The vertex of the given function is (0,4)
What is a quadratic equation?
A quadratic equation is a second-order polynomial equation with a single variable such as x, where ax²+bx+c=0. with a ≠ 0 . Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution. Real or complicated solutions are both possible.
identify the coefficients a and b of the quadratic function
y =ax² +bx+c-------(1)
a=2, b=0
x-coordinate of the vertex is x= -b/2a = -(0)/(2(2)) = 0
Substitute x=0 into given equation to get y-coordinate of the vertex
y= 2(0)² + 4 = 0+4 = 4
Vertex= (x,y) = (0,4)
The vertex of the given function is (0,4)
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A cell phone plan charges $47.35 per month plus $13.94 in taxes, plus $0.60 per minute for calls beyond the 400-minute monthly limit. Write a piecewise-
defined function to model the monthly cost C(x) (in S) as a function of the number of minutes used for the month.
C(x).
18
for (Choose one) Y
for (Choose one) ▼
X
!!
The two pieces relate to the number of minutes used, since there's the 400-minute limit.
Piece #1: When you use less than or equal to 400 minutes:
Cost calculation: $47.35 + $13.94 = $61.29
Piece #2: When you use more than 400 minutes:
Cost calculation: $47.35 + $13.94 + $0.60(x-400)
The x-400 piece is because you're only charged the $0.60/minute beyond the 400 minutes, so 401 minutes needs just 1 minute of extra charge
Cost calculation cleaned up: 61.29 + 0.60x - 240 = 0.6x - 178.71
Now it looks weird to have that -178.71, but keep in mind that this is only used if x > 400.
[tex]C(x) = \left \{ {{61.29 ~~~~~~~~~~~~~~ \text{ if } ~0 \leq x\leq 400} \atop {0.6x - 178.71~~~~ \text{ if } x > 400} \right.[/tex]
Your system might not require the "0≤x", but it technically should be there.
A research firm estimates the number of people who watch a television show. One rating point means that about 1,800,000 households watched the show. The top-rated television show during a certain week had a rating of 10.2. About how many households watched the show that week?
Based on the rating information of 10.2, a total of 1,800,000 households watched the show that week is 18360000 household.
How do ratings work?An evaluation of something's quality or appeal is given a rating. a 10 out of 10 value-for-money rating, as an illustration. The president's standing among the public is at its lowest point since assuming office.
Position is synonymous with ranking, evaluation, appraisal, and categorisation. Additional Ratings
Since 1 rating point is given = 1,800,000
Rating point = 1,800,000 household
Rating point = 10.2 × 1,800,000 household.
Rating point =18360000 household.
Therefore, correct to state that the number of households that watched the show that week are 18360000 household.
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Help!!!!
I am very lost!
The height of the plane to the nearest metres is 1023 metres. Therefore, the answer is A.
How to find the height of the plane?A pilot flying over the gulf of Mexico sees an island at an angle of depression of 12 degrees. At this time the horizontal distance from the plane to the island is 4812 metres .
Therefore, the height of the plane can be found as follows:
The situation forms a right angle triangle.
Using trigonometric ratios,
tan 12 = opposite / adjacent
tan 12° = x / 4812
cross multiply
x = 4812 tan 12°
x = 4812 × 0.21255656167
Therefore,
x = 1022.82217476
x = 1023 metres.
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what is y:x if 4x-6y=7x+2y
Please Answer Quick!
Answer:
x = 5/2
y = 1/2
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
[tex]\qquad \sf \dashrightarrow \: 4x - 6y = 7x + 2y[/tex]
[tex]\qquad \sf \dashrightarrow \: 4x - 7x = 2y + 6y[/tex]
[tex]\qquad \sf \dashrightarrow \: 8y = - 3x[/tex]
[tex]\qquad \sf \dashrightarrow \: y = - \dfrac{3}{8} x[/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{y}{x} = - \dfrac{3}{8} [/tex]
[tex]\qquad \sf \dashrightarrow \: {y}:{x} = - {3}:{8} [/tex]
That's our required ratio ~
write the sentence as an equation
n and 328 more is the same as 13
The equation which correctly represents the sentence in discuss as required is; n + 328 = 13.
Which sentence correctly represents the equation?It follows from the task content that the equation which correctly represents the sentence given in the task content is to be determined.
The word phrase; n and 328 more can be represented as; n + 328.
Therefore, n and 328 more is the same as 13 can be represented as; n + 328 = 13.
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A plane traveled 4160 miles with the wind in 6.5 hours and 3900 miles against the wind in the same amount of time.
Find the speed of the plane in still air and the speed of the wind.
...
Answer:s
Step-by-step explanation:
The "-8" and "+8" on the left
cancel, leaving x by itself. What
number do we get on the right?
Enter the number that belongs in the green box.
X-8=6
+8+8
x = [?]
ha
This is a two-part question:
1. Jack's gasoline-powered model airplane travels in a circle while the cord is held. How far does it travel in 5 full circles if the cord is 15 ft.?
2. Last Saturday Jack flew his airplane 100 times around a circle with a cord of 50 ft. If Jack increases the length of the cord by 10 ft and fly it for 100 circles, how much further will the plane travel?
1. The plane travelled a distance of 471.239 ft
2. The plane would travel further by 6283.185 ft
What is circumference?
The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle.
If you move along a full circle of a radius 'r', the distance covered by you is equal to [tex]2\pi r[/tex]
Part 1:
Given that, Jack's aeroplane travels in a circle of a cord of length 15ft for 5 times
The total distance travelled by plane is [tex]15*2\pi *15[/tex]
[tex]=150\pi[/tex]
= 471.239 ft
Part 2:
Given that, Jack flew his aeroplane 100 times with a cord of 50 ft.
The total distance covered by the plane is 100 * (2*50*[tex]\pi[/tex])
If he increases the length by 10 ft, The cord will now be 60 ft.
The total distance it would cover then is 100 * (2*60*[tex]\pi[/tex])
Now,
100 * (2*60*[tex]\pi[/tex]) - 100 * (2*50*[tex]\pi[/tex])
= 100 * (2*(60-50))*[tex]\pi[/tex])
= 100 * 2 * 10 * [tex]\pi[/tex]
= 2000 * [tex]\pi[/tex]
= 6283.185 ft
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BUDGET
Income
Expenses
Rent
Groceries
Utilities
Total Expenses
Net income
Instruction
Class Activity 1
January February March
$2200
$1200
$125
$69.51
$2200
$1225
$110.1
$82.71
$2200
$1225
$79.16
$73.04
1) Bold and center align the column headings and "merge and center" the title.
2) Format all numbers with "$" to 2 decimal places.
3) Calculate totals for each type of expense and for each month. Also, calculate a grand total for all 3 months of
expenses.
4) Calculate net income for each month (total income minus total expenses).
Class Activity (Contd.)
5) Add another column to calculate the percentage of total expenses for each category by
dividing each category's total by the grand total.
6) Create two different unique charts. Each chart must represent different information on the
table.
7) Each chart must be on a different Excel page and each page tab must be labelled
according to the chart.
