The equation represents a direct proportion
The proportionality constant is 1.2
How to determine the type of the equationFrom the question, we have the following parameters that can be used in our computation:
a=1.2b
The above equation is a proportional linear equation
A proportional linear equation is represented as
y = kx
Where
The constant of proportionality is k
Using the above as a guide, we have the following:
The equation a=1.2b is a direct proportion and the proportionality constant is 1.2
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Determine the average rate of change of this function over the interval
-2 ≤ x ≤ 4. f(x₂)—ƒ(x1)
I
x2-x1 OR y2-91
x2-x1
The points will be found in the table of the calculator. Use the points (-2,-3)
and (4, 21)
The average rate of change of the function over the interval -2 ≤ x ≤ 4 is given as follows:
4.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output divided by the change in the input.
The two points in this problem are given as follows:
(-2, -3) and (4,21).
Hence the change in the output is of:
21 - (-3) = 24.
The change in the input is of:
4 - (-2) = 6.
Hence the rate is of:
24/6 = 4.
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A shop sells bagels for $5 per dozen. You can use the table to answer the questions. Explain your reasoning.
number of bagels price in dollars
12 5
How many bagels can you buy for $50?
The number of bagels when you buy for $50 will be 120 bagels.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
A shop sells bagels for $5 per dozen.
Let 'x' be the number of bagels and 'y' be the total cost. Then the equation is given as,
y / x = 5 / 12
12y = 5x
The number of bagels when you buy for $50 will be given as,
12(50) = 5x
600 = 5x
5x = 600
x = 120
The number of bagels when you buy for $50 will be 120 bagels.
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one recipe calls for 1/3cup of oil the second recipe calls for 1/3 cup of oil Ernesto has one cup of oil does Ernesto have enough oil to make both recipes
Yes, Ernesto has enough oil to make both recipes. Each recipe calls for 1/3 cup of oil, and he has one cup of oil. Therefore, he has enough oil to make both recipes with some oil left over.
The diagram shows the graph of y = x² - 4x + 6, with a tangent drawn to the
curve at x = 3.
Use the tangent to estimate the gradient of the curve at
=
3.
Algebra 1
Write an exponential function that is in the family of
f(x) = 2x with a vertical shrink and translation down 5?
Image attached
The exponential function of the family f(x) = 2^x with a vertical shrink and a translation down 5 units is given as follows:
A. f(x) = 0.5(2)^x - 5.
How to define the function?The parent function is defined as follows:
f(x) = 2^x.
For the vertical shrink, the function is multiplied by a constant that has an absolute value less than one, hence:
f(x) = 0.5(2)^x.
For the translation down 5 units, the number 5 is subtracted from the definition of the function, hence:
A. f(x) = 0.5(2)^x - 5.
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18. The area of a playground is 204y * d ^ 2 The width of the playground is 5 yd longer than its length.
The playground's length and breadth are 12 yards and 17 yards, respectively.
The playground's area is 204 square yards, according to the statistics provided in the inquiry.
204 square yards is the area.
The playground's breadth is 5 yards more than its length.
Let the playground be 'l' yards long.
The playground's width will then be (l + 5) yards.
The formula for the playground area is Length × Width.
A = Length x width
204 = l (l + 5)
204 = + 5l
+ 5l - 204 = 0
+ 17l - 12l - 204 = 0
l (l + 17) -12 (l + 17) = 0
(l + 17) (l - 12) = 0
(l + 17) = 0 or (l - 12) = 0
l = -17 or l = 12
The length value cannot be negative.
As a result, the length is 12 yards.
The breadth is thus equal to l + 5.
Width = 12 + 5
17 yards wide
As a result, the length is 12 yards and the breadth is 17 yards.
Option (b) is the right answer.
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A playground has a surface area of 204 yd2. The playground's breadth is 5 yards greater than its length. Determine the playground's length and breadth.
a.) 17 yards in length, 22 yards in breadth
b.) 12 yard length, 17 yard breadth
c.) 22 yard length, 17 yard breadth
d.) 17 yard length, 12 yard breadth
30 POINTS
A system of linear equations is shown in the graph. How many solutions does the system have?br />
a coordinate plane with one line that passes through the points 0 comma 4 and 3 comma 3 and another line that passes through the points 0 comma negative 1 and 3 comma negative 2
One solution at (0, 4)
One solution at (−3, 0)
Infinitely many solutions
No solution
The correct option regarding the number of solutions of the sustem of equations is given as follows:
No solution.
