For each equation, determine whether it represents a direct variation, an inverse variation, or neither.
Find the constant of variation when one exists and write it in simplest form.
Answers
The types of variation and their constants are;
1) Direct variation with constant of variation as -1/4
2) Direct variation with constant of variation as ³/₂
How to Interpret Mathematical Variations?A variation is defined as a relation that exists between a set of values of one variable and then a set of values of other variables.
In variation, if the variables change proportionately that is they either increase together or decrease together, then they are said to vary directly.
1) We are given the equation;
4y = -x
Now, y is the output while x is the input and so we make y the subject to get; y = -¹/₄x
Now, writing the relationship between y and x as a variation, we will have; y ∝ x
For this to be equal, there has to be a constant of proportionality which means; y = kx
Comparing with our equation tells us that;
This is a direct variation with constant of variation as -1/4
2) We are given the equation;
3x = 2y - 7
Rearranging gives;
2y = 3x + 7
y = ³/₂x + 7
Now, the greater the value of x, the greater the value of y and as such this is also a direct variation with the constant of variation being 3/2.
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Related Questions
What are the coordinates of the point that is one half the distance between A(-1, -2) and B(6, 12)?
Enter your answer by filling in the boxes.
Answers
The coordinates of the point that is one half the distance between A and B is (5/2, 11/2)
How to determine the coordinates of the point that is one half the distance between A and B?
The point with the distance that is one half the distance between A and B is the midpoint of A and B.
The coordinate of the midpoint of a line is the half x values and y values. Thus: Xm = (X1 + X2)/2 and Ym = (Y1 + Y2)/2
where m is the midpoint
Given: A(-1, -2) and B(6, 12)
X1 = -1, Y1 = -2 and X2 = 6, Y2 = 12
Xm = -1+6 /2 = 5/2
Ym = -2+12 = 11/2
Therefore, the coordinates of the point that is one half the distance between A(-1, -2) and B(6, 12) is (5/2, 11/2)
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The population of city A is 24% less than the population of city B, so city A's population is _____% of city B's.
Answers
Answer:
76%
Step-by-step explanation:
100%-24%=76%
How many ways can the letters in the word CHEWY be arranged to form a five letter code
Answers
Answer:
60 ways;
GOOD LUCK!
Step-by-step explanation:
The word CHEWY has 5 letters, Therefore, it can be arranged in 5!/2! = 120/2 = 60 ways.
Write an equation in standard form of the line that passes through (-4,1) and has the slope m=3
An equation in standard form is ____ = -13
Answers
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ 3}(x-\stackrel{x_1}{(-4)}) \implies y -1= 3 (x +4) \\\\\\ y-1=3x+12\implies y=3x+13\implies -3x+y=13\implies \boxed{3x-y=-13}[/tex]
Rewrite as equivalent rational expressions with denominator (5c+9)(c−3)(c−8): 8/5c^2-6c-27, 2c/5c^2-31c-72
Answers
The equivalent rational expression with the same denominator as given will be 8(c - 8)/[(c - 3)(5c - 9)(c - 8)] and 2c(c - 3)/[(c - 3)(5c - 9)(c - 8)].
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
As per the given expression,
8/(5c² - 6c - 27) , 2c/(5c² - 31c - 72)
Now, take the first denominator,
5c² - 6c - 27 = 5c² - 15c + 9c - 27
⇒ 5c(c - 3) - 9(c - 3)
⇒ (c - 3)(5c - 9)
Take the second denominator
5c² - 31c - 72 = 5c² - 40c + 9c - 72
⇒ 5c(c - 8) + 9(c - 8)
⇒ (c - 8)(5c + 9)
Therefore, the expression converts as,
8/[(c - 3)(5c - 9)] , 2c/[(c - 8)(5c + 9)]
8/[(c - 3)(5c - 9)] = 8(c - 8)/[(c - 3)(5c - 9)(c - 8)]
2c/[(c - 8)(5c + 9)] = 2c(c - 3)/[(c - 3)(5c - 9)(c - 8)]
The denomiantor of both expression are same.
Hence "The equivalent rational expression with the same denominator as given will be 8(c - 8)/[(c - 3)(5c - 9)(c - 8)] and 2c(c - 3)/[(c - 3)(5c - 9)(c - 8)]".