Here are the steps to complete the budget, as described in the instructions:
Bold and center align the column headings:Highlight the column headings (Income, Expenses, Rent, Groceries, Utilities, Total Expenses, Net Income)Right-click and select "Format Cells"In the "Font" tab, select "Bold" and "Center" alignClick "OK"How to merge and center the title:Type the title "BUDGET" in cell A1Highlight cells A1 to G1Right-click and select "Merge and Center"The title will now be centered across the entire rowFormat all numbers with "$" to 2 decimal places:Highlight the cells containing numbersRight-click and select "Format Cells"In the "Number" tab, select "Currency" and set decimal places to 2Click "OK"Calculate totals for each type of expense and for each month:
To calculate the total expenses for each month, add up the amounts in the Rent, Groceries, and Utilities columnsFor example, in January the total expenses would be $125 + $69.51 + $82.71 = $277.22To calculate the grand total expenses for all 3 months, add up the total expenses for each monthFor example, the grand total expenses would be $277.22 + $110.10 + $73.04 = $460.36Calculate net income for each month:
To calculate the net income for each month, subtract the total expenses from the total incomeFor example, in January the net income would be $2200 - $277.22 = $1922.78Add another column to calculate the percentage of total expenses for each category:
Create a new column to the right of the Utilities columnLabel this new column "Percentage of Total Expenses"In the first cell of this column, divide the value in the Rent column by the grand total expenses and multiply by 100For example, in January the calculation would be =($125/$460.36)*100 = 27.11%Copy this formula down to the last row of dataCreate two different unique charts:
Go to the "Insert" tab and select the type of chart you want to create (e.g. bar chart, pie chart, line chart, etc.)Highlight the data you want to include in the chartClick the "Insert" button to create the chartRepeat the process to create a second chart on a different Excel pageLabel each page tab according to the chart:
Right-click on the first chart's page tab and select "Rename"Type in a descriptive label for the chart (e.g. "Expense Breakdown Chart")Repeat the process for the second chart page tab.Read more about budgets here:
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Line ℓ has equation y=-x+4. Find the distance between ℓ and the point F(-1 7)
Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
To find the distance between a line and a point, we need to find the perpendicular distance from the point to the line. Here's the step-by-step process:
Find the equation of the line perpendicular to ℓ that passes through point F(-1, 7): Since the slope of line ℓ is -1, the slope of the perpendicular line will be the negative reciprocal of -1, which is 1. To find the equation of the line, we need a point and the slope. Point F(-1, 7) will be used, and the slope is 1.
Using the point-slope form of a line, we can write the equation of the perpendicular line passing through point F as: y - 7 = 1(x + 1). Simplifying, we get: y = x + 8.
To find the point of intersection between the two lines, we can substitute the equation of line ℓ into the equation of the perpendicular line:
-x + 4 = x + 8
Solving for x, we get x = 6. Substituting x = 6 into the equation of line ℓ, we get:
y = -6 + 4 = -2
So, the point of intersection between the two lines is (6, -2).
To find the distance between the point F and the line ℓ, we can use the distance formula:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) is the point F(-1, 7) and (x2, y2) is the point of intersection (6, -2).
So, substituting the values into the formula:
distance = √((6 - (-1))^2 + ((-2) - 7)^2) = √((7)^2 + (9)^2) = √(49 + 81) = √(130) = approximately 11.3
Therefore, the distance between the line ℓ and point F is approximately 11.3 units.
can someone pls give me the percent equation to these? 100 points to the fellow that does and brainiest if correct. Also pls hurry, its due today
6.5% of $400 is
what number?
12.5% of $100 is
what number?
130 is what percent
of 650?
$5.40 is what
percent of $4.50?
$8.40 is what
percent of $28?
56% of what
number is $21.84?
$495 is 55% of
what number?
120 is what percent
of 400?
4% of 975 is what
number?
Answer:
Step-by-step explanation:
You just need to remember to first convert percentages to decimal form by dividing the percent by 100. Then you can work out the calculations.
Also, remember that if the problem is asking you to find a percentage, you need to turn your decimal answer to a percentage by multiplying by 100.