What is the solution to the system of equations?We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.
The line going through points (0,4) and (3,3) is given as follows:
y = -0.33x + 4.
The line going through points (0,-1) and (3,-2) is given as follows:
y = -0.33x - 1.
The two functions have the same slope, hence they are parallel lines, and thus the number of solutions is of zero.
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3
Solve the problem. Show your work.
Kasim has 7 square platters of equal size.
Each side of each platter is 0. 4 meters long.
Kasim places all the platters in a row with
no gaps between the sides. How long is the
row of platters?
Step 1: Calculate the length of one platter. To calculate the length of one platter, multiply 0.4 meters by 4 sides, which gives us a total of 1.6 meters.
Step 2: Calculate the length of the row of platters. To calculate the length of the row of platters, multiply the length of one platter (1.6 meters) by the number of platters (7), which gives us a total of 11.2 meters.
Therefore, the row of platters is 11.2 meters long.
What exactly are algebraic word issues? The process of converting phrases into equations and then solving those equations is known as solving algebraic word problems. a single variable, and. In a real-world situation, the variable typically stands for an unknowable quantity.
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what theorems, properties, or strategies are common to the proof of the triangle proportionality theorem and the proof of converse of the triangle proportionality theorem?'
Common theorems, properties, or strategies to the proof of the Triangle Proportionality Theorem and its converse include using similarity and congruence, angle-angle criterion, and transitive property of equality.
The Triangle Proportionality Theorem states that if a line is drawn parallel to one side of a triangle to intersect the other two sides, then the ratio of the lengths of the intersecting lines is equal to the ratio of the lengths of the corresponding sides of the triangle.
The converse of the Triangle Proportionality Theorem states that if two pairs of corresponding sides in two triangles are proportional, then the two triangles are similar.
Overall, these theorems, properties, and strategies form the basis for proving both the Triangle Proportionality Theorem and its converse, and they are used to establish the relationships between the lengths of sides and angles in triangles.
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A car rental company charges a flat fee of $25 per day plus an additional $0.20 per mile driven. If a customer rents a car for 3 days and drives a total of 150 miles, what is their total rental cost?
Answer & Step-by-step explanation:
To find the total rental cost, we need to add the flat fee to the mileage charge. Here are the steps:
1. Multiply the number of rental days by the flat fee: 3 days x $25/day = $75
2. Multiply the total miles driven by the mileage rate: 150 miles x $0.20/mile = $30
3. Add the flat fee and the mileage charge to get the total cost: $75 + $30 = $105
Therefore, the customer's total rental cost is $105.
Hope it helps!Answer:
105$
Step-by-step explanation:
Is (x − 2) a factor of f(x) = x3 − 2x2 + 2x + 3? Use either the remainder theorem or the factor theorem to explain your reasoning.
Answer:
(x - 2) is not a factor of f(x)
Step-by-step explanation:
We can use the Remainder Theorem to check if (x - 2) is a factor of f(x) = x^3 - 2x^2 + 2x + 3.
The Remainder Theorem states that if we evaluate a polynomial at a specific value and the result is zero, then that value must be a root of the polynomial and therefore the polynomial can be divided by the corresponding linear factor.
So, if we plug in x = 2 into f(x), we get:
f(2) = 2^3 - 2 * 2^2 + 2 * 2 + 3
= 8 - 8 + 4 + 3
= 7
Since f(2) is not equal to zero, it follows that (x - 2) is not a factor of f(x).
Alternatively, we could use the Factor Theorem, which states that a polynomial is divisible by (x - a) if and only if f(a) = 0. Since f(2) is not equal to zero, (x - 2) is not a factor of f(x).
3x-y=18
-2y=-6x-120
solve the system of equations!
show your work!! :)
The system is inconsistent.
The two lines are parallel and never intersect.
====================================================
Work Shown:
Solving the 1st equation for y.
3x-y=18
-y=18-3x
y = -(18-3x)
y = -18+3x
y = 3x-18
Plugging that into the other equation to solve for x.
-2y=-6x-120
-2(y)=-6x-120
-2(3x-18)=-6x-120
-6x+36=-6x-120
-6x+6x=-120-36
0x = -156
0 = -156
We arrive at a false statement.
Therefore, this system has no solutions
The system is inconsistent.
If you were to use a graphing tool like Desmos or GeoGebra, then you'll see the two lines are parallel. They never intersect to form a solution.
