Please calculate the volume of a solid oblique pyramid with a triangular base, given that the base has a length of 8 inches and a height of 6 inches, and the height of the pyramid is 10 inches. Round your answer to the nearest cubic inch.

The eigenvalues of the given matrix are approximately -1.8478, 0.8478, and 2, and the corresponding eigenvectors are approximately [-0.577, -0.577, -0.577], [0.6614, -0.6614, 0], and [0.577, 0.577, 0.577].

To find the eigenvalues and eigenvectors of the given matrix:

Let A be the given matrix:

A = [[0, 1, 1],

    [1, 0, 1],

    [1, 1, 0]]

To find the eigenvalues, we need to solve the characteristic equation det(A - λI) = 0, where λ is the eigenvalue and I is the identity matrix.

The characteristic equation becomes:

det([[0-λ, 1, 1],

    [1, 0-λ, 1],

    [1, 1, 0-λ]]) = 0

Expanding the determinant, we have:

-(λ³ - 2λ - 2) = 0

Simplifying, we get:

λ³ - 2λ - 2 = 0

Now we solve this equation to find the eigenvalues:

By analyzing the equation or using numerical methods, we find that the eigenvalues are approximately:

λ₁ ≈ -1.8478

λ₂ ≈ 0.8478

λ₃ ≈ 2

To find the eigenvectors, we substitute each eigenvalue back into the equation (A - λI) * v = 0 and solve for v.

For λ₁ ≈ -1.8478:

(A - λ₁I) * v₁ = 0

Solving this equation, we find the eigenvector v₁ associated with λ₁ as:

v₁ ≈ [-0.577, -0.577, -0.577]

For λ₂ ≈ 0.8478:

(A - λ₂I) * v₂ = 0

Solving this equation, we find the eigenvector v₂ associated with λ₂ as:

v₂ ≈ [0.6614, -0.6614, 0]

For λ₃ ≈ 2:

(A - λ₃I) * v₃ = 0

Solving this equation, we find the eigenvector v₃ associated with λ₃ as:

v₃ ≈ [0.577, 0.577, 0.577]

Therefore, the eigenvalues of the given matrix are approximately -1.8478, 0.8478, and 2, and the corresponding eigenvectors are approximately [-0.577, -0.577, -0.577], [0.6614, -0.6614, 0], and [0.577, 0.577, 0.577].

For more questions on eigenvalues:

https://brainly.com/question/15586347

#SPJ8

Answer:

A

Step-by-step explanation:

3x16

+

4x18
+

5x17

Answer:

there is no solution

Step-by-step explanation:

x + y = 6 → (1)

x + y = 4 → (2)

subtract (2) from (1) term by term

(x - x) + (y - y) = 6 - 4

0 + 0 = 2

0 = 2 ← false statement

this false statement indicates the equations have no solution

The correct option that would be sufficient to prove the right triangles ∆WXZ and ∆WYX is (A) WZ/WX = XW/YW

The perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.

Considering the smaller right triangle ∆WXZ and the bigger triangle ∆WYX;

the side WZ of ∆WXZ will correspond to the side WX of ∆WYX and similarly, side XW of ∆WXZ will correspond to the side of ∆WYX

so we can we the proportion as;

WZ/WX = XW/YW

Therefore, the proportion WZ/WX = XW/YW would be sufficient to prove the right triangles ∆WXZ and ∆WYX

Read more about right triangle here:https://brainly.com/question/2920412

#SPJ1

Answer:

[tex]\dfrac{(x+6)^2}{25}-\dfrac{(y+8)^2}{144}=1[/tex]

Step-by-step explanation:

To write the equation of the hyperbola with foci (7, -8) and (-19, -8), and vertices (-1, -8) and (-11, -8), we first need to determine the orientation of the hyperbola.

As the y-values of the foci are the same, the foci are located horizontally from the center of the hyperbola, and therefore the hyperbola is horizontal (opening left and right).

The standard equation for a horizontal hyperbola is:

[tex]\boxed{\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1}[/tex]

where:

The center of a hyperbola is the midpoint of the vertices.

