Review the graph.

On a coordinate plane, a circle has center (4, 0) and radius 4. Another circle has center (2, negative 3) and radius 6. The area inside of the first circle and outside of the second circle between the 2 circles is shaded.

Which system of inequalities is shown in the graph?

36 > (x + 3)2 + (y – 2)2 and 16 > (x – 4)2 + y2
36 > (x – 2)2 + (y + 3)2 and 16 > (x – 4)2 + y2
36 < (x + 3)2 + (y – 2)2 and 16 > (x – 4)2 + y2
36 < (x – 2)2 + (y + 3)2 and 16 > (x – 4)2 + y2

The volume of the given triangular prism is approximately 104.76075 cubic inches.

To calculate the volume of a triangular prism, you need to multiply the area of the triangular base by the height of the prism.

Given that the triangular base has sides measuring 9 inches each, we can find the area of the base using the formula for the area of an equilateral triangle:

Area = [tex](\sqrt(3) / 4) * side^2[/tex]

where "side" represents the length of one side of the triangle. In this case, the side length is 9 inches.

Area = [tex](\sqrt(3) / 4) * 9^2\\ = (\sqrt(3) / 4) * 81\\ = (1.732 / 4) * 81\\ = 1.732 * 81 / 4\\ = 139.681 / 4[/tex]

    = 34.92025 square inches

Now that we have the area of the triangular base, we can calculate the volume of the prism by multiplying it by the height of the prism:

Volume = Base Area * Height

      = 34.92025 square inches * 3 inches

      = 104.76075 cubic inches

Therefore, the volume of the given triangular prism is approximately 104.76075 cubic inches.

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Answer: Triangle C.

Step-by-step explanation:

We can find the area of the triangles by multiplying the base by the height and dividing by 2. The given formula is A = [tex]\frac{bh}{2}[/tex].

    A = [tex]\frac{bh}{2} =\frac{4}{2} =2[/tex]

    B = [tex]\frac{bh}{2} =\frac{4}{2} =2[/tex]

    C = [tex]\frac{bh}{2} =\frac{3}{2} =1.5[/tex]

    D = [tex]\frac{bh}{2} =\frac{4}{2} =2[/tex]

    E = [tex]\frac{bh}{2} =\frac{4}{2} =2[/tex]

We can see that the triangle with the different area is triangle C. It has an area of 1.5 units², while the rest have an area of 2 units².

Answer: To determine if the ordered pair (x, y) is a solution of the given system of equations, you need to substitute the values of x and y into each equation and check if both equations hold true.

Given system of equations:

2x - y = 1

5x - 3y = 1

Let's substitute the values of x and y from the ordered pair (x, y) into each equation:

For equation 1:

2x - y = 1

Substituting x = 2 and y = -1:

2(2) - (-1) = 4 + 1 = 5

For equation 2:

5x - 3y = 1

Substituting x = 2 and y = -1:

5(2) - 3(-1) = 10 + 3 = 13

Now, compare the results of each equation with the right-hand side of the respective equation:

For equation 1: 5 (left side) ≠ 1 (right side)

For equation 2: 13 (left side) ≠ 1 (right side)

Since both equations do not hold true when substituting the values of x = 2 and y = -1, the ordered pair (2, -1) is not a solution of the given system of equations.

Step-by-step explanation: Hope this helps!

The simplified form of the expression, 10a⁻⁸b⁻² / 4a³b⁵ is 5 / 2a¹¹b⁷

The expression can be simplified using the properties of the exponents as follows;

Therefore,

10a⁻⁸b⁻² / 4a³b⁵

Hence, using the indices law for exponents,

10a⁻⁸b⁻² / 4a³b⁵ = 5a⁻⁸b⁻² / 2a³b⁵

Therefore,

5a⁻⁸b⁻² / 2a³b⁵ = 5 / 2 a⁻⁸⁻³b⁻²⁻⁵

Hence,

5 / 2 a⁻⁸⁻³b⁻²⁻⁵ = 5 / 2 a⁻¹¹b⁻⁷

Therefore,

5 / 2 a⁻¹¹b⁻⁷ = 5 / 2a¹¹b⁷

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Answer:

h(- 1) = - 1 , h(0.75) = 1 , h(1) = 1

Step-by-step explanation:

h(- 1) has x = - 1 in the interval - 2 ≤ x ≤ - 1 , then

h(- 1) = - 1

h(0.75) has x = 0.75 in the interval 0 < x ≤ 1 , then

h(0.75) = 1

h(1) has x = 1 in the interval 0 < x ≤ 1 , then

h(1) = 1

A) The new coordinates after a 90° clockwise rotation are (3, -2).

