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)
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I seQuestion 10nd you a picture in few minutes
8.) The inequality that describes the possible number of calories X, you can eat during the rest of the day would be < 1200. That is option A.
9.) The value of X would be = 3.
How to determine the quantity of calories you will eat for the day?For question 8.)
The quantity of calories for each day < 2200. That is;
1 day < 2200
The calories consumed for breakfast = 350
The calories consumed for lunch = 650
The total calories consumed = 350+650 = 1000 calories.
The amount of calories needed to be consumed the more = 2200-1000 = 1200
Therefore the quantity of calories needed more < 1200 calories.
For question 9.)
t(X) = 3x - 5
where;
t(X) = 4
That is;
4 = 3x - 5
3x=4+5
3x = 9
X = 9/3 = 3
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A coordinator will select 6 6 songs from a list of 6 6 songs to compose an event's musical entertainment lineup. How many different lineups are possible
The requried, there is only 1 possible lineup of 6 songs from a list of 6 songs.
To determine how many different lineups are possible, we can use the formula for combinations, which is:
nCk = n! / (k!(n-k)!)
where n is the total number of items, k is the number of items being selected, and the exclamation mark denotes the factorial function.
In this case, we have n = 6 (the total number of songs) and k = 6 (the number of songs to be selected). So we can plug these values into the formula:
6C6 = 6! / (6!(6-6)!) = 6! / (6!0!) = 1
Therefore, there is only 1 possible lineup of 6 songs from a list of 6 songs.
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The equation y = 2x2 – 4x – 3 models the cross-section of a sculpture that sits in the water, where x is horizontal distance, and y is height above sea level. At what two x-values is the sculpture at sea-level?
The two x-values where the sculpture at sea-level are x = 2.581 and x = -0.581
At what two x-values is the sculpture at sea-level?From the question, we have the following parameters that can be used in our computation:
y = 2x^2 - 4x - 3
When the sculpture at sea-level, the value of y is 0
So, we have
2x^2 - 4x - 3 = 0
When solved graphically, we have
x = 2.581 and x = -0.581
Hence, the x values are x = 2.581 and x = -0.581
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how do you find the area of a trapizoid
Answer:
By using the formula down below you can find the area of a trapezoid
A = [tex]\frac{a+b}{2}[/tex]h
↑ Area
A = Base
B = Base
H = Height
Example.
A = 12
B = 4
H = 2
First “ A “ + “ B “ =
12 + 4 = 16
16 / 2 = 8
8 x “ h “
8 x 2 = 16
Answer is 16
Thus the answer is, above
So if you look that up then it will show you how to find the area of a trapizoid
In school please help me
Answer:
Step-by-step explanation:
4992223553535
your in school ask a teacher
CAN SOMEONE HELP WITH THIS QUESTION?✨
Help
Applying the Solution to a 3X3 System
At a family reunion, there only blood relatives, consisting of children, parents, and grandparents, in attendance. There were 400 people total. There were twice as many parents as grandparents, and 50 more children than parents. How many children, parents, and Grandparents were in attendance?
Show up all steps please
Solving the system of equations, the number of children, parents, and Grandparents who were in attendance are 190, 140 and 70 respectively.
Let C, P and G denotes the number of children, parents and the grandparents in the function.
We get the system of equations,
C + P + G = 400 [equation 1]
P = 2G ⇒ G = P/2 [equation 2]
C = P + 50 [equation 3]
Substituting 2 and 3 in 1,
(P + 50) + P + (P/2) = 400
2P + P/2 = 350
5/2 P = 350
P = 140
C = P + 50 = 140 + 50 = 190
G = P/2 = 140/2 = 70
Hence the number of parents = 140, grandparents = 70 and children = 190.
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Assistance needed thank you
By using the head to tail, the addition of the vectors [tex]\vec a + \vec b[/tex] is (3, -5).
How to add vectors by using the head to tail method?In Geometry, a vector is typically composed of two end points. First, is the starting point which is commonly known as a "tail" and the second (ending) point that is commonly known as a "head."
Additionally, the head to tail method of adding two vectors requires drawing the first vector ([tex]\vec a[/tex]) on a graph and then placing the tail of the second vector ([tex]\vec b[/tex]) at the head of the first vector. Finally, the resultant vector would be drawn from the tail of the first vector ([tex]\vec a[/tex]) to the head of the second vector ([tex]\vec b[/tex]).
Next, we would add the two (2) vectors algebraically as follows;
[tex]\vec a + \vec b[/tex] = (4, -3) + (-1, -2)
[tex]\vec a + \vec b[/tex] = [(4 + (-1)), (-3 + (-2))]
[tex]\vec a + \vec b[/tex] = [(4 - 1), (-3 - 2)]
[tex]\vec a + \vec b[/tex] = (3, -5).
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Can anyone help me with this question? please.
The population mean is calculated as the sum of all observations in the population, divided by the number of objects in the population.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.
Hence the population mean is calculated as the sum of all observations in the population, divided by the number of objects in the population.
Missing InformationThe problem is incomplete, hence the procedure to obtain the mean of a data-set, in this case the population, is presented.
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Dylan is putting a gold ribbon around the lid of a rectangular box. The lid ha a width of 6(1/4) inches and a length of 4(5/8) inches. The ribbon costs $1.50 per Inch. How much will it cost Dylan to p gold ribbon around the perimeter of the lid? $13.88 $21.75 $32.63 $43.36
The value of cost of the perimeter of the lid is, $32.625
Given that;
Dylan is putting a gold ribbon around the lid of a rectangular box. The lid ha a width of 6(1/4) inches and a length of 4(5/8) inches.
Hence, The value of perimeter of the lid is,
⇒ P = 2 (6 1/4 + 4 5/8)
⇒ P = 2 (25/4 + 37/8)
⇒ P = 2 (50/8 + 37/8)
⇒ P = 2 (87/8)
⇒ P = 87/4 inches
Since, The ribbon costs $1.50 per Inch.
Hence, Total cost for lid is,
⇒ 1.50 × 87/4
⇒ $32.625
Thus, The value of cost of the perimeter of the lid is, $32.625
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For each relation, decide whether or not it is a function.
Answer:
relation 1-function
relation 2-not a function
relation 3-function
relation 4-funtion
The data shows the weight of the potting soil brought by each student. Draw a line plot and answer the questions below. 1 1/2 kg 3/4 kg 1 1/2 kg Title: 1 kg 1 1/2 kg 2 kg 3/4 kg 2 kg 3/4 kg Roading and Math for K-5 2 kg 2 kg 2 kg 2 1/2 kg 3/4 kg 1 kg 1. How many students brought 3/4 kg of soil? 2. How many students brought less than 1 1/2 kg? 3. How many students brought 1 kg or more? 4. How many fewer students brought 1 kg than 2 kg? 5. How many students brought more than 1 1/2 kg but less than 2 1/2 kg? 6. How much soil was brought by all the students together?
Answer:
|
| 3/4 kg
| x
|
| x
| x
| x
| x
| x
| x
|_________
1 kg 1 1/2 kg 2 kg 2 1/2 kg
Two students brought 3/4 kg of soil.
Four students brought less than 1 1/2 kg of soil (the ones who brought 3/4 kg and the one who brought 1 kg).
Eight students brought 1 kg or more of soil.
Two fewer students brought 1 kg than 2 kg (two students brought 1 kg and four students brought 2 kg).
Two students brought more than 1 1/2 kg but less than 2 1/2 kg (the ones who brought 2 kg).
The total amount of soil brought by all the students is:
Copy code
1 1/2 kg + 3/4 kg + 1 1/2 kg + 1 kg + 2 kg + 3/4 kg + 2 kg + 2 kg + 2 kg + 2 1/2 kg + 3/4 kg
= 19 3/4 kg
Step-by-step explanation:
Answer:
Step-by-step explanation:
it is timed by 1 1/2kg
[Two home-improvement stores (Great Home and Super Home) in a growing urban area are interested in expanding their market share. Both are interested in expanding the size of their store and parking lot to accommodate potential growth in their customer base. Two possible actions for both the firms are: ‘increase the size of the store and parking lot’ and ‘do not increase the size of the store and parking lot’. Payoffs are defined in terms of increase in annual profits in $million. The following table describes the payoffs for both the firms to alternative actions taken by each of them. Note, Great Home’s payoffs are given first and Super Home’s payoff are given second.]
Super Home
Increase
Do not increase
Great Home Increase
($1.5 million, $1m) ($3.4m, $0.4m)
Do not increase
($0.6m $3.2m) ($2.5m, $2m)
“You can delete this table as well from your submitted file”.
a) [Let’s say, each store is pursuing its own best interest. What will be a rational (or dominant) strategy for Super Home to follow? Explain in 3-4 sentences. What will be a rational (or dominant) strategy for Great Home to follow? Explain in 3-4 sentences. (4 marks)]
b) [What will be the annual profit growth for each store, if they both follow their dominant strategy? Define Nash Equilibrium and identify the Nash Equilibrium in the table above. (4 marks)]
c) [Suppose the owners of Super Home and Great Home meet for a friendly game of golf one afternoon and happen to discuss a strategy to optimize profit. What should the joint strategy be they should both agree to? What will annual profit growth be for each store under this agreement? (2 marks)]
a) For Super Home, the superior (or dominant) tactic is to magnify the size of the store and parking lot. This is, regardless of what Great Home does, Super Home's payoff is amplified when it expands its size ($1m vs $0.4m if Great Home amplifies; $3.2m vs $2m if Great Home passes).
What is the best strategy for Great Home?Similarly, for Great Home, the logical (or dominant) strategy is also to expand the size of the store and parking lot. This is because, although unrelated to Super Home's decision, Great Home's payoff is augmented when it enlarges its size ($1.5m vs $0.6m if Super Home magnifies; $3.4m vs $2.5m if Super Home disallows).
b) If both stores implement their authoritative plan, Great Home will witness an annual profit growth of $1.5 million, and Super Home will observe an annual profit growth of $1 million.
A Nash Equilibrium comprehends a state wherein each player chooses their finest ploy given the stratagems selected by the other participant(s), and no player can modify their consequence through exclusively adapting their strategy. In this case, the Nash Equilibrium exists in (Increase, Increase), which spans over the payoffs ($1.5m, $1m).
c) The conjunctive approach both stores should commit to would be for Great Home to amplify the size of its store and parking lot, and Super Home to renounce increasing its size.
Under this harmonized approval, the annual profit growth for Great Home will come out at $3.4 million, and for Super Home, it will arrive at $0.4 million. This system gives rise to a higher collective gain compared to the Nash Equilibrium.
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PLEASE HURRY
Let v = 5i - 2j Find ||4v||
The magnitude of the vector 4v is 4 times the magnitude of v, which is equal to 4 √29.
Given the vector v = 5i - 2j, we can find the magnitude or norm of the vector ||v|| using the formula:
||v|| = √(v · v)
where · denotes the dot product of the vector with itself.
Substituting the values of the vector v, we have:
||v|| = √((5i - 2j) · (5i - 2j))
Expanding the dot product using the distributive law, we get:
||v|| = √(25i² - 20ij + 4j²)
Since i² = j² = 1 and ij = ji = 0, we can simplify this expression to:
||v|| = √(25 + 4) = √29
Thus, the magnitude of the vector v is √29.
Now, we need to find the magnitude of the vector 4v. Using the property that ||kv|| = |k| ||v|| for any scalar k and vector v, we have:
||4v|| = |4| ||v|| = 4 √29
In summary, the magnitude of the vector v is √29, and the magnitude of the vector 4v is 4 √29.
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-24=8(y-8)-4y??????????????
Answer:
[tex]\sf y=10[/tex]Step-by-step explanation:
[tex]\sf -24=8(y-8)-4y[/tex]
[tex]\sf 8\left(y-8\right)-4y=-24[/tex]
Expand:-
[tex]\sf 8\left(y-8\right)-4y[/tex][tex]\sf 8y-64-4y[/tex][tex]\sf 4y-64[/tex][tex]\sf 4y-64=-24[/tex]
Add 64 to both sides:-
[tex]\sf 4y-64+64=-24+64[/tex][tex]\sf 4y=40[/tex]Divide both sides by 4:-
[tex]\sf \cfrac{4y}{4}=\cfrac{40}{4}[/tex][tex]\sf y=10[/tex]________________________
Q14 20 students take a maths test. Their tutor records the scores. The list below shows
their scores:
15, 24, 6, 8, 29, 6, 12, 17, 24, 22, 25, 30, 18, 3, 11, 7, 18, 27, 28, 27
Present these scores in three suitable groups
The scores of the maths students recorded by their tutor presented in three suitable groups are 1 - 10, 11 - 20, 21 - 30.
How to present scores in groups?Math test scores: 15, 24, 6, 8, 29, 6, 12, 17, 24, 22, 25, 30, 18, 3, 11, 7, 18, 27, 28, 27
The group of scores when divided into 3;
Group frequency
1 - 10 5
11 - 20 6
21 - 30 9
Therefore, the groups 1 - 10, 11 - 20, 21 - 30 have the frequency 5, 6 and 9 respectively.
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pleas
HELP IMMEDIATELY
Answer:
144ft^3
Step-by-step explanation:
To start, we have your formula: [tex]V=\frac{1}{2} (bh) (l)[/tex]
b = base length of the triangle.
h = height of the triangle.
l = length of the prism
Fill in for each of those values:
[tex]V = \frac{1}{2} (6x6)(8)[/tex]
[tex]V=\frac{1}{2} (36)(8)[/tex]
[tex]V=(18)(8)[/tex]
[tex]V=144[/tex]
Your answer, because it is a 3D shape, should be cubed, so:
[tex]V=144ft^{3}[/tex]
Bacteria in a dirty glass triple 4 hours. If there are 25 bacteria to start, how many in the glass
after 1 day?
If the number of bacteria triples every 4 hours, then after 1 day (24 hours), the number of bacteria will triple 6 times.
Tripling a number 6 times is the same as multiplying it by 3 raised to the power of 6, or 3^6.
So, if there are 25 bacteria to start, the number of bacteria after 1 day will be:
25 x 3^6 = 25 x 729 = 18,225 bacteria.
Answer:
Step-by-step explanation:
It is not possible to accurately determine the number of bacteria in the glass after 4 hours without additional information such as the rate of bacterial growth, the environmental conditions, and whether any bacteria were removed or added during that time.
A bag of apples weighs 8 7 8 pounds. A crate of bananas is 6 times as heavy as the apples. How much heavier are the bananas than the apples?
The crate of bananas is heavier than the bag of apples by 53 1/4 pounds.
How much heavier are the bananas than the apples?An apple and a banana are both kinds of fruits. They both weigh differently.
Weight of a bag of apple = 8 7/8 pounds
Weight of a crate of bananas = 6 times as heavy as the apples
= 6 × 8 7/8
= 6 × 71 /8
= 426 / 8
= 53 1/4 pounds
Therefore, the weight of a crate of bananas is 53 1/4 pounds
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Which shows the correct first step to solving the system of equations in the most efficient manner?
3x+2y-17
x+4y=19
O x=-4y+19
-2y+17
3
O x-
O4y=-x+19
Oy=-3x+17
Answer:
(a) x = -4y +19
Step-by-step explanation:
You want to know a good first step for solving the system of equations in an efficient manner.
3x +2y = 17x +4y = 19SubstitutionOne way to solve these equations is by substitution. To do that, we typically write an expression for one of the variables in terms of the other. It is efficient to choose a variable that already has a coefficient of 1.
Here, a useful first step is to solve the second equation for x:
x = -4y +19
__
Additional comment
Then the solution proceeds with substitution for x:
3(-4y +19) +2y = 17
-10y +57 = 17
-10y = -40
y = 4
x = -4(4) +19 = 3
The solution is (x, y) = (3, 4).
Another reasonable first step is to subtract the second equation from twice the first:
2(3x +2y) -(x +4y) = 2(17) -(19)
5x = 15
x = 3
3 +4y = 19 . . . . . . substitute for x in the second equation
y = (19 -3)/4 = 4
The "addition" or "elimination" method shown second is also shown using 5 steps, but these are generally more complicated steps than the ones shown for the "substitution" solution. It appears the substitution solution probably is "the most efficient" in this case.