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The structured question below,
5x10^-10/3x10^-9
1x10^-9/3.5x10^-9
Answers
Answer:
1.667×10^-12.857×10^-1Step-by-step explanation:
You want the result of a division operation performed on numbers written in scientific notation.
In each case, the result number will have a repeating decimal fraction. We show 4 significant figures in the answer. The number of significant figures you need to use will depend on what you're using the answer for. If you are required to match the precision of the numbers here, you will want to use 1 significant figure.
The rules of exponents apply, so the exponent of the result will be the difference of the exponents of numerator and denominator. As always, if the numerator mantissa is smaller than the denominator mantissa, the result will be a fraction, so adjustment of the exponent will be necessary.
5×10^-10/(3×10^-9)= (5/3)×10^(-10-(-9)) = 1.667×10^-1
1×10^-9/3.5×10^-9= (1/3.5)×10^(-9-(-9)) = 0.2857×10^0 = 2.857×10^-1
__
Additional comment
Any scientific or graphing calculator and any spreadsheet can accept input in scientific notation and format the output in the same way.
You need to be careful with the way you enter the multiplier. Most calculating platforms accept the E notation shown in the attachment. If you use multiplication (×10^-9, for example), then the denominator number will need to be enclosed in parentheses. The third line of the second attachment shows the result of not using parentheses: the multiplier intended for the denominator instead multiplies the result of the division. (This behavior is required by the Order of Operations.)
Find the values of x and y.
Answers
Answer:
y=60°, x=60°
Step-by-step explanation:
X=60° Angles in a Equaliteral triangles are all 60°
Alternate angle to get the base angle close to y
Y=60° because of Isoceless angles
Samuel is taking a multiple choice test with a total of 100 points available. Each question is worth exactly 5 points. What would be Samuel's test score (out of 100) if he got 9 questions wrong? What would be his score if he got xx questions wrong?
Answers
If Samuel answers 9 questions wrong, his score will be 55 points, and if he answers x questions wrong his score is:
f(x) = 100 - x*5
What will be Samuel's score if he got 9 questions wrong?
We know that there are 100 points available, and each question gives 5 points, then the number of questions is given by the quotient:
100/5 = 20
There are 20 questions.
So, if you answer 9 wrong, then you answer:
20 - 9 = 11 correctly
Then your score is:
11*5 = 55
Your score will be 55 points.
And again, each answer gives 5 points, so if you answer x questions wrong your score will be the linear equation:
f(x) = (20 - x)*5
f(x) = 100 - x*5
Where x is an integer between 0 and 20.
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When you add an integer to +3, a negative sum or postive sum is possible. Use an example to show each possibilty.
Answers
It is true that when you add an integer to +3, a negative sum or postive sum is possible. An example is 2 + 3 = 5 and -4 + 3 = -1
How to calculate the value?It should be noted that from the information,we want to prove that addition of +3 to an integer can either be negative or positive.
This will be:
= 2 + 3
= +5
In this case, it gives a positive number.
Also, -4 + 3
= -1
This gives a negative number.
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What is the equation of this graphed line?
Answers
Answer:
y = 2x +2
Step-by-step explanation:
You want the equation of the line through points (-4, -6) and (2, 6).
SlopeThe slope of the line is given by the formula ...
m = (y2 -y1)/(x2 -x1)
m = (6 -(-6))/(2 -(-4)) = 12/6 = 2
Point-slope equationThe point-slope equation of a line is ...
y -k = m(x -h) . . . . . line with slope m through point (h, k)
Using the point (2, 6) and the found value of slope, an equation for the line can be written:
y -6 = 2(x -2) . . . . point-slope equation for the line
Slope-intercept equationSolving this equation for y and simplifying, we get the slope-intercept equation of the line.
y = 2x -4 +6 . . . . . eliminate parentheses, add 6
y = 2x +2 . . . . . . . . simplify; slope-intercept equation
will reward brainliest please help!!!
Dianelys accepted a new job at a company with a contract guaranteeing annual raises. In the first year, Dianelys' salary will be $40000, and she will get a raise of $2500 every year. Make a table of values and then write an equation for S,S, in terms of n,n, representing Dianelys' salary after working nn years for the company.