I used x to represent what we are looking for:
6.5% of $400 = x
0.065 * 400 = $26
12.5% of 100 = x
0.125 * 100 = $12.5
x of 650 = 130
130/650 = 0.2 which equals 20%
x of $4.50 = $5.40
5.40/4.50 = 1.2 which equals 120%
x of $28 = $8.40
8.40/28 = 0.3 which equals 30%
56% of x = $21.84
21.84/0.56 = 39
55% of x = $495
495/0.55 = 900
x of 400 = 120
120/400 = 0.3 which equals 30%
4% of 975 = x
0.04 * 975 = 39
Answer:
See below
Step-by-step explanation:
a. 6.5% of $400:
[tex]= \frac{65}{100}[/tex]× ($400)
= $260
b. 12.5% of $100:
[tex]= \frac{12.5}{100}[/tex] × ($100)
= $12.5
c. 130 is what percent of 650:
[tex]=\frac{130}{650}[/tex]×100%
= 20%
d. $5.40 is what percent of $4.50:
[tex]= \frac{5.40}{4.50}[/tex]×100%
= 120%
e. $8.40 is what percent of $28:
[tex]= \frac{8.40}{28}[/tex]× 100%
= 30%
f. 56% of what number is $21.84:
=[tex]\frac{56}{100}[/tex]× number = $21.84
∴ Number = [tex]\frac{100}{56}[/tex]×$21.84
= $39
g. $495 is 55% of what number:
= $495 = [tex]\frac{55}{100}[/tex]× Number
∴Number = [tex]\frac{100}{55}[/tex]×($495)
= $900
h. 120 is what percent of 400:
= [tex]\frac{120}{400}[/tex]×100%
= 30%
i. 4% of 975 is what number:
= [tex]\frac{4}{100}[/tex]×975
= 39
NEED HELP ASAP!!!
Due today
Answer:
20 cubic yards
Step-by-step explanation:
You want to know the volume in cubic yards of a layer of topsoil that is 6 inches deep over an area 31 feet by 34 feet.
UnitsYou know that ...
36 inches = 1 yard3 feet = 1 yardThen the dimensions of the volume being applied are ...
6 inches = 6/36 yards
31 feet = 31/3 yards
34 feet = 34/3 yards
VolumeThe volume is the product of the dimensions of the space:
V = LWH
V = (31/3 yd)(34/3 yd)(6/36 yd) ≈ 19.519 yd³
About 20 cubic yards are needed to fill the garden.
An observer standing at the top of a vertical cliff spots a house in the adjacent valley at an angle of depression of 12 degrees. The cliff is 60 meters tall. How far is the house from the base of the cliff?
Distance of the house from the base of the cliff is 282.27 m.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
From the figure attached,
AB = Height of the cliff = 60 m
Let the distance between the base of the cliff and the house 'C' = x m
If the angle of depression = 12°
Then angle of elevation of the top of the cliff from the house = 12°
Now from right triangle ABC,
tan12=60/x
x=60/tan 12
x=60/0.21256
x = 282.27 m
Therefore, distance of the house from the base of the cliff is 282.27 m.
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Decide which of the two given prices is better and explain why. Storage locker A rents for $33/yd^2 per month. Storage locker B rents for $1.49/ft^2 per week. (Assume 1 month=4 weeks.)
B is significantly more affordable and better than A, renting for $1.62 per square foot.
Yard and feet conversion:Yard and feet are used to estimate the length. Both of the units are used in the royal and US customary system of measurements. The value of one yard is equal to three feet.
To compute Square yard to Square Feet, where Square yard is equal to 9 Square Feet, multiply the value in Square yard by 9. one can also use the Square yard to Square Feet calculator.
1 yard² = 9 feet²
A rents for $33 per yard squared
hence A rents $33 for 9 feet squared
hence A rents $3.67 per feet squared( $33/9) which is costlier than $1.49 per feet squared
Thus, as B is more economical, it is better.
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A cell phone plan charges $47.35 per month plus $13.94 in taxes, plus $0.60 per minute for calls beyond the 400-minute monthly limit. Write a piecewise-
defined function to model the monthly cost C(x) (in S) as a function of the number of minutes used for the month.