The table lists recommended amounts of food to order for party guests. and are hosting a graduation party for 40 guests. They know there will also be guests stopping by who may have come from other parties. For ordering purposes, they will count each of these "drop-in" guests as half a guest. How much of each food item should and order for a graduation party with drop-in guests?
To order enough food for a graduation party with drop-in guests, they should order:
112 + 1.4x pieces of fried chicken
14.64 + 0.183x pounds of meat
41 + 0.5125x pounds of lasagna
If we consider each "drop-in" guest as half a guest, then the total number of guests becomes:
40 + 0.5x, where x is the number of "drop-in" guests.
To determine how much of each food item to order, we can use the recommended amounts as a guide and scale them up based on the total number of guests:
Fried chicken: 28 pieces for 10 guests, so we need 28 * (40 + 0.5x) / 10 = 112 + 1.4x pieces.Meat: 3.66 pounds for 10 guests, so we need 3.66 * (40 + 0.5x) / 10 = 14.64 + 0.183x pounds.Lasagna: 10.25 pounds for 10 guests, so we need 10.25 * (40 + 0.5x) / 10 = 41 + 0.5125x pounds.So, to order enough food for a graduation party with drop-in guests, they should order:
112 + 1.4x pieces of fried chicken
14.64 + 0.183x pounds of meat
41 + 0.5125x pounds of lasagna
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The equations for two savings accounts for the same Initial amount of $1125 and an interest rate of 1.875% accrued differently are shown in the table. Savings Account A A = 21.09t + 1125 Savings Account B JAN 1 A = 1125 1+ (1. 0.01875 2 2t Complete the statement. After 9 years, savings account [DROP DOWN 1] will have more money because it is modeled by [DROP DOWN 2] where the investment [DROP DOWN 3].
Savings Account B will have more money after 9 years because it is modeled by the exponential equation, and the investment grows exponentially with time
We have,
To determine which savings account has more money after 9 years, we can evaluate the amount of money in each account using the given equations.
For Savings Account A, the equation is:
A = 21.09t + 1125
Substituting t = 9 (since we're interested in the amount after 9 years), we get:
A = 21.09(9) + 1125 = 1300.81
So, after 9 years, Savings Account A will have $1300.81.
For Savings Account B, the equation is:
A = 1125(1 + 0.01875/2)^(2t)
Substituting t = 9, we get:
A = 1125(1 + 0.01875/2)^(2(9)) = 1318.98
So, after 9 years, Savings Account B will have $1318.98.
Therefore,
Savings Account B will have more money after 9 years because it is modeled by the exponential equation, and the investment grows exponentially with time
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If the area of triangle abc is 21 square units, find sinA if b=14 and c=9
Applying the formula for the area of triangle using sine, we have:
sin A = 1/3 (A ≈ 19.5°).
How to Find the Area of a Triangle Using Sine Rule?Given that a triangle has the following parameters:
Area of triangle ABC = 21 square units
Side b = 14 units
Side c = 9 units
Thus, applying the area of a triangle using the sine rule, we have the following formula:
Area = 1/2 * b * c * sin A
Plug in the values:
21 = 1/2 * 14 * 9 * sin A
2 * 21 = 126 * sin A
42 = 126 * sin A
42/126 = sin A
sin A = 1/3
A = sin^(-1)(1/3)
A ≈ 19.5°
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Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 15(0.94)
The exponential function in this problem represents a decay, with a percentage rate of 6%.
How to define an exponential function?An exponential function has the definition presented as follows:
y = ab^x.
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The function is classified as growth or decay as follows:
Growth: |b| > 1.Decay: |b| < 1.The function in this problem is defined as follows:
y = 15(0.94)^x.
As |b| = 0.94 < 1, the function is a decay function, and the rate is obtained as follows:
1 - r = 0.94
r = 1 - 0.94
r = 0.06
r = 6%.
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How much running area is there?