Answers
1. Dianely's salary can be represented with the following table of values for 5 years as follows:
Year Salary
1 $40,000
2 $42,500
3 $45,000
4 $47,500
5 $50,000
2. The equation to model Dianely's salary after n years is S = 40,000 + 2,500n.
What is an equation?An equation is a mathematical statement equating two or more mathematical expressions.
Equations use variables, numbers, mathematical operands, and the equation symbol (=).
Dianely's initial salary = $40,000
Salary raise per year = $2,500
Dianely's salary after n years in equation form, S = 40,000 + 2,500n.
Table of Values for Dianely's Salary:Year Salary
1 $40,000
2 $42,500 (40,000 + 2,500)
3 $45,000 (42,500 + 2,500)
4 $47,500 (45,000 + 2,500)
5 $50,000 ($47,500 + 2,500)
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A new cruise ship line has just launched 3 new ships: the Pacific Paradise, the Caribbean Paradise, and the
Mediterranean Paradise. The Caribbean Paradise has 23 more deluxe staterooms than the Pacific Paradise. The
Mediterranean Paradise has 30 fewer deluxe staterooms than three times the number of deluxe staterooms on the
Pacific Paradise. Find the number of deluxe staterooms for each of the ships if the total number of deluxe staterooms
for the three ships is 518.
Answers
Answer:
Mediterranean Paradise has 30 fewer deluxe staterooms than three times the number of deluxe staterooms on the
Pacific Paradise.
Step-by-step explanation:
not really sure what to do here??
Answers
Answer:
[tex]d=-6[/tex]
[tex]a_9=-49[/tex]
Step-by-step explanation:
If the first term of a sequence is [tex]-1[/tex] and the second term is [tex]-7[/tex], then each successive term in the sequence is [tex]6[/tex] less than the previous term. The common difference is [tex]-6[/tex] ( [tex]d=-6[/tex] ).
The formula representing the arithmetic sequence is:
[tex]a_n=-6n+5[/tex]
Therefore, the ninth term in the sequence is:
[tex]a_9=-6(9)+5[/tex]
[tex]a_9=-54+5[/tex]
[tex]a_9=-49[/tex]
7
7
^
Why is randomization important?
Select the statement that best answers the question.
to ensure all treatment groups receive experimental units
to ensure all treatment groups are roughly equivalent regarding the experimental units
to ensure that all treatment groups are roughly equivalent regarding the variability within the experimental units
4) Intro
English
Answers
The correct answer is Option A.
Randomization important because it is used to ensure all treatment groups receive experimental units .
What is randomization ?Randomization is mostly used in experiments to establish a cause and effect link and regulate the underlying variable. Also, the evidence is strengthened by randomizing an experiment. Good. To ensure that the outcomes are accurate, randomization is mostly used in experiments.Every experimental unit has the same chance of receiving any therapy, and treatments are distributed to them entirely at random. -A random number table, computer, program, etc. are used to perform randomization.Fixed allocation randomization and adaptive randomization are the two main categories of randomization techniques. The majority of trials employ fixed randomization, in which subjects are assigned to the intervention or comparator with a probability that remains constant over the course of the investigation.
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Answer:
the answer is c. to ensure that all treatment groups are roughly equivalent regarding the variability within the experimental units
Step-by-step explanation:
a piece of pipe is 40in. long. It is cut in to 3 pieces. the longest piece is 3 times as long as the middle sized piece and the shortest piece is 23 in. shorter than the longest piece. Find the lengths of all 3 pieces of pipe.
Answers
The length of shortest piece is 4 inches, middle sized piece is 9 inches and that of longest piece is 27 inches.
According to the question,
We have the following information:
A piece of pipe is 40in. long. It is cut in to 3 pieces. The longest piece is 3 times as long as the middle sized piece and the shortest piece is 23 in. shorter than the longest piece.
Let's take the length of middle sized piece to be x inches.
