The general form of the equation of the Quadratic function is y = (-1/9) x2-(14/9) x-43/9.
The general form of the equation of the Quadratic function is y = (-1/9) x2-(14/9) x-43/9.
The general form of the equation of a quadratic function given the vertex and a point on the graph, we can use the vertex form of the quadratic equation y = a( x- h) 2 k where( h, k) represents the vertex of the parabola. In this case, the vertex is(- 7, 6) and the point is(- 10, 5). We can substitute these values into the equation to get 5 = a(- 10-(- 7)) 2 6 Simplifying farther 5 = a(- 10 7) 2 6 5 = a(- 3) 2 6 5 = 9a 6 Now, we can break for' a' a = 5- 6 9a = -1 a = -1/ 9 Substituting this value back into the equation, we get y = (-1/9)( x-(- 7)) 2 6
Simplifying farther y = (-1/9)( x 7) 2 6 Expanding and rearranging, we can write the equation in general form y = (-1/9)( x2 14x 49) 6 y = (-1/9) x2-(14/9) x-49/9 6 y = (-1/9) x2-(14/9) x-43/9 So, the general form of the equation of the quadratic function is y = (-1/9) x2-(14/9) x-43/9.
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Q1.
A fall in the price of good X from GH¢6 to GH¢4 causes a decrease in the quantity of good Y
demanded from 1,100 to 900. What is the cross-price elasticity of demand between good X and
good Y?
(a) 0.5
(b) -0.5
(c) 2.0
(d) 3.5
The cross-price elasticity of demand between good X and good Y will be 0.5. Thus, the correct option is A.
Given that5:
Old Quantity = 1,100
New Quantity = 900
The percentage change of good Y is calculated as,
P = ((900 - 1,100) / 1,100) * 100
P = (-200 / 1,100) * 100
P = -18.18%
Next, let's calculate the percentage change in the price of good X:
Old Price = GH¢6
New Price = GH¢4
The percentage change in the price of good X is calculated as,
P = ((4 - 6) / 6) * 100
P = (-2 / 6) * 100
P = -33.33%
The cross-price elasticity of demand is calculated as,
⇒ (-18.18% / -33.33%)
⇒ 0.546 or 0.5
Thus, the correct option is A.
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The width of a rectangle is 3 feet and the area is 18 square feet , what is perimeter of the rectangle?
Answer:
18 ft
Step-by-step explanation:
area = length × width
length = area/width
length = 18 ft² / 3 ft
length = 6 ft
perimeter = 2(length + width)
perimeter = 2(6 ft + 3 ft)
perimeter = 2(9 ft)
perimeter = 18 ft
Answer:
[tex]\mathrm{18ft.}[/tex]
Step-by-step explanation:
[tex]\mathrm{We\ have,}\\\mathrm{Width\ of\ rectangle(b)=3ft.}\\\mathrm{Area\ of\ rectangle(A)=18\ sq.\ ft}\\\mathrm{Let\ the\ length\ of\ the\ rectangle\ be\ 'l'\ and\ its\ perimeter\ be\ 'P'.}\\\mathrm{Now,}\\\mathrm{Area\ of\ rectangle=l\times b}\\\mathrm{or,\ 18=l\times 3}\\\mathrm{or,\ l=6ft.}\\\mathrm{So\ the\ length\ of\ rectangle\ is\ 6\ feet.}\\\mathrm{Finally,\ perimeter\ of\ rectangle\ is\ given\ by\ the\ formula:}\\\mathrm{P=2(l+b)=2(6+3)=2(9)=18ft.}\\[/tex]
[tex]\mathrm{\therefore Perimeter\ of\ rectangle\ is\ 18\ feet.}[/tex]
Mr. Khumalo has a Standard Bank Account. The cash deposiverser d counter (branch deposit) services includes air for of R10,39 plus K1,95 per R100 or part thereof, with a mininium charge of R16,00. What is the minimum amount that a person can be chaped for a cash deposit Mr Khumale deposited R4 550,00 over the counter at Standard Bank (2)
The minimum amount that Mr. Khumalo can be charged for the cash deposit is R99.12.
To calculate the minimum amount charged for a cash deposit over the counter at Standard Bank, we'll use the given information.
The deposit charge includes an initial fee of R10.39, and an additional fee of K1.95 per R100 or part thereof, with a minimum charge of R16.00.
First, we calculate the additional fee based on the deposit amount:
Additional fee = (Deposit amount / 100) x K1.95
For Mr. Khumalo's deposit of R4,550.00:
Additional fee = (4,550.00 / 100) x 1.95
Additional fee = 88.725
Next, we compare the additional fee to the minimum charge of R16.00:
If the additional fee is less than the minimum charge, the minimum charge applies. Otherwise, the additional fee is charged.