R = 20 ft
I WILL MARK YOU BRAINLIEST AND GIVE 30 POINTS
With a radius of 20 feet and 10 rounds traversed, the total distance equates to approximately 1256.6 feet.
How to solveWhen calculating the circumference (C) of a circle, the formula 2 * π * radius (R) is employed.
Taking into consideration R = 20 feet, we shall arrive at the following figure:
C = 2 * π * 20
C ≈ 2 * 3.14159265359 * 20
C ≈ 125.66 feet
If we use this calculation to determine the total distance covered after running 10 laps around a track, our equation morphs into Circumference (C) multiplied by the Number of laps (L).
When L equals 10, it follows that:
Total distance ≈ 125.66 feet * 10
Total distance ≈ 1256.6 feet
Therefore, with a radius of 20 feet and 10 rounds traversed, the total distance equates to approximately 1256.6 feet.
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What is the total distance covered after running 10 laps around a circular track with a radius of 20 feet?
Need answer ASAP please!
What is the total perimeter
Answer:
12 + 3 + 12 + (1/2)π(3) = 27 + (3/2)π ft
= 31.71 ft
Determining Slope and y-Intercept A coordinate plane with 4 lines. The first line is labeled a(x) and passes through (2, negative 4) and (0, 2) and continues past (negative 1, 5). The second line is labeled f(x) and passes through (negative 6, negative 6), (negative 3, 0), and (0, 6). The third line is labeled g(x) and passes through (negative 2, negative 7), (0, negative 3), (1, negative 1) and (2, 1). The fourth line is labeled h(x) and passes through (negative 6, negative 6), (0, negative 3), and (6, 0). When Janelle woke up, it was –3 degrees Fahrenheit outside. As the morning progressed, the temperature rose 2 degrees every hour. Which line on the graph could represent this scenario? a(x) f(x) g(x) h(x
A line on the graph which could represent this scenario is: C. g(x), the third line is labeled g(x) and passes through (negative 2, negative 7), (0, negative 3), (1, negative 1) and (2, 1).
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided about Janelle when she woke up, the temperature can be modeled by this equation:
y = mx + c
y = 2x + (-3)
y = 2x - 3
Therefore, the table of values can be generated as follows;
x y
0 -3
1 -1
2 1
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Use the long division method to find the result when 4x³ + 8x² + 13x + 15 is
divided by 2x + 3.
Answer:
2x2+x+5
Step-by-step explanation:
PLEASE HELP. The steps to derive the quadratic formula are shown below:
Step 1 ax2 + bx + c = 0
Step 2 ax2 + bx = − c
Step 3
Provide the next step to derive the quadratic formula.
a times the quantity x squared plus b over a times x end quantity equals negative c
x(ax + b) = −c
x squared over a plus b over a times x equals negative c over a
x squared over a plus b over a equals negative c over a
Answer:
Step 3: Divide both sides of the equation in Step 2 by a to get x² + (b/a)x = -c/a.
HELP ME PLEASE ITS DUE TODAY!!! The following data shows the number of times a class of 7th graders ate breakfast over a 30-day period.
{4, 18, 22, 25, 15, 12, 22, 14, 19, 30, 24, 20, 21, 24, 29, 16, 20, 27, 24, 25}
Part A: Determine the best graphical representation to display the data. Explain why the type of graph you chose is an appropriate display for the data. (2 points)
Part B: Explain, in words, how to create the graphical display you chose in Part A. Be sure to include a title, axis label(s), scale for axis if needed, and a clear process of how to graph the data. (2 points)
The best graphical representation to display the data would be a Histogram. This is appropriate because it will display the distribution and frequency of the grades, thus making it easy to compare the classes. To create the graph, you will use bars to depict the range of figures. This is on the x-axis while the y-axis will contain the frequency of occurrence.
How to design a histogramDesigning a histogram requires an understanding of the range of values, the frequency of occurrence, and the general picture that the graph is meant to paint in the mind of the reader.
So, for the histogram above, you can have a title like The distribution of 7th graders' breakfast over a 30-day period. Next, you label the x and y axis and plot the figures based on the information provided.
Learn more about histograms here:
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#SPJ1