From the data points given, the linear equation is obtained as y = 6x - 3.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The data points given are -
X = 1, 2, 3, 4, 5
f(x) = 3, 9, 15, 21, 27
The slope of the line is given as m.
The slope can be deduced using the formula -
(y2 - y1) / (x2 - x1)
m = (9 - 3) / (2 - 1)
m = 6/1
m = 6
The slope-intercept form of a equation is y = mx + b
Substitute the values of x, y and m in the equation -
3 = 6(1) + b
3 = 6 + b
b = 3 - 6
b = -3
So, the equation becomes -
y = 6x - 3
This equation forms a straight line in the graph.
Therefore, y = 6x - 3 is a linear equation.
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Figure ABCDE has vertices A(−2, 3), B(2, 3), C(5, −2), D(0, −4), and E(−2, −2). Plot the points on your own coordinate grid and connect the points in alphabetical order. Decompose Figure ABCDE into rectangles and triangles. Part A: How many triangles and rectangles did you make? (1 point) Part B: Use Figure ABCDE created on your coordinate grid to find the lengths, in units, of Sides AB and AE. (4 points) Part C: What is the area of Figure ABCDE? Show your work. (5 points)
Figure ABCDE has vertices A(−3, 3), B(2, 3), C(5, −2), D(0, −3), and E(−3, −2) So the Area of figure = 36.5 sq units
To Find: Plot the points
Decompose Figure ABCDE into rectangles and triangles.
lengths of Sides AB and AE.
area of Figure ABCDE
Plot ( x , y) ( x , y)
If x is positive, start right away from the origin. If it's negative, turn left.
If +ve, move y upward; if -ve, move y downward.
Plotted and labeled points
A(−3, 3), B(2, 3), (2, 3),
AB's length is five.
A(−3, 3) E(−3, −2).
AE length is 5
two triangles and one rectangle
area of a rectangle equal 5 * 5, or 25 square units.
The right angle triangle's area is equal to (1/2) * 5 * 3 = 7.5 square units.
another triangle's area is equal to (1/2) * 8 * 1 square units.
Figure's surface area is 25 + 7.5 + 4 = 36.5 sq units.
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Which system of equations has a solution of (3/5,-13/10)?
A value we can put in place of a variable (such as x) that makes the equation true and the answer is 13/-10
What is meant by variable ?A number that is capable of taking on any one of a range of values.
A variable's symbolic representation.
Something which can change.
A variable that could alter in a scientific experiment.
A property that can be measured and given varied values is known as a variable.
Variables include things like height, age, income, province of birth, school grades, and kind of dwelling.
Independent, dependent, and controlled variables make up the three primary variables. A automobile driving down various surfaces is one example.
A variable in programming is a value that can change based on external factors or data that has been supplied to the program.
3x+5y
= 0x+5y
=-3x+y
=-3/5x + y
= 3/5 13x + 10y
=0x + 10y
=13x+y
=13/- 10
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a manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 418 gram setting. is there sufficient evidence at the 0.10 level that the bags are overfilled? based on a 24 bag sample, the manufacturer decides to reject the null hypothesis. what is the conclusion?
There is sufficient evidence at 0.10 level of significance that the machine is overfilling the bags. So the option 1 is correct.
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 418 gram setting.
For the given question,
The Hypothesis for the test would be:
H(0): μ = 418
H(1): μ > 418
The fact that the null hypothesis is rejected means that there is enough data to conclude that the machine is significantly overfilling the bags at the 0.10 level of significance.
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The complete question is:
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 418 gram setting. Is there sufficient evidence at the 0.10 level that the bags are overfilled? Based on a 24 bag sample, the manufacturer decides to reject the null hypothesis. What is the conclusion?
1. There is sufficient evidence at the 0.10 level of significance that the machine is overfilling the bags.
2. There is not sufficient evidence at the 0.10 level of significance that the machine is overfilling the bags.
• Kwan is planting a garden. He plants vegetables in
1
of the garden. He uses
2
of the
5
vegetable garden for radishes. Kwan wants to know how much of the whole garden
he is using to plant radishes.
Kwan is utilizing 8% of the entire garden to plant radishes.
Kwan is planting a garden and he is utilizing 1/5 of the garden to plant vegetables. That implies that 1 out of 5 pieces of the garden is being utilized to grow vegetables.
He then, at that point, expresses that he utilizes 2/5 of that 1/5 region for radishes. That implies that 2/5 of the area utilized for vegetables is being utilized to grow radishes.
To find the fraction of the entire garden that is being utilized for radishes, we want to join the two fractions. We can do this by multiplying them together.
At the point when we multiply 1/5 by 2/5, we get 2/25. This fraction can likewise be communicated as a rate by multiplying it by 100.
2/25 * 100 = 8%
So, Kwan is utilizing 8% of the entire garden to plant radishes.
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Rewrite the following without an exponent.
(5/3)^-3
Iman ate 1/3 of a bag of popcorn.
His 4 friends ate equal shares of the remaining popcorn.
Which expression represents the popcorn that each friend ate?
Answer: 1/3 per friend.
Step-by-step explanation:1/3 1/6*4= 3/3 or 1 whole bag. to find the 1/6, 2/3 multiply by 1/4= 2/12 or 1/6 of popcorn per friend
An alligators tail length is proportional to its body length. An alligator with a body length of 2.5 feet has a tail length of 2.8 feet. What is the tail length of an alligator whose body length is 9.2 feet?
Answer:
4.34
Step-by-step explanation:
proportional: 2.8/2.5 =1.12
body + tail = body + 1.12 body = 2.12 body = 9.2.
so body = 9.2/2.12 = 4.34
3 ( � − 2 ) + � − 1 = 3(x−2)+x−1= 5 5
Answer: The equation provided is already solved, on the left side of the equation it shows the step by step solution of the equation:
3(x-2)+x-1 = 3(x-2) + x - 1 = 5
3x - 6 + x - 1 = 5
Combining like terms
4x - 7 = 5
Adding 7 to both sides
4x = 12
Dividing both sides by 4
x = 3
So the value of x that makes the equation true is x = 3
Step-by-step explanation:
if alen eats 7 apples and then 4 oranges 2 bananas how much calsium has he goten
Answer:
So there are 11 mg of calcium in apples.
38 mg of calcium in oranges.
And 6 mg of calcium in bananas.
So if he ate 7 apples, that adds up to:
7 * 11 = 77 mg of calcium.
4 oranges adds up to:
4 * 38 = 152 mg of calcium
2 bananas adds up to:
2 * 6 = 12 mg of calcium.
In total:
77 + 152 + 12 = 241
Alen ate 241 mg of potassium
Step-by-step explanation:
Hope it helps! =D
Simplify the expression to a polynomial in standard form:(-x+4)(3x^2+3x+5)
deci nu știi să faci matematică?
What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer?
The amount of money Rashon would need to invest is equal to $8,300.46.
How to determine the value of equivalent quarterly interest rate?Mathematically, the compound interest on an investment can be calculated by using this mathematical expression:
A(t) = P(1 + r/n)^{nt}
Where:
A represents the future value.r represents the interest rate.n represents the number of times compounded.P represents the principal.T represents the time measured in years.In this scenario, Rashon's investment is compounded quarterly at an interest rate of 6.9% as follows:
Quarterly interest rate = 0.069/4
Quarterly interest rate = 0.01725%
20,200 = P(1 + 0.01725)^{4 × 13}
20,200 = P(1.01725)^52
20,200 = 2.4336P
Principal, P = 20,200/2.4336
Principal, P = $8,300.46.
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Answer:
In this scenario, Rashon's investment is compounded quarterly at an interest rate of 6.9% as follows:
Quarterly interest rate = 0.069/4
Quarterly interest rate = 0.01725%
20,200 = P(1 + 0.01725)^{4 × 13}
20,200 = P(1.01725)^52
20,200 = 2.4336P
Principal, P = 20,200/2.4336
Principal, P = $8,300.46.
The polygon in the diagram is a square with center P. The answer options are below:
144.0in
72.0in
24.0in
36.0in
Refer to image for other info
The area of square = 72.0 in The surface area of a shape is measured using the area.use square units for area when you can multiply the length to determine the area .
Option B is correct.
What is area of square?The quantity of square units required to completely fill a square is known as the area of a square. The region that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area. The measurement is made using square units, with square metres serving as the standard unit (m²).
Area of square = Side ²
side=6√2
Area=?
Area of square = ( 6√2)²
72 .0 inches.
Why square units for area?This is because the sum of two lengths is used to calculate an area. If those are, for instance, measured in meters, you would multiply some meters by others. Consequently, the expression for the area in square meters. Similar to volume: You divide three lengths by.
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a tank with a capacity of 400l is full of a mixture of water and chlorine with a concentration of 0.05g of chlorine per liter. in order to reduce the concentration of chlorine, fresh water is pumped into the tank at a rate of 4 l/s. the mixture is kept stirred and is pumped out at a rate of 10 l/s. find the amount of chlorine in the tank as a function of time.
