the cost of two apples is thrice the cost of grapes write a linear equation in two variables
Answers
Answer:
\(2x-3y=0\\\\\)
Step-by-step explanation:
Let the cost of apples be x and the cost of grapes be y, then according to the word problem we have,
\(2x=3y\)
Therefore, the required linear equation is \(2x-3y=0\\\)
What is a linear equation?A linear equation is an algebraic equation whose variables do not exceed the power of order 1.
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Related Questions
Which of the following statements about “vesting periods” is TRUE?
Answers
question 9 of 10 explain how you can determine the sign of the sum of two integers if one integer is positive and the other integer is negative.
Answers
To determine the sign of the sum of two integers when one integer is positive and the other is negative, we can follow a simple rule based on their magnitudes.
If the magnitude of the positive integer is greater than the magnitude of the negative integer, the sum will be positive. This is because the positive integer outweighs the negative integer, resulting in a positive value.
On the other hand, if the magnitude of the negative integer is greater than the magnitude of the positive integer, the sum will be negative. In this case, the negative integer dominates and determines the sign of the sum.
In both scenarios, the sign of the larger magnitude integer takes precedence and determines the sign of the sum. It is important to note that the sum will always have the sign of the integer with the larger magnitude, regardless of the specific values of the integers involved.
By considering the magnitudes of the integers, we can easily determine the sign of their sum when one integer is positive and the other is negative.
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Look at this diagram:
If TV and WY are parallel lines and m
Answers
If TV and WY are parallel lines, then m∠VUX = 53°.
What are parallel lines?
Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines. Parallel lines intersect at infinity is another way to put it.
It is given that line segment TV and WY are parallel to each other.
A line ZS intersect the parallel lines.
The measure of m∠TUS = 53°.
The measure of m∠VUX = m∠TUS as they are both vertically opposite angles and hence they are same.
Therefore, m∠VUX = 53°.
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a cylinder with a height of 17 centimeters and a radius of 8 centimeters is filled with water. if the water is then poured into the rectangular prism shown, will it overflow? write an argument that can be used to defend your solution.
Answers
Answer:
The volume of a cylinder is calculated by multiplying the area of the base by the height. The area of the base of a cylinder is πr², where r is the radius of the cylinder. In this case, the radius is 8 centimeters, so the area of the base is 201.06 cm². The height of the cylinder is 17 centimeters, so the volume of the cylinder is 3417.02 cm³.
The volume of a rectangular prism is calculated by multiplying the length, width, and height. In this case, the length is 15 centimeters, the width is 12 centimeters, and the height is 9 centimeters. The volume of the rectangular prism is 1620 cm³.
Since the volume of the cylinder is less than the volume of the rectangular prism, the water will not overflow.
Here is an argument that can be used to defend this solution:
The volume of the cylinder is calculated by multiplying the area of the base by the height.
The area of the base of a cylinder is πr², where r is the radius of the cylinder.
In this case, the radius is 8 centimeters, so the area of the base is 201.06 cm².
The height of the cylinder is 17 centimeters, so the volume of the cylinder is 3417.02 cm³.
The volume of a rectangular prism is calculated by multiplying the length, width, and height.
In this case, the length is 15 centimeters, the width is 12 centimeters, and the height is 9 centimeters.
The volume of the rectangular prism is 1620 cm³.
Since the volume of the cylinder is less than the volume of the rectangular prism, the water will not overflow.
Step-by-step explanation:
37
The figure shows the positions of three players at a moment of a water polo match. Player A throws the ball to Player B, who then throws the
Player C.
Distance (m)
16
12
00
4
m
0
0
Player A
4
(8,4)
8
Player B
Player C
How far did player A throw the ball?
(18, 7)
12 16 20 24
Distance (m)
Round all answers to the nearest tenth of a meter.
How far did player B throw the ball?
(24, 14)
28 x
Answers
Answer:
can you take picture of your questions
Answer: these are the asnwers
Step-by-step explanation: :)
d) if 36 reindeer are randomly selected, what is the probability their mean weight is less than 100kg
Answers
When 36 reindeer are chosen at random, the probability that the mean weight is less than 100 kg is 0.1492.
