Relating tables to equations a 2-column table with 3 rows. column 1 is labeled x with entries 2, 4, 5. column 2 is labeled y with entries 5, 10, 12.5. use the information in the table to find the constant of proportionality and write the equation. the constant of proportionality is . the equation that represents this proportional relationship is .
Answers
The constant of proportionality is 2.5.
What is constant of proportionality?Firstly, there is proportional relationship.
Two values x and y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.
x = ky
The constant k is called constant of proportionality.
Given that,
A 2-column table with 3 rows.
Column 1 is labeled x with entries 2, 4, and 5.
Column 2 is labeled y with entries 5, 10, and 12.5.
Based on the above information, the calculation is as follows:
5/2 = 2.5 , so it comes 2.5
10/ 4 = 2.5 so it comes 12 and so on
Hence, The constant of proportionality is 2.5.
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Related Questions
Please help need by tomorrow it would be very very very appreciated
Answers
Answer and step-by-step explanation:
Graphing y = -2x - 6:
y = -2x - 6 is in the slope-intercept form of a line. The general equation for the slope-intercept form is given by:y = mx + b, where
m is the slope,and b is the y-intercept.Since the y-intercept is at (0, -6), mark this point on the graph.
We can think of slope as rise over run. We can think of -2 as the fraction -2/1.Thus, a slope of -2 means that you rise (move down) -2 units each time and run (move right) 1 unit each time.Thus, you can subtract 2 from the y-coordinate and add 1 to the x-coordinate of (0, -6) to find another point on the line.
(0 + 1, -6 - 2)
(1, -8).
Thus, mark the point (1, -8).
We can keep subtracting 2 from every y-coordinate and adding 1 to every x-coordinate until we exceed the numbers on the graph.
I'll attach a picture from the Desmos graphing calculator that shows you where to draw each point.
After you finish drawing the points, make the line by connecting the points.
Graphing x - 4y = 28:
We can convert x - 4y = 28 to slope-intercept form by isolating y. We'll first need to subtract x from both sides:(x - 4y = 28) - x
-4y = -x + 28
Now we need to divide both sides by -4 to fully find the slope-intercept form:(-4y = -x + 28) / -4
y = -x/-4 + 28/-4
y = 1/4x - 7
Since the y-intercept is at (0, -7), mark this point on the graph.
A slope of 1/4 means that you rise (move up) 1 unit and run (move right) 4 units.Thus, you can add 1 to the y-coordinate and add 4 to the x-coordinate of (0, -7) to find another point on the line.(0 + 4, -7 + 1)
(4, -6)
Thus, mark the point (4, -6)
We can keep adding 1 to every y-coordinate and adding 4 to every x-coordinate until we exceed the numbers on the graph.
I'll attach a picture from the Desmos graphing calculator that shows you where to draw each point.
After you finish drawing the points, make the line by connecting the points.
HELPP this is due tomorrow
254 people were surveyed regarding their favorite gemstone 54%chose diamonds 6%chose saphires 30% chose emeralds 10% rubies. How many people did not choose emeralds or rubies?
Answers
Answer:
152.4
Step-by-step explanation:
30%+10%=40%
100%-40%=60%
254*0.60=152.4
. Let U={0,1,2,3,4,5,6,7,8,9},A={2,4,5,7,8,9}, and B={1,2,5,6,8}. Find the following: (a) A∪B (b) A∩B (C) ∣A∣ (D) ∣B∣ (E) ∣A∪B∣ F) ∣A∩B∣
Answers
From the provided sets we obtain; A∪B = {1, 2, 4, 5, 6, 7, 8, 9}, A∩B = {2, 5, 8}, ∣A∣ = 6, ∣B∣ = 5, ∣A∪B∣ = 8, ∣A∩B∣ = 3
Let's calculate the values based on the provided sets:
U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {2, 4, 5, 7, 8, 9}
B = {1, 2, 5, 6, 8}
(a) A∪B (union of A and B):
A∪B = {1, 2, 4, 5, 6, 7, 8, 9}
(b) A∩B (intersection of A and B):
A∩B = {2, 5, 8}
(c) ∣A∣ (cardinality of A, i.e., the number of elements in A):
∣A∣ = 6
(d) ∣B∣ (cardinality of B, i.e., the number of elements in B):
∣B∣ = 5
(e) ∣A∪B∣ (cardinality of the union of A and B):
∣A∪B∣ = 8
(f) ∣A∩B∣ (cardinality of the intersection of A and B):
∣A∩B∣ = 3
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100 POINTS IF U GET THIS RIGHT!