Since the additional fee of R88.725 is greater than the minimum charge of R16.00, the additional fee will be charged.
Finally, we add the initial fee and the additional fee to get the total charge:
Total charge = Initial fee + Additional fee
Total charge = R10.39 + R88.725
Total charge = R99.115
Therefore, the minimum amount that Mr. Khumalo can be charged for the cash deposit is R99.12.
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Help me with this please!
The solution is: Option D has the correct data points and so is the right answer.
We have,
A function is a mathematical way of representing relation between two variables.
The function given is
y = 2x²
For x = - 2, y = -2(- 2)² = -8
For x = - 1, y = -2(- 1)² = -2
For x = 0, y = -2(0)² = 0
For x = 1, y = -2(1)² = -2
For x = 2, y = -2(2)² = -8
the table of x-y will be:
x - 2 - 1 0 1 2
y -8 -2 0 -2 -8
The graph is attached with the answer.
The parabola opens downward and has the data points as mentioned above .
The Graph B best represents a parabola ,
Therefore Option D is the correct answer.
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complete question:
Complete the following table using the equation: Y = negative 2 x Squared x -2 -1 0 1 2 y Plot the points on a graph and determine which graph best represents the equation. Graph A On a coordinate plane, a parabola opens up. It goes through (negative 1, 2), has a vertex at (0, 0), and goes through (1, 2). Graph B On a coordinate plane, a parabola opens down. It goes through (negative 1, negative 1), has a vertex at (0, 0), and goes through (1, negative 1). a. 8, 2, 0, 2, 8; Graph A b. -8, -2, 0, -2, -8; Graph A c. 8, 2, 0, 2, 8; Graph B d. -8, -2, 0, -2, -8; Graph B Please select the best answer from the choices provided A B C D
Two watches, one set accurately and the other delayed by 9 minutes per hour compared to the correct time.
If we set both watches to 8:00 AM, after how many hours will the delayed watch meet the accurate watch again?
Submit only a number
Answer: To determine when the delayed watch will meet the accurate watch again, we need to find the number of hours it takes for the delayed watch to catch up by 9 minutes.
Since the delayed watch falls behind by 9 minutes per hour, it will catch up by 9 minutes after every hour. Therefore, it will take 1 hour for the delayed watch to catch up by 9 minutes.
Hence, the delayed watch will meet the accurate watch again after 1 hour.
Submit the number: 1
Ivan places a basketball with radius 4.75 in. inside a cube-shaped box with side length 9.5 in. How many cubic inches of packing foam does Ivan need to fill the empty space in the bo: Use 3.14 for , and round your answer to the nearest cubic inch
Answer:
To find the volume of the empty space in the box, we need to subtract the volume of the basketball from the volume of the box.
Volume of the basketball = (4/3) * π * r^3
= (4/3) * 3.14 * (4.75 in)^3
Volume of the box = side length^3
= (9.5 in)^3
Empty space volume = Volume of the box - Volume of the basketball
Empty space volume = (9.5 in)^3 - (4/3) * 3.14 * (4.75 in)^3
Calculating this equation will give us the volume of the empty space in cubic inches. Rounding the answer to the nearest cubic inch will provide the amount of packing foam needed to fill the empty space.
100 Points! Algebra question, photo attached. Please show as much work as possible. Thank you!
A. The distributions of the periods is that using the five number summary is that
The 7th Period has higher minimum and lower maximumThe 3rd period is more spread (from the quartiles)The 7th Period has higher medianB. The box and whisker plot of the periods is attached
A. Comparing the distributions of the periodsFrom the question, we have the following parameters that can be used in our computation:
7th Period
66, 72, 77, 78, 78, 80, 82, 84, 84, 87, 88, 88, 89, 89, 90 92, 92, 93, 94, 94 96, 96
3rd Period
52, 60, 62, 64, 64, 65, 68, 71, 72, 74, 75, 76, 78, 79, 83, 84, 85, 88, 89, 93, 94, 97
The distributions of the periods will be compared using the five-number summaries
Using a graphing tool, the five-number summaries are:
7th Period
Minimum: 66Lower Quartile Q1: 79.5Median: 88Upper Quartile Q3: 92.25Maximum: 963rd Period
Minimum: 52Lower Quartile Q1: 64.75Median: 75.5Upper Quartile Q3: 85.75Maximum: 97B. Creating a box and whisker plot of the periodsThe box and whisker plot of the periods is added as an attachment
From the box and whisker plot attached, we can see the five-number summaries of the periods
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Clara graphed her reading fluency scores for 6 weeks. 99, 88, 97, 107, 100, 109 What is the median of the scores?