The amount of chlorine in the tank as a function of time is:
C(t) = 0.05 * e^(-6/400*t)
Let C(t) be the concentration of chlorine in the tank at time t and V(t) be the volume of the tank at time t.
At t=0, we know that:
C(0) = 0.05 g/l
V(0) = 400 l
As fresh water is pumped in at a rate of 4 l/s and the mixture is pumped out at a rate of 10 l/s, the rate of change of the volume of the tank is:
dV/dt = 4 - 10 = -6 l/s
As the concentration of chlorine is being diluted by the addition of fresh water, the rate of change of the concentration is proportional to the rate of change of the volume. So we can write:
dC/dt = - k * C(t) * (dV/dt)
where k is a proportionality constant.
We can integrate the above equation with respect to time to find the concentration of chlorine in the tank as a function of time:
C(t) = C(0) * e^(-kt)
In order to find the value of k we can use the initial condition C(0) = 0.05 g/l and V(0) = 400l
0.05 = C(0) * e^(-k*0)
0.05 = C(0)
so we can substitute this value into the above equation and solving for k:
C(0) = 0.05 = 0.05 * e^(-k*0)
0.05 = 0.05
so k = -6/400
Finally, the amount of chlorine in the tank as a function of time is:
C(t) = 0.05 * e^(-6/400*t)
This equation expresses the amount of chlorine in the tank as a function of time t. As time goes on, the concentration of chlorine will decrease exponentially.
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You bought a fish tank in the shape of a rectangular prism. The dimensions are n, n=6, and n=18. Use the formula V=lwh to write a polynomial in standard form for the volume of the fish tank. Show all work
If the dimensions of the rectangular fish tank are n , 6 and 18 , then the polynomial in the standard form for Volume of fish tank is V = 108n .
The dimensions of the fish tank in shape of rectangular prism re :
length = n , width = 6 and height = 18 ;
the formula to be used to calculate the volume of rectangular fish tank is written as : Volume = length × Width × Height ;
substituting the values in the volume formula ,
we get ;
Volume of tank = n × 6 × 18 ;
= n × 108 ;
= 108n .
Therefore , the polynomial in the standard form can be written as V = 108n .
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96x2let be the inverse function of . take to be an output of the function . that is, and . (a) which statement best describes ?
The output of a function is returned by the inverse function, which also returns the initial value. Consider the inverse relationship between the functions f and g: f(g(x)) is g(f(x)) is x.
How can you determine a function's inverse?Write the function y as a function of x, i.e., y = f(x), and then solve for x as a function of y, to determine the inverse of a function.
steps for determining a function's inverse.
In the equation expressing the function, swap out f(x) with y.
Swap out x and y. To put it another way, swap out every x for a y and vice versa.
Solve for y.
Change y to f-1 (x).
The output of a function is returned by the inverse function, which also returns the initial value. Consider the inverse relationship between the functions f and g: f(g(x)) = g(f(x)) = x.
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Write a function g(x) with a graph that is the reflection of the graph of f across the x-axis.
f(x) = - square root 14x
The function g(x) with a graph that is the reflection of the graph of f(x) = - square root 14x across the x-axis is given as follows:
[tex]g(x) = \sqrt{14x}[/tex]
How to obtain the function g(x)?The parent function f(x) is defined as follows:
[tex]f(x) = -\sqrt{14x}[/tex]
The rule for a reflection over the x-axis is given as follows:
g(x) = -f(x).
Meaning that only the signal of the function is changed.
Removing the negative signal, the function g(x) is then defined as follows:
[tex]g(x) = \sqrt{14x}[/tex]
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El departamento de teatro de la escuela está organizando una producción y planea cobrar $10 por entrada y $5 por una entrada para niños. Necesitan ganar por lo menos $3,000 cada noche para cov s. El auditorio tiene capacidad para 400 personas.
The four inequalities are a + c ≤ 400, 10a + 5c ≥ 3000, a ≥ 0 and c ≥ 0. The club must sell 200 children tickets and 200 adult tickets.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The value for one ticket is - $10
The value for one children's ticket is - $5
The total amount that need s to be earned is - $3000
The number of seats in the auditorium is - 400
Let the number of children be = c and the number of adults be = a.
Then the inequality will be -
a + c ≤ 400
10a + 5c ≥ 3000
a ≥ 0
c ≥ 0
The inequalities will have a straight line as (≤,≥) symbols are used in the inequalities.
Write the two inequalities in equation form -
a + c = 400....(1)
10a + 5c = 3000 or 2a + c = 600....(2)
Subtract equation (1) from (2) -
2a + c - (a + c) = 600 - 400
2a + c - a - c = 200
a = 200
a = 200
Substitute the value of a in equation (1) -
200 + c = 400
c = 400 - 200
c = 200
So, the intersection point is (200,200) and the number of children is 200 whereas the number of adults is 200.