If x−4y=−10 and 2x+9y=−3 are true equations, what would be the value of 3x+5y?
Answer:
3x+5y = -13
Step-by-step explanation:
Since there are two variables, you must solve for one of them first. One way we can do that is through elimination.
X seems the easiest to eliminate.
We can subtract the two equations.
x - 4y = -10
- 2x+9y = -3
If we subtract it like this, it wouldn't eliminate any variables. So, let's multiply the first equation by 2 so both equations have 2x.
2x - 8y = -20
- 2x+9y = -3
Now, subtract the equations.
-17y = -17
We can solve for y now.
y = 1
Since we have y's value, we can solve for x. Plug y back into one of the equations.
x - 4(1) = -10
x - 4 = -10
x = -6
Now that we have both the x and y values, simply plug it into 3x+5y.
3(-6) + 5(1)
-18 + 5
-13
So the answer is -13
fwam took a taxi from his house to the airport. the taxi company charged a pick-up fee of $3.80 plus $2.25 per mile. the total fare was $33.05, not including the tip. write and solve an equation which can be used to determine mm, the number of miles in the taxi ride.
The equation that represents the whole scenario is 3.80 + 2.25(x) = 33.05 and the number of miles is 13.
Finding the number of miles:Here we will use the linear equation concept to solve the problem. Since we don't know the number of miles represent it with a variable 'x' and form a Linear equation according to the given condition in the problem. Now solve the resultant equation for the value of variable 'x'
Here we have
The taxi company charged a pick-up fee of $3.80 plus $2.25 per mile. the total fare was $33.05, not including the tip.
Let 'x' be the number of miles in the taxi ride
Total cost to travel 'x' mile = 3.80 + 2.25(x)
From the given data, the total fare was $33.05
=> 3.80 + 2.25(x) = 33.05
=> 2.25x = 33.05 - 3.80
=> 2.25x = 29.25
=> x = 29.25/2.25
=> x = 13
Therefore,
The equation that represents the whole scenario is 3.80 + 2.25(x) = 33.05 and the number of miles is 13.
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Please help
Find CD.
1.) 4.5
2.) 5.3
3.) 5.5
4.) 6.3
Answer:
CD = 6.3
Step-by-step explanation:
triangles CFG and CDE are similar, so their side lengths are proportional
this means CD/CF = CE/CG
since we don't know CF, we need to first solve for CF in order to find CD
luckily, we know CD = CF + FD, and FD is given:
CD/CF = CE/CG -> (CF + FD) / (CF) = CE/CG
multiply both sides by CF to get CF + FD = CE * CF / CG
move the terms with CF to one side, and the constants to the other side:
CF - CF(CE/CG) = -FD
solve for CF:
CF(1-(CE/CG)) = -FD, CF = FD / ((CE/CG) - 1) = (1.8)/(((2.4+6)/(6)) - 1) = 4.5
Since CD = CF+FD, CD = 4.5 + 1.8 = 6.3
Your friend determines whether x and y are proportional. Is your friend correct? Explain
Answer: How can you tell whether X and Y are proportional?
Step-by-step explanation: How can you tell whether X and Y are proportional?
To know if a relationship is proportional, you should look at the ratios between the two variables. If the ratio is always the same, the relationship is proportional. If the ratio changes, the relationship is not proportional. please select brainiest if right
A small country emits 115,000 kilotons of carbon dioxide per year. in a recent global agreement, the country agreed to cut its carbon emissions by 1.6% per year for the next 11 years. in the first year of the agreement, the country will keep its emissions at 115,000 kilotons and the emissions will decrease by 1.6% in each successive year. how many total kilotons of carbon dioxide would the country emit over the course of the 11 year period, to the nearest whole number?
The total kilotons of carbon dioxide would the country emits over the course of the 11-year period will be 2.23 x 10 ⁻¹⁵ kilotons.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a small country emits 115,000 kilotons of carbon dioxide per year. in a recent global agreement, the country agreed to cut its carbon emissions by 1.6% per year for the next 11 years.
The total kilotons of carbon dioxide would the country emits over the course of the 11-year period will be calculated as:-
Amount = 115000 x ( 0.016)¹¹
Amount = 2.23 x 10 ⁻¹⁵ kilotons.
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The probability of a high school basketball team winning any game is 58%. This team is in a six-game tournament,
and the games are played independently of one another. Let X represent the number of games the team might win
in this tournament. What are the mean and standard deviation of X?