A standard error is the standard deviation of its sampling distribution or an interpretation of that standard deviation.
Given,
Mean of the weights = 102.4 kg
Standard deviation = 13.9 kg
To determine the probability that the mean weight of 36 reindeer will be less than 100 kg, first compute the standard error using the formula,standard error, \(\sigma_x=\frac{\sigma}{\sqrt{n}}\)
Where, \(\sigma\)=standard deviation
n= number of reindeer
substitute the values in the formula,
\(\sigma_x=\frac{13.9}{\sqrt{36}}\\\\\sigma_x=2.31667\)
Now,
\(P(x < 100)=P(x < \frac{100-102.4}{2.316})\\\\=P(z < -1.04)\)
from z-score table,
=0.1492
Thus, the probability the their mean weight is less than 100 kg is 0.1492.
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Your question is incomplete, here is the complete question.
The weight of male reindeer of the R. Santa Claus subspecies is normally distributed with mean 102.4 kg and standard deviation 13.9 kg
if 36 reindeer are randomly selected, what is the probability their mean weight is less than 100kg?
If the price of a yo-yo in a shop increased by 20% and is now $6.00, what was the original price?
Answers
Answer: Original Price: $5
Step-by-step explanation:
x+0.2x=6
1.2x=6
x=5
Original Price: $5
Answer:1.20$
Step-by-step explanation:
so with some problems like this what you can do is multiply the numbers you’re given especially with percentages this makes it really easy to solve all you need to do is multiply the 6$ and the 20% by making the 20% into a decimal and for this problem the 20% would be 0.2. and after you’ve done that you multiply the 6$ with 0.2 and you should get your answer
What is the area of this compound figure?
Answers
The area of the composite figure is equal to 99 mm² square milimetresmetres.
How to calculate for the area of the figureThe composite figure can be observed to be made up of two horizontal rectangle, and a vertical rectangle, so we shall calculate for the areas of the three figures and then add the result to get the total area of the composite figure as follows:
area of the bigger horizontal rectangle = 11 mm × 3 mm
area of the bigger horizontal rectangle = 33 mm²
area of the smaller horizontal rectangle = 5 mm × 2 mm
area of the smaller horizontal rectangle = 10 mm
area of the vertical rectangle = 14 mm × 4 mm
area of the vertical rectangle = 56 mm²
total area of the composite figure = 33 mm² + 10 mm² + 56 mm²
total area of the composite figure = 99 mm²
Therefore, the area of the composite figure is equal to 99 mm² square milimetres.
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(a) Show that the vectors u1 = (2, 0, 3), u2 = (−3, 0, 2) and u3 = (0, 7, 0) form an orthogonal basis for R 3 .(b) Write v = (1, 2, 3) as a linear combination of u1 = (2, 0, 3), u2 = (−3, 0, 2) and u3 = (0, 7, 0).
Answers
Main Answer:The linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3
Supporting Question and Answer:
How can we express a vector as a linear combination of vectors using a system of equations?
To express a vector as a linear combination of vectors using a system of equations, we need to find the coefficients that multiply each given vector to obtain the desired vector. This can be done by setting up a system of equations, where each equation corresponds to the components of the vectors involved.
Body of the Solution:
(a) To show that the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3, we need to demonstrate two conditions: orthogonality and linear independence.
Orthogonality: We need to show that each pair of vectors is orthogonal, meaning their dot product is zero.u1 · u2 = (2)(-3) + (0)(0) + (3)(2) = -6 + 0 + 6 = 0
u1 · u3 = (2)(0) + (0)(7) + (3)(0) = 0 + 0 + 0 = 0
u2 · u3 = (-3)(0) + (0)(7) + (2)(0) = 0 + 0 + 0 = 0
Since the dot product of every pair of vectors is zero, they are orthogonal.
2.Linear Independence: We need to show that the vectors u1, u2, and u3 are linearly independent, meaning that no vector can be written as a linear combination of the other vectors.