B) The new coordinates after a 180° rotation are (-2, -3).

C) The new coordinates after a 270° clockwise rotation are (-3, 2).

To determine the new coordinates of point P when it is rotated about the origin by different angles, we can use the rotation formulas. Let's assume the original coordinates of point P are (x, y).

a) 90° clockwise rotation:

In a 90° clockwise rotation, the new x-coordinate (x') is obtained by replacing x with y and changing the sign. The new y-coordinate (y') is obtained by replacing y with -x.

x' = y

y' = -x

So, the new coordinates of point P after a 90° clockwise rotation are (y, -x).

b) 180° rotation:

In a 180° rotation, the new x-coordinate (x') is obtained by changing the sign of x, and the new y-coordinate (y') is obtained by changing the sign of y.

x' = -x

y' = -y

So, the new coordinates of point P after a 180° rotation are (-x, -y).

c) 270° clockwise rotation:

In a 270° clockwise rotation, the new x-coordinate (x') is obtained by replacing x with -y. The new y-coordinate (y') is obtained by replacing y with x and changing the sign.

x' = -y

y' = x

So, the new coordinates of point P after a 270° clockwise rotation are (-y, x).

To illustrate with an example, let's assume the original coordinates of point P are (2, 3).

a) 90° clockwise rotation:

x' = 3

y' = -2

The new coordinates after a 90° clockwise rotation are (3, -2).

b) 180° rotation:

x' = -2

y' = -3

The new coordinates after a 180° rotation are (-2, -3).

c) 270° clockwise rotation:

x' = -3

y' = 2

The new coordinates after a 270° clockwise rotation are (-3, 2).

These calculations demonstrate how the coordinates of a point change when it undergoes rotations of different angles about the origin.

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The probability of picking a black checker, replacing it, and then picking another black checker from a bag of six black checkers and four red checkers is (6/10) * (6/10) = 36/100 = 0.36 or 36%.

In the first pick, there are six black checkers out of a total of ten checkers (six black checkers and four red checkers), so the probability of picking a black checker is 6/10 or 0.6.

Since the checker is replaced after the first pick, the bag remains the same for the second pick. In the second pick, the probability of picking another black checker is also 6/10 or 0.6.

To find the overall probability, we multiply the probabilities of the individual events, resulting in 0.6 * 0.6 = 0.36 or 36%.

To explain further, the probability is determined by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, the favorable outcome is picking a black checker twice, and there are six black checkers available for each pick.

The total number of possible outcomes is the total number of checkers in the bag, which is ten. By multiplying the probabilities of the two independent events (picking a black checker on the first and second picks), we obtain the probability of both events occurring consecutively. Thus, the probability of picking a black checker, replacing it, and then picking another black checker is 0.36 or 36%.

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The choice between these tests depends on the assumptions of normality, variance equality, and the nature of the data.

The choice between using an independent t-test with equal variance, independent t-test with unequal variance, or the Wilcoxon signed test depends on the nature of the data and the assumptions that can be made.

The independent t-test assumes that the data is normally distributed and that the variances in the two groups being compared are equal. It is appropriate when the data meets these assumptions and the objective is to compare means between two independent groups.

However, if the assumption of equal variances is violated, an independent t-test with unequal variance (also known as Welch's t-test) can be used. It does not assume equal variances and provides a more robust analysis in such cases.

On the other hand, the Wilcoxon signed test (also known as the Wilcoxon signed-rank test) is a non-parametric test used when the data does not meet the assumptions of normality or when dealing with ordinal or skewed data. It is typically used to compare paired samples or matched data, where each observation in one group is paired with a corresponding observation in the other group.

The independent t-test with equal variance is appropriate for normally distributed data with equal variances. The independent t-test with unequal variance is used when the assumption of equal variances is violated. The Wilcoxon signed test is employed for non-parametric data or when dealing with paired samples.

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The length of the final cut paving stone is 5 feet.

In this question, we have a sidewalk that is 54.5 feet long and the paving stones that will be used are 5.5 feet long.

The worker has to place 9 full paving stones and cut the final stone to fit.

We are required to find the length of the final cut paving stone.

