Answer:
As supply rises, prices generally decrease.--true
As demand decreases, costs generally increase.--false
As supply decreases, prices increase.--true
The average rate of change describes how much a quantity changes as price increases.--false
As demand rises, the price of the product decreases.--false
Step-by-step explanation:
The letters in the word HORSES are arranged in a row.How many unique arrangements are there of the letters?
Enter your answer in the box.
_____ arrangements
Answer:
180
Step-by-step explanation:
The word HORSES has 6 distinct letters, so we can arrange them in 6! = 720 ways if all the letters were unique.
However, in this case, the letters E and S are repeated twice. Therefore, we must divide by the number of arrangements of the repeated letters to avoid counting the same arrangement more than once.
The letter E appears twice, so there are 2! = 2 ways to arrange the E's within the word. Similarly, the letter S appears twice, so there are 2! = 2 ways to arrange the S's within the word.
Thus, the total number of unique arrangements of the letters in the word HORSES is:
6! / (2! × 2!) = 720 / 4 = 180
Therefore, there are 180 unique arrangements of the letters in the word HORSES.
At Jamie's bank, 20 bankers manage personal loans and 15 bankers manage business loans. Of those, 3 bankers manage both. If the bank only offers these two types of loans, how many bankers does it employ? A. 17 B. 32 C. 35 D. 38
The bank employs a total of 32 bankers, and the answer is not listed among the options provided. The correct option is B.
Let's denote the number of bankers who manage only personal loans as P and the number of bankers who manage only business loans as B. Then, we can use the following information to form equations:
There are 20 bankers who manage personal loans, which means P + 3 bankers in total manage personal loans.
There are 25 bankers who manage business loans, which means B + 3 bankers in total manage business loans.
The bank has a total of X bankers.
Using these equations, we can solve for X as follows:
P + 3 = 20 (equation 1)
B + 3 = 25 (equation 2)
P + B + 3 = X (equation 3)
Solving equation 1 for P, we get P = 17.
Solving equation 2 for B, we get B = 12.
Substituting P = 17 and B = 22 into equation 3, we get:
17 + 12 + 3 = X
Simplifying, we get X = 32.
Therefore, the bank employs a total of 32 bankers, and the answer is not listed among the options provided.
To know more about finance calculation follow
https://brainly.com/question/15299975
#SPJ1
The functions fand g are defined as follows.
f(x)=2x²-3x g(x)=-4x-1
Find f(-4) and g (5).
f(-4) = ?
g (5) = ?
Answer:
f(- 4) = 44 , g(5) = - 21
Step-by-step explanation:
to evaluate f(- 4) substitute x = - 4 into f(x)
f(- 4) = 2(- 4)² - 3(- 4) = 2(16) + 12 = 32 + 12 = 44
to evaluate g(5) substitute x = 5 into g(x)
g(5) = - 4(5) - 1 = - 20 - 1 = - 21
Can someone please help me and give me the answer ASAP
1. The lateral surface area of the prism is 200 units²
2. The lateral surface area of the cylinder is 125.6 cm²
What is lateral surface area?The lateral surface area is the area of the lateral surface.
The lateral surface area of a prism is expressed as;
LSA = (a+b+c)h
or perimeter of the base × height
LSA = (6+12+7)8
= 25 × 8
= 200 units²
The lateral surface area of a cylinder
= 2πrh
r = 4cm and h = 5cm
LSA = 2 × 3.14 × 4 × 5
LSA = 40 × 3.14
= 125.6cm²
learn more about lateral surface area from
https://brainly.com/question/12506372
#SPJ1
Find the sum of the first 5 terms of the geometric sequence 3, -9, 27,....
The sum of the first 5 terms of the sequence is 183.
We have,
The first term of the sequence is 3 and the common ratio is -3.
We can use the formula for the sum of the first n terms of a geometric sequence:
Sn = a(1 - r^n) / (1 - r)
where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.
Plugging in the values we have:
S5 = 3(1 - (-3)^5) / (1 - (-3))
Simplifying:
S(5) = 3(1 + 243) / 4
S(5) = 3(244) / 4
S(5) = 183
Therefore,
The sum of the first 5 terms of the sequence is 183.
Learn more about geometric sequence here:
https://brainly.com/question/2321576
#SPJ1
X
-3
-1
1
-1
y
5
2
-1
4
The table above:
The task here is to determined where the table given is a function. Thus we can state that the above table is NOT a function. This is called Non-Function Relation.