CG)-{8
for (Choose one) ▼
for (Choose one)
X
The piecewise function for the given problem is;
C(x) = $61.29 x ≥ 400
C(x) = $61.29 + 0.6(x - 400) if x ≥ 400
How to identify the Piecewise Function?A piecewise function is defined as a function that has different definitions depending on which values of x are being used. Piecewise functions are called "piecewise" due to the fact that they are made of "pieces" with different function definitions. To evaluate a piecewise function for a given value of x, find which interval your value fits in, and then use that definition of the function to evaluate.
First, we will find the monthly cost if the 400-minute monthly limit is not exceeded. Then, the total cost would be;
47.35 + 13.94 = 61.29 with just the plan and taxes. So if x ≤ 400, then;
C(x) = 61.29
Now if the 400 minutes is exceeded, the bill will also include $0.60 per additional minute. To find the number of additional minutes, we can take the total number of minutes x and subtract 400. In general, the cost would be;
C(x) = $61.29 + 0.6(x - 400) if x ≥ 400
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You have a wire that is 35 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minimum?
The circumference of the circle is 110 m.
What is the circumference of the circle?Let us assume that the wire has been cut into two equal halves thus the radius of the circle would be 35 m/2 = 17.5 m
Then;
C = 2πr
C = circumference
r = radius
"pi" is a mathematical constant approximately equal to 3.14 and "r" is the radius of the circle. If the diameter of the circle is known, the radius can be calculated by dividing the diameter by 2.
C = 2 * 3.142 * 17.5
C = 110 m as we can see here
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Find a positive angle less than 360° that is coterminal with the given angle
-1025°
The positive coterminal angle less than 360° is, 55°
What are coterminal angles ?Angles with the same initial and terminal sides but a multiple of 360° degree difference are known as coterminal angles (or a full rotation). In other words, you can create an angle that is coterminal with the original angle by taking it and adding or subtracting 360 degrees (or any multiple of 360 degrees).
To find a positive angle that is coterminal with -1025°,
we can add or subtract any multiple of 360° until we get an angle between 0° and 360°.
Adding 1080° (which is 3 revolutions of 360°) to -1,025° gives us:
= -1,025° + 1080°
= 55°
Since this angle is less than 360°,
Therefore, a positive angle less than 360° that is coterminal with -1025° is 55°.
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Select the correct answer. What is the value of x in the equation 1,331x3 − 216 = 0? A. B. C. D.
Answer: x=0.545455
Step-by-step explanation:
add 216 to both sides
divided both sides by 1331
take cube root
in 4x to the fifth +1 what would the end behavior of the graph be?[
The end behavior of the given fucntion is [tex]x\rightarrow \infty , y\rightarrow-\infty\\x\rightarrow-\infty, y\rightarrow\infty[/tex].
What is end behavior of function.?End behavior of a equation is defined as behavior of graph of the function at the ends of the x-axis.
Given, [tex]4x^{5} +1[/tex].
We have to find the end behavior of the graph.
The corresponding graphical representation is given below:
From the graph it is clearly known that as,
Value of x increases ⇒Value of y decreases.
That is x approaches positive infinity and y approaches negative infinity.
i.e., [tex]x\rightarrow \infty , y\rightarrow-\infty\\x\rightarrow-\infty, y\rightarrow\infty[/tex]
Hence, the end behavior of the given equation is [tex]x\rightarrow \infty , y\rightarrow-\infty\\x\rightarrow-\infty, y\rightarrow\infty[/tex].
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If m4=75°, then what is m8
Which choices are equivalent to the expression below?
Check all that apply.
√24
A. 4.√6
B. 2 √6
C. √4.6
D. 24
E. 8.√6
F. √12
The value equivalent to the expression is (2)√6 and option B is the correct answer.
What is prime factorization?Finding the prime factors of a given number, such as a composite number, is done through the process of prime factorization. The prime numbers are the only components in these factors. A number with just the number itself and factor 1 is said to be a prime number.
the quantities that are multiplied to produce new quantities. For instance, the factors of 15 are 3 and 5, or 3 + 5 = 15.