To find the length of the final cut paving stone, we first need to find the total length covered by the 9 full paving stones. We can do this by multiplying the length of each stone (5.5 feet) by the number of stones placed (9).

Total length covered by 9 full paving stones = 5.5 feet × 9 = 49.5 feet Next, we can subtract this total length from the length of the sidewalk to find out how much length is left for the final stone.

Length left for final stone = Length of sidewalk - Total length covered by 9 full paving stones= 54.5 feet - 49.5 feet = 5 feet.

Finally, we know that the worker has to cut the final stone to fit, so the length of the final cut paving stone will be equal to the length of the remaining space. Length of final cut paving stone = Length left for final stone= 5 feet.

Therefore, the length of the final cut paving stone is 5 feet.

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The probability of selecting two Democrats from the political discussion group is 3/8 or approximately 0.375.

The probability of selecting two Democrats from the group can be calculated using the concept of probability. In this case, we have a total of 10 Democrats out of 16 total group members.

The probability of selecting the first Democrat is 10/16, since there are 10 Democrats out of 16 group members.

After selecting the first Democrat, there are 9 Democrats left out of 15 remaining group members. Therefore, the probability of selecting the second Democrat is 9/15.

To find the probability of both events occurring, we multiply the individual probabilities together.

So the probability of selecting two Democrats in succession is (10/16) * (9/15) = 3/8 or approximately 0.375.

In summary, the probability of selecting two Democrats from the political discussion group is 3/8 or approximately 0.375.

This means that there is a 37.5% chance of choosing two Democrats if two members are selected randomly and in succession.

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By using a statistical calculator, the actual sample mean and sample standard deviation are:

Actual sample mean = 46.1500.

Actual ample standard deviation = 8.6256.

In Mathematics and Geometry, the sample mean for any set of data can be calculated by using the following formula:

Mean = ∑x/(n - 1)

In Mathematics and Geometry, the sample standard deviation for any set of data can be calculated by using the following formula:

Standard deviation, δx = √(1/N × ∑(x - [tex]\bar{x}[/tex])²)

By using a statistical calculator, the actual sample mean and sample standard deviation are as follows;

Actual sample mean = 46.1500.

Actual ample standard deviation = 8.6256.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The domain of the relation S is the set of all x-values from the ordered pairs in the relation. In this case, the given ordered pairs are (3, p), (3, 0), (4, g), and (1, 4).

To find the domain, we collect all the unique x-values from these ordered pairs.

From the given pairs, we have x = 3, x = 4, and x = 1. However, note that (3, p) and (3, 0) have the same x-value of 3. When considering the domain, we only need to list unique x-values.

Therefore, the domain of the relation S can be expressed as:

domain = {1, 3, 4}

Moving on to the range of the relation S, it refers to the set of all y-values from the ordered pairs.

From the given pairs, we have y = p, y = 0, y = g, and y = 4. Similarly, we need to consider only unique y-values when determining the range.

Thus, the range of the relation S can be expressed as:

range = {0, 4, g, p}

It's important to note that the specific values of g and p are not given in the question. So, in the range, g and p are considered as distinct symbols representing unknown values.

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The random variable given in the accompanying table is discrete.

A discrete random variable can only take on a countable number of distinct values. In this case, the random variable represents the number of girls, and the values it can take are 0, 1, 2, 3, and 4. These values are countable and separate from each other, indicating that the random variable is discrete.

The probabilities assigned to each value also support the notion of discreteness. Each probability represents the likelihood of observing a specific number of girls, indicating that the random variable is defined for specific outcomes.

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The expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2) Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

The property of exponents that must be applied to the expression p^(1/2) to derive p as the result is the Power of a Power Property.

The Power of a Power Property states that when a power is raised to another power, the exponents are multiplied.

For instance, consider the expression p^(1/2). We can apply the Power of a Power Property to this expression as follows: p^(1/2) = (p^(1/2))^1 By applying the Power of a Power Property, the exponent (1/2) is multiplied by the exponent 1, giving a result of 1/2.

Therefore, the expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2)Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

So we have derived p as the result using the Power of a Power Property.

In summary, we must apply the Power of a Power Property to the expression p^(1/2) to derive p as the result.

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The safe amount of dose to administer in this situation is 15mL

To solve this problem, we can use the following steps:

Calculate the amount of drug in 1 mL of the solution.

Divide the desired dose by the amount of drug per mL.