Given that the vertices are (-1, -8) and (-11, -8), we can use the midpoint formula to find the coordinates of the center:

[tex](h,k)=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)[/tex]

[tex](h, k)=\left(\dfrac{-1-11}{2},\dfrac{-8-8}{2}\right)[/tex]

[tex](h, k)=\left(-6,-8\right)[/tex]

The value of "a" is the distance between the center of the hyperbola and each vertex.  To find the value of a, calculate the distance between the x-coordinates:

[tex]a=-1-(-6)=5[/tex]

[tex]a=-6-(-11)=5[/tex]

The value of "c" is the distance between the center of the hyperbola and each focus.  Given that the foci are (7, -8) and (-19, -8), and the center is (-6, -8), to find the value of c, calculate the distance between the x-coordinates:

[tex]c = 7-(-6)=13[/tex]

[tex]c = -6-(-19)=13[/tex]

Now we have determined the values of a and c, we can use c² = a² + b² to find the value of b:

[tex]c^2 = a^2 + b^2[/tex]

[tex]13^2 = 5^2 + b^2[/tex]

[tex]169 = 25 + b^2[/tex]

[tex]b^2=144[/tex]

[tex]b=12[/tex]

Finally, substitute the found values of a, b, h and k into the standard equation of a hyperbola:

[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex]

[tex]\dfrac{(x-(-6))^2}{5^2}-\dfrac{(y-(-8))^2}{12^2}=1[/tex]

[tex]\dfrac{(x+6)^2}{25}-\dfrac{(y+8)^2}{144}=1[/tex]

Therefore, the equation of the hyperbola with foci (7, -8) and (-19, -8), and vertices (-1, -8) and (-11, -8) is:

[tex]\boxed{\dfrac{(x+6)^2}{25}-\dfrac{(y+8)^2}{144}=1}[/tex]

The function Sam can use to figure his total earnings for the day, based on the number of people he serves, is E(n) = 42 + 5n.

To calculate Sam's total earnings for the day, we need to consider both his hourly wages and the tips he receives based on the number of people he serves. Let's break it down step by step.

First, we know that Sam earns $7 per hour as his wage. Since he works for 6 hours, his earnings from wages alone would be $7 multiplied by 6, which equals $42.

Next, Sam also earns about $5 in tips for each person he serves. We can represent the number of people Sam serves as "n". Therefore, his total tip earnings would be $5 multiplied by "n", which gives us 5n.

To calculate Sam's total earnings for the day, we add his earnings from wages and tips together. So the function representing his total earnings, "E", can be written as:

E(n) = 7(6) + 5n

Simplifying further, we get:

E(n) = 42 + 5n

For more such questions on number

https://brainly.com/question/24644930

#SPJ8

Answer:

Step-by-step explanation:

[tex]\angle x=\angle y=\angle z=90\deg\ \text{(angle in a semi-circle is a right angle)}[/tex]

All 3 angles are examples of the theorem which states that any angle coming off the diameter of a circle going to the edge of the circle will form a right angle.

The pairs of angles that are vertical angles in the figure are R and T.

In the figure provided, vertical angles are formed by the intersection of two lines. Vertical angles are always congruent (equal in measure) to each other.

Looking at the given options:

R and T are vertical angles because they are formed by the intersection of lines.

P and D are not vertical angles. They are adjacent angles formed by the intersection of lines, but they are not directly opposite each other.

Therefore, the pairs of angles that are vertical angles in the figure are:

R and T

for such more question on vertical angles

https://brainly.com/question/1821791

#SPJ8

Answer:

- 8a²

Step-by-step explanation:

using the rule of exponents

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m - n)}[/tex]

given

[tex]\frac{80a^9}{-10a^7}[/tex]

= [tex]\frac{80}{-10}[/tex] × [tex]a^{(9-7)}[/tex]

= - 8 × a²

= - 8a²

Part 1- The lower class boundary for the first class is 100.

Part 2- Approximately 75% of students take exactly two courses.

Part 1:

To find the lower class boundary for the first class, we need to consider the given class intervals. The lower class boundary is the smallest value within each class interval.

Given the class intervals:

100 - 104

105 - 109

110 - 114

115 - 119

120 - 124

125 - 129

130 - 134

The lower class boundary for the first class interval (100 - 104) would be 100.

So, the lower class boundary for the first class is 100.

Part 2:

To determine the percentage of students who take exactly two courses, we need to calculate the relative frequency for that particular category.

Given the data:

of Courses Frequency Relative Frequency Cumulative Frequency

1 23 0.4423 23

2 - 39

3 13 0.25 -

We can see that the cumulative frequency for the second class (2 courses) is 39. To find the relative frequency for this class, we need to divide the frequency by the total number of students surveyed, which is 52.