The mean (expected value) of X is 3.48, and the standard deviation of X is 1.27.
Basketball Game Win StatsMean (Expected Value) of X:The mean or expected value of X, representing the number of games the team might win, can be calculated using the formula:
E(X) = n * p
where:
n = number of games (6)
p = probability of winning each game (0.58)
So, E(X) = 6 * 0.58 = 3.48
Standard Deviation of X:The standard deviation of X, representing the spread of the distribution, can be calculated using the formula:
SD(X) = √(n * p * (1 - p))
where:
n = number of games (6)
p = probability of winning each game (0.58)
So, SD(X) = √(6 * 0.58 * (1 - 0.58)) = 1.27
Therefore, the mean of X is 3.48, and the standard deviation of X is 1.27.
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Here is a clock face. For each time given, name the number the second hand points at.
1. 15 seconds after 1:00.
2. 30 seconds after 1:00.
3. 1 minute after 1:00.
4. 5 minutes after 1:00.
Based on the given time; the number the second hand points at are;
1. 15 seconds after 1:00 - The seconds hand points at 32. 30 seconds after 1:00 - The seconds hand points at 63. 1 minute after 1:00 - The seconds hand points at 124. 5 minutes after 1:00 - The seconds hand points at 12Which number is the second hand pointing at?There are a total of 12 numbers on a clock starting from 1 and ending at 12
There are 60 strokes or lines with equal spaces on a clock
Each stroke or line represents a second
60 seconds = 1 minutes
1. 15 seconds after 1:00.
= The seconds hand points at 3
2. 30 seconds after 1:00.
The seconds hand points at 6
3. 1 minute after 1:00.
1 minutes = 60 seconds
The seconds hand points at 12
4. 5 minutes after 1:00
5 minutes = 300 seconds
The seconds hand points at 12
Therefore, the seconds hand of the given time points at 3, 6, 12 and 12 respectively.
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I need help on this hmh assignment
Suppose you know that ∠S and ∠Y are complementary and that m∠S = 2(m∠Y) − 30°. Find m∠Y.
Answer:
Step-by-step explanation:
Since ∠S and ∠Y are complementary, we have:
∠S + ∠Y = 90°
We also know that:
m∠S = 2(m∠Y) − 30°
Substituting the second equation into the first equation, we get:
2(m∠Y) − 30° + ∠Y = 90°
Combining like terms:
3(m∠Y) = 120°
Dividing both sides by 3:
m∠Y = 40°
Therefore, m∠Y is 40 degrees.
A bird flies from the bottom of a canyon that is 62 2/5
feet below sea level to a nest that is 504 1/2
feet above sea level. What is the difference in elevation between the bottom of the canyon and the bird's nest
Step-by-step explanation:
The difference in elevation between the bottom of the canyon and the bird's nest is 504 1/2 - (-62 2/5) = 504 1/2 + 62 2/5 = 566 5/5 = 566 feet
Answer:
Step-by-step explanation:
Say sea level is 0.
Bottom of the canyon is -62.4ft and bird's nest is 504.5ft
Subtract.
504.5 - 62.4 = 442.1ft
solve the following systems of linear equations using substitution
6x - y = -7 and 5x + y = -4
Answer:
(-1,1)
Step-by-step explanation:
1. Rearrange either equation to isolate one of the variables. Lets use 6x - y = -7 :
6x - y = -7
-y = -7 - 6x
y = 7+6x
2. Now use this definition of x in the second equation:
5x + y = -4
5x + (7+6x) = -4
11x = -11
x = -1
3. Now use x = -1 in either equation to find y:
6x - y = -7
6 (-1) - y = -7
-y = -1
y = 1
The solution is (-1,1)
See the attached graph.
3. the table below shows world population size from different points in history. create a function to model this data. what type of model best fits the data? what would the expected world population be in 2017? research and compare your prediction with the known value.
A polynomial regression model is a good choice for this data, as it can fit the trend of increasing population growth over time.
What do you mean by function?A function is a mathematical concept that assigns a unique output value for each input value.
In mathematical notation, a function is usually expressed as "f(x)" where "x" is the input and "f(x)" is the corresponding output. For example, a function could be defined as f(x) = x^2, which means that for any value of x, the function will calculate and return the square of that value.
To model the world population data, we can use a mathematical function to fit the data points. A polynomial regression model is a good choice for this data, as it can fit the trend of increasing population growth over time.