The amount of drug in 1 mL of the solution is:

The other options are not safe because they would either deliver too much or too little medication. 20 mL would deliver 1000 mg, which is twice the desired dose. 4 mL would deliver only 60 mg, which is not enough medication. 2 mL would deliver only 30 mg, which is also not enough medication.

Therefore, the correct answer is 15 mL.

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To solve the problem, let's break it down step by step:

Given information:

- Point q is on a bearing of 120°, at a distance of 80m from point p.

- Point r is on a bearing of 045° and a distance of 150m from point q.

i) Distance between p and q:

Since point q is 80m away from point p, the distance between them is simply 80m.

ii) Bearing of point p from point r:

To find the bearing of point p from point r, we need to add the angles of the bearings. The bearing from q to p is 120°, and the bearing from r to q is 45°. Adding them gives us:

Bearing of p from r = 120° + 45° = 165°

iii) How far west of r is q:

To determine how far west of r point q is, we need to consider the bearing of r and the distance between r and q. The bearing of r is 45°, which means it is in the northeast direction. Since we want to find how far west q is, we need to subtract 45° from 180° to get the southwest direction. This indicates that q is west of r.

To calculate the distance, we use the cosine rule:

Distance between r and q = s[tex]\sqrt(80^2 + 150^2 - 2 * 80 * 150 * cos(180° - 45°)) ≈ 162.97m[/tex]

Therefore, q is approximately 162.97m west of r.

iv) Perpendicular distance from q to |PR|:

To find the perpendicular distance from q to the line segment PR, we can use the formula for the area of a triangle:

Perpendicular distance = (2 * Area of triangle PQR) / PR

First, we need to calculate the area of triangle PQR. Using the formula:

Area of triangle PQR = (1/2) * base * height

We can use the side PQ as the base and the distance from q to the line segment PR as the height. From the given information, we know that PQ has a length of 80m and the distance from q to |PR| is the same as the distance between r and q (162.97m). Calculating the area:

Area of triangle PQR = (1/2) * 80 * 162.97 ≈ 6518.8

Now we can calculate the perpendicular distance:

Perpendicular distance = (2 * 6518.8) / 150 ≈ 87.12m

Therefore, the perpendicular distance from q to |PR| is approximately 87.12m, rounded to 2 decimal places.

In summary:

i) The distance between p and q is 80m.

ii) The bearing of point p from r is 165°.

iii) Point q is approximately 162.97m west of r.

iv) The perpendicular distance from q to |PR| is approximately 87.12m.

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Answer:

{(0,0)}

Step-by-step explanation:

Since only (0,0) works, then the relation R in roster form must be {(0,0)}

To find the height of the cylinder when the volume is given as 1500 in³ and the radius is 7 inches, we can use the formula for the volume of a cylinder:

Volume = π * r² * h

Substituting the given values, we have:

[tex]1500 = 3.14 * 7^2 * h1500 = 3.14 * 49 * h1500 = 153.86 * h[/tex]

To solve for h, we divide both sides of the equation by 153.86:

h = 1500 / 153.86

h ≈ 9.75

Rounding the answer to the nearest hundredth, the height of the cylinder is approximately 9.75 inches.

Therefore, the height of the cylinder is 9.75 inches.

Note: It is important to use the accurate value of π, which is approximately 3.14159, for precise calculations. However, in this case, since you specified to use 3.14 for π, I have used that approximation to calculate the height.

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The statements about the measures of the center that are factual include the following:

A) The mean for Group A is less than the mean for Group B.

B) The median for Group A is less than the median for Group B.

C) The mode for Group A is less than the mode for Group B.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [∑x]/n

Where:

Mean for Group B = (1+1+1+2+2+3+3+3+3+5)/10

Mean for Group B = 2.4

Median for Group B = (3+2)/2 = 2.5.

Mean for Group A = (1+1+1+1+1+2+2+2+2+3)/10

Mean for Group A = 1.6

Median for Group A = (1+2)/2 = 1.5

Therefore, the mean and median for Group A is less than the mean and median for Group B.

In conclusion, all of the other three answer choices are correct since answer option D and E are not factual.

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Yes, deductive thinking does start with a given set of rules or premises that are already accepted as true.

Deductive thinking is a logical process of reasoning in which one starts with a general premise or set of premises, and then uses logic to draw a specific conclusion based on those premises. This type of thinking is often used in mathematics, science, and philosophy.

In deductive reasoning, the premises are considered to be true and the conclusion necessarily follows from the premises. For example, if the premise is "All mammals have fur" and the conclusion is "A dog is a mammal", then the conclusion necessarily follows from the premise.

