The answer is:
vertex: (4,-5); focus: (4,2); directrix: y=-12
The vertex of the parabola is (4, -5), the focus is (4, 2), and the directrix is the line y = -12.
To determine the vertex, focus, and directrix of a parabola given by the equation y = {1{28}(x - 4)² - 5, we must first identify the standard form of a parabolic equation, which is y = a(x - h)² + k where (h, k) is the vertex of the parabola. In this case, we can see that the vertex (h, k) is (4, -5).
The focus of a parabola is a fixed point from which the distance to any point on the parabola is equal to the distance from that point to the directrix.
The directrix is a fixed straight line. The distance between the vertex and the focus, denoted as 4p, can be determined from the coefficient a in the standard form, where a = {1}/{4p} or p = {1}/{4a}. Thus, p = {1}/{4({1}/{28})} = 7. The focus is then at (h, k + p) = (4, -5 + 7) = (4, 2).
The directrix has the equation y = k - p, so it will be y = -5 - 7 = -12. The parabola opens upwards because the value of a is positive.
In summary, the vertex of the parabola is (4, -5), the focus is (4, 2), and the directrix is the line y = -12.
What's an equation for A new plasma-screen television costs $5250. A family makes a down payment of $552 and pays off the balance in 24 equal monthly payments. ...?
Final answer:
To find the amount for the monthly payments for a plasma-screen TV, subtract the down payment from the total cost and divide by the number of installments. The equation is: Monthly Payment = (Total Cost - Down Payment) / Number of Installments, which calculates to $195.75.
Explanation:
The student is seeking to find an equation that represents the cost of a plasma screen television being paid off with a down payment and equal monthly installments. Given the total cost of the television is $5250 and the down payment is $552, we can start by calculating the remaining balance after the down payment, which will be paid in 24 equal monthly payments.
First, subtract the down payment from the total cost to find the balance that needs to be paid in installments:
Total cost of television: $5250Down payment: -$552Balance to be paid in monthly installments: $5250 - $552 = $4698Next, we divide the balance by the number of monthly payments to find the amount of each payment:
Number of monthly payments: 24Monthly payment amount: $4698 / 24 = $195.75Therefore, the equation that represents the monthly payment after the down payment is:
Monthly Payment = (Total Cost - Down Payment) / Number of Installments
Applying the given numbers we get:
Monthly Payment = ($5250 - $552) / 24
Plugging in the values:
Monthly Payment = $4698 / 24 = $195.75
I put 80 POINTS into question please answer
In January 2008, the temperature in parts of Minnesota fell from -48 F to −12 F over a 24-hour period. What was the average temperature change per hour?
Answer:
-40
Step-by-step explanation:
What is the axis of symmetry of the function f(x) =-(x+9)(x-21)
Answer:
x = 6
Step-by-step explanation:
The given equation is [tex]f(x)=-(x+9)(x-21)[/tex]
We write the equation in standard form of parabola [tex]f(x)=ax^2+bx+c[/tex] using FOIL
[tex]f(x)=-(x+9)(x-21)\\\\f(x)=-(x^2-21x+9x-189)\\\\f(x)=-x^2+12x+189[/tex]
Now, we know that the axis of symmetry passes through the vertex. Hence, in order to find the vertex of the parabola, we find the x coordinate of the vertex.
x coordinate of the vertex is [tex]-\frac{b}{2a}[/tex]
Here, a = -1 b = 12
[tex]-\frac{b}{2a}\\\\=-\frac{12}{2\cdot(-1)}\\\\=-(-6)\\\\=6[/tex]
Therefore, the axis of symmetry is x = 6
find m KTL. Please I need help
The John Deere company has found that the revenue from sales of heavy-duty tractors is a function of the unit price p that it charges. The revenue R is given by the following function.
R(p)= (-1/2)p^2+1520p
What unit price p should be charged to maximize revenue? Give your answer correct to the nearest dollar. ...?
To maximize revenue for John Deere's heavy-duty tractors, the optimal unit price is found by determining the vertex of the provided quadratic revenue function R(p). Using the vertex formula, the unit price p that maximizes revenue is $1520.
Maximizing Revenue for John Deere Heavy-Duty Tractors
To find the unit price that maximizes revenue for John Deere heavy-duty tractors, we need to analyze the revenue function R(p) provided, which follows a quadratic format:
R(p) = [tex](-1/2)p^2[/tex] + 1520p
To find the maximum revenue, we can use the fact that the vertex of a parabola described by a quadratic equation y = ax^2 + bx + c provides the maximum or minimum value of the function. Since our equation is in the form of a parabola opening downwards (because the coefficient of p^2 is negative), the vertex will give us the maximum revenue point.