To find the expected world population in 2017, we would need to estimate the polynomial regression model using the data points provided and then evaluate the model at the year 2017.
Research shows that the actual world population in 2017 was approximately 7.5 billion, which is higher than our estimated value based on the limited data points provided. This highlights the importance of considering additional factors and data when making predictions about the world population.
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The complete question is
A savings account pays interest at a rate of R% per year.
Nick invests £8 500 in the account for one year.
At the end of the year, Nick pays tax on the interest at a rate of 30%.
After paying tax, he gets £166.60
Work out the value of R.
Answer:
The Value of R is 20%.
Step-by-step explanation:
Let R be the interest rate (in percentage) per year. The interest earned after one year would be R% of £8,500, which is (R/100) * £8,500 = £(R * 85)/100.
After paying tax, the amount Nick receives would be (R * 85)/100 * (100 - 30)/100 = £(R * 85 * 70)/10000.
Since Nick receives £166.60 after paying tax, we have:
£(R * 85 * 70)/10000 = 166.60
Solving for R, we get:
R = (10000 * 166.60) / (85 * 70) = 20.0.
Therefore, the interest rate R is 20%.
What iS the ratio for cos b?
Answer:
12/37
Step-by-step explanation:
Given right triangle ABC with sides AB=37, BC=12, and CA=35, you want the cosine of angle B.
CosineThe cosine of an angle in a right triangle is ...
Cos = Adjacent/Hypotenuse
The leg adjacent to angle B is BC=12. The hypotenuse is AB=37.
Using these values, the cosine of B is ...
cos(B) = BC/BA
cos(B) = 12/37
Find the minimum value of c=x+y
Answer:
The minimum value of C is 14
Step-by-step explanation:
Sketch the graph of the constraints using
2x + y = 20
with intercepts (0, 20) and (10, 0)
2x + 3y = 36
with intercepts (0, 12) and (18, 0)
The solution to both are above the lines
Solve 2x + y = 20 and 2x + 3y = 36 to find the point of intersection at (6, 8)
Then the coordinates of the vertices of the region formed are
(0, 20), (6, 8) and (18, 0)
Evaluate the objective function at each vertex to determine minimum value
C = 0 + 20 = 20
C = 6 + 8 = 14
C = 18 + 0 = 18
Thus the minimum value of C is 14 when x = 6 and y = 8
Hope this helped to get you answer!
What happens as x approaches zero from the positive direction?
What happens as x approaches zero from the negative direction?
What is the domain of the function?
all real numbers x
all positive real numbers x
all negative real numbers x
all real numbers x, except x = 0
The domain of the function is all real numbers , except x = 0
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
Let the domain of the function be represented as D
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
When the value of the x of function approaches zero from the positive direction , the function f ( x ) gets larger
And , when the value of the x of function approaches zero from the negative direction , the function f ( x ) gets larger in the negative direction
Now , the domain of the function will be all the real numbers except 0
Hence , the domain of the function is all real numbers except 0
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Ten times a number r plus one-fifth of a number s equals thirteen. Five times the number r plus one-tenth of the number s
equals eight. What are the two numbers?
th
Answer: No Solution
Step-by-step explanation: When you use the elimination method on second equation by multiplying it by 2 you get two equations that add up to a different solution. Since the variable coefficients are the same on both, there will be no solution.
Alex the electrician needs 34 yards of electrical wire to complete his job. He has a coil of wiring in his workshop. The coiled wire is 18 inches in diameter and is made up of 21 circles of wire. Will this coil be enough to complete the job? Let Pi be 3. 14
Alex will not be able to complete his job. According to the measurement given for the coil, the electrician will not be able to complete the job.
The circumference of the coil of wiring can be calculated with
C= 2πr
where r is the radius and π= 3.14
The radius can be calculated by dividing the diameter by 2. Then:
r= 18 inches ÷ 2
r= 9 inches
Convert 9 inches to yards (1 yard= 36 inches)
(9 inches)(1 yard ÷ 36 inches) = 0.25 yard
Substitute this radius into the formula:
C= 2(3.14)(0.25 Yard)
C= 1.57 Yard
Since there are 21 circles of wire, we need to multiply C= 1.57 yards by 21
C = (1.57 Yard)(21) = 32.97 Yard
The coil has 32.97 yards of wire and Alex needs 34 yards, therefore, this coil will not be enough to complete the job.
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