The correct statement according to the given equation is statement (D)"They have a single solution since they have various y-intercepts but the same slopes."
What is the equation?
The relationship between two terms on either side of an equal sign is easily demonstrated using a simple equation.
Additionally, one or more of the four arithmetic operations that simple equations do include addition, fundamental arithmetic, multiplication, and division.
The three possible forms of the equation system are point-slope form, standard form, and slope-intercept form.
So, given equations:
y = 1/2 * x - 3
y = - 1/2 * x - 3
As we are aware, a line's slope-intercept form is:
y = m x + c
Therefore, it is clear from equations 1 and 2 that:
m1 = 1/2 and c1 = -3
m2 = -1/2 and c2 = -3
Therefore, the correct statement according to the given equation is statement (D)"They have a single solution since they have various y-intercepts but the same slopes."
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Complete question:
A system of equations is given below. y=1/2x-3 and -1/2x-3. Which of the following statements best describes the two lines?
a. They have the same slope but different y-intercepts, so they have no solution.
b/. They have the same slope but different y-intercepts, so they have one solution.
c. They have different slopes but the same y-intercept, so they have no solution.
d. They have different slopes but the same y-intercept, so they have one solution.
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
Band students at Yardley High School sell candy every year as a fundraiser. Last year, they sold 53 boxes of truffles and 54 boxes of peanut brittle, raising a total of $428. This year, they sold 67 boxes of truffles and 54 boxes of peanut brittle, from which they raised $484. How much does the band earn from each item?
The band earns $ from each box of truffles and $ from each box of peanut brittle.
A box of truffles costs $4.00 each
A box of peanut brittle costs $4.00 each
What is the algebra of equation?
A mathematical statement in which two expressions are rendered equal to one another is known as an algebraic equation. A variable, coefficients, and constants make up an algebraic equation in most cases.
Here, we
Let t = boxes of truffles and p = peanut brittle
53t + 54p = 428...(1)
67t + 54p = 484...(2)
On solving equations (1) & (2), we get
14t = 56
t = 4
53t + 54p = 428
53(4) + 54p = 428
212 + 54p = 428
54p = 216
p = 4
Hence,
A box of truffles costs $4.00 each
A box of peanut brittle costs $4.00 each
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Which of the following is an example of the Closure Property of multiplication for the set of whole numbers?
A. 74 + 59 = 59 + 74
B. 65 × 3 = 3 × 65
C. 6× 4 = 24
D (2 + 4) + 5 = 2 + (4 + 5)
Answer:
Step-by-step explanation:
The correct option is A 6
×
4 = 24
Closure property of multiplication for whole numbers states that product of two whole numbers a and b is always a whole number c.
Only options B and C have a multiplication sign. Of them, option B is of the form a
×
b = b
×
a
So 6
×
4 = 24 is an example for closure property of multiplication.
two airplanes are flying in the air at the same height: airplane a is flying east at $$ mi/h and airplane b is flying north at $$ mi/h. if they are both heading to the same airport, located $$ miles east of airplane a and $$ miles north of airplane b, at what rate is the distance between the airplanes changing?
The distance between the airplanes changing is -390.
Calculation:The miles from the airport to Airplane A can be calculated as follows: a = 30 -250t, where t is in hours.
Similar to airplane A, airplane B's distance from the airport can be expressed as...b = 40 -300t
Using the Pythagorean theorem, one can calculate the separation (d) between the aircraft:
d^2 = a^2 + b^2
Depending on the passage of time, we have...2dd' = 2aa' + 2bb', and d' = (aa' + bb')/d.
The values of its variables at t=0 must be determined in order to determine the numerical value of thisa = 30 -2500 = 30 a' = -250 b = 40 -3000 = 40 b' = -300
d = √(a²+b²) = √(900+1600) = 50
Then, d' = (30(-250) +40(-300))/50 = -19500/50 = -390
At a speed of 390 miles per hour, the space between the aircraft is closing.
How far apart are the equation's two planes?The distance between the two planes is going to be the square root of six, therefore if we solve for d, multiply both sides of this equation by the square root of six, we obtain six is equal to negative d, or d is equal to negative six.
How widely apart are commercial airplanes?For a commercial airliner, separation will typically be at least 3 miles laterally or 1,000 feet vertically (as stated in the question). The 5 mile rule is applied laterally in the enroute environment, at greater operating speeds over 10,000 feet, depending on the kind of radar and distance from the antennae.
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C'D'
is a translation of
CD
. Write the translation rule.
-
Translation is one of the four types of mathematical transformations that may be applied to a function graph.