The formula for the p-coordinate (horizontal axis) of the vertex of a parabola is given by -b/(2a). In this case, a = -1/2 and b = 1520, therefore:
p = -b/(2a) = -1520/(2 * (-1/2)) = -1520/(-1) = 1520
Hence, the unit price p should be set at $1520 to maximize revenue for the sale of heavy-duty tractors. This value is already an integer, so rounding to the nearest dollar is not necessary.
Rosa works due north of home. Her husband Juan works due east. They leave for work at the same time. By the time Rosa is 7 miles from home, the distance between them is one mile more than Juan's distance from home. How far from home is Juan? ...?
lisa is 6 years older than Tom. Their father's age is twice the sum of their ages. How old is lisa if her dad is 32?
If $1,000 is invested in an account that pays 4% interest compounded annually, an expression that represents the amount in the account at end of three years can be given by which of the following equations?
A. 1000+0.4^3
B. 1000(0.3)^3
C. 1000(1.04)^3 ...?
What are the solutions to the equation x2 = 64?
A.
8 only
B.
32 and –32
C.
8 and –8
D.
32 only
The number of times one needs to use the completely filled cone to completely fill the cylinder with water is
Answer:
Step-by-step explanation:
Given that there is a cone and cylinder with equal radius and height.
Recall volume formula for cone and cylinder as
Volume of cone = [tex]\frac{1}{3} \pi r^2 h[/tex]
Volume of cylinder =[tex]\pi r^2 h[/tex]
Thus we find that cylinder has a greater volume and ratio is 3:1
Hence 3 times if filled up with a cone the cylinder will be completely full
Elisa has a DVD collection. She has 10 horror movies, 20 comedies and 15 action movies. If she picks one at random to watch, what is the probability that it is an action movie?
Michael and kathryn bowl together and their combined total score for one game was 425 points. Michael's score was 70 less than twice kathryn's. which system of equations models the problem if x represents kathryn's score and y represents michael's score ?
A. x+y=70
y=2x-425
B. x-y=425
y=2x-70
C.x+y=425
y=2x-70
D. x+y=425
y=2x+70
Answer:
Option C is correct
[tex]x+y = 425[/tex]
[tex]y = 2x-70[/tex]
Step-by-step explanation:
Here, x represents Kathryn's score and y represents Michael's score.
As per the statement:
Michael and Kathryn bowl together and their combined total score for one game was 425 points.
⇒[tex]x+y = 425[/tex]
It is also given that Michael's score was 70 less than twice Kathryn's.
⇒[tex]y = 2x-70[/tex]
Therefore, the system of equations models the problem is:
[tex]x+y = 425[/tex]
[tex]y = 2x-70[/tex]
There are 6 female goldfish for every 10 male goldfish in an aquarium. there are 216 female goldfish in the aquarium. how many goldfish are in the aquarium
Answer:
In Total=560
Step-by-step explanation:
216/6=36
36*10=360
216+360=560
You are buying potato chips at the grocery store. You have a manufacturers coupon for a $1.00 off and the store is offering 20% off if you buy 2 bags. You decide to buy 2 bags of potato chips. How do you compute your final cost?
A. Subtract $1.00 off each bag and then multiply by .20
B. Multiply each bag by .20, subtract $1.00 off of each bag, and then add them together.
C. Add the two bags together, multiply by .80, and then subtract $1.00.
D. Subtract $1.00 from the first bag, then add them together, and then multiply by .80.
Answer:
The correct option is: C. Add the two bags together, multiply by .80, and then subtract $1.00.
Step-by-step explanation:
First you need to add the prices of two bags for getting the total sales price.
Now, the store is offering 20% off, that means you need to pay 80% of the total sales price. For finding the amount, we need to multiply the total sales price by 0.80
Then, you have a manufacturers coupon for a $1.00 off. So, for fining the final price, you need to subtract that $1.00 from the last result.
Thus, the correct option will be......
C. Add the two bags together, multiply by .80, and then subtract $1.00.
multiply (x-4)(x^2-5x-6) ...?
Answer:
The answer is: [tex]x^3-9x^2+14x+24[/tex]
Step-by-step explanation:
The given expression is: [tex](x-4)(x^2-5x-6)[/tex]
For getting the product, we need to distribute [tex](x-4)[/tex] with each term in the second parenthesis. So.....
