FIFA created a football with a 21 cm circumference out of leather. If 10% of the leather is wasted, the cost of leather with labour is Rs. 25 per square centimetre. All total, Rs. 31,173.90 worth of leather was purchased to produce one football.
The diameter of the leather used to make the football is 21 cm, so its radius is 10.5 cm (half of the diameter).
The formula for calculating a sphere's surface area can be used to determine how much leather is required to produce a football:
Surface area = [tex]4\pi r^2[/tex]
Surface area = 4π[tex](10.5)^2[/tex]
Surface area = 1385.44 sq. cm
If 10% of the leather is wasted, then the actual amount of leather used is 90% of the total leather bought. So, we need to calculate the cost of 90% of the leather:
Cost of leather = 90% of the total leather cost
Cost of leather = 0.9 x 1385.44 sq.cm x Rs. 25/sq.cm
Cost of leather = Rs. 31,173.90
Therefore, the total cost of the leather bought to make the football, including the labour cost, is Rs. 31,173.90.
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a pet needs 5 mg/kg of albon po sid on day 1, then 2.5 mg/kg po sid for 5 more days. the medication is available in 125-mg tablets and the pet weighs 25 lb. how many tablets will be dispensed for the owner?
The pet will need 3 tablets of Albon for the treatment. This can be answered by the concept of Simple mathematics.
To calculate the required dosage, we need to convert the pet's weight from pounds to kilograms, which gives us 11.36 kg. On day 1, the pet requires 5 mg/kg of Albon, which amounts to 56.8 mg. Since each tablet contains 125 mg, we need to give the pet 0.454 tablets (56.8/125) which we will round up to 1 tablet. For the next 5 days, the pet requires 2.5 mg/kg of Albon, which amounts to 28.4 mg.
Therefore, we will give the pet 0.227 tablets (28.4/125) which we will round up to 1/4 of a tablet (0.25 tablets) each day. So, over the course of 6 days, the total number of tablets needed will be 1 + (0.25 x 5) = 2.25, which we will round up to 3 tablets.
Therefore, the owner will need to be dispensed with 3 tablets of Albon for the pet's treatment.
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perform a follow-up analysis of the test in exercise 38 by finding the individual compo- nents of the chi-square statistic. which cell(s) contrib- uted most to the final result and in what direction?
The cell that contributed most to the final result was Cell (1,2) with a contribution of 8.44.
How Cell (1,2) was contributed most to the final result?we need to calculate the expected frequencies for each cell in the contingency table. We can use the formula:
Expected frequency = (row total x column total) / grand total
The grand total for the table is 80, so we can calculate the expected frequencies for each cell as follows:
Expected frequency of Cell (1,1) = (44 x 42) / 80 = 23.1
Expected frequency of Cell (1,2) = (44 x 38) / 80 = 20.9
Expected frequency of Cell (2,1) = (36 x 42) / 80 = 18.9
Expected frequency of Cell (2,2) = (36 x 38) / 80 = 17.1
Next, we need to calculate the contribution of each cell to the chi-square statistic. We can do this by subtracting the expected frequency from the observed frequency, squaring the result, and then dividing by the expected frequency.
The contributions of each cell to the chi-square statistic are as follows:
Contribution of Cell (1,1) = (37 - 23.1)2 / 23.1 = 8.30
Contribution of Cell (1,2) = (7 - 20.9)2 / 20.9 = 8.44
Contribution of Cell (2,1) = (9 - 18.9)2 / 18.9 = 4.52
Contribution of Cell (2,2) = (27 - 17.1)2 / 17.1 = 6.04
Finally, we can sum up the contributions of all the cells to get the chi-square statistic:
Chi-square statistic = 8.30 + 8.44 + 4.52 + 6.04 = 27.30
The cell that contributed most to the final result was Cell (1,2) with a contribution of 8.44. This cell had an observed frequency of 7, which was much lower than the expected frequency of 20.9. This indicates that there is a significant association between the two variables in this cell, and it is driving the overall result of the test.
In conclusion, by breaking down the chi-square statistic into its individual components, we can identify the cells that contribute most to the result and gain a deeper understanding of the relationship between the variables.
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what is the product of these binomials [tex](x-9)(x+2)=
The product of the binomials (x-9) and (x+2) is x² - 7x - 18.
How to calculate the product of these binomials?To find the product of the binomials (x-9) and (x+2), we can use the FOIL method, which stands for First, Outer, Inner, Last.