We can determine linear independence by forming a matrix with the vectors as its columns and performing row operations to check if the matrix can be reduced to the identity matrix.
[A | I] = [u1 | u2 | u3 | I] =
[2 -3 0 | 1 0 0]
[0 0 7 | 0 1 0]
[3 2 0 | 0 0 1]
Performing row operations:
R3 - (3/2)R1 -> R3
R1 <-> R2
[1 0 0 | -3/2 1 0]
[0 1 0 | 0 1 0]
[0 0 7 | 0 0 1]
Since we can obtain the identity matrix on the left side, the vectors u1, u2, and u3 are linearly independent.
Therefore, the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3.
(b) To write v = (1, 2, 3) as a linear combination of u1, u2, and u3, we need to find the coefficients x, y, and z such that:
v = xu1 + yu2 + z*u3
Substituting the given vectors and coefficients:
(1, 2, 3) = x(2, 0, 3) + y(-3, 0, 2) + z(0, 7, 0)
Simplifying the equation component-wise:
1 = 2x - 3y
2 = 7y
3 = 3x + 2y
From the second equation, we can solve for y:
y = 2/7
Substituting y into the first equation:
1 = 2x - 3(2/7)
1 = 2x - 6/7
7 = 14x - 6
14x = 13
x = 13/14
Substituting the found values of x and y into the third equation
3 = 3(13/14) + 2(2/7)
3 = 39/14 + 4/7
3 = 39/14 + 8/14
3 = 47/14
Therefore, we have determined the values of x, y, and z as follows:
x = 13/14
y = 2/7
z = 47/14
Thus, we can write the vector v = (1, 2, 3) as a linear combination of u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) as:
v = (13/14)u1 + (2/7)u2 + (47/14)u3
Therefore, v can be expressed as a linear combination of the given vectors.
Final Answer:Therefore,the linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3
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The linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3
To express a vector as a linear combination of vectors using a system of equations, we need to find the coefficients that multiply each given vector to obtain the desired vector. This can be done by setting up a system of equations, where each equation corresponds to the components of the vectors involved.
Body of the Solution:
(a) To show that the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3, we need to demonstrate two conditions: orthogonality and linear independence.
Orthogonality: We need to show that each pair of vectors is orthogonal, meaning their dot product is zero.
u1 · u2 = (2)(-3) + (0)(0) + (3)(2) = -6 + 0 + 6 = 0
u1 · u3 = (2)(0) + (0)(7) + (3)(0) = 0 + 0 + 0 = 0
u2 · u3 = (-3)(0) + (0)(7) + (2)(0) = 0 + 0 + 0 = 0
Since the dot product of every pair of vectors is zero, they are orthogonal.
2.Linear Independence: We need to show that the vectors u1, u2, and u3 are linearly independent, meaning that no vector can be written as a linear combination of the other vectors.
We can determine linear independence by forming a matrix with the vectors as its columns and performing row operations to check if the matrix can be reduced to the identity matrix.
[A | I] = [u1 | u2 | u3 | I] =
[2 -3 0 | 1 0 0]
[0 0 7 | 0 1 0]
[3 2 0 | 0 0 1]
Performing row operations:
R3 - (3/2)R1 -> R3
R1 <-> R2
[1 0 0 | -3/2 1 0]
[0 1 0 | 0 1 0]
[0 0 7 | 0 0 1]
Since we can obtain the identity matrix on the left side, the vectors u1, u2, and u3 are linearly independent.
Therefore, the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3.