Length of longest piece = 3x inches
Length of shortest piece = (3x-23) inches
Now, we have the following expression:
x+3x+3x-23 = 40
7x-23 = 40
Adding 23 on both the sides:
7x = 40+23
7x = 63
Dividing by 7 on both the sides:
x = 63/7
x = 9 inches
Length of longest piece = 3*9 inches
Length of longest piece = 27 inches
Length of shortest piece = (27-23) inches
Length of shortest piece = 4 inches
Hence, the length of shortest piece is 4 inches, middle sized piece is 9 inches and that of longest piece is 27 inches.
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lee has seven 5-dollar bills and 6 quarters
in his pocket. How much money would he have
left in his pocket if he buys a leather jacket
worth $35.20.
Answers
Answer:
Lee would have $1.30 left.
Step-by-step explanation:
7 x 5 = $35
6 x .25 = $1.50
Altogether, Lee has $36.50 before buying the jacket
$36.50 - 35.20 = $1.30
If its 50 degrees outside and it drops 70 degrees, how cold will it get?. (Please give steps also..)
Answers
Answer:
Step-by-step explanation:
50
A couple bought a rental house for $195,000 it’s assessed value was $180,000 if the tax rate is $1.50 per $100 of assessed value what is the monthly contribution the lender will require for taxes round to the nearest cent
Answers
Step-by-step explanation:
there is no interest and such involved. it is a straight forward calculation to allow the lender to accumulate enough funds (= the ESCROW account as part of the mortgage account structure) to be able to pay the taxes once a year on behalf of the owners.
so, the tax is $1.50 for every $100 of the assessed value of the house.
how many $100 units are in that value ?
180,000 / 100 = 1,800 units.
that means the tax for that house is
1800 × 1.5 = $2,700
in order for the lender to accumulate $2,700 in the ESCROW account in a year (= 12 months), the monthly contribution has to be
2700 / 12 = $225.00
find the percentage increase if a number 3/8 increase to 3/4
Answers
Answer:
37,
Step-by-step explanation:
It takes 36 pounds of seed to completely plant a 6 acre field. How many acres can be planted per pound of seed?
Answers
Answer: 6 lbs per acre
Step-by-step explanation: just divide 36 by 6 and you get 6. To check your answer multiply 6 and 6. Then you get 36 and know your answer is right.
It is expected that 750 people will attend
the concert. In fact, 600 people attended.
600 is what percent of the expected
number?
Answers
600 is the 80% of the the expected number
Number of people that expected to attend the concert = 750 people
Number of people that attended the concert = 600 people
600 is what percent of the expected number = ( Number of people that attended the concert ÷ Number of people that expected to attend the concert ) × 100
Substitute the values in the equation
600 is what percent of the expected number = (600 / 750) × 100
Divide the terms in bracket first
= 0.8 × 100
Multiply the given terms
= 80%
Hence, 600 is the 80% of the the expected number
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Use point-slope form to write the equation of a line that passes through the
point (14,-17) with slope -2.
Answers
Answer:
[tex]y+17=-2(x-14)[/tex]
Step-by-step explanation:
The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex].
p=(-3,7); m=-1 graph line containing the point p and having slope m.
Answers
The equation of the line is x+y-4=0.
What is an equation?
A formula known as an equation uses the equals sign (=) to express how two expressions are equal.
Main Body:
we know that one point form of a line is
y-y₁= m(x-x₁) , where m= slope
now given is a point (-3,7) and m=-1
y-7 =(-1)(x+3)
x+y-4=0
Hence the answer is x+y-4 =0
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In Exercises 27-30, give the measure of the angle in radians and
degrees. Give exact answers whenever possible.
sin¹ (0.5)
Answers
The measure of the angle for the given trigonometric function is 30°.
Given that, [tex]sin^{-1}(0.5)[/tex].
What are trigonometric angles?Trigonometric angles are the angles in a right-angled triangle using which different trigonometric functions can be represented. Some standard angles used in trigonometry are 0º, 30º, 45º, 60º, 90º.
Trigonometry angle can be expressed in terms of trigonometric ratios as,
θ = [tex]sin^{-1[/tex] (Perpendicular/Hypotenuse)
θ =[tex]sin^{-1[/tex] (0.5)
= [tex]sin^{-1[/tex] (1/2)
= 30°
Therefore, the measure of the angle for the given trigonometric function is 30°.