First: Multiply the first terms of each binomial: xx = x²
Outer: Multiply the outer terms of each binomial: x × 2 = 2x
Inner: Multiply the inner terms of each binomial: -9 × x = -9x
Last: Multiply the last terms of each binomial: -9 × 2 = -18
Now we can add up these four products to get the final answer:
x² + 2x - 9x - 18
Simplifying this expression, we get:
x² - 7x - 18
Therefore, the product of the binomials (x-9) and (x+2) is x² - 7x - 18.
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a bug ran along a number line at a speed at 11 units per minutes. It never changes direction. If the bug is at 100 units at 7:15,where could it be at 7:20
Answer:
Step-by-step explanation:
Answer:
155 Units
Step-by-step explanation:
Rate of Bug (given) = 11 units PER MINUTE
It never changed direction, so it was going in positive direction (assume).
In 7:15 pm (evening), it was at Point 100,
We want the point at which it was at 7:20 pm.
7:20pm - 7:15pm = 5 minutes
So, time passed 5 minutes. It's rate is 11 units PER MINUTE, so in 5 mins:
11 * 5 = 55 units
Assuming he is going in positive direction, the bug will be at:
100 + 55 = 155 Units
PLEASE HELP! 10 POINTS! URGENT!
Answer: 32
Step-by-step explanation:
Multiply by reciprocal. -> y >or= 32
32=32
24<32
16<32
8<32
What is the volume?
5 1/3in
3 3/4 in
4 in
can't get this rule answer. I got it wrong...
The two true statements about the axis of symmetry are the first and second ones, so the correct option is the second one (counting from the top)
What can we say about the axis of symmetry?The axis of symmetry is a of a quadratic equation is a line that cuts the parabola in two equal halves.
For a quadratic of the form:
y = ax² + bx + c
Where the vertex is (h, k)
The axis of symmetry is the line of the form:
x = h
Then the two true statements are i and ii, the third and fourth statements are false because the vertex can be either a maximum or minimum, so we can't apply these restrictions.
Then the correct option is the second one.
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Scott has been working out to get in shape. Each night, he does 3 bent-leg sit-ups for every 2 straight-leg sit-ups. If Scott does 10 straight-leg sit-ups every night, how many sit-ups does he do altogether?
Scott does 35 sit-ups altogether every night.
What is ratio?A ratio is a comparison of two quantities, expressed as the quotient of one quantity divided by the other. Ratios can be written in different forms, such as using a colon (:) or a fraction (/).
According to question:For every 2 straight-leg sit-ups, Scott does 3 bent-leg sit-ups. Therefore, the ratio of straight-leg sit-ups to bent-leg sit-ups is 2:3.
If Scott does 10 straight-leg sit-ups every night, we can use this ratio to find out how many bent-leg sit-ups he does.
First, we can write the ratio as a fraction:
2/5 = 10/x
where x is the number of bent-leg sit-ups Scott does.
To solve for x, we can cross-multiply:
2x = 50
x = 25
Therefore, Scott does 25 bent-leg sit-ups every night.
To find the total number of sit-ups Scott does every night, we can add the number of straight-leg sit-ups to the number of bent-leg sit-ups:
10 + 25 = 35
Therefore, Scott does 35 sit-ups altogether every night.
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The diameter of the circle above is 6cm what is the circumference of the circle?
Answer:
A
Step-by-step explanation:
r=d/2
=6/2 =3
2πr
2×3.14×3
=18.84
An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 2662 feet and Plane B is taking off. Plane A is gaining altitude at 25.25 feet per second and Plane B is gaining altitude at 85.75 feet per second. How many seconds will pass before the plane are at the same altitude? What will their altitude be when they’re at the same altitude?
I need helppppppppp please help me I don’t understand
Answer:
m∠2 = 130°
m∠3 = 25°
m∠4 = 25°
Step-by-step explanation:
Opposite angles of rhombi are congruent. Therefore,
m∠1 = m∠2 = 130°
The measures of the interior angles of a triangle add to 180°. Using this information, along with the isosceles triangle theorem, we can solve for m∠3 (which is also congruent to m∠4):
m∠2 + 2(m∠3) = 180°
↓ substituting in m∠2
130° + 2(m∠3) = 180°
↓ subtracting 130° from both sides
2(m∠3) = 50°
↓ dividing both sides by 2
m∠3 = 25°
m∠3 = m∠4 = 25°
C is between A and D , and B is the midpoint of AC . If BC=2 and BD=7 , find AD
Answer:
AD = 9
Step-by-step explanation:
B is the midpoint of AC and BC = 2 so AC = 4.
BD is given as 7 so all we need to do is add up the given values:
AC + BD - BC = AD
4 + 7 - 2 = 9
Find the perimeter of AIJK. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale. F 35 349 499 978 H GJ K 49° 44 34
Using the equation and cross-multiplication method, we know that the perimeter of the triangle IJK is 180.4 units.
What are triangles?A triangle is a polygon with three edges and three vertices.
It belongs to the basic geometric shapes.
A triangle having vertices A, B, and C is known as triangle ABC.
Any three locations in Euclidean geometry that are not collinear result in a distinct triangle and a distinct plane.
The closed, two-dimensional shape known as a triangle has three sides, three angles, and three vertices.
A triangle is part of a polygon.
So, we know that:
We must ascertain the value of x in order to determine the triangle's perimeter, IJK.
Using the ratio of comparable triangles and the triangles above, we have:
HF/KI = FG/IJ
Where,
HF = 35, KI = 77, FG = 27 and IJ = x
By changing the values, we obtain:
35/77 = 27/x
Take the cross product of the aforementioned equation, and we have:
35x = 27*77
x = 27*77/35 = 27 * 11/5 = 59.4
The triangle's perimeter is thus equal to the sum of its sides:
△IJK = 44 + 77 + 59.4 = 180.4
Therefore, using the equation and cross-multiplication method, we know that the perimeter of the triangle IJK is 180.4 units.
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Correct question:
Watch the help video on the perimeter of AIJK. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.
A fourth grade class surveys students as to their shoe size.
Which type of graph would best display the results of this survey?
A. Circle graph
B. Histogram
C. Line plot
D. Blox plot
The best type of graph to display the results of this survey would be a histogram. A histogram is a graph that uses bars to represent the frequency distribution of a set of data. In this case, the shoe sizes would be grouped into intervals (e.g., 1-3, 4-6, 7-9, etc.) and the height of each bar would represent the number of students who have shoe sizes within that interval. A histogram is an effective way to show the overall pattern of the distribution of shoe sizes in the class.
A circle graph, also known as a pie chart, is useful for showing parts of a whole. It may not be the best choice for this survey since it does not show the distribution of shoe sizes as effectively as a histogram would.
A line plot, also known as a dot plot, is useful for showing the frequency of individual values in a small data set. It may not be the best choice for this survey since it may not be practical to list every individual shoe size.
A box plot, also known as a box-and-whisker plot, is useful for showing the distribution of a large data set. It may not be the best choice for this survey since the data set is likely to be small, and a histogram would be more appropriate for displaying the results.
5c + 4c + 2 and 5c + 2[2c] + 1]
The final expression is 9c + 2.
What is an equation?
In mathematics, an equation asserts the equality of two expressions, usually separated by an equal sign (=). An equation is formed when two expressions are set equal to each other. The expressions can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
To simplify the expressions:
5c + 4c + 2 = 9c + 2
In this expression, we can add the coefficients of the like terms 5c and 4c to get 9c. Then we simply combine the constant term 2.
5c + 2[2c + 1] = 5c + 4c + 2
In this expression, we can distribute the 2 outside the brackets to get:
5c + 2(2c) + 2(1) = 5c + 4c + 2
Then, as in the previous expression, we can combine the like terms 5c and 4c to get 9c and simplify to get:
9c + 2
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Write a counterexample to prove this is false:
Yes, The function with a frequency of 2 has a greater period than a function with a frequency of 1/2.
What does the word" function" signify in calculation?
As a set of inputs with one for each, a function is defined as a relationship between them. A function, expressed simply, is an association between inputs where each input is connected to one and only one affair. A sphere, codomain, or range exists for every function. generally, f( x), where x is the input, is used to represent a function.
frequency of f(x) = 1/period of f(X)
2 = 1/[tex]T_{f}[/tex]
[tex]T_{g}[/tex] = 1/2
frequency of g(X) = 1/period of g(X)
1/2 = 1/[tex]T_{g}[/tex]
[tex]T_{f}[/tex] = 2
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The areas of two circles are 92 2 and 62 2
respectively. Find the radius of the circle
having its area equal to the sum of the areas of the two circles.
Answer:
formula for area of a circle = πr²
πr² = 92cm² first circle
πr² = 62cm² second circle
now to find the radius of a circle having the sum of the other circle.
πr² = 92 + 62
3.142 × r² = 154
r² = 154/3.142
r² = 49.013
take square root of both sides
r = √49.013
r = 7.000cm ≈ 7cm
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used
The tiles to the correct boxes to complete the pairs-
A: [tex](-3^{-2} )^{0}[/tex] = 1; B: [tex]3^{3}.3^{1}. 3^{2} .3^{-12}[/tex] [tex]= 1/729[/tex] C: [tex]-3^{5} / -3^{8}[/tex] = -1/27 ; D: [tex]-3^{-3}. 3^{-3}[/tex] = - 1/729.
Explain about the indices:We can determine how many times a phrase has been multiplied by itself using an index, which is a tiny number.
Indexes is the plural of index.
Remember that a power is the result of a particular number of identical factors? For instance, the number [tex]3^{7}[/tex] is a power, where the base is the number 3, and the index or exponent is the number 7.
Given number with exponents :
A: [tex](-3^{-2} )^{0}[/tex]
[tex]= (-3^{0} )\\= 1[/tex]
B: [tex]3^{3}.3^{1}. 3^{2} .3^{-12}[/tex]
[tex]= 3^{3 + 1 + 2 -12}[/tex]
[tex]= 3^{-6}\\= 1/729[/tex]
C: [tex]-3^{5} / -3^{8}[/tex]
[tex]= -3^{5-8}\\= - 3^{-3}\\\= -1/27[/tex]
D: [tex]-3^{-3}. 3^{-3}[/tex]
[tex]= -3^{-3 - 3}\\= -3^{-6}\\\\= -1/729[/tex]
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Shama draws a model of her garden on the coordinate grid. Each unit on the
grid represents 1 foot. Shama buys 1 plant for every 4 square feet of the garden.
How many plants does Shama buy?
y
87
7
6
5
4
3
2
1
0
1 2 3 4 5 6 7 8 9 10
X
14 plants
10 plants
7 plants
18 plants
Done->
Shama needs to buy 10 plants for her garden.
Calculating the number of plants she buysFrom the graph, we have
Area = 8 * 5 = 40
To determine how many plants Shama needs to buy, we need to use the given rule that she buys 1 plant for every 4 square feet of the garden.
Therefore, we can divide the total area of the garden by 4 to find how many plants she needs to buy:
Number of plants = Area of garden ÷ 4
Substituting the given values, we get:
Number of plants = 40 ÷ 4
Number of plants = 10
Therefore, Shama needs to buy 10 plants for her garden.
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A large to-go order at a local coffee shop consists of 20 cups of coffee. Five of the cups of coffee have sugar, 12 of the cups of coffee have artificial sweetener, and the others are black, containing no sugar or sweetener. Suppose an experiment involves a person taking a cup of coffee from this order. The person does not put that coffee back with the others, and then takes another coffee from the order. What is the probability that the person selects 2 coffees with artificial sweetener? Express your answer as a simplified fraction.
The probability that the person selects 2 coffees with artificial sweetener is 33/95.
How to find the Probability?Let A be the event that the first cup of coffee has artificial sweetener, and B be the event that the second cup of coffee also has artificial sweetener.
We want to find the probability of the intersection of A and B, i.e., the probability that both cups have artificial sweetener. We can use the formula for conditional probability:
According to given data:P(A and B) = P(B|A) * P(A)
where P(B|A) is the probability of B given that A has occurred, and P(A) is the probability of A.
The probability of selecting a cup of coffee with artificial sweetener on the first draw is:
P(A) = 12/20
After the first cup has been drawn, there are now 11 cups with artificial sweetener left in the order, out of a total of 19 cups (since one cup has already been drawn). Therefore, the probability of selecting another cup with artificial sweetener on the second draw, given that the first cup had artificial sweetener, is:
P(B|A) = 11/19
So the probability of selecting two cups with artificial sweetener is:
P(A and B) = P(B|A) * P(A) = (11/19) * (12/20) = 33/95
Therefore, the probability that the person selects 2 coffees with artificial sweetener is 33/95.
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the grand canyon is 1600 meters deep at its deepest point. a rock is dropped from the rim above this point. express the height of the rock as a function of the time t in seconds. how long will it take the rock to hit the canyon floor? a(t)
The grand canyon is 1600 meters deep at its deepest point. a rock is dropped from the rim above this point. express the height of the rock as a function of the time t in seconds. It will take approximately 18.05 seconds for the rock to hit the canyon floor.