Answers
Answer:
164.22
Step-by-step explanation:
Area = length x width
Area = 11.9 x 13.8
164.22 = 11.9 x 13.8
Evaluate a + 4 when a =87
Answers
Answer:
81
Step-by-step explanation:
a+4
Let a = 87
87+4
81
Henry has a box in the shape of a
square pyramid. He wants to wrap
the box with paper. If the base has
side lengths of 5 in. and the lateral
height is 8 in., about how much
wrapping paper will he need?
Answers
The amount of wrapping paper that he needs to cover the pyramid will be 105 square inches.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
Henry has a box in the shape of a square pyramid.
He wants to wrap the box with paper.
If the base has side lengths of 5 in. and the lateral height is 8 in.
Then the amount of the wrapping paper that he needs to cover the pyramid will be
\(\rm Area = 4 \times \dfrac{1}{2} \times 5 \times 8 + 5 \times 5\\\\\\Area = 80 + 25\\\\\\Area = 105 \ in^2\)
Thus, the amount of wrapping paper that he needs to cover the pyramid will be 105 square inches.
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=
Solve the system of equations – 2x – 4y = -30 and -x + y = 6 by
combining the equations.
Answers
Answer:
X=1
Y=7
Step-by-step explanation:
Add both equations
(-2x) -4y +(-x) +y=-24
-3x-3y=-24. Take - 3 common factor
-3(x+y)=-24. Devide both sides by - 3
X+y=8
Adding the second equation with x+y=8
-x+y +x+y=14
2y=14
Y=7
In equation (x+y=8) substitute y with 7
X+7=8
X=1
Part A
MONEY Samir plan to buy a new video game ytem which will cot at leat $450. He earn $6 per hour babyitting and $10 per hour tutoring. Let x be the number of hour babyitting and y be the number of hour tutoring. Part A Select the inequality that repreent the number of hour Samir could work to earn enough to buy the game ytem. Part A
Select the inequality that repreent the number of hour Samir could work to earn enough to buy the game ytem. A) y≥ − 0. 6x 45
B) y ≥ − 123x 75
C) y > 123x − 75
D) y > 6x 10
Answers
Answer:
Step-by-step explanation:
The required inequality is y ≥ - 0.6x + 45 which represents the number of hours Samir could work to earn enough to buy the game system. which is the correct answer would be an option (A).
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
The video game system will cost at least $450.
He earns $6 per hour babysitting and $10 per hour tutoring.
Let x be the number of hours babysitting and y be the number of hours of tutoring.
According to the given situation, we can write the inequality would be as:
⇒ 6x + 10y ≥ 450
Rearrange the terms of variables in the above inequality,
⇒ 10y ≥ 450 - 6x
Divided by 10 into both sides of the above inequality,
⇒ 10y/10 ≥ 450/10 - 6x/10
⇒ y ≥ 45 - 0.6x or
⇒ y ≥ - 0.6x + 45
Thus, the required inequality is y ≥ - 0.6x + 45 which represents the number of hours Samir could work to earn enough to buy the game system.
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Find the solution for the system that satisfies the conditions at t = 0. y!1 = -13y1 + 56y2, y1(0) = 1
Y2 = -4y1 + 17y2, y2(0) = 1 (y1(t), y2(t))=
Answers
To find the solution for the given system of differential equations, we can use the initial conditions at t = 0 to determine the values of y1(0) and y2(0), which are both given as 1.
Using these initial conditions, we can solve the system of equations:
y1' = -13y1 + 56y2,
y2' = -4y1 + 17y2.
To solve this system, we can express it in matrix form:
Y' = AY,
where Y = [y1, y2] and A is the coefficient matrix:
A = [-13 56]
[-4 17].
The solution to this system can be found by diagonalizing the coefficient matrix A. Let's calculate the eigenvalues and eigenvectors:
The eigenvalues λ can be found by solving the characteristic equation det(A - λI) = 0, where I am the identity matrix:
det(A - λI) = (-13 - λ)(17 - λ) + 4*56 = λ^2 - 4λ + 8 = (λ - 2)^2 + 4.
Solving the characteristic equation, we get λ = 2 ± 2i.
For each eigenvalue, we can find the corresponding eigenvector by solving the system (A - λI)V = 0:
For λ = 2 + 2i, we have the eigenvector V1 = [4 - 2i, 1].
For λ = 2 - 2i, we have the eigenvector V2 = [4 + 2i, 1].
Now, we can write the general solution as:
Y(t) = c1V1e^(λ1t) + c2V2e^(λ2t),
where c1 and c2 are constants determined by the initial conditions.
Plugging in the initial conditions at t = 0:
Y(0) = c1V1 + c2V2 = [1, 1],
we can solve for c1 and c2: c1V1 + c2V2 = [1, 1].
Solving this system of equations, we can find the values of c1 and c2.
Finally, substituting the values of c1, c2, V1, V2, λ1, and λ2 into the general solution, we obtain the specific solution for the given initial conditions at t = 0: Y(t) = [y1(t), y2(t)].
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if you have 15 points which average to about 100% how many points would you need to get half
Answers
Answer:
7.5 so about 7 or 8
Step-by-step explanation:
convert decimal to fractions
1.8 and 0.2
Answers
Answer:
1.8 = 18/10 = 9/5
0.2 = 2/10 = 1/5
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Is -2–9 positive or negative
Answers
Answer:
Negitve
Step-by-step explanation:
-2 -9= -11
Keep going left in the number line
✽ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ✽
➷ I think it's negative because \(-2 - 9 = -11\)
I'm not really sure, sorry!
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
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Sara is having a dinner party for four friends and needs to reduce the serving size of the meatloaf recipe. She uses the equation x/4=5 How many servings did the recipe originally make?
Answers
Answer:
\(x \4 = 5 \\ x = 5 \times 4 = 20 \\ x = 20.\)
Jordan throws a ball from a cliff 12 feet above the ground with an initial velocity of 32 feet per second. In the following functions, h(t) represents the height of the ball above the ground, in feet, with respect to time, t, in seconds, after the ball was thrown. Which of the following functions models the amount of time the ball is in the air?
h(t)= -4(t-1)^2 +3
h(t)= -16(t-1)^2 -4
h(t)= -16(t-1)^2 +12
h(t)= -16(t-1)^2 +28
Answers
Answer:
Your answer will be the third function
Step-by-step explanation:
The base function you need to know is h(t)= 1/2at^2
Your acceleration in this problem is going to be gravity which they give to you, 32 feet per second squared. Since the ball is falling, it means it will have negative acceleration. Now you have the equation h(t)= -16t^2. The final step is to add the initial height from which the ball was dropped giving you: h(t)= -16t^2 +12
If PQR is an equilateral triangle, solve for y. PQ = 14y - 59 QR = 9y+1
Answers
Answer:
y=12
Step-by-step explanation:
For the data shown in the scatter plot below, identify a point apart from the main cluster?
A (1, 4)
B (3, 5)
C (8, 7)
D(4, 7)
Answers
Answer:
C. (8, 7)Step-by-step explanation:
There are 2 points that are apart from the main cluster:
(8, 7) and (8.5, 7.5)One of them is included in the answer choices:
C. (8, 7)How do you show that f and G are inverses of each other?
Answers
First make the graph of the functions, then if the two graphs are symmetric with respect to the line y = x (mirror images over y = x ), then they are inverse functions.
Symmetric
A figure or shape that can be divided into two equal parts by a line is called symmetric figures.
Inverse Functions
The inverse function of a function f is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by F^-1.
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If you have 6 periods per day at school and math is 1 of them, what percentage of your school day is spent in math?
Answers
Answer:
16.67% of your day is spent in math class.
Step-by-step explanation:
The total would be 100% and then since you have 6 periods we divide 100 by 6 to get 16.67%. So 16.67% of your day is spent in math class.
what percent of 64 is 16? Answer without the percent sign
Answers
Answer:
25 percent
Step-by-step explanation:
Dividing 64 by 16 will give you the answer of 0.25
0.25 expressed as a percentage is written as 25%
Answer:
25 percent
16 is the 25 percent of 64
what are the zeros of the polynomial function f(x)=x^3-9x^2+29x?
Answers
Answer:
Step-by-step explanation:
(1): "x2" was replaced by "x^2". 1 more similar replacement(s).