The use of a set of rules or premises is an essential feature of deductive thinking because it allows for logical reasoning and inference to take place. By starting with a set of accepted premises, one can use logic to deduce new information or conclusions.

In summary, deductive thinking does start with a given set of rules or premises that are already accepted as true. These rules or premises are used to draw specific conclusions based on logical reasoning and inference.

Answer:

Step-by-step explanation:

0.14x + 0.06(20,500 - x) = 2,670.00

0.14x + 1,230 - 0.06x = 2,670.00

0.08x + 1,230 = 2,670.00

0.08x = 2,670.00 - 1,230

0.08x = 1,440.00

x = 1,440.00 / 0.08

x = 18,000.00

invested $18,000.00 in the bond account and $2,500.00 (20,500 - 18,000) in the certificate of deposit account.

The value of the expression [tex]\sqrt{a^2 + 12} + |b|[/tex] when a = -2 and b = 14 is 18.

Given the expression in the question:

[tex]\sqrt{a^2 + 12} + |b|[/tex]

When a = -2 and b = 14

To determine the value of the expression [tex]\sqrt{a^2 + 12} + |b|[/tex] when a = -2 and b = 14, we substitute the given values into the expression and simplify.

[tex]\sqrt{a^2 + 12} + |b|[/tex]

Plug in a = -2 and b = 14

[tex]\sqrt{(-2)^2 + 12} + |14|\\\\Simplify\\\\\sqrt{4 + 12} + |14|\\\\\\\sqrt{16} + |14|\\\\\\4 + 14\\\\18[/tex]

Therefore, the value of the expression is 18.

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The population of Ohio   has grown at a slower rate compared to Florida since 1900.

The city of Florida has experienced   a more significant increase in recent decades.

Currently, her population is   larger than that of Ohio. Ohio's population   was around 4.5 million in 1900,reaching about 7.5 million in 1950.

In the 1900s as well, Florida's population   was about 0.9 million in 1900 and around 2.7 million in 1950. By 2020,Florida's population had   grown to about 21.5 million, while Ohio's population was about 11.7 million.

hence, while both populations are growing one is growing at a faster rate that that is Florida.

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The 99% confidence interval for the population standard deviation (σ) is approximately 29.53 < σ < 150.33.

To construct a 99% confidence interval for the population standard deviation (σ), we can use the chi-square distribution. The formula for the confidence interval is:

Lower bound: (n - 1) * s^2 / χ^2(α/2, n-1)

Upper bound: (n - 1) * s^2 / χ^2(1 - α/2, n-1)

Where:

n is the sample size (11 in this case)

s is the sample standard deviation (given as 9)

α is the significance level (1 - confidence level), which is 0.01 for a 99% confidence level

χ^2(α/2, n-1) is the chi-square critical value at α/2 with n-1 degrees of freedom

χ^2(1 - α/2, n-1) is the chi-square critical value at 1 - α/2 with n-1 degrees of freedom

To find the critical values from the chi-square distribution table, we need to determine the degrees of freedom, which is n - 1 = 11 - 1 = 10 in this case.

Using the chi-square distribution table or a statistical calculator, the critical values are approximately 2.763 and 23.209 for χ^2(α/2, 10) and χ^2(1 - α/2, 10), respectively.

Substituting the values into the formula, we have:

Lower bound: (11 - 1) * 9^2 / 23.209 ≈ 29.53

Upper bound: (11 - 1) * 9^2 / 2.763 ≈ 150.33

Therefore, the 99% confidence interval for the population standard deviation (σ) is approximately 29.53 < σ < 150.33.

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Answer:

4x - 3 - 2x + 5 = 6 - 3x + 2 + 5x

2x + 2 = 2x + 8

2 ≠ 8, so this equation has no solutions.

Answer:

No solution

Step-by-step explanation:

Given:

[tex]4x-3-2x+5=6-3x+2+5x[/tex]

rearrange terms so like terms are together

[tex]4x-2x-3+5=6+2-3x+5x[/tex]

combine like terms

[tex]2x+2=8+2x[/tex]

subtract 2x to both sides

[tex]2\neq 8[/tex]

2 doesn't equal 8, meaning that there are 0 solutions to this problem.

Hope this helps! :)

The box plots provide visual representations of the distribution of salaries at two companies, Company A and Company B. To compare the ranges and medians of the data sets, we examine the characteristics of each box plot.