Relative Frequency = Frequency / Total Number of Students

Relative Frequency for 2 courses = 39 / 52 ≈ 0.75 (rounded to 4 decimal places)

To convert this to a percentage, we multiply the relative frequency by 100.

Percentage of students taking exactly two courses = 0.75 * 100 ≈ 75%

Therefore, approximately 75% of students take exactly two courses.

for such more question on lower class boundary

https://brainly.com/question/7949481

#SPJ8

Question

Part 1.

Data was collected for 300 fish from the North Atlantic. The length of the fish (in mm) is summarized in the GFDT below.

Lengths (mm) Frequency

100 - 104 1

105 - 109 16

110 - 114 71

115 - 119 108

120 - 124 83

125 - 129 18

130 - 134 3

What is the lower class boundary for the first class?

class boundary =

Part 2

In a student survey, fifty-two part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below:

Please round your answer to 4 decimal places for the Relative Frequency if possible.

# of Courses Frequency Relative Frequency Cumulative Frequency

1 23 0.4423 23

2   39

3 13 0.25

What percent of students take exactly two courses? %

The regression line is y = -0.1471x + 2.2386.

To determine the regression line using the LinReg(ax+b) function, we input the given data into the calculator and obtain the values for a and b in the regression equation.

Using the LinReg(ax+b) function with the given data, we have:

X: {14.56, 13.58, 12.69, 14.87, 15.68, 14.28}

Y: {0.25, 0.84, 0.71, 0.65, 0.35, 0.61}

After performing the regression analysis, we obtain the regression equation as follows:

y = -0.2012x + 3.4986

Therefore, the regression line is y = -0.2012x + 3.4986.

Please note that the numerical values provided for a and b are rounded to four decimal places for simplicity.

To check the regression line, we can substitute the given x-values into the equation and compare the calculated y-values with the actual y-values to verify the accuracy of the regression line.

For similar question on regression line.

https://brainly.com/question/17004137

#SPJ8

0.612 can be rewritten as the simplified fraction 153/250.

Question: Rewrite as a simplified fraction. 0.612
To rewrite 0.612 as a simplified fraction, we need to convert the decimal into a fraction.
Step 1: Count the number of decimal places.
In this case, 0.612 has three decimal places.
Step 2: Write the decimal as a fraction with the decimal part as the numerator and the denominator as the place value of the rightmost digit.
Since there are three decimal places, the denominator will be 1000 (10 raised to the power of 3).
0.612 = 612/1000
Step 3: Simplify the fraction.
To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator. In this case, both the numerator and denominator are divisible by 4.
612/1000 = (612 ÷ 4) / (1000 ÷ 4) = 153/250

Fore more such questions on simplified fraction

https://brainly.com/question/78672

#SPJ8

Answer: 8/9

Step-by-step explanation:

64/72            Divide both the top and bottom by 8

8/9

Answer:

(Sumita plans to deposit Rs. 21000 in any bank for 3 years. (a) Define compound interest. (b) How much amount will she get at 10% simple interest when she deposits it in a bank N ? Calculate it. (c) How much amount will she get at 9% interest being compounded annually when she deposits it in another bank M?Calculate it. (d) Which bank is better to deposit the sum and how much more amount will she get (e) from the bet

(a) Compound interest is the interest earned on both the initial principal amount and any accumulated interest from previous periods. Unlike simple interest, which is calculated only on the principal amount, compound interest takes into account the interest that has been added to the principal over time.

(b) To calculate the amount Sumita will get at 10% simple interest when she deposits Rs. 21,000 in bank N for 3 years, we can use the formula for simple interest:

Simple Interest = (Principal * Rate * Time) / 100

In this case:

Principal (P) = Rs. 21,000

Rate of interest (R) = 10%

Time (T) = 3 years

Simple Interest = (21,000 * 10 * 3) / 100

Simple Interest = 6,300

Amount = Principal + Simple Interest

Amount = 21,000 + 6,300

Amount = Rs. 27,300

Therefore, Sumita will get Rs. 27,300 at 10% simple interest when she deposits it in bank N.

(c) To calculate the amount Sumita will get at 9% interest compounded annually when she deposits Rs. 21,000 in bank M for 3 years, we can use the formula for compound interest:

Compound Interest = Principal * [(1 + Rate/100) ^ Time] - Principal

In this case:

Principal (P) = Rs. 21,000

Rate of interest (R) = 9%

Time (T) = 3 years

Compound Interest = 21,000 * [(1 + 9/100) ^ 3] - 21,000

Calculating the compound interest:

Compound Interest = 21,000 * (1.09^3) - 21,000

Compound Interest ≈ 21,000 * 1.29503 - 21,000

Compound Interest ≈ 27,139.63 - 21,000

Compound Interest ≈ Rs. 6,139.63

Amount = Principal + Compound Interest

Amount = 21,000 + 6,139.63

Amount ≈ Rs. 27,139.63

Therefore, Sumita will get approximately Rs. 27,139.63 at 9% interest compounded annually when she deposits it in bank M.

(d) To determine which bank is better to deposit the sum, we compare the amounts received in bank N (simple interest) and bank M (compound interest).

In bank N, Sumita will receive Rs. 27,300, while in bank M, she will receive approximately Rs. 27,139.63.

Comparing the amounts, we can see that Sumita will get a slightly higher amount in bank N.

(e) The amount she will get from the better bank (bank N) is Rs. 27,300 - Rs. 27,139.63 = Rs. 160.37 more than bank M.

Step-by-step explanation:

hope it help

Answer:

40, 50, 30 Yes

13, 5, 12 Yes

10, 10, 15 Yes

41, 9, 40 Yes

Step-by-step explanation:

16, 10, 6

10 + 6 = 16

No

40, 50, 30

30 + 40 > 50

Yes

13, 5, 12

5 + 12 > 13

Yes

70, 20, 25

20 + 25 < 70

No

10, 10, 15

10 + 10 >15

Yes

41, 9, 40

9 + 40 > 41

Yes

Answer:

the effective tax rate for a taxable income of $175,000 is approximately 21.02%.

Step-by-step explanation:

Let's break down the income into the corresponding tax brackets:

The first $10,275 is taxed at a rate of 10%.

Tax on this portion: $10,275 * 0.10 = $1,027.50

The income between $10,276 and $41,175 is taxed at a rate of 12%.

Tax on this portion: ($41,175 - $10,276) * 0.12 = $3,710.88

The income between $41,176 and $89,075 is taxed at a rate of 22%.

Tax on this portion: ($89,075 - $41,176) * 0.22 = $10,656.98

The income between $89,076 and $170,050 is taxed at a rate of 24%.

Tax on this portion: ($170,050 - $89,076) * 0.24 = $19,862.88

The income between $170,051 and $175,000 is taxed at a rate of 32%.

Tax on this portion: ($175,000 - $170,051) * 0.32 = $1,577.44

Now, sum up all the taxes paid:

$1,027.50 + $3,710.88 + $10,656.98 + $19,862.88 + $1,577.44 = $36,836.68

The effective tax rate is calculated by dividing the total tax paid by the taxable income:

Effective tax rate = Total tax paid / Taxable income

Effective tax rate = $36,836.68 / $175,000 = 0.21024 (rounded to the nearest hundredth)

Answer:

all real numbers

Step-by-step explanation:

Try a negative number, a positive number and zero for x.

All of them work.

Answer: all real numbers

Answer:

I wish you good luck in finding your answer

Answer: 115

Step-by-step explanation:

Answer:

Step-by-step explanation:

(x^3 - 10x + K)/(X+3) = 6 GIVEN

for different values of x there are many possible values of k some i will show

when we substitute x=1

we get k=33

at x=2

weget k=42

so many values are possible for k

because there is no intervel in question which restrics us from taking different values of x or k so you take any value of x you will get different values of k

Answer: D

Step-by-step explanation:

Hope it helps

Step-by-step explanation:

h,k   center is  0,0 and radius is 8

(x-0)^2  + ( y-0)^2 = 8^2

x^2  + y^2  = 64

IM NOT SURE, DO YOU WANT ME TO WORK IT OUT FOR YOU?

Answer:

incorrect

Step-by-step explanation:

as 7 * 6 = 42 and r is 10

so 6r3 is incorrect

and 7 * 7 = 49 and r is 3

so 7r3 is correct

(a) To find the assets in 2011 using the given information: A. To find the assets in 2011, substitute 11 for x and evaluate to find A(x).

In 2011 the assets are about $669.6 billion

(b) To find the assets in 2016 using the given information: B. To find the assets in 2016, substitute 16 for x and evaluate to find A(x).

In 2016 the assets are about $931.5 billion.

(c) To find the assets in 2019 using the given information: B. To find the assets in 2019, substitute 19 for x and evaluate to find A(x).

In 2019 the assets are about $1135.4 billion.

Based on the information provided, we can logically deduce that the assets for a financial firm can be approximately represented by the following exponential function:

[tex]A(x)=324e^{0.066x}[/tex]

where:

For the year 2011, the cost (in billions of dollars) is given by;

x = (2011 - 2007) + 7

x = 4 + 7

x = 11 years.

Next, we would substitute 11 for x in the exponential function:

[tex]A(11)=324e^{0.066 \times 11}[/tex]

A(11) = $669.6 billions.

Part b.

For the year 2016, the cost (in billions of dollars) is given by;

x = (2016 - 2007) + 7

x = 9 + 7

x = 16 years.

Next, we would substitute 16 for x in the exponential function:

[tex]A(16)=324e^{0.066 \times 16}[/tex]

A(16) = $931.5 billions.

Part c.

For the year 2019, the cost (in billions of dollars) is given by;

x = (2019 - 2007) + 7

x = 12 + 7

x = 19 years.

Next, we would substitute 19 for x in the exponential function:

[tex]A(19)=324e^{0.066 \times 19}[/tex]

A(19) = $1135.4 billions.

Read more on exponential functions here: brainly.com/question/28246301

#SPJ1

Answer: [tex](-\infty, 6) \cup (6, \infty)[/tex]

Step-by-step explanation:

Polynomials are continuous for all reals, so we only need to consider the rational part. Since the denominator is undefined at [tex]x=6[/tex], there is a vertical asymptote at [tex]x=6[/tex].

Answer:

a. To fill in the missing data in the table, we can use the information given in the table along with the fact that the total number of employees is 186.

For value A: Since the total number of employees with no college credit is 28, and the total number of men is 79, we can subtract the number of men with some college (C) and college graduates (15) from the total number of men to find the missing value A. So A = 79 - C - 15.

For value B: Since the total number of women is 186, we can subtract the number of women with some college (D) and college graduates (22) from the total number of women to find the missing value B. So B = 186 - D - 22.

For value C: Since the total number of employees with some college is 81, and we have already determined the values A and D, we can subtract A and D from the total number of employees with some college to find the missing value C. So C = 81 - A - D.

For value D: Similarly, we can subtract B and E from the total number of women to find the missing value D. So D = 186 - B - E.

For value E: Since the total number of college graduates is 37 (15 men + 22 women), we can subtract the number of college graduates among men (15) from the total to find the missing value E. So E = 37 - 15.

For value F: Since the total number of employees is 186, we can subtract the total number of men (79) from the total to find the missing value F. So F = 186 - 79.

b. Joint relative frequency refers to the proportion of individuals that fall into a particular combination of categories. For example, the joint relative frequency of men with no college credit is the number of men with no college credit divided by the total number of employees (28/186). These data are joint and relative because they represent the proportion of individuals in a specific category combination relative to the total population.

c. To summarize the data using conditional relative frequency, we can calculate the proportion of individuals in each category given a specific condition. For example, we can calculate the conditional relative frequency of women who are college graduates by dividing the number of women who are college graduates (22) by the total number of women (186). Similarly, we can calculate the conditional relative frequency of men with some college by dividing the number of men with some college (C) by the total number of men (79).

To summarize the data using marginal relative frequency, we can calculate the proportion of individuals in each category by dividing the number of individuals in that category by the total number of individuals. For example, we can calculate the marginal relative frequency of men by dividing the total number of men (79) by the total number of employees (186). Similarly, we can calculate the marginal relative frequency of college graduates by dividing the total number of college graduates (37) by the total number of employees (186).

d. The data in the table can be analyzed to determine if there is an association or relationship between the variables. If the values in the table change depending on the categories of the other variable, then the variables are dependent. In this case, the data is dependent because the number of individuals with certain educational levels (no college credit, some college, college graduate) varies based on their gender. For example, there are different proportions of men and women in each educational category, indicating a relationship between gender and education level.

Step-by-step explanation:

The missing values in the two-way frequency table are filled based on the given values and the composition of the table. The table represents joint relative frequency, which is the proportion of specific groups in the total population. We can summarize the data using marginal and conditional relative frequencies, and the data are considered dependent because an employee's education level depends on their gender.

To fill in the missing values of the two-way frequency table, we need to use the given numbers and the rules of the two-way frequency table. Here are the strategies used for filling in the values for A through F:

The table will also represent joint relative frequency because each cell represents the joint occurrence of two categories (gender and education level). For example, the number of male employees with no college credit (28) divided by the total number of employees (186) is a joint relative frequency.

We may summarize the table data using conditional relative frequency and marginal relative frequency. The marginal relative frequency is the total of each row or column divided by the grand total. The conditional relative frequency would be, for example, the proportion of women among those with no college credit.

The data are dependent because the education level depends on whether the employee is a man or a woman.

https://brainly.com/question/16148316

#SPJ2

Answer:

No

Step-by-step explanation:

To determine if the average number of miles flown per passenger increased by one-third between 1966 and 1976, we need to compare the increase in miles flown during that period.

According to the given table:

To find the increase in miles flown, subtract the 1966 value from the 1976 value:

[tex]\begin{aligned}\sf Increase\; in\; miles\; flown &= \sf 831 \;miles - 711\; miles\\&= \sf 120\; miles\end{aligned}[/tex]

Therefore, the average number of miles flown per passenger between 1966 and 1976 increased by 120 miles.

To check if the increase is one-third of the initial value, we need to calculate one-third of the 1966 value:

[tex]\begin{aligned}\sf One\;third \;of \;711 \;miles &= \sf \dfrac{1}{3} \times 711\; miles\\\\ &= \sf \dfrac{711}{3} \; miles\\\\&=\sf 237\;miles\end{aligned}[/tex]

Since the increase in miles flown (120 miles) is not equal to one-third of the initial 1966 value (237 miles), the statement that the average number of miles flown per passenger increased by one-third between 1966 and 1976 is not true.

Answer:

[tex]\textsf{The parabola has a vertex at $\left(\:\boxed{-3}\:,\boxed{-7}\:\right)$, has a p-value of $\boxed{-1}$ and it}[/tex]

[tex]\textsf{$\boxed{\sf op\:\!ens\;to\;the\;left}$\:.}[/tex]

Step-by-step explanation:

The given directrix of the parabola is x = -2, which is a vertical line.

The directrix is perpendicular to the axis of symmetry. Therefore, this means that the parabola has a horizontal axis of symmetry.

The focus of a parabola is a fixed point located inside the curve. The x-coordinate of the given focus is x = -4. As this is to the left of the directrix, it means that the parabola opens to the left.

The standard form of a horizontal parabola is:

[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]

where:

As the focus is (-4, -7), then:

[tex]\begin{aligned}(h+p, k)&=(-4,-7)\\\\\implies k&=-7\\\implies h+p&=-4\end{aligned}[/tex]

As the directrix is x = -2, then:

[tex]h - p=-2[/tex]

To find the value of h, sum the equations involved h and p to eliminate p:

[tex]\begin{array}{crcccr}&h &+& p& =& -4\\+&h& -& p& = &-2\\\cline{2-6}&2h&&& =& -6\\\cline{2-6}\\\implies &h&&&=&-3\end{array}[/tex]

To find the value of p, substitute the found value of h into one of the equations:

[tex]\begin{aligned}-3 - p&=-2\\p&=-3+2\\p&=-1\end{aligned}[/tex]    

Therefore, the values of h, k and p are:

The parabola has a vertex at (-3, -7), has a p-value of -1 and it opens to the left.

The parabola has a vertex at (-3, y), has p-value of 1 and it equation is

(x + 3)² = 4y.

To find the equation of the parabola with the given focus and directrix, we can use the standard form equation of a parabola:

(x - h)² = 4p(y - k)

where (h, k) is the vertex of the parabola and "p" is the distance from the vertex to the focus (and also from the vertex to the directrix).

Given:

Focus: (-4, -7)

Directrix: x = -2

1. Finding the vertex:

Since the directrix is a vertical line, the vertex lies on the line that is equidistant from the focus and directrix. In this case, it lies on the line x = (-4 + (-2))/2 = -3.

Therefore, the vertex of the parabola is (-3, y).

2. Finding the p-value:

The distance from the vertex to the focus (and also to the directrix) is the same. In this case, the distance is |-3 - (-4)| = 1.

Therefore, the value of "p" is 1.

3. Writing the equation of the parabola:

Using the vertex (-3, y) and the p-value of 1, we can write the equation of the parabola:

(x - h)² = 4p(y - k)

(x - (-3))² = 4(1)(y - y)

Simplifying, we get:

(x + 3)² = 4(y - y)

(x + 3)² = 4y

So, the equation of the parabola is (x + 3)² = 4y.

The vertex of the parabola is (-3, y) and the p-value is 1.

Learn more on equation of parabola here;

https://brainly.com/question/29635857

#SPJ1