The given expression is √24.
Find the prime factorization of 24:
2 | 24
2 | 12
2 | 6
3 | 3
| 1
Thus, √24 can be written as:
√24 = √(2)²(2)3
√24 = (2)√6
Hence, the value equivalent to the expression is (2)√6 and option B is the correct answer.
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When number is multiplied by 9 the product is 72. find the number
Answer: 8
Step-by-step explanation: 9 x 8 = 72
help me please dont know what im doing
The amount of natural oil needed to make 869 liters of Petrolyn oil is given as follows:
1520.75 liters.
How to obtain the amount of natural oil?The necessary amount of natural oil is obtained applying the proportions in the context of this problem.
Considering the ratio given in the problem, a rule of three is established, as follows:
7 liters of natural oil - 4 liters of Petrolyn oil.
n liters of natural oil - 869 liters of Petrolyn oil.
Applying cross multiplication, the desired amount is obtained as follows:
4n = 7 x 869
n = 7 x 869/4
n = 1520.75 liters.
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Piecewise linear relations
The required piecewise linear relations are f(x) = 4 if [0, 2), and f(x) = -2x + 8 if [2, 4).
What is a piecewise function?A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).
The graph is given in the question, as shown
f(x) = 2x + 4 if [-2, 0]
This the sub-function define between the interval [-2, 0].
f(x) = 4 if [0, 2)
This the sub-function define between the interval [0, 2).
f(x) = -2x + 8 if [2, 4)
This the sub-function define between the interval [2, 4).
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What is the surface area of the box?
A. 160 square inches
B. 46 square inches
C. 92 square inches
D. 184 square inches
Answer:
D
Step-by-step explanation:
Front
5x4 = 20
Back
5x4 = 20
Top
5x8 = 40
Bottom
5x8 = 40
Right side
8x4 = 32
Left side
8x4 = 32
Add all the sides
20 + 20 + 40 + 40 + 32 +32 = 184
The following data represent the weights (in grams) of a
random sample of 50 candies
(a) Determine the sample standard deviation weight
SH gram
(Round to two decimal places as needed)
0.98
0.85
0.92
0.98
0.71
Part 1 of 6
0.88
0.86
0.75
0.85
0.85
0.86
0.78
0.75
0.75
0.74
Cm
0.82
0.85
0.91
0.78
0.72
O
081
0.81
0.81
0.81
0.84
Points: 0 of 4
087
0.85
0.89
0.77
0.85
0.97
0.74
0.89
0.82
0.86
0.82
084
0.91
0.87
0.94
0.85
0.71
0.83
0.87
0.94
0.81
0.81
0.78
0.77
0.85
The sample standard deviation weight of the 50 candies is, 0.07 grams.
What is standard deviation ?The amount of variation or dispersion in a set of data values is measured by standard deviation. A statistical calculation is used to determine how far the values vary from the mean (average) value. While a high standard deviation suggests that the data values are more dispersed, a low standard deviation suggests that the data values tend to be close to the mean.
To find the sample standard deviation weight,
we can use the formula:
[tex]s = \sqrt{((1/(n-1))} \sum((x - \bar x)^{2} ))[/tex]
where n is the sample size, x is the weight of each candy, [tex]\bar x[/tex] is the sample mean weight, and sum() means to add up the values.
We can first find the sample mean weight:
[tex]\bar x[/tex]= (0.98 + 0.85 + 0.92 + 0.98 + 0.71 + 0.88 + 0.86 + 0.75 + 0.85 + 0.85 + 0.86 + 0.78 + 0.75 + 0.75 + 0.74 + 0.82 + 0.85 + 0.91 + 0.78 + 0.72 + 0.81 + 0.81 + 0.81 + 0.84 + 0.87 + 0.85 + 0.89 + 0.77 + 0.85 + 0.97 + 0.74 + 0.89 + 0.82 + 0.86 + 0.82 + 0.84 + 0.91 + 0.87 + 0.94 + 0.85 + 0.71 + 0.83 + 0.87 + 0.94 + 0.81 + 0.81 + 0.78 + 0.77 + 0.85) / 50
[tex]\bar x[/tex] = 0.8456
Next, we can calculate the sample standard deviation:
s = √((1/(50-1)) x ((0.98-0.8456)² + (0.85-0.8456)² + ... + (0.77-0.8456)² + (0.85-0.8456)²))
s = sqrt(0.0045916)
s = 0.0678
Rounding to two decimal places, the sample standard deviation weight is 0.07 grams.
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What is the frequency of the function given? f(x)=9cos(4πX)+10
Answer:
Step-by-step explanation:
The frequency of a cosine function is related to the number of cycles that the function completes in a unit interval (usually in 2π radians).
The frequency of a cosine function with the form f(x) = A * cos(Bx + C) is given by B/(2π), where A, B, and C are constants.
For the function f(x) = 9cos(4πx) + 10, the frequency is given by 4π / (2π) = 2 cycles per unit interval.
So, the frequency of the function f(x) = 9cos(4πx) + 10 is 2 cycles per unit interval.
Enter the letter of the graphed function(image)
answer c)
cross x at x = -2, x = 3, and x = 1
the square root tells us that it bounces off that location rather than intercepting
7x + 14y = 28
5x+10y= 20
Solve for x and y using elimination
The value of x is [0,∞] and y is [0,∞]. The solution has been obtained by using the elimination method.
What is elimination method?
The elimination approach involves removing one of the variables from the system of linear equations by employing addition or subtraction together with multiplication or division of the variable coefficients.
We are given two equations as
7x + 14y = 28 ....(1)
5x + 10y = 20 ....(2)
Now, on multiplying equation (1) by 10, we get the equation as
70x + 140y = 280 ....(3)
On multiplying equation (2) by 14, we get the equation as
70x + 140y = 280 ....(4)
Since, we are getting the same equations so, the system has infinitely many solutions.
Hence, the value of x is [0,∞] and y is [0,∞].
Learn more about elimination method from the given link
https://brainly.com/question/25427192
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The Function F(T)=575,000/1+4000e^-T describes the number of people, F(T) , who have become ill with ebola T weeks after the initial outbreak in a particular community.
How many people became ill with ebola when the epidemic began?
How many people were infected 6 weeks after the initial breakout? Round to the nearest whole number of people?
What is the limiting size of the infected population? That is, how many people were infected at t = (infinity sign goes after = sign)? Round to the nearest whole number of people.
Step-by-step explanation:
you have to be careful when typing questions and particularly formulae and expressions here. automatic text conversion has the habit of transforming e.g. fractions into one line divisions without any brackets.
what your wrote here :
575,000/1 + 4000e^-T = 575,000 + 4000e^-T
that cannot be the function.
I am sure it must be
F(T) = 575,000/(1 + 4000e^-T)
right ?
I am basing the rest of my answer on that assumption.
how many people became ill, when the outbreak began ? that means T = 0.
F(0) = 575,000/(1 + 4000e^-0) =
= 575,000/(1 + 4000×1) =
= 575,000/(4001) = 143.7140715... ≈ 144 people
6 weeks after the outbreak
F(6) = 575,000/(1 + 4000e^-6) =
= 575,000/(1 + 4000/(e^6)) =
= 575,000/(1 + 9.915008707...) =
= 575,000/10.915008707... =
= 52,679.75642... ≈ 52,680 people
limit t -> infinity
F(infinity) = 575,000/(1 + 4000e^-infinity) =
= 575,000/(1 + 4000/(e^infinity)) =
= 575,000/(1 + 0) = 575,000 people