The height of a rock dropped from the rim of the Grand Canyon can be expressed as a function of time, t, in seconds. To do this, we will use the free-fall equation, which states that the height of an object in free fall is given by:
a(t) = -1/2 * g * t^2 + h
where:
- a(t) is the height of the rock at time t,
- g is the acceleration due to gravity (approximately 9.81 meters per second squared),
- t is the time in seconds, and
- h is the initial height of the rock (1600 meters, in this case).
For the rock dropped from the rim of the Grand Canyon, the function becomes:
a(t) = -1/2 * 9.81 * t^2 + 1600
To find how long it will take the rock to hit the canyon floor, we need to find the value of t when the height, a(t), is equal to 0 (i.e., the rock reaches the floor).
0 = -1/2 * 9.81 * t^2 + 1600
Now, we'll solve for t:
1/2 * 9.81 * t^2 = 1600
t^2 = (1600 * 2) / 9.81
t^2 ≈ 325.99
t ≈ √325.99
t ≈ 18.05 seconds
Therefore, it will take approximately 18.05 seconds for the rock to hit the canyon floor.
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Out of 980 pizzas, only 196 are stuffed crust, so how many will be stuffed crust out of 5000 pizzas?
Step-by-step explanation:
192080 because we multiply its 980×196 =182080
Write an exponential function
y = abx
for a graph that passes through
(2, 1)
and
(3, 4).
An exponential function y = abx for a graph that passes through (2, 1) and (3, 4) is [tex]y = (1/16)(4)^x[/tex].
To write an exponential function in the form[tex]y = ab^x[/tex] that passes through the points (2, 1) and (3, 4), follow these steps:
Step 1: Write the general form of the exponential function:
[tex]y = ab^x[/tex]
Step 2: Plug in the coordinates of the first point (2, 1):
[tex]1 = ab^2[/tex]
Step 3: Plug in the coordinates of the second point (3, 4):
[tex]4 = ab^3[/tex]
Step 4: Solve for "a" and "b" using the equations from Steps 2 and 3.
We have two equations:
1)[tex]1 = ab^2[/tex]
2) [tex]4 = ab^3[/tex]
Divide equation 2 by equation 1 to eliminate "a":
[tex](4/1) = (ab^3)/(ab^2)[/tex]
4 = b.
Now that we have found "b," we can find "a" by plugging "b" back into either equation 1 or 2.
We'll use equation 1:
[tex]1 = a(4)^21 = a(16)[/tex]
a = 1/16
Step 5: Write the final exponential function using the values of "a" and "b":
[tex]y = (1/16)(4)^x[/tex].
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What is the circumference of the circle pictured below? (Use π = 3.14
For the given circle the circumference is 34.54.
What is circumference?
Circumference is the distance around the edge of a circle or any curved, circular object. It can be thought of as the perimeter of a circle.
The circumference of a circle is given by the formula:
C = πd
where d is the diameter of the circle.
Substituting the given value of the diameter, we get:
C = π(11)
Using π = 3.14, we can evaluate the expression:
C = 3.14(11)
C = 34.54
Therefore, the circumference of the circle is 34.54 (rounded to two decimal places).
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whoever tells me the correct answer wins
The commute times are shorter for City A but more predictable for City B. Thus, option c is correct.
What is interval?In mathematics, an interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set. An interval can be written using interval notation, which uses parentheses, square brackets, or a combination of both to indicate whether the endpoints of the interval are included or excluded.
The interval [1, 5] represents a set of real numbers that includes all the numbers between 1 and 5, including 1 and 5 themselves. The square brackets indicate that the endpoints of the interval are included in the set. The left bracket "[" indicates that the interval includes the number 1, and the right bracket "]" indicates that the interval includes the number 5.
In interval notation, we can write this interval as:
[1, 5] = {x | 1 ≤ x ≤ 5}
This means that the set of all real numbers x, such that x is greater than or equal to 1 and less than or equal to 5, is equal to the interval [1, 5].
Graphically, we can represent this interval on a number line as follows:
|-----|-----|-----|-----|-----|
0 1 2 3 4 5
The interval [1, 5] is the closed interval between 1 and 5, including both endpoints, so we use closed circles to indicate that the endpoints are included in the interval:
|-----|-----|-----|-----|-----|
0 1 2 3 4 5
[ ○-----○ ]
1 5
The interval includes all the numbers on the number line between 1 and 5, including 1 and 5 themselves, but no other numbers outside of that range.