(x, y) = (x + a, y + b)
Describe translation.In mathematics, a translation is the up, down, left, or right movement of a form. Because the translated shapes appear to be exactly the same size as the original ones, they are consistent with one another. Just one or more routes have been altered. There is no change in the form because it is just being moved from one location to another.
Rule of TranslationWhen the shape is moved towards the left by k units, then replace x with x - k.
When the shape is moved towards the right by k units, then replace x with x + k.
When the shape is moved up by k units, then replace y with y + k.
When the shape is moved down by k units, then replace y with y - k.
Example: What are the new coordinates when the translation (x, y) → (x - 2, y + 3) is applied to the point (2, 5).
Solution:
The coordinates of old point (preimage) are (x, y) = (2, 5). Now, applying the given translation to this point,
x - 2 = 2 - 2 = 0
y + 3 = 5 + 3 = 8
Thus, the coordinates of the translated point (image) are (0, 8).
This was the example of translation.
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the number of tropical fish that an aquarium can hold depends on the volume of the fish tank. the interior dimensions of the fish tank are 22 cm, 42 cm, and 50 cm. each fish requires 10,000 cubic centimeters of water. how many tropical fish will this fish tank hold?
The number of tropical fish that this fish tank hold is 5 fish
Given that,
The volume of the fish tank determines how many tropical fish can be kept in an aquarium. The fish tank's inside measures 22 cm, 42 cm, and 50 cm. Water volume needed per fish is 10,000 cubic centimeters.
Dimensions of fish tank :
Length = 22 cm
Width = 42 cm
Height = 50 cm
Volume of fish tank = length x breadth x height
= 22 * 42 * 50
= 46200 cm³
Each fish requires 10,000 cubic centimeters of water.
So, tank will hold number of fishes = 46200 / 10000
= 4.62
Hence tank will hold 5 fish.
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Given sine (30 degrees) = one-half and cosine (30 degrees) = startfraction startroot 3 endroot over 2 endfraction, use trigonometric identities to find the the value of cot(30°). one-half startfraction startroot 3 endroot over 3 endfraction startfraction startroot 3 endroot over 2 endfraction startroot 3 endroot
Given that sin 30 degree = 1/2 and cos 30 degree = Squareroot 3/2the value of cot(30°) is = Squareroot 3
Sine 30°=1/2
Cos 30° = √3/2
Sin 30 degrees has a value of 0.5. Sin 30 can also be expressed in radians as sin /6. The triangle's angles and side length are related by the trigonometric function, often known as an angle function.
The sine function, cosine function, and tangent function are the three trigonometric ratios that are the most well-known.
The ratio of the adjacent side to the hypotenuse is referred to as the cosine function. If the right triangle's angle is 30 degrees, then the cosine value at this angle, or the value of Cos 30 degrees, is expressed as 3/2.
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Answer:
3
Step-by-step explanation:
Question 1
What is their rate of change (speed) in Section A? Remember to include units.
Question 2
What is the rate of change of (speed) in section B? Remember to included units
Question 3
What is their rate of change of (speed) in section D (hours 7-10)? Remember to include units
Question 4
During which section was the person moving at the highest speed? What was their speed? Defend your answer
Question 5
During which section did the person travel the farthest? How did they travel?
Question 6
BONUS: write a short (paragraph) scenario that tells the story about where on the graph came from. You can be as creative as you want!
Please only comment if you will give me all these answers thank you!
The rate of change or the speed of the different sections and the distance answers are below;
1) 2 m/s
2) 0 m/s
3) 3 m/s
4) Section C
5) Section A
How to solve distance time graph?1) The formula for the slope is;
Slope = (y₂ - y₁)/(x₂ - x₁)
Taking two coordinates in section A, we can find the slope which gives us the speed;
Speed = (50 - 0)/(25 - 0)
Speed = 2 m/s
2) Section B shows that the speed is constant and as such the rate of change of speed 0 m/s
3) Rate of change of section C is;
Speed = (80 - 50)/(70 - 60)
Speed = 3 m/s
4) The section that the person was moving at the highest speed is 3 m/s which is section C.
5) The section that the person travelled the farthest is section A which was 50 meters.
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how many ways can i select 3 objects out of 30
Answer:
10 times.
Step-by-step explanation:
because 10 x 3 = 30.
If the 3 objects are selected from 30. Then the number of combinations will be 4,060.
What are permutation and combination?A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.
A won and a punctuation mark are used to represent the combination of all positive integers that are less than or equal to the provided positive integer.
The 3 objects are selected from 30. Then the combination is given as,
⇒ ³⁰C₃
⇒ [30!][(30 - 3)! x 3!]