What is the reason for the above assertion?The table given above is suggestive of the relationship between the values of x and y given.
It may be inferred that x values are the input values while the y values are the output.
So the criteria for the values on the table to constitute a function is that each input value (x) must be associated with only one value of y.
From the table, it is clear to see that this rule if violated. You have the x value (-1) being associated with the y values of 2 and 4 respectively, hence, it is proper to conclude that the table is NOT a function.
This is called a Non-Function Relation.
Learn more about Function Relation:
https://brainly.com/question/6241820
#SPJ1
What is the slope of 5x-4y=-24
Answer: The slope is -5/4
m=-5/4
If an a × b matrix is multiplied by a c x d matrix, what must be true in order to get an
answer?
The condition that must be true in order to get a correct answer will be that the number found in the columns of the first matrix must be equal to the numbers in the rows of the second matrix.
What is a matrix?A matrix is a rectangular arrangement of numbers that can be used to demonstrate mathematical properties. Often, two or three matrices can be evaluated to determine an outcome.
For the given matrices, a × b and c x d the only way to arrive at a correct answer will be if the figures found in the columns of the first matrix equal the figures found in the rows of the second matrix.
Learn more about matrices here:
https://brainly.com/question/94574
#SPJ1
answer this please i need help with this problem
The value of x in the triangle is 1/√3
We know that tan function is the ratio of opposite side and adjacent side
In triangle, for angle 60 degrees the opposite side is 1 unit
Adjacent side is x units
tan 60 = opposite side/adjacent side
√3= 1/x
We need to find value of x
Apply cross multiplication
x=1/√3
Hence, the value of x in the triangle is 1/√3
To learn more on trigonometry click:
https://brainly.com/question/25122835
#SPJ1
Can someone help me please????????????????????????????????????
The percentage error for each of the given situations are:
1) 23%
2) 21%
3) 11%
4) 16.67%
5) 43%
How to find the percent error?The formula for percent error is:
Percentage Error = ((Actual Number – Estimated Number)/ Estimated number) * 100%
1) Estimated Number = 2310
Actual Number = 3000
Thus:
Percent Error = (3000 - 2310)/3000 * 100%
Percent error = 23%
2) Estimated Number = 17600
Actual Number = 21300
Thus:
Percent Error = (21300 - 17600)/17600 * 100%
= 21%
3) Estimated Number = 4.5
Actual Number = 4
Thus:
Percent Error = (4 - 4.5)/4.5 * 100%
= 11%
4) Estimated Number = 15000
Actual Number = 12500
Thus:
Percent Error = (12500 - 15000)/15000 * 100%
= 16.67%
5) Estimated Number = 350
Actual Number = 200
Thus:
Percent Error = (200 - 350)/350 * 100%
= 43%
Read more about Percent Error at: https://brainly.com/question/5493941
#SPJ1
What is the volume of this prism?44 cubic units
88 cubic units
102 cubic units
Not enough information.
The volume of the prism will be 88 cubic units. Then the correct option is B.
Given that:
Length, L = 4 units
Width, W = 4 units
Height, H = 5.5 units
The volume of the prism is given as,
V = L x W x H
The volume of the prism is calculated as,
V = 4 x 4 x 5.5
V = 88 cubic units
The volume of the prism will be 88 cubic units. Then the correct option is B.
More about the rectangular prism link is given below.
https://brainly.com/question/12649592
#SPJ1
The complete question is given below.
The position (in meters) of a particle per respect to time (in seconds) is defined by the
following functions (t)=t4-16t³+72t² +5. Find the maximal and minimal value for
the speed of the particle for t E [1, 7].
The maximum of 1,159 m/s occurs when t = 7, and the minimum of 16 m/s occurs when t = 6.
How to calculate the valueIt should be noted that upon deriving v(t), an equation of 12t² - 96t + 144 is produced. Subsequently, v'(t) must be set to zero, resulting in a quadratic equation of 12t² - 96t + 144 = 0, requiring division of both sides by 12 to produce t² - 8t + 12 = 0.
The quadratic can now be factored to obtain (t - 2)(t - 6) = 0, indicating that critical points lie on the values t = 2 and t = 6.
After calculating these values— v(1) = 100 m/s, v(2) = 64 m/s, v(6) = 16 m/s and v(7) = 1159 m/s—it is clear that the maximum of 1,159 m/s occurs when t = 7, and the minimum of 16 m/s occurs when t = 6.
Learn more about speed on
https://brainly.com/question/13943409
#SPJ1
1. An account is opened with an initial deposit of $6,500
and earns 3.6% interest compounded semi-annually.
What will the account be worth in 20 years?
The balance of the account after 20 years is given as follows:
A(20) = $13,268.58.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for this problem are given as follows:
P = 6500, r = 0.036, n = 2, t = 20.
Hence the balance of the account after 20 years is given as follows:
A(20) = 6500 x (1 + 0.036/2)^(2 x 20)
A(20) = $13,268.58.
More can be learned about compound interest at https://brainly.com/question/24274034
#SPJ1
What is the length of AB
The length of AB in the right triangle is 8 units.
How to find the side of a right triangle?The sides of a right angle triangle can be found as follows:
The right angle triangle has one of its angles as 30 degrees. The side AB can be found using trigonometric ratios.
Hence,
sin 30 = opposite / hypotenuse
where
opposite side = AB
hypotenuse side = 16 units
Therefore,
sin 30 = AB / 16
cross multiply
AB = 16 sin 30
AB = 16 × 0.5
AB = 8 units
Therefore,
AB = 8 units
learn more on triangle here: brainly.com/question/25950519
#SPJ1
Nicole‘s mother put tiles on a section of the kitchen floor. The section included 5 rows with 13 tiles in each row. Each tile cost $2. How much money did Nicole’s mother spend on the tiles?
If each tile cost $2 then the amount spend by Nicole’s mother on tiles is $130
Given that Nicole‘s mother put tiles on a section of the kitchen floor.
The section included 5 rows with 13 tiles in each row
Each tile cost $2.
To find the total amount spend by Nicolas mother on tiles we have to find the number of tiles
Number of tiles =5×13
=65 tiles
Now let us find the amount
Total amount on tiles = 2×65
=$130
Hence, if each tile cost $2 then the amount spend by Nicole’s mother on tiles is $130
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
Which account will make more money, an account that starts out with $4,500 with a 7.75% APR
compounded monthly or an account that begins with $5,500 with a 6.75% APR continuously
compounded? Calculate the two accounts for 10yrs, 20yrs, 50yrs, 85yrs.
Answer:
second account makes more for the first 20 years; after 20.6 years, the first account makes more.first account: 10 yrs: $9743; 20 yrs: $21096; 50 yrs: $214,137; 85 yrs: $3,198,369second account: 10 yrs: $10802; 20 yrs: $21216; 50 yrs: $160,734; 85 yrs: $1,706,582Step-by-step explanation:
You want to compare the future values of two accounts after 10, 20, 50, and 85 years:
$4500 at 7.75%, compounded monthly$5500 at 6.75%, compounded continuouslyCompounded monthlyThe formula for account value with compounding monthly is ...
A = P(1 +r/12)^(12t) . . . . . . principal P invested at rate r for t years
A = 4500(1 +0.075/12)^(12·t) . . . . . using given values for P and r
The first line of calculator output shown in the attachment gives the value after 10, 20, 50, and 85 years.
Compounded continuouslyThe formula for account value with continuous compounding is ...
A = P·e^(rt)
A = 5500·e^(0.0675t) . . . . . using given values for P and r
The second line of calculator output shown in the attachment gives the value after 10, 20, 50, and 85 years.
You will notice this (second) account has higher value up to 20 years, then lower value after that.
The account with the higher interest rate will make more money after the "break-even" period of about 20.6 years.
__
Additional comment
We have rounded the account values to the nearest dollar. For the purpose of value comparison, three significant figures would be sufficient.
The second attachment shows the different account values over the long term. You can see the higher interest rate really makes a difference.
The third attachment shows the shorter-term account values, and the "break-even" time period of about 20.6 years, when the values in both accounts are about $22,063.
Using the graphing function on your calculator, find the solution to the system
of equations shown below.
OA. No solution
B. x = -8, y = 2
OC. x= 12, y = 3
D. More than 1 solution
3y-12x=18
2y-8x=12
SUBMIT
The solution to the system of equations is (d) More than 1 solution
Finding the solution to the system of equationsFrom the question, we have the following parameters that can be used in our computation:
3y-12x=18
2y-8x=12
Using the graphing function on a calculator, we have the solution to be
Infinite many solutions
This is so because the equations 3y-12x=18 and 2y-8x=12 are equivalent equations
Read more about system of equations at
https://brainly.com/question/13729904
#SPJ1
Ravi is saving money to buy a game. The game costs $12, and so far he has saved one-fourth of this cost. How much money has Ravi saved?
Answer:
$3
Step-by-step explanation:
since $12 is 4/4 and he save 1/4 its 12÷4
Answer:
$3
Step-by-step explanation:
12 divided by 4 is 3
(3+3)+(3+3)
6+6
= 12
HELP ASAP I NEED DONE WITHIN 5 MINUTES OR A LITTLE MORE AND ALSO BRAINLIEST
The line plot represents the afterschool activities at 19 middle schools.
A horizontal number line starting at 0 and increasing by units of two up to 30. There is one dot above 6, 8, and 26. There are two dots above 10, 12, 18, 20, and 22. There are three dots above 14 and 16. The title is Afterschool Activities, and the number line is labeled Number of Activities.
Which statement best describes the spread and distribution of the data?
The data is symmetric with an approximate range of 20. The lowest value of 6 might mean that most students did not participate in activities.
The data is skewed with an approximate range of 20. The most frequent number of activities was 16 or more, which might mean that most of the students participated in the activities.
The data is symmetric with an approximate range of 20. The most frequent number of activities was 14 and 16, which might mean about half of the students in each class participated.
The data is bimodal with an approximate range of 20. This means that the most frequent number of activities was either 4 or 26, which might mean that the activities vary in each school.
Answer: the best answer is option A: the data is symmetric with an approximate range of 20. The lowest value of 6 might mean that most students did not participate in activities.
Step-by-step explanation: From the line plot, we can see that the data is not symmetric because the dots are not equally distributed on both sides of the plot. Therefore, we can eliminate options A and C.
Option D suggests that the data is bimodal, meaning that there are two peaks in the distribution. However, there is no clear indication of two peaks in the plot. Therefore, we can eliminate option D.
Option B suggests that the data is skewed, and the most frequent number of activities is 16 or more. However, this is not the case as the highest number of dots is above 14 and 16. Therefore, we can eliminate option B.
Customer: "I don't think that your questions are relevant to our discussion
A. Let me explain how my questions are related to our discussion.
B. I didn't mean to sound negative. Let me start over.
C. I am trying to be nice. I think you took what I said the wrong way.
D. I am very interested in what you have to say.
E. I apologize that you do not find them helpful.
The best response to such statement will be "Let me explain how my questions are related to our discussion" which is option (A)
What you should know about Customer DissatisfactionThe statement the customer made shows that he is disappointed with whatever the situation is.
Customer dissatisfaction refers to the feeling of displeasure, frustration, or disappointment that a customer experiences when their expectations are not met by a product or service they have purchased or received. It can arise from various factors, such as poor quality, ineffective communication, slow response times, inadequate support, or a mismatch between customer needs and what is being offered.
To prevent customer dissatisfaction, businesses must focus on providing high-quality products and services, being responsive and attentive to customer needs, and proactively addressing any issues or concerns that arise.
Learn more about customer dissatisfaction here:
https://brainly.com/question/26313265
#SPJ1
The pairs of polygons below are similar. Give the scale factor, perimeter ratio, and area ratio of Figure A to Figure B
1.) The scale factor = 4
The perimeter ratio = 1:3
The area ratio = 1:16
How to calculate the scale factor of the given shapes?To calculate the scale factor of the given shapes, the formula that should be used would be ;
Scale factor = Bigger dimensions/ Smaller dimensions
Length of the bigger rectangle (B) = 16
Length of the smaller rectangle (A) = 4
The scale factor = 16/4 = 4
The perimeter = 2(l+w)
length B = 16
width B = 8
perimeter B = 2(16+8)
= 2(24) = 48
Length A = 4
width A = 2
perimeter A =2(4+2)
= 16
The perimeter ratio = A:B = 16:48 = 1:3
Area = length×width
length A = 4
width A = 2
Area A = 4×2 = 8
length B = 16
width B = 8
area B = 8×16= 128
Area ratio of A:B = 8:128 = 1:16
Learn more about area here:
https://brainly.com/question/28470545
#SPJ1
A contractor can by two types of wood. she got 45 expensive wood and 60 cheap wood for the same total price. if the 45 expensive wood cost $3.00 more than the 60 cheap wood, then which equation below shows the correct relationship between the 2 types of wood that she purchased. Also (x =price of the 60 cheap wood)
A.45(x+3)=60x
B.45(x-3)=60x
C.60(x-3)=45x
D.60(x+3)=45x
Answer:
A. 45(x+3)=60x
Step-by-step explanation:
PLEASE HELP I DON'T UNDERSTAND THIS!!!!!
Answer:
C. (4, 0)
Step-by-step explanation:
(x, y)
a. (4, 3)
y = 12 - 3x
3 = 12 - 3(4)
3 = 12 - 12
3 = 0 false
b. (-4, 4)
y = 12 - 3x
4 = 12 - 3(-4)
4 = 12 + 12
4 = 24 false
c. (4, 0)
y = 12 - 3x
0 = 12 - 3(4)
0 = 12 - 12
0 = 0 true
d. (0, 4)
y = 12 - 3x
4 = 12 - 3(0)
4 = 12 - 0
4 = 12 false.
Answer: C (4, 0)
Step-by-step explanation:
your function y = 12 - 3x
They are asking which of those points are on the line
(x, y) this is a format of a point where you can plug in x for x and y for y.
a. (4, 3) x=4 y=3 substitute and see if your answer is true
3 = 12 -3(4)
3 = 0 this is not true so (4, 3) is not a solution
b. (-4,4) x= -4 y=4
4 = 12 - 3(-4)
4 = 24 not true
c. (4, 0) x=4 y=0
0 = 12-3(4)
0 = 0 true (4,0) is a solution
d. (0, 4)
4 = 12 - 3 (0)
4=12
cos xº [Hint: Change degree into radian] find the derivative from definition
The derivative of the function cos(xº) in radians is y' = -sin(xπ/180)
Finding the derivative of the functionFrom the question, we have the following function definition that can be used in our computation:
cos(xº)
Changing the degree into radian, we have
cos(xπ/180)
Express as a function
So, we have
y = cos(xπ/180)
When the cosine function is differentiated, we have
y' = -sin(xπ/180)
Hence, the differentiated function is y' = -sin(xπ/180)
Read more about derivative at
https://brainly.com/question/5313449
#SPJ1
The volume of the triangular pyramid below is 210 units³. Find the value of x.
The value of x as shown in the triangular prism is 14 unit.
What is traingular pyramid?Triangular pyramids are formed solely from triangles. The 3 triangular sides slant upwards to form the triangular base.
To calculate the value of x of the rectangular pyramid, we use the formula below
Formula:
V = bhH/6............................. Equation 1Where:
V = volume of the Pyramidb = Base of the triangleh = Height of the triangleH = Height of the pyramidFrom the diagram and the question,
Given:
V = 210 unit³b = 10h = 9 H = xSubstitute these values into equation 1 and solve for x
210 = (10×9×x)/6210 = 15xx = 210/15x = 14 unitHence, the value of x is 14 unit.
Learn more about triangular pyramid here: https://brainly.com/question/30517561
#SPJ1
A new cylindrical can with a diameter of 7 cm is being designed by a local company. The surface area of the can is 180 square centimeters. What is the height of the can? Estimate using 3.14 for pi , and round to the nearest hundredth. Apply the formula for surface area of a cylinder SA =TB+PH.
The height of the can is approximately 1.26 cm.
The formula for the surface area of a cylinder is:
SA = 2πr² + 2πrh
where r is the radius of the cylinder and h is its height.
Since the diameter of the can is 7 cm, the radius is 7/2 = 3.5 cm.
We are given that the surface area of the can is 180 square centimeters, so we can set up an equation:
180 = 2π(3.5)² + 2π(3.5)h
Simplifying:
180 = 24.5π + 7πh
180 = 45.5πh
h = 180 / (45.5π)
h = 1.25924790139
h ≈ 1.26 cm (rounded to the nearest hundredth)
To learn more about the cylinder;
https://brainly.com/question/16134180
#SPJ1
CAN SOMEONE HELP WITH THIS QUESTION?
The numeric value of the function f(x) at x = 5 is given as follows:
f(5) = 74.75.
How to obtain the function f(x)?The second derivative of the function f(x) is given as follows:
f''(x) = 2x + 6sin(x).
Integrating the second derivative, the first derivative of the function is given as follows:
f'(x) = x² - 6cos(x) + K.
When x = 0, y' = 2, hence the constant K is given as follows:
2 = -6 + K
K = 8.
Hence:
f'(x) = x² - 6cos(x) + 8.
Integrating the first derivative, the function is given as follows:
f(x) = x³/3 - 6sin(x) + 8x + K.
When x = 0, y = 4, hence the constant K is given as follows:
K = 4.
Then:
f(x) = x³/3 - 6sin(x) + 8x + 4.
The numeric value at x = 5 is given as follows:
f(5) = 5³/5 - 6sin(5) + 8(5) + 4
f(5) = 74.75.
More can be learned about integrals at https://brainly.com/question/22008756
#SPJ1
please help, asap. for an assignment
The value of m in terms of other variables of the right angle triangle is: m = √(p² - n²)
How to use pythagoras theorem?Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle.
The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a² + b² = c²
However, it can also be written in the form of c² = a² + b²
From the given triangle, we can write as:
p² = m² + n²
m² = p² - n²
m = √(p² - n²)
Read more about pythagoras theorem at: https://brainly.com/question/231802
#SPJ1
Is the relation a function?
No, the relation is not a function.
Is the given relation a function?Given the relation in the question:
x: -2, -4, -1, -4, 5, 3
y: 1, -3, 2, 8, 0, -1
A function is simply a relationship that maps one input to one output.
To determine whether the relation is a function, we need to check whether each x-value in the relation is associated with a unique y-value.
Looking at the x-values, we see that there are repeated values of -4, which means that there are multiple y-values ( -3 and 8 ) associated with x = -4.
The mapping of x to y is not well-defined for all values of x, since one value of x is associated with multiple values of y, hence, it is not a function.
Learn more about functions here: brainly.com/question/2541698
#SPJ1
NO LINKS!! URGENT HELP PLEASE!!!
Find the equation of a parabola with a vertex at (-2, 6) and that passes through the (-4, -5)
Answer:
[tex]\frac{-11}{4} (x + 2)^2 + 6.[/tex]
Step-by-step explanation:
As we know that
The standard equation of a parabola with vertex at point (h,k) is given by:
[tex]y = a(x-h)^2 + k[/tex]
where (h,k) is the vertex
and "a" is a coefficient that determines the direction and shape of the parabola.
We know that the vertex of our parabola is (-2, 6),
so we can substitute those values into the equation to get:
[tex]y = a(x + 2)^2 + 6[/tex]
Now finding a.
Since the parabola passes through point (-4, -5). Substituting these coordinates into the equation, we get:
-5 = a(-4 + 2)^2 + 6
-5 =a(-2)^2+6
-5=4a +6
-5-6=4a
4a=-11
a =- 11/4
Substituting the value of an equation second, we get
[tex]\frac{-11}{4} (x + 2)^2 + 6.[/tex]
Therefore, the equation of the parabola with a vertex at (-2, 6) and passing through (-4, -5) is y =
[tex] \frac{-11}{4} (x + 2)^2 + 6[/tex]
Answer:
[tex]y=-\dfrac{11}{4}(x+2)^2+6[/tex]
Step-by-step explanation:
The vertex form of a parabola is:
[tex]\boxed{y=a(x-h)^2+k}[/tex]
where:
(h, k) is the vertex."a" is the leading coefficient.Given the vertex is at (-2, 6), substitute h = -2 and k = 6 into the equation:
[tex]y=a(x-(-2))^2+6[/tex]
[tex]y=a(x+2)^2+6[/tex]
To find the value of a, substitute the point (-4, -5) into the equation and solve for a:
[tex]\begin{aligned}-5&=a(-4+2)^2+6\\-5&=a(-2)^2+6\\-5&=4a+6\\-5-6&=4a+6-6\\-11&=4a\\\dfrac{-11}{4}&=\dfrac{4a}{4}\\-\dfrac{11}{4}&=a\\a&=-\dfrac{11}{4}\end{aligned}[/tex]
Substitute the found value of a back into the equation:
[tex]y=-\dfrac{11}{4}(x+2)^2+6[/tex]
Therefore, the equation of a parabola with a vertex at (-2, 6) and that passes through the point (-4, -5) is:
[tex]\boxed{y=-\dfrac{11}{4}(x+2)^2+6}[/tex]