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I need help with the whole page please help!
The following points are 5 or more units apart: A and B, G and D, G and F, G and E, F and E, E and B, (4, 3 and (4, -2), (6, -2) and (0, -2), (3, -7) and (3, -1)
Identifying the points that are 5 or more units apartWhen two points on a graph are 5 or more units apart, it means that there is a significant difference in the values of the function at those points.
For example, if we have two vertical or horizontal points (x1, y1) and (x2, y2) on a graph such that |x1 - x2| ≥ 5, it means that the x-values of the two points are at least 5 units apart.
Similarly, if |y1 - y2| ≥ 5, it means that the y-values of the two points are at least 5 units apart.
Using the above as a guide, the following points are 5 or more units apart
A and B, G and D, G and F, G and E, F and E, E and B, (4, 3 and (4, -2), (6, -2) and (0, -2), (3, -7) and (3, -1)
The point that is 8 or more units apart from NWe have
N = (6, 8)
The point that is 8 or more units apart from N could be
Point = (6, 8 + at least 8)
So, we have
Point = (6, 8 + 9)
Point = (6, 17)
Hence, the point is (6, 17)
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the weights of bags filled by a machine are normally distributed with a standard deviation of 0.04 kg and a mean that can be set by the operator. at what level should the mean be set if it is required that only 1% of the bags weigh less than 9.5 kg?
At μ = 10.0932 level should the mean be set if it is required that only 1% of the bags weigh less than 9.5 kg.
Given Data:
σ = 0.04 kg
x = 9.5 kg
We want to determine μ such that: P(X ≤ 9.5)= 1% = 0.01
Thus, we know here probability of x is 0.1 which is less than 9.5
so here Z is -2.326 by the standard table
Determine the z-score in the normal probability table in the appendix that has a probability closest to 0.01:
Then, we have here 1% to left when Z is - 2.326
Now,
The value corresponding to the z-score is then the mean increased by the product of the z-score and the standard deviation:
x = μ+ zσ
= μ− 2.33(0.04) = μ - 0.0932
Since , P(X ≤ 9.5) = 0.95% = 0.095, we know that x also has to be equal to 9.5:
μ− 0.0932 = 9.5
Add 0.0932 to each side of the previous equation:
μ = 10+ 0.0932
= 10.0932
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The radius of a circle is 18 kilometers. What is the circle's area?
Answer: 1017.36 km²
Step-by-step explanation:
Area of Circle = πr² = 3.14×18×18 = 1017.36 km²
pls do not answer if you do not know the answer. I have had this problem many times and do not want to report anyone today. 45 points.
The quadratic function f(x) has roots of -2 and 6, and it passes through the point (1, 15).
What is the vertex form of the equation of f(x)?
f(x) = (x - 2)² +16
f(x) = (x + 2)² + 16
f(x) = -(x - 2)² + 16 f
(x) = -(x + 2)² + 16
Answer:
To find the vertex form of the quadratic equation, we need to first find the equation in standard form, which is:
f(x) = a(x - r)(x - s)
where r and s are the roots of the quadratic equation and a is a constant.
From the problem statement, we know that the roots of the quadratic equation are -2 and 6. Thus, we can write:
f(x) = a(x + 2)(x - 6)
To find the value of a, we can use the point (1, 15) that the function passes through. We substitute x = 1 and f(x) = 15 into the equation:
15 = a(1 + 2)(1 - 6)
15 = -15a
Thus, a = -1.
Substituting this value of a into the equation, we get:
f(x) = -(x + 2)(x - 6)
To convert this equation into vertex form, we need to complete the square. We can do this by adding and subtracting (2/2)² = 1 from the equation:
f(x) = -(x + 2)(x - 6) + 1 - 1
= -(x + 2)² + 16
Therefore, the vertex form of the equation of f(x) is f(x) = -(x + 2)² + 16.
Step-by-step explanation:
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In an orchard, there are 12 apple trees, 24 orange trees, and a cherry tree. What is the ratio of orange trees to cherry trees?
Answer: 24:1
Step-by-step explanation:
In the first step, you have to acknowledge how many of each tree there are in the question asked.
There is one cherry tree and 24 orange trees.
So the ratio of orange trees to cherry trees would be 24:1