Therefore, the graph is obtained.
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The school drama department is putting on a production and plans to charge $10 per ticket and $5 for a children's ticket. They need to earn at least $3,000 each night for cover the cost. The auditorium has a capacity for 400 people.
Write and graph a system of four inequalities that describe how many of each type of ticket the club must sell to meets its goal.
James has x quarters. His brother has 4 times as many quarters as James has. How may quarters do they have altogether?
The total number of quarters James and his brother will be 5x
Addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.
James has x quarters while his brother has 4 times as many quarters as James.
So, for determining the value of the total number of quarters James's brother have we will multiply the value of the total number of quarter James have by 4.
So, the value of the total quarter James's brother has = 4*x = 4x
Now for determining the total number of quarters of James and his brother we will add both values.
The total number of quarters James and his brother will be= x+4x = 5x
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How do I solve for the missing value
The missing value in the triangle is given as follows:
28.
How to obtain the missing value?The theorem used to solve this problem is given as follows:
A line parallel to one side of a triangle divides the other two proportionately.
As 28 - 16 = 12, the proportional relationship between the side lengths is given as follows:
12/21 = 16/x.
Applying cross multiplication, the value of x is obtained as follows:
12x = 21(16)
Simplifying by 4, we have that:
3x = 21(4)
Simplifying by 3, we have that:
x = 7 x 4
x = 28.
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Mrs. Cooper paid more than $22 for a pack of hand towels. Each towel cost $2.85. The hand towels were available in packs of 4, 5, 6, and 8. Use the inequality to find the minimum number of towels, t, in the pack.
Using inequality, the minimum number of towels in the pack is t = 6.
How to Find Minimum Number Using Inequality?We can start by using the inequality 2.85t > 22, where t is the number of towels in the pack.
To find the minimum number of towels, we can use the smallest possible value for t that satisfies the inequality. Since the hand towels were available in packs of 4, 5, 6, and 8, we can use t = 4 in the inequality:
2.85(4) > 22
Simplifying the left side of the inequality gives:
11.4 > 22
This is not true, so t = 4 does not satisfy the inequality.
Next, we can use t = 5:
2.85(5) > 22
Simplifying the left side of the inequality gives:
14.25 > 22
This is also not true, so t = 5 does not satisfy the inequality.
We can keep doing this for t = 6, and t = 8, we will find out t=6 is the minimum value of t that satisfies the inequality.
2.85(6) > 22
Simplifying the left side of the inequality gives:
17.1 > 22
This is true, so t = 6 is the minimum number of towels in the pack.
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Find two positive numbers satisfying the given requirements.
The product is 154 and the sum is a minimum.
The required two positive numbers are 11 and 14 which product is 154 and the sum is a minimum.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.
The product is 154 and the sum is a minimum.
As per the question, the required solution would be as:
product sum
1 x 154 1 + 154 = 155
2 x 77 2 + 77 = 79
11 x 14 11 + 14 = 25
7 x 22 7 + 22 = 29
Here, we can arrange these numbers as:
25 < 29 < 79 < 155
This means the sum (11 + 14 = 25) is a minimum.
So the minimum value = 11
And the maximum value = 14
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White Oak is 15 miles from River City. What would its distance be on the map? WHOEVER ANSWERS GETS 30 POINTS
When White Oak is 15 miles from River City and the scale is 1 in.=3 mi, the distance in the map is 5 inches.
How to explain the scale?The ratio that describes the relationship between the actual figure and its model is called the scale. It serves as a representation of the actual figures in smaller units on maps. A scale of 1:5, for instance, means that 1 on the map is equivalent to the size of 5 in the real world.
A scale of 1:5, for instance, means that the size of 1 unit in the drawing corresponds to the size of 5 units in the real world. A scale of 1:5 is evident, for instance, if a giraffe that stands 150 inches tall in real life is depicted on the drawing as 30 inches tall.
In this case, when White Oak is 15 miles from River City and the scale is 1 in.=3 mi, the distance in the map is:
= 15 / 3
= 5 inches.
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On a Cartesian plane sketch the region which represents the set of points for which x<2 and y>or= to 2
The inequality for this problem is defined as follows:
x < 2.y >= 2.The Cartesian plan representation of the inequality is given by the image presented at the end of the answer.
How to graph the inequality?The two conditions for the inequality are given as follows:
x < 2.y >= 2.These conditions are plotted as follows:
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To the nearest hundredth find the value of x
Answer:
x = 14.83 (to the nearest hundredth)
Step-by-step explanation:
Following the Pythagoras' Theorem,
a² + b² = c²
x² + 6² = 16²
x² = 220
∴ x = 14.83 (to the nearest hundredth)
Rachel is making a tent. The triangular piece of fabric for the front of her tent has an area of 24 ft. ². Find the height of the fabric if it is 6 feet long at it's base. 
The height of the fabric is 8 ft.
Now, According to the question:
Rachel is making a tent.
The triangular piece of fabric for the front of her tent has an area of 24 [tex]ft^2[/tex]
and, it is 6 feet long at it's base.
We have to find the height of the fabric .
Now, Based on the given condition:
Formulate the problem:
24 × 2 ÷ 6
Cross out the common factor:
4 × 2
Calculate the product or quotient :
= 8
Hence, the height of the fabric is 8 ft.
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How do you find the general solution of an exact differential equation?
The general solution of an exact differential equation can also be found by solving the associated homogenous equation and adding the particular solution obtained from the original equation.
1. Identify the exact differential equation.
2. Find the integrating factor by multiplying the equation by an expression of the form e^(f(x)).
3. Multiply the integrating factor with the equation to make it exact.
4. Integrate both sides of the equation to obtain the general solution.
5. Check the solution by differentiating it to confirm that it satisfies the original equation.
6. Add the particular solution obtained from the original equation to the homogenous solution to get the general solution.
The general solution of an exact differential equation can be found by using an integrating factor. An integrating factor is a function of the independent variable which can be multiplied with the equation in order to make it exact. Once the equation has been made exact, it can be solved using the standard integration techniques. In addition, the general solution can be found by solving the associated homogenous equation and then adding the particular solution obtained from the original equation.
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Graph y= 1/3x-3 .I just need to know the plots
Answer: Points: (0, -3), and (9, 0)
Step-by-step explanation:
In order to graph an equation, you find 2 pairs of points and then just connect them into a line. (The x intercepts and the y intercepts are helpful)
One pair: (x, y) = (0, -3)
Another pair: (x, y) = (9, 0)
Now just connect them to get the line :>
The graphs shows the speed of a car for 30 seconds. A) using a single appropriate trapezium , estimate the distance travelled by the car during this time . B) is your answer an overestimate or underestimate ?
The distance travelled by the car during this time by using single appropriate trapezium is 26.25 and the answer provided is an underestimate
Estimate the distance travelled by the car during this time?A) Using a single appropriate trapezium, the estimated distance travelled by the car during the 30 seconds is approximately 55 metres.
This is calculated by taking the area of the trapezium formed by the two points of the speed graph: 8m/s and 6m/s.
The area is calculated by taking the average of the two points, multiplied by the time duration:
Area = (8+6/2) * 30
Area = 7*30
Area = 210
The area of the trapezium is then divided by the speed of the car at the start of the journey (8m/s) to get the estimated distance travelled:
Distance = 210/8
Distance = 26.25
This is rounded up to give an estimated distance travelled of 55 metres.
B) The answer of 55 metres is an underestimate of the actual distance travelled by the car. This is because the trapezium method only takes into account the start and end points of the graph, and not any of the other points in between. The actual distance travelled by the car is likely to be higher as the speed of the car is likely to have been greater at points in between the start and end points.
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Bryson's Dad is 38 years old. If this is four years than three times Bryson's age, how old is Bryson?
The age of Bryson today is 11 1/3 years
How to determine the age of Bryson today?From the question, we have the following mathematical statements:
Bryson's dad age = 38
Bryson's dad age = 4 + 3 * Bryson's age
Represent Bryson's age with x
So, we have the following equation
Bryson's dad age = 38
Bryson's dad age = 4 + 3x
substitute the known values in the above equation, so, we have the following representation
4 + 3x = 38
Evaluatet the like terms
3x = 34
Divide by 3
x = 11 1/3 years
Hence, Bryson's age as per the mathematical statement is 11 1/3 years
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need the answer asap ! thank you to whoever helps ! <3
The system that has the solution (-2, -2, -2) is the one in option C.
x + 2y = -6
y + 2z = -6
x - y - z = 2
Which system of equations has the given solution?We want to see which of the given systems has the solution (-2, -2, -2).
To check that, we only need to evaluate all the equations of the system on these values and see if all the equations are true.
If we look at the third system we will get:
x + 2y = -6
y + 2z = -6
x - y - z = 2
Replacing all the values of the point we get:
-2 + 2*(-2) = -6
-2 + 2*(-2) = -6
-2 + 2 + 2 = 2
All these equations are true, thus, the correct option is C.
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