[tex](x-4)(x^2-5x-6)\\ \\ =x^2(x-4)-5x(x-4)-6(x-4)\\ \\ =x^3-4x^2-5x^2+20x-6x+24 \ [using\ distribution\ rule]\\ \\ =x^3-9x^2+14x+24\ [combining\ like\ terms][/tex]
So, the answer is: [tex]x^3-9x^2+14x+24[/tex]
Choose the answer that solves the equation:
7 – 3 + 5 × (6 – 2) = ?
A) 0
B) 16
C) 24
D) 36
Answer:b
Step-by-step explanation:
What is the solution to this inequality?
16 + x > 30
A. x > 14
B. x >-14
C. x > -46
S. x > 46
Owners of a recreation area are filling a small pond with water. They are adding water at a rate of
25
liters per minute. There are
600
liters in the pond to start.
Let
W
represent the amount of water in the pond (in liters), and let
T
represent the number of minutes that water has been added. Write an equation relating
W
to
T
, and then graph your equation using the axes below
The equation relating W to T is W = 600 + 25T.
Given:
The initial amount of water in the pond is 600 liters.
The water is being added at a rate of 25 liters per minute.
As time (T) increases, the amount of water in the pond (W) will increase due to the constant addition of 25 liters per minute.
The equation can be written as follows:
W = 600 + 25T
In this equation, 600 represents the initial amount of water in the pond (at T = 0), and 25T represents the additional water added for each minute of time (T).
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Mikel traded Australian dollars for Thai baht at an exchange rate of 1 Australian dollar = 29.3225 Thai baht. He gave the exchanger a total of $1900 and was charged a flat fee of $40. Approximately how many Thai baht does Mikel have?
Simplify. √24
A √38
B √212
C √26
D √46
To simplify √24, we find its prime factors, pair them up, and bring one number from each pair outside the square root. The remaining numbers stay under the square root. The correct answer is 2√6. The options provided in the question are all incorrect.
Explanation:The problem is asking us to simplify √24, which is a typical Mathematics question in Middle School. Here are the steps we need to take:
Find the prime factors of 24. They are 2, 2, 2, and 3.Group the factors in pairs. We have one pair of 2's.Take one number from each pair outside the square root symbol. So, we have 2.The remaining numbers (2 and 3) stay under the square root symbol, multiplied together to give 6.Therefore, √24 simplifies to 2√6.
All the options provided (A √38, B √212, C √26, D √46) are incorrect.
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After a certain number of moves in a chess game, the ratio of black pieces to white pieces is 4 to 3. If there are 12 black pieces on the board, which proportion can be used to find the number of white pieces?
To find the number of white pieces when the ratio of black pieces to white pieces is known, set up a proportion and solve for the missing variable. In this case, the number of white pieces is 9.
To find the number of white pieces, we can use the proportion 3/4 = W/12, where W represents the number of white pieces.
Cross multiply to get 3*12 = 4*W
Therefore, 36 = 4W
Divide by 4 to find that W = 9.
Solve the system of equations below by graphing them with a pencil and paper. Enter your answer as an ordered pair.
y = 2x - 3 y = -2x + 5 ...?
Answer:
Solution is (2,1)
Step-by-step explanation:
In order to graph both lines ,we need to find the X and Y intercepts for both equations
Lets take equation y =2x -3
To find y intercept ,we plug x =0 ,we get y =2(0)-3 = 0-3 =-3
Y intercept is (0,-3) Which is point 'C' in the graph
To find X intercept ,we plug y =0 ,we get 0 = 2x-3 or x = 3/2 or 1.5
X intercept is (1.5,0) Which is point D in the graph.
Lets take equation y =-2x+5
To find y intercept ,we plug x =0 ,we get y = -2(0)+5 = 0+5 = 5
Y intercept is (0,5) which is point A in the graph .
To find X intercept ,we plug y =0 ,we get 0 =-2x+5 or x = 5/2 or 2.5
X intercept is (2.5,0) which is point B on the graph
After getting intercept of both lines ,we plot both lines
In the graph Blue line shows y=2x-3 and Red line shows y =-2x+5
both lines intersect at point E which is called the solution of both equation
which is given to be (2,1)
2. mrs. barlow's math class took a test yesterday. out of 70 students, 70% of them passed. how many of mrs. barlow's students passed the test?
The radius of a cylindrical water tank is 5.5ft, and its height is 8ft
. What is the volume of the tank? Use the value 3.14 for π, and round your answer to the nearest whole number.Be sure to include the correct unit in your answer.
The volume of the cylindrical water tank with a radius of 5.5 feet and a height of 8 feet is 760 cubic feet after rounding to the nearest whole number.
To calculate the volume of a cylindrical water tank, we use the formula V = , where V represents volume, is the constant Pi, approximately equal to 3.14, r is the radius of the cylinder, and h is its height.
Given that the radius r is 5.5 feet and the height h is 8 feet, substituting these values into the formula gives us:
V = 3.14 * (5.5ft) * 8ft
First calculate the radius squared:
5.5ft * 5.5ft = 30.25ft
Now, calculate the volume:
V = 3.14 * 30.25ft * 8ft = 3.14 * 242ft = 759.88ft
After rounding to the nearest whole number, the volume is 760 cubic feet.
356 added to the product of 56 and an unknown number is equal to -832 what is the equation for the given statement
The Answer:
356+56y=-832
Your math teacher allows you to choose the most favorable measure of central tendency of you test scores to determine your grade for the term. On six tests you earn scores of 89,81,85,82,89 and 89. What is your grade to the nearest whole number, and which measure of central tendency should you choose?
Answer:
89; the mode
Step-by-step explanation:
Final answer:
The best measure of central tendency for the student's test scores is the mode, which is 89. The mean and median are 86 and 87 respectively, but the mode gives the highest score, hence it is the most favorable for determining the student's final grade.
Explanation:
The question asks for the most favorable measure of central tendency for a student's test scores to determine their final grade. The test scores provided are 89, 81, 85, 82, 89, and 89.
To find the most favorable measure, we need to calculate the mean (average), median, and mode of the test scores. The mean is calculated by adding all the scores together and dividing by the number of tests. The median is the middle number when the scores are listed in order, and the mode is the number that appears most frequently.
Calculating the mean: (89 + 81 + 85 + 82 + 89 + 89) / 6 = 85.83, which we round to the nearest whole number as 86.
To find the median, we order the scores: 81, 82, 85, 89, 89, 89. Since there are an even number of scores, the median is the average of the two middle numbers, in this case, 85 and 89. Thus, the median is (85 + 89) / 2 = 87.
The mode is the most frequent score, which is 89.
Out of the mean, median, and mode, the mode is the highest and most favorable measure of central tendency for the student, resulting in a final grade of 89 when rounded to the nearest whole number.
What is the median for the following set of data? 2, 5, 7, 8, 11, 11, 12
What is 40.53 ounces converted to liters?
You have been asked by the police department to find three locations the Acute Perps gang is likely to hit in the coming weeks. Because the gang sticks to a triangular pattern, the locations could be a translation, reflection, or rotation of the original triangle. For this step, identify and label three points on the coordinate plane that are a translation of the original triangle. Next, use the coordinates of your translation along with the distance formula to show that the two triangles are congruent by the SSS postulate. You must show all work with the distance formula.
Note:
Images with coordinates or original and translated triangles are attached.
Answer:
The coordinates for the given triangle are A(6,3), B(6,-3) and C(-2,-3), respectively.
Let us translate this triangle by -6 units along the x-axis and +3 units along the y-axis. This means that 6 will be subtracted from each of the abcissas (x-points) and 3 will be added to each ordinates (y-points). Hence, our translated triangle will have the following coordinates: A'(0,6), B'(0,0) and C'(-8,0), respectively.
Now to prove that both triangles are congruent, we use the SSS postulate, which states that:
"If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent."
Distance between two point P1 and P2 will be:
[tex]|P_1P_2|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Now using distance formula to find sides of triangle ABC and triangle A'B'C'.
For Triangle ABC:
|AB| = [tex]\sqrt{(6-6)^2+(-3-3)^2} =\;6\;units[/tex]
|AC| = [tex]\sqrt{(-2-6)^2+(-3-3)^2} =\;10\;units[/tex]
|BC| = [tex]\sqrt{(-2-6)^2+[-3-(-3)]^2} =\;8\;units[/tex]
For Triangle A'B'C':
|A'B'| = [tex]\sqrt{(0-0)^2+(0-6)^2} =\;6\;units[/tex]
|A'C'| = [tex]\sqrt{(-8-0)^2+(0-6)^2} =\;10\;units[/tex]
|B'C'| = [tex]\sqrt{(-8-0)^2+(0-0)^2} =\;8\;units[/tex]
Hence, as the distances are equal, the two triangles are congruent by SSS postulate.
what's 6 diveded by 711