Step by step solution :
STEP
1
:
Equation at the end of step 1
(((x3) + 32x2) + 29x) + 30 = 0
STEP
2
:
Checking for a perfect cube
2.1 x3+9x2+29x+30 is not a perfect cube
Trying to factor by pulling out :
2.2 Factoring: x3+9x2+29x+30
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 29x+30
Group 2: x3+9x2
Pull out from each group separately :
Group 1: (29x+30) • (1)
Group 2: (x+9) • (x2)
he groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
2.3 Find roots (zeroes) of : F(x) = x3+9x2+29x+30
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
Write an algebraic expression for the word phrase.
10 times the product of g and h
Answers
Answer:
10(g*h)
Step-by-step explanation:
the * is supposed to mean times/multiply
since it is an expression you do not put y= or f(x)= or anything like that
Answer:
10(g*h)
Step-by-step explanation:
"Product" means multiply so you would want to multiply g and h together. You put it in parenthesis because you want to multiply the solution you get from multiplying g and h by 10. To show this, you can simply just put the 10 in front of the parenthesis as that implies multiplication.
PLEASE HELP SUPER FAST AND ILL GIVE BRAINLEST
Describe in words a sequence of transformations that maps ∆ABC to ∆A''B''C''.
Write an ordered-pair rule for each transformation in the sequence.
Answers
Transformations that maps ∆ABC to ∆A''B''C'' is \(A^{''}(8,-2)\\B^{''}(5,-2)\\C^{''}(7,0)\)
What is coordinate plane ?A coordinate plane is a two-dimensional surface made up of two number lines. It is produced when a horizontal line crosses the origin, which is the location where the X-axes and Y-axes meet. The numbers on a coordinate grid are used to find points. Using a coordinate plane, you may graph points, lines, and many other things. It functions as a map and gives precise driving instructions between two spots.
Reflection about x - axes (x,y)→(x,-y)
Reflection about y - axes (x,-y)→(-x,-y)
combined reflection is reflection about origin.
\(A^{'}(5,-3) \\B^{'}(2,-3)\\\)
\(C^{'}(4,-1)\)
Shift upward by 1 unit and on right hand side by 3 units
(x,y)→(x+3;y+1)
=\(A^{''}(8,-2)\\B^{''}(5,-2)\\C^{''}(7,0)\)
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How many solutions does the system have?
y= -2x - 4
y= 3х + 3
Answers
Answer:
One solution
Step-by-step explanation:
The system has one solution and that is (-1.4, -1.2)
differences between mean and median 1. you're given n = 5 measurements: 0, 7, 1, 1, 4. find the mean, median, and mode. show your work (don't use the calculator; show the calculations.) (2 points)
Answers
The mode of this set of numbers is 1,the median of this set of numbers is 1.
Mean: To find the mean of this set of 5 numbers, we first add them together and divide by the number of measurements. 0 + 7 + 1 + 1 + 4 = 13. 13 divided by 5 (the number of measurements) is 2.6. Therefore, the mean of this set of numbers is 2.6.
Median: To find the median of this set of 5 numbers, we first need to arrange them in order from least to greatest. 0, 1, 1, 4, 7. The median is the middle number, so it is 1. Therefore, the median of this set of numbers is 1.
Mode: To find the mode of this set of 5 numbers, we need to look for the number that appears most often. In this set, the number 1 appears twice while the rest of the numbers appear only once. Therefore, the mode of this set of numbers is 1.
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Find the slope of the line that passes through (3,11) and (7, 10)
Answers
the slope of the line will be:
\(m=\frac{11-10}{3-7}=-\frac{1}{4}\)The point (2,-4), (x,y), A, and B all lie on the line. Find an equation relating x and y (Hint: The lope formula)
Answers
The point (2,-4), (x,y), A, and B all lie on the line. An equation relating x and y is m(x-2)=y+4.
The points (2, -4), (x, y) are lie on the line.
The slope formula is the vertical change in y divided by the horizontal change in x, sometimes called rise over run. The slope formula uses two points, (x1, y1) and (x2, y2), to calculate the change in y over the change in x. Slope is a ratio that includes how y changes for every unit increase of x.
The slope formula,
m\((x_{2}-x_{1})= y_{2}-y_{1}\)
Here, \(x_{1} = 2, x_{2}= x, y_{1}= -4\) and \(y_{2}= y\)
Now, we have to substitute the values in the formula,
\(m=\frac{y-(-4)}{x-2}\)
\(m= \frac{y+4}{x-2}\)
m(x-2)= y+4
Therefore, the equation is m(x-2)=y+4.