The range of a data set represents the difference between the maximum and minimum values. Looking at the box plots, we can determine that the range of Company A's salaries is larger than the range of Company B's salaries.

This can be inferred by observing the lengths of the whiskers, where the whiskers in Company A's box plot extend further in both the upper and lower directions compared to Company B's box plot.

The median of a data set represents the middle value when the data is arranged in ascending or descending order. Comparing the medians of the two box plots, we can determine that the median of Company A's salaries is higher than the median of Company B's salaries.

This is evident by comparing the positions of the medians within the boxes. In Company A's box plot, the median is closer to the upper quartile, indicating a higher median salary, while in Company B's box plot, the median is closer to the lower quartile, suggesting a lower median salary.

In summary, the range of salaries at Company A is larger than that of Company B, indicating a wider spread of salary values. Additionally, the median salary at Company A is higher than the median salary at Company B, suggesting a higher central tendency or midpoint in the distribution of salaries.

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Answer:

864

Step-by-step explanation:

80/100 simplified is 4/5

so you do 4/5 of 1080

which is 1080 divided by 5 that is 216

and then 216 x 4 which is 864

Answer:

5x + y = 4

Step-by-step explanation:

2x + (y + x) = 2x + x + y = 3x + y

Next, we can subtract 3x from both sides of the equation to isolate the variable y on one side:

2x + (y + x) - 3x = 4 - 3x

2x + y = 4 - 3x

Finally, we can rearrange the equation to have the variables followed by the constant on the right-hand side of the equation:

2x + 3x + y = 4

5x + y = 4

So, the equation is standard form is 5x + y = 4

2x + (y + x) = 4

When a + is found in front of an expression inside a parenthesis, the expression stays the same.

2x + y + x = 4

Group like terms. If a term has no coefficient, its coefficient is considered to be 1.

2x + 1x

We group like terms by adding their coefficients.

(2 + 1)x = 3x

3x + y4

The linear inequality is Efe-x < 78.Hence, the required expression for the average marks is (92 + 85 + 65 + Efe-x)/4. The linear inequality for the information that average marks are less than 80 is Efe-x < 78.

Given data:The marks scored by the four students in a mathematics test are ESI-92, Seth-85, Mary-65, Efe-x.We are required to write down an expression for the average marks. Also, we need to check if the average marks are less than 80 and write a linear inequality for the information.

Average of the marks:In order to find out the average of the marks scored by the four students, we add up the marks and divide by the total number of students. Let us do this:Average of the marks scored by the four students= (ESI-92 + Seth-85 + Mary-65 + Efe-x)/4= (92 + 85 + 65 + Efe-x)/4Let's now simplify this expression.Linear Inequality:Given that if the average marks are less than 80, we need to write a linear inequality for this information.

Let us do this:Average marks < 80(92 + 85 + 65 + Efe-x)/4 < 80Multiplying both sides by 4, we get:92 + 85 + 65 + Efe-x < 4 × 80Now, adding all the marks, we get:242 + Efe-x < 320Subtracting 242 from both sides, we get:Efe-x < 320 - 242Efe-x < 78

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Answer:

y = 17/4

Step-by-step explanation:

To determine the equation of the directrix of a parabola, we need to first identify the focus of the parabola. The general equation of a parabola is y = ax² + bx + c. Comparing this with the given equation y = 12x² - 6x + 10, we can say that a = 12, b = -6 and c = 10.

Now, to find the focus, we can use the formula, (h, k + (1/4a)) where h and k are the coordinates of the vertex. The vertex of this parabola can be determined by using the formula, h = -b/2a and k = c - b²/4a.

Substituting the values of a, b, and c in these formulas, we get;

h = -(-6)/2(12) = 1/4

k = 10 - (-6)²/4(12) = 9/2

So, the coordinates of the vertex are (1/4, 9/2).

Now, substituting these values in the formula, we get the focus as;

(h, k + (1/4a)) = (1/4, 9/2 + (1/4(12))) = (1/4, 23/4)

Hence, the focus of the parabola is (1/4, 23/4).

Now, the equation of the directrix of the parabola is y = k - (1/4a). Substituting the values of k and a in the formula, we get;

y = 9/2 - (1/4(12)) = 9/2 - 1/4 = 17/4

Therefore, the equation of the directrix is y = 17/4.

Hence, the equation of the directrix of the given parabola is y = 17/4.