(b) To write v = (1, 2, 3) as a linear combination of u1, u2, and u3, we need to find the coefficients x, y, and z such that:
v = xu1 + yu2 + z*u3
Substituting the given vectors and coefficients:
(1, 2, 3) = x(2, 0, 3) + y(-3, 0, 2) + z(0, 7, 0)
Simplifying the equation component-wise:
1 = 2x - 3y
2 = 7y
3 = 3x + 2y
From the second equation, we can solve for y:
y = 2/7
Substituting y into the first equation:
1 = 2x - 3(2/7)
1 = 2x - 6/7
7 = 14x - 6
14x = 13
x = 13/14
Substituting the found values of x and y into the third equation
3 = 3(13/14) + 2(2/7)
3 = 39/14 + 4/7
3 = 39/14 + 8/14
3 = 47/14
Therefore, we have determined the values of x, y, and z as follows:
x = 13/14
y = 2/7
z = 47/14
Thus, we can write the vector v = (1, 2, 3) as a linear combination of u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) as:
v = (13/14)u1 + (2/7)u2 + (47/14)u3
Therefore, v can be expressed as a linear combination of the given vectors.
Therefore, the linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3
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a circle has central angle 144° and its arc length is 4 units. ind the arc length and area of the sector
Answers
A circle has central angle 144° and arc length of 4 units. The area of the corresponding sector is 7.96 square units.
A sector of a circle is an area enclosed by two radii and an arc. The formula for the area of a sector is given by:
Area of sector = (central angle/360°) x πr²
Hence, we must find the radius of the circle first using the arc length information.
Arc length = (central angle/360°) x 2πr
4 = (144°/360°) x 2πr
r = 4 x 360°/(144° x 2π)
= 1.59 units
The area of the circle is given by:
A = πr²
= = π(1.59²) = 7.96 square units
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please help ASAP !!
Choose the system of equations that matches the following graph:
Picture included!
Answers
Answer:
Choice 2
Step-by-step explanation:
If im wrong im so sorry
If im right can i hav brainliest plz?
Answer:
b
Step-by-step explanation:
So you start at x-axis work your way down to the y-axis and you get your answer.
Write this number in
scientific notation.
572,900.000
[?]×10[]
![Write this number inscientific notation.572,900.000[?]10[]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/wFXBbc3ndvtiIZgsv6duJFbua2qbMjBk.png)
Answers
The number in the exponential scientific form is A = 5.729 x 10⁸
Given data ,
Let the number be represented as A
Now , the value of A is
A = 572,900,000
On simplifying , we get
From the laws of exponents , we get
The exponential form of a number is a way of representing a number using exponents, where the base is typically a number greater than 1
So , the value of A is
When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
A = 5.729 x 10⁸
Hence , the scientific form is A = 5.729 x 10⁸
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How many possible outcomes are therefor any set of linear systems?
Answers
The answer is three
None, one or infinitely many solutions
x=5 y = 3, x² + 3(x +y)=
HELP FAST
Answers
9514 1404 393
Answer:
49
Step-by-step explanation:
Put the variable values in place of the corresponding variables, and do the arithmetic.
x² +3(x +y) =
5² +3(5 +3) = 25 +3(8) = 25 +24 = 49
For the bar graph, what is the total population surveyed?
A)303
B)3,030
C)3,030,000
D)303,000
PLEASE HELP ASAP ILL GIVE BRAINLIEST
Answers
Add all the numbers of population surveyed
Answer:
A should be right i just add every thing toghter
Step-by-step explanation:
2 4 6 8 10 12 Find the interquartile range (IQR) of the data set,
Answers
The interquartile range of the data set is equal to 6.
What is an interquartile range?The interquartile range is a measure of statistical dispersion, or data spread. The IQR is also known as the midspread, middle 50%, or middle 50%.
The interquartile range is a measurement of a data set's "middle fifty." A range is a measurement of where a set's beginning and end are located.
Given data set is 2 4 6 8 10 12. The upper range is 8 10 12 and the lower range is 2 4 6.
Calculate the median of the upper range and the lower range and subtract it.
Median upper range = 10
Median lower range = 4
The interquartile range is calculated as,
IQR = 10 - 4 = 6
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Am I suppose to substitute the variables with random numbers in order to answer these questions???
Translation A maps (x, y) to (x + n, y + 1). Translation B maps (x, y) to (x +s, y + m).
1. Translate a point using Translation A, followed by Translation B. Write an algebraic rule for the final image of the point after this composition.
2. Translate a point using Translation B, followed by Translation A. Write an algebraic rule for the final image of the point after this composition.
3. Compare the rules you wrote for parts (a) and (b). Does it matter which translation you do first? Explain your reasoning.
Answers
9514 1404 393
Answer:
(x, y) ⇒ (x +n +s, y +1 +m)(x, y) ⇒ (x +s +n, y +m +1)they are identical in effect; order does not matterStep-by-step explanation:
Substitute the expressions.
A then BAfter the first translation, the value of x is (x+n). Put that as the value of x in the second translation.
x ⇒ x +s . . . . . . . . . the definition of the second translation
(x+n) ⇒ (x+n) +s . . . the result after both translations
The same thing goes for y. After the first translation, its new value is (y+1).
y ⇒ y +m . . . . . . . . the definition of the second translation
(y+1) ⇒ (y+1) +m . . . the result of both translations
Then the composition of A followed by B is (x, y) ⇒ (x +n +s, y +1 +m).
__
B then AThe same reasoning applies. After the B translation, the x-coordinate is (x+s) and the y-coordinate is (y+m). Then the A translation changes these to ...
x ⇒ x +n . . . . . . . . . . definition of translation A
(x+s) ⇒ (x+s) +n . . . . translation A operating on point translated by B
y ⇒ y +1 . . . . . . . . . . . definition of translation A
(y+m) ⇒ (y+m) +1 . . . . translation A operating on point translated by B
The composition of B followed by A is (x, y) ⇒ (x + s + n, y + m + 1).
__
You should recognize that the sums (x+n+s) and (x+s+n) are identical. The commutative and associative properties of addition let us rearrange the order of the terms with no effect on the outcome.
The two translations give the same result in either order.
5n = (n + 3) n+ (n + 3) (−8)
how would this be in a verbal sentence?
Answers
Answer: Five times a number is equal to the addition of three more than that number times the number itself and (-8) times 3 more than that number.
Please help me with this homework
Answers
Answer:
answer is |-1| < 7
Answer:
{-1}<7 Hope it helped brainiest plz
Step-by-step explanation:
7 is greater than {-1} because it's a negative number and 7 is a positive.
one thousand two hundred and seventy deer are living on an island that is eight hundred and thirty square kilometers in size. what is the population density of the deer per square kilometer?
Answers
you divide the population by the size, and in turn you would get 1.53
hope this helped!! :)
A studio charges a sitting fee of 25$ plus 7$ per each portrait sheet ordered. Write an expression that can be used to find the total cost to have photographs taken. Then the cost of purchasing twelve portrait sheets.
Answers
Hi
let's call X number of photo ordered.
So total Cost is C(x) = 7X+ 25
Il let you calculate for X = 12 . Have fun
Scenario A. The manager at Dunder-Mifflin Paper Company interested in understanding how a company's employee benefits influence employee satisfaction. In 2020 the company implemented a new benefits package that included optional benefits such as childcare, eldercare, and retirement packages. The manager compares the employee satisfaction ratings from before and after the new benefits package was implemented.
1. What is the independent variable for Scenario A?
a. The employee benefits package
b. The work from home policy
c. Employee productivity
d. The employees at the company
e. The office layout (floorplan)
Answers
The independent variable for Scenario A is given as follows:
a. The employee benefits package.
What are dependent and independent variables?In the case of a relation, we have that the independent and dependent variables are defined by the standard presented as follows:
The independent variable is the input of the relation.The dependent variable is the output of the relation.In the context of this problem, we have that the input and the output of the relation are given as follows:
Input: Employee benefits package.Output: Employee satisfaction.Hence the independent variable for Scenario A is given as follows:
a. The employee benefits package.
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All students in a year group were asked how they travelled to school.
The results were as follows:
a.
150 students walked
b.
83 students took the bus
Work out the percentage for
each transport type.
c.
57 students were driven in
d.
10 students cycled in
Answers
Step-by-step explanation:
there are
150 + 83 + 57 + 10 = 300 students in total.
so,
100% = 300
1% = 100%/100 = 300/100 = 3
a.