Answer:
99.5
Explanation:
First, you would put the numbers into order from least to greatest.
99, 88, 97, 107, 100, 109
Which would be:
88, 97, 99, 100, 107, 109
Median is the middle of the number line, so you would cross off a number from each side until you find the middle.
99, 100
You would end up with two numbers, which you will have to find the mean of. In order to do so, you need to add them together then divide by 2 because there are 2 numbers.
99 + 100 = 199
199/2 = 99.5
answer the following questions
The value of the trigonometric ratio indicated in the question for each are:
1) tan Z = 3/4, 2) sin C = 3/4, 3) tan Z = 20/21, 4) cos X = 3/5, 5) cos A = 5/13 and 6) tan Z = 3/4
Given are certain right angled triangles. We have to find the value of each of the trigonometric ratio indicated.
1) tan Z = opposite side / adjacent side
= YX / YZ
= 24/32 = 3/4
2) sin C = Opposite side / Hypotenuse
= AB / AC
= 24/40 = 3/5
3) tan Z = opposite side / adjacent side
= YX / YZ
= 20/21
4) cos X = adjacent side / Hypotenuse
= XY / XZ
= 15/25 = 3/5
5) cos A = adjacent side / Hypotenuse
= AB / AC
= 15/39 = 5/13
6) tan Z = opposite side / adjacent side
= YX / YZ
= 27/36 = 3/4
Hence the ratios are found.
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You deposit $300 in an account that earns simple interest at an annual rate of 6.5%.
If no other deposits or withdrawals were made, what is the total amount of money in the account at the end of 8 years?
Total amount of money in the account will be $456.
How much money will be in the account after 8 years?Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest.
The formula for simple interest is: Simple Interest = Principal × Rate × Time
Principal (P) is $300
Rate (R) is 6.5%
Time (T) is 8 years.
Simple Interest = $300 × 0.065 × 8
Simple Interest = $156
Total Amount = Principal + Simple Interest
Total Amount = $300 + $156
Total Amount = $456.
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An apple orchard's workers pick 14,446 apples in the month of October. A sample of 109 of these apples shows that 48 of them are damaged and bruised. What is the best estimate of the number of apples picked at the orchard in October that are bruised and damaged?
A computer is $699 on the installment plan.
Down payment: $100 Payments: $58 a month for 12 months
How much was Marge's finance charge on the computer?
$796
$97
$696.36
Answer:
Therefore, Marge's finance charge on the computer is $97.
Step-by-step explanation:
To calculate Marge's finance charge on the computer, we need to find the total amount she will pay for the computer through the installment plan and subtract the original purchase price.
Down payment = $100
Total amount paid for the computer = Down payment + Monthly payment * Number of months
Total amount paid = $100 + ($58 * 12)
Total amount paid = $100 + $696
Total amount paid = $796
Finance charge = Total amount paid - Purchase price
Finance charge = $796 - $699
Finance charge = $97
Therefore, Marge's finance charge on the computer is $97.
Triangle FGH, with vertices F(-5,-7), G(-2,-5), and H(-6,-2), is drawn inside a rectangle, as shown below.
The area of the triangle FGH is equal to 13√10 unit²
Given that the vertices;
F(-5,-7), G(-2,-5), and H(-6,-2)
We have to find the area of the triangle as;
Area of triangle = 1/2bh²
Here,
Area of triangle FGH = 1/2 (GH) (FG)²
Now,
Length of FG = √26
Length of GH = √10
Then,
Area of triangle FGH = 1/2 (GH) (FG)²
Area of triangle = 1/2 × √10 × √26²
Area of triangle = 1/2 × √10 × 26
Area of triangle FGH = 13√10
Therefore,
The area of the triangle FGH = 13√10 unit²
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A law firm hires the same number of lawyers every year.At the end of 12 years, the firm has hired 48 lawyers.How many lawyers has the firm hired on the last 5 years?
Answer:
20 lawyers
Step-by-step explanation:
48 ÷ 12 = 4
which means every year 4 lawyers are hired
5 × 4 = 20
so this means the law firm has hired 20 lawyers in the last 5 years
Please help. Any uncessary answers will be reported.
In the Pythagorean Planet, it is a tradition that you can only marry someone when the sum of the square of the bride and the groom combined is the square of the age of the brides father. The pythagorean Juniper got married when she was 33 years old, at that time her father was over 500 years old. How old was the groom?
