd) Price($)
P 220 16.50
Q 300 21.64
R 250 19.99
S 150 23.99
the finishing line with lowest cost per yard is
Select one:
a. S
b. P
c. R
d. Q
To find the fishing line with the lowest cost per yard, we need to calculate the cost per yard for each type of fishing line. This can be done by dividing the price ($) by the length (yd) for each line.
For line P: Cost per yard = $16.50 / 220 yd ≈ $0.075 per yd
For line Q: Cost per yard = $21.64 / 300 yd ≈ $0.072 per yd
For line R: Cost per yard = $19.99 / 250 yd ≈ $0.080 per yd
For line S: Cost per yard = $23.99 / 150 yd ≈ $0.160 per yd
Comparing the cost per yard for each line, we can see that line Q has the lowest cost per yard, which is approximately $0.072 per yd.
Therefore, the fishing line with the lowest cost per yard is:
b. Q
the perimeter of this polygon is Answer cm (rounded to the nearest cm).
To find the perimeter of the polygon, we would need additional information about the polygon, such as the number of sides and the length of each side. Please provide more details about the polygon so that I can calculate the perimeter for you.
the perimeter of this polygon is Answer cm (rounded to the nearest cm). the interior 11.2 cm per side triangle and 51.4 degree per triangle
Given that the polygon consists of triangles with a side length of 11.2 cm and an interior angle of 51.4 degrees, we can proceed to calculate the perimeter.
Since the interior angle is given, we can calculate the exterior angle of each triangle:
Exterior angle = 180 degrees - interior angle = 180 - 51.4 = 128.6 degrees
To find the number of sides in the polygon, we can use the relationship between the exterior angle and the number of sides:
Number of sides = 360 degrees / exterior angle = 360 / 128.6 ≈ 2.8
Since a polygon must have a whole number of sides, we round the number of sides to the nearest whole number:
Number of sides ≈ 3
Given that each side of the triangle is 11.2 cm and there are 3 sides, the perimeter of the polygon is:
Perimeter = 11.2 cm * 3 = 33.6 cm
Therefore, the perimeter of the polygon is approximately 33.6 cm (rounded to the nearest cm).
Jessica has a summer job that pays time and half for overtime (over 40 hours in a week). Jessica's hourly rate of pay is $7.00/hour. The graph that best represents this scenario is
Apologies, but as a text-based AI, I am unable to directly show or generate graphs. However, I can describe the scenario for you:
To represent Jessica's scenario on a graph, we can plot her total earnings as a function of the number of hours worked in a week.
For the first 40 hours, her earnings per hour will be $7.00, represented by a straight line on the graph with a slope of $7.00/hour. The equation of this line would be:
Earnings = $7.00/hour * Number of Hours
For any hours worked beyond 40, her earnings will be time and a half, or $7.00/hour * 1.5 = $10.50/hour. This overtime earnings can be represented by another straight line on the graph but with a steeper slope of $10.50/hour. The equation of this line would be:
Overtime Earnings = $10.50/hour * (Number of Hours - 40)
To complete the graph, we can plot the total earnings as a function of the number of hours worked. The total earnings can be calculated by adding the earnings for the first 40 hours and the overtime earnings. The equation for total earnings would be:
Total Earnings = Earnings + Overtime Earnings
I hope this description helps you visualize the scenario on a graph. If you have any specific questions or need further assistance, please let me know!
Triangle ABC = Triangle CDE the two triangle are congruent because they follow the Answer concurrency pattern
I'm sorry, but the statement you provided is incorrect. Congruent triangles are not determined by concurrency patterns.
Triangles are considered congruent (meaning they have the same size and shape) if their corresponding sides and angles are equal. This can be determined through various methods, such as side-angle-side (SAS), side-side-side (SSS), or angle-side-angle (ASA) congruence criteria.
To prove that Triangle ABC and Triangle CDE are congruent, you would need to provide information about their corresponding sides and angles. Without additional information, we cannot determine their congruence.
Concurrency patterns, on the other hand, refer to lines or points that intersect at a common point, such as concurrent lines meeting at a point of concurrency (e.g., medians intersecting at the centroid). This concept is not directly related to triangle congruence.
Marshal is defrosting some chicken in his microwave. The chicken weighs 1.95kg. According to his cookbook 0.5kg of chicken takes 7 minutes to defrost. With this in mind, Marshal should set his microwave timer to exactly:
Select one:
a. 14 minutes
b. 27 minutes and 18 seconds
c. 10 minutes and 15 seconds
d. 27 minutes and 30 seconds
To determine the time Marshal should set his microwave timer to defrost the chicken, we can set up a proportion based on the given information:
0.5kg takes 7 minutes
1.95kg takes x minutes
We can set up the proportion as follows:
0.5kg / 7 minutes = 1.95kg / x minutes
To solve for x, we can cross multiply and then divide:
0.5kg * x minutes = 1.95kg * 7 minutes
0.5x = 13.65
Divide both sides by 0.5:
x = 13.65 / 0.5
x = 27.3 minutes
Therefore, Marshal should set his microwave timer to exactly 27 minutes and 18 seconds (option b).
A 12 inch by 16 inch poster was produced using a scale factor of 4. The largest dimension of the original image is
Select one:
a. 64 in
b. 48 in
c. 4 in
d. 3 in
To find the largest dimension of the original image, we need to reverse the scaling that was applied using the scale factor of 4.
If the dimensions of the scaled poster are 12 inches by 16 inches, and the scale factor is 4, we can divide each dimension by 4 to find the corresponding dimensions of the original image.
12 inches / 4 = 3 inches
16 inches / 4 = 4 inches
Therefore, the largest dimension of the original image is 4 inches (option c).
The width of a snowflake on a spherical red ornament is 3 cm. on a similar a gold ornament the snowflake is 15 cm wide.
The linear scale factor that represents the enlargement from the red ornament to the gold one is Answer.
The red ornament is filled with is 71 cm^3 of gel. The amount of gel required to fill the gold ornament is Answer cm^3.