150 / 3 = 50%
b.
83 / 3 = 27 2/3 % or 27.66666...%
c.
57 / 3 = 19%
d.
10 / 3 = 3 1/3 % or 3.333333...%
What is the sum of all exterior angles in a polygon?
Answers
Sophie used the equation y = x + 1 to represent that the length of a piece of fabric needed for a craft project (y) is always 1 inch greater than the length of the object made with the fabric (x). Which graph represents four solutions to Sophie's equation?
Answers
Answer: Last graph, the one with the points (1, 2), (2, 3), (3, 4), and (4, 5)
Step-by-step explanation:
We have the equation y = x + 1
Now we can replace x by different values to get pairs (x, y).
if x = 1, we have:
y = 1 + 1 = 2
then we have the pair (1, 2)
if we have x = 2, then:
y = 2 + 1 = 3
Then we have the pair (2, 3)
So we need to find the graph that has these points.
The only graph that has the points (1, 2) and (2, 3) is the last graph.
Jacy has $1,000 to invest in either a fund that pays approximately 4.6% per year or in a savings account with an annual interest rate of 1.8%. Write a polynomial function S(x) to represent the interest Jacy will earn in 1 year by investing x dollars in the fund and the remainder in the savings account.
Answers
Answer:
.046x
Step-by-step explanation:
Use the diagram to the right to determine whether BC. DE. Justify your answer. AD = 15, DB = 12, AE = 10, and EC = 8. The cut part is BC (top to bottom)
Answers
Explanation:
AD = 15, DB = 12, AE = 10, and EC = 8
To determine if line BC is parallel to line DE, we will find the ratio of thier corresponding sides. if it is equal, they are parallelf
. prove that either 2⋅10500 15 or 2⋅10500 16 is not a perfect square. is your proof constructive or nonconstruc- tive?
Answers
This is a non-constructive proof because it does not provide an explicit example of a number that is not a perfect square, but rather shows that such a number must exist.
How to determine perfect square number?We can prove that either 2 × 10⁵⁰⁰ + 15 or 2 × 10⁵⁰⁰ + 16 is not a perfect square using non-constructive proof.
Suppose that there exist integers a and b such that:2 × 10⁵⁰⁰ + 15 = a² and 2 × 10⁵⁰⁰ + 16 = b²
Let's observe both the equations:
2 × 10⁰⁰ + 15 ≡ 3 (mod 4)2 × 10⁵⁰⁰ + 16 ≡ 0 (mod 4)
As we can see, the first equation is congruent to 3 (mod 4), which implies that it cannot be a perfect square.
Similarly, the second equation is congruent to 0 (mod 4), which means that it is a perfect square. This contradicts our assumption that both equations are perfect squares.
Therefore, we can conclude that either 2 × 10⁵⁰⁰ + 15 or 2 × 10⁵⁰⁰ + 16 is not a perfect square.
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what is the exact value of the expression? tan(π6) sin(5π3)⋅cos(−3π4)
Answers
The exact value of the expression tan(π/6) sin(5π/3)⋅cos(-3π/4) is -√3/2.
We have tan(π/6). The angle π/6 is equivalent to 30 degrees. The tangent of 30 degrees is √3/3.
We have sin(5π/3). The angle 5π/3 is equivalent to 300 degrees. In the unit circle, the sine value at 300 degrees is -√3/2.
Finally, we have cos(-3π/4). The angle -3π/4 is equivalent to -135 degrees. In the unit circle, the cosine value at -135 degrees is -√2/2.
Multiplying these values together, we have (√3/3) * (-√3/2) * (-√2/2). Simplifying, we get (√3 * √3 * √2) / (3 * 2 * 2) = (√3 * √2) / 12.
Taking the negative sign into account, the final value is -√3/2, which is approximately -0.866.
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Bill spends 28% of his monthly salary on rent. If his rent is 525
dollars a month, how much is his monthly salary?
‼️PLEASE HELP ME‼️‼️‼️‼️‼️‼️