The triangle is solved using the Pythagoras theorem
Given data ,
Let's denote the age of the groom as G. According to the tradition in the Pythagorean Planet, the sum of the squares of the bride's age (33) and the groom's age (G) combined should be equal to the square of the bride's father's age (F).
The equation representing this condition is:
33² + G² = F²
We are given that at the time of the wedding, the bride's father was over 500 years old. Let's denote his age as F and rewrite the equation accordingly:
33² + G² = (500 + F)²
Hence , the equation is 33² + G² = (500 + F)²
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Write with fractional exponents. (Do not use parentheses.)
Answer:
4[tex]y^{\frac{3}{2} }[/tex]
Step-by-step explanation:
using the rule of exponents/ radicals
[tex]\sqrt[n]{a^{m} }[/tex] = [tex]a^{\frac{m}{n} }[/tex]
then
4 [tex]\sqrt{y^{3} }[/tex]
= 4[tex]y^{\frac{3}{2} }[/tex]
A soccer player jumps up and heads the ball while it is 7 feet above the ground. If the function
y = -16t squared + 20t + 7 represents this situation, about how long will it take the ball to hit the ground?
Answer:
3.3 seconds
Step-by-step explanation:
To find the time it takes for the ball to hit the ground, we need to solve the equation y = 0, since the ball will be on the ground when its height (y) is zero.
The equation given is:
y = -16t^2 + 20t + 7
Setting y to zero:
0 = -16t^2 + 20t + 7
To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, factoring may not be straightforward, so let's use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = -16, b = 20, and c = 7. Substituting these values into the quadratic formula:
t = (-20 ± √(20^2 - 4(-16)(7))) / (2(-16))
t = (-20 ± √(400 + 448)) / (-32)
t = (-20 ± √848) / (-32)
Simplifying further:
t = (-20 ± √(16 * 53)) / (-32)
t = (-20 ± 4√53) / (-32)
Now we have two possible solutions for t:
t1 = (-20 + 4√53) / (-32)
t2 = (-20 - 4√53) / (-32)
Since time cannot be negative in this context, we can disregard the negative solution.
t ≈ (-20 + 4√53) / (-32)
Calculating this value:
t ≈ 3.3 seconds (rounded to one decimal place)
Therefore, it will take approximately 3.3 seconds for the ball to hit the ground.
Please help I’ll mark you as brainliest if correct!
The cosD is √53/9 from the given triangle which is adjacent side by hypotenuse
The triangle DEF is a right triangle
We know that cosine function is a ratio of adjacent side and hypotenuse
The adjacent side of angle D is DE
We have to find the length of DE by using Pythagoras theorem
DE²+EF² =DF²
DE²+28=9²
DE²=81-28
DE²=53
Take square root on both sides
DE=√53
So cosD=√53/9
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What is the perimeter of the shape?
8 m
4 m
11 m
4 m
4 m
11 m
4 m
A system of equations is created by using the line represented by 2 x + 4 y = 0 and the line represented by the data in the table below.
x
y
–1
8
3
–4
5
–10
6
–13
What is the x-value of the solution to the system?
A specific X-value for the solution ,-4 is not equal to -3/2.
The x-value of the solution to the system of equations, we need to solve the given equation and the line represented by the data in the table. Let's begin by examining the first equation, 2x + 4y = 0.
We can rewrite this equation in terms of y:
4y = -2x
y = (-2/4)x
y = (-1/2)x
Now, let's use the data from the table to create a system of equations:
For the first data point (-1, 8):
y = (-1/2)x
8 = (-1/2)(-1)
8 = 1/2
Since 8 is not equal to 1/2, the first data point does not satisfy the equation.
For the second data point (3, -4):
y = (-1/2)x
-4 = (-1/2)(3)
-4 = -3/2
Again, -4 is not equal to -3/2, so the second data point does not satisfy the equation.
We can continue this process for the remaining data points, but from the information given, it seems that none of the data points satisfy the equation. Therefore, there is no solution to the system of equations.
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the ratio of the heights of two cylinders is 1:3. if the volume of the smaller cylinder is 67cm3, find the volume of the larger cylinder
PLEASE ANSWER ASAP
The volume of the larger cylinder is 201 cm³.
Given that,
Ratio of the heights of two cylinders = 1 : 3
We have to find the volume of the larger cylinder.
The formula to find the volume of a cylinder is,
Volume of cylinder = π r² h, where r is the radius and h is the height of the cylinder.