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The sum of 3 consecutive even integers is 18
Answers
Answer:
4,6,8
Step-by-step explanation:
Let x = 1st even integer
x+2 =2nd even integer
x+4 =3nd even integer
x+ x+2 + x+4 = 18
Combine like terms
3x+6 = 18
Subtract 6 from each side
3x+6-6=18-6
3x= 12
Divide by 3
3x/3 =12/3
x = 4
x+2 = 6
x+4 = 8
In a direct variation, y = 16 when x = 4. Write a direct variation equation that shows therelationship between x and y.Write your answer as an equation with y first, followed by an equals sign.Submit
Answers
For a direct variation, there is always a constant between both variables usually represented by k.
That means for every value of y, the contant is multiplied by x.
Therefore;
\(\begin{gathered} 16=4k \\ k=\frac{16}{4} \\ k=4 \\ \text{The equation that shows the relationship betw}een\text{ x and y is;} \\ y=4x \end{gathered}\)Detemine which equation has the same solutions as the equation below.
4X² + 32X - 28 = 0
A. (X+4)²=23
B. 4(X+4)²=36
C. (X+8)²=57
D. 4(X+8)²=28
Answers
The answer is B i hopes this helps
A recent study in KZN showed that 50% of the cars traveling on highways were above the speed limit. A random sample of 9 cars on these highways is taken. Let X denote the number of speeding cars. What is the probability that the number of speeding cars is at least 9? (Rounded to 3 decimal places) What is the expected number of speeding cars, E[X]? (Rounded to one decimal place) What is the variance of the distribution of X? (Rounded to 1 decimal place) What is the standard deviation of the distribution of X? (Rounded to 1 decimal place) Suppose the average speeding fine per car is R2174. What is the expected fines generated by the next 9 cars?
Answers
Probability that the number of speeding cars is at least 9: 0.009 Expected number of speeding cars, E[X]: 4.5 Variance of the distribution of X: 2.25 Standard deviation of the distribution of X: 1.5 Expected fines generated by the next 9 cars: R19566.
To solve the given problem, we need to assume that the number of cars on the highways follows a binomial distribution with parameters n = 9 (number of trials) and p = 0.5 (probability of a car being above the speed limit).
Probability that the number of speeding cars is at least 9:
Since the probability of a car being above the speed limit is 0.5, the probability of a car not being above the speed limit is also 0.5.
To find the probability of having at least 9 speeding cars, we sum up the probabilities of having 9, 10, 11, ..., up to 9 cars. Mathematically, it can be represented as P(X ≥ 9) = P(X = 9) + P(X = 10) + P(X = 11) + ... + P(X = 9).
Using the binomial probability formula, P(X = k) = (n choose k) * p^k * (1 - p)^(n - k), we can calculate the probabilities for each value of k and then sum them up:
P(X ≥ 9) = P(X = 9) + P(X = 10) + P(X = 11) + ... + P(X = 9)
= [C(9, 9) * 0.5^9 * 0.5^(9 - 9)] + [C(9, 10) * 0.5^10 * 0.5^(9 - 10)] + [C(9, 11) * 0.5^11 * 0.5^(9 - 11)] + ...
Evaluating this expression, we find that P(X ≥ 9) ≈ 0.009 (rounded to 3 decimal places).
Expected number of speeding cars, E[X]:
The expected value of a binomial distribution is given by the formula E[X] = n * p. Therefore, in this case, the expected number of speeding cars is E[X] = 9 * 0.5 = 4.5 (rounded to one decimal place).
Variance of the distribution of X:
The variance of a binomial distribution is calculated using the formula Var(X) = n * p * (1 - p). Substituting the values, we get Var(X) = 9 * 0.5 * (1 - 0.5) = 2.25 (rounded to one decimal place).
Standard deviation of the distribution of X:
The standard deviation is the square root of the variance. Therefore, the standard deviation of the distribution of X is sqrt(2.25) = 1.5 (rounded to one decimal place).
Expected fines generated by the next 9 cars:
Since the average speeding fine per car is R2174, the expected fines generated by a single car is R2174. Therefore, the expected fines generated by the next 9 cars would be 9 * R2174 = R19566.
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