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a packet of crisps weighs 32 grams to the nearest gram. a multipack of crisps contains 10 packets. work out the least and the greatest weights of the multipack. you can ignore the weight of the multipack wrapper
Answers
If a multipack of crisps contains 10 packets. the least and the greatest weights of the multipack is 315, 325.
How to determine the least and greatest weight?Range = 31.5≤ x < 32.5
Range = 31.5≤ 10 < 32.5
Hence,
Lowest and greatest possible for 32 grams
Lowest possible = 31.5 grams
Greatest possible =32.4 grams
Since multipack of crisps contain is 10 packets hence.
Least weight = 31.5 grams × 10
Least weight =315
Greatest weight = 32.5 grams × 10
Greatest weight = 325
Therefore 315 and 325 are the weight.
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The sum of a number and 4 times the number
Write two equivalent expressions for each statement.
Answers
Let the number be n.
Then the expression is:
The sum of a number and 4 times the numbersum = n + 4nsum = 5nAnswer:
4x + x5xStep-by-step explanation:
Forming the expression,
→ 4x + x
Let's solve the expression,
→ 4x + x
→ 5x
Hence, the answer is 5x.
Determine the slope-intercept form of the equation of the line parallel to y = -4/3x + 11 that passes through the point (–6, 2). y = x +
Answers
The equation of the line in slope-intercept form is y = -4x/3-6 when the line is parallel to y = -4x/3+11.
According to the question,
We have the following information:
The line is parallel to y = -4/3x + 11 and passes through the point (–6, 2).
Now, we know that the following formula is used to find the equation of the line:
y-y' = m(x-x')
In this case, m is the slope of the line.
m = -4/3
We have the following values:
x' = -6 and y' = 2
Now, we have the following expression:
(y-2) = -4/3(x+6)
y-2 = -4x/3-8
Adding 2 to both sides of the equation:
y = -4x/3-8+2
y = -4x/3-6
Hence, the equation of the line in slope-intercept form is y = -4x/3-6 when the line is parallel to y = -4x/3+11.
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The animals at a safari park include camels,
kangaroos and meerkats.
There are 12 more kangaroos than there are
camels.
There are 3 times as many meerkats as there
are camels.
There are the same number of kangaroos as
there are meerkats.
How many camels are there at the safari park?
Answers
m = 3c
k = m
Equating the RHS of the first two equations gives
3c = c + 12
2c = 12
c = 6
There are 6 camels
Does the compound event consist of two mutually exclusive events?
Two dice are rolled. The sum of the dice is a 3 or a 9.
Answers
Probability = number of desired event occurrences/number of events in sample space = 9/36 = 1/4
What is meant by probability?Probability is the branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely it is that a claim is true. The probability of an event is a number between 0 and 1, with 0 signifying impossibility and 1 expressing certainty.
A compound event is made up of two separate events.
Here is a table of probable sums of two die rolls. Die 1 and Die 2 values are listed along the side and top. The figures are roughly near the middle. The sum of Die 1 = 2 and Die 2 = 2 is 4, for example.
Die 2
Die1 1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
Rolling two dice yields 6 * 6 = 36 possible outcomes, or 36 possible sums. There are 36 occurrences in the sample space.
Looking at the table, a 3 or a 9 happens as the sum 9 times, resulting in 9 of the 36 potential occurrences having a sum of 3 or 9.
Probability = number of desired event occurrences/number of events in sample space = 9/36 = 1/4
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A circular plot with 1000 ft diameter is watered by a spray irrigation system. To the
nearest square foot, find the area that is watered as the sprinkler rotates 90°.
Answers
The area that is watered as the sprinkler rotates 90° is 196,250.
What is the area of the circular plot?
The space a circle takes up in a two-dimensional plane is known as the area of the circle. Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. A = πr², where r is the circle's radius, is the formula for calculating a circle's surface area.
Here, we have
Diameter = 1000ft
Radius = 500
Then, we apply the area of a circle and get
= (90/360)× π×(500)²
= 62,500 × π
= 196,250
Hence, the area that is watered as the sprinkler rotates 90° is 196,250.
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