Let height of smaller cylinder = h
Height of larger cylinder = 3h
π r² (h) = 67
Volume of larger cylinder = π r² (3h)
= 3 [π r² (h)]
= 3 × 67
= 201 cm³
Hence he volume is 201 cm³.
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Use the image to answer the question pls and Ty
LOTS OF POINTS Can someone provide the correct answer, and tell me what I did wrong here?
The height of the given triangle will be 13.416 cm.
Given a right-angle triangle that has a hypotenuse of 14 cm, height of x, and base of 4 cm.
The Pythagorean theorem is a fundamental principle in geometry that establishes a relationship between the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Applying the Pythagorean theorem, we can write:
[tex]14^2 = 4^2 + x^2[/tex]
Simplifying the equation:
[tex]196 = 16 + x^2[/tex]
Subtracting 16 from both sides:
[tex]180 = x^2[/tex]
Taking the square root of both sides:
x = √180 = 6√5
Simplifying the square root:
x ≈ 13.416 cm
Therefore, the height (x) of the right-angle triangle is approximately 13.416 cm.
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Calculate the monthly loan payment
Loan amount: 60000
Down payment: 4000
Interest rate: 13%
Term: 60 months (5 years)
The monthly loan payment for a $60,000 loan with a $4,000 down payment, 13% interest rate, and a term of 60 months is approximately $1,289.49.
To calculate the monthly loan payment, we need to use the loan amount, down payment, interest rate, and term.
Loan amount: $60,000
Down payment: $4,000
Principal amount: Loan amount - Down payment = $60,000 - $4,000 = $56,000
Interest rate: 13% per annum (or 0.13 as a decimal)
Monthly interest rate: 13% / 12 = 0.0133 (approx.)
Term: 60 months (5 years)
Now, let's calculate the monthly loan payment using the formula for a fixed-rate loan:
Monthly payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
P = Principal amount
r = Monthly interest rate
n = Total number of payments
Substituting the values into the formula:
Monthly payment = $56,000 * (0.0133 * (1 + 0.0133)^60) / ((1 + 0.0133)^60 - 1)
Using a calculator, the approximate monthly loan payment comes out to be $1,289.49.
Therefore, the monthly loan payment for a $60,000 loan with a $4,000 down payment, 13% interest rate, and a term of 60 months is approximately $1,289.49.
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During one year, the population of a town increased by 2% but during the next year it diminished by 2%. If at the end of the second year the population was 6,25,000, what was the population at the beginning?
Answer:
614,818.71
Step-by-step explanation:
hope it helps
Answer:
6,25,250
Step-by-step explanation:
let initaial population be "x"
after increasing by 2%
x'=x+x*2%
x'=102x/100
x' is decreased by 2% and population reached 625000,so,
625000=102x/100-2%*102x/100
625000=102x/100-51x/2500
625000=2499x/2500
2499x=625000*2500
x=1562500000/2499
x=625250.1
complete population is only counted so,
x=625250
initial population =625250
which word means a location in space?
a. line
b. plane
c. point
d. ray
Answer:
C.
Step-by-step explanation:
I think the answer is C. or a point because a point is like a location in space and the question is asking which word means a location in space.
what is the value of the underlined digit in the number 27,416,385. 4 is the underlined number.
The value of the underlined digit in the number 27,416,385.( 4 is the underlined number.) is the hundred thousandths place.
How can the digits be known?The symbols, from 0 to 9 can be described as a digit. For instance, the numbers 2 and 3 are used to represent the number 23. however amount is represented by a number.
It should be noted that It may be expressed using one, two, three, or even more digits however only single symbol used to represent a number is a digit in the case above we can see that 4 is the hundred thousandths place.
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Solve for b.
7b - 20 - 4b = -5
b = [?]
The value of b from the Equation 7b - 20 - 4b = -5 is 5.
An equation is a mathematical statement that states the equality between two expressions. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, etc.
We have the Equation:
7b - 20 - 4b = -5
Now, add 20 both side we get
7b - 20 - 4b + 20 = -5 + 20
7b - 4b = 15
Now, combine like terms
3b = 15
Now, divide both side by 3 we get
3b/3 = 15/3
b= 5
Thus, the value of b is 5.
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Solve for
x
x
5
=
8
9
Give your answer as an improper fraction in its simplest form.
Answer:
[tex]x[/tex] × 5 = 89
∴ [tex]x[/tex] = 89 ÷ 5
= [tex]\frac{89}{5}[/tex] (improper fraction)
If 10 teenagers can eat 72 slices of pizza, how many slices are needed to feed 20 teenagers?