Simplify the expression, then we have
⇒ [30 x 29 x 28 x 27!] / [(27! x 3 x 2 x 1)]
⇒ (30 x 29 x 28) / (3 x 2 x 1)
⇒ 24,360 / 6
⇒ 4,060
If the 3 objects are selected from 30. Then the number of combinations will be 4,060.
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One basketball costs $2 more than another. The sum of their costs is $146. How much does each basketball cost?
Answer:
$72 and $74
Step-by-step explanation:
Let the cheaper ball cost x.
x + x + 2 = 146
2x = 144
x = 72
x + 2 = 74
Answer: $72 and $74
PLS HELP ME NEED FOR MATH PLS
y = 25x + 263 this equation represents how much money she will have, including her saving.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
We have,
The saved amount of $263 by Jenna,
and also she earns $25 per day
if x represents the number of days she works,
and let's take y as the total amount she will have.
Then the equation becomes:
y = 25x + 263
Hence, y = 25x + 263 this equation represents how much money she will have, including her saving.
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1) Is the triangle right angled?
8cm
16cm
18cm
Answer: No the triangle with sides 8cm 16 cm 18cm can't be a right angle triangle because of the Pythagoras theorem which states that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
Step-by-step explanation:
Hope this was helpful
Answer:
no it is not a right angled triangle the Pythagoras theorem
Kayla tried to find the median from the following table, which shows the number of chin-ups she did
last week. However, she made a mistake.
Day
Number of chin-ups
Here is Kayla's work:
=
5+7+9+4+5
5
30
5
Mon Tue Wed Thu Fri
5 7 9 4 5
= 6
"The median is 6 chin-ups per day."
What mistake did Kayla make?
Answer:
Kayla Calculated the Mean instead of the median.
Step-by-step explanation:
If Kayla's work is the sum of all the numbers, she is calculating the mean.
In addition to the 407 inch diagonal, the rectangle slab is 379 inches wide.
What is the length of the side of the slab in inches?
By using Pythagorean theorem ,148 is the length of the side of the slab in inches .
What is the Pythagorean theorem in plain English?
The Pythagorean Theorem states that the squares on the hypotenuse of a right triangle, which is the side that faces the right angle, are equal when added together.
This is written as a2 + b2 = c2 in the usual algebraic notation.
12 inches = 1 feet
feet measurment = 407/12 = 33.91 feet
In triangle ABC
Using PYTHAOREAN THEOREM
l² + b² = h²
l = √h² - b²
l = √407² - 379²
l = √165649 - 143641
l = √22008
l = 148.35
l ≈ 148
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identify the number and type of solutions for the equation 9x2 − 12x 4 = 0.
Answer:
9x^2-12x+4=0
Step-by-step explanation:
you can use factorization method or Quadratic method (Almighty formular).
The number of the solution of the equation is 2 and the solution is equal and real which is 2/3.
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.
The quadratic equation is ax² + bx + c = 0. Then the discriminant is given as,
D = b² - 4ac
If D > 0, then the roots are real and distinct root.If D = 0, then the roots are real and equal roots.If D < 0, then the roots are imaginary roots.The equation is given below.
9x² - 12x + 4 = 0
The discriminant is given as,
D = (-12)² - 4 x 9 x 4
D = 144 - 144
D = 0
Then the roots of the equation is given as,
9x² - 12x + 4 = 0
(3x)² - 2 · 3x · 2 + (2)² = 0
(3x - 2)² = 0
x = 2/3
The number of the solution of the equation is 2 and the solution is equal and real which is 2/3.
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Consider the following graph. у 5 5 -4 -3 2 1 1 2. 2 3 4 5 6 (a) Find the interval(s) on which fis increasing. (Enter your answer using interval notation.) (b) Find the interval(s) on which fis decreasing. (Enter your answer using interval notation.) (c) Find the open interval(s) on which fis concave upward. (Enter your answer using interval notation.) (d) Find the interval(s) on which fis concave downward. (Enter your answer using interval notation.) (e) Find the coordinates of the point(s) of inflection. (x,y) = -([ The graph of the derivative f' of a function fis shown. y= f'(x) A 0 2 X 4 6 (a) on what intervals is fincreasing? (Enter your answer using interval notation.) On what intervals is f decreasing? (Enter your answer using interval notation.) (b) At what values of x does f have a local maximum or local minimum? (Enter your answers as a comma-separated list.)
Answer:
Consider the following graph
(a) Find the interval(s) on which fis increasing. (Enter your answer using interval notation.) = (1,3)U(4,6).
(b) Find the interval(s) on which fis decreasing. (Enter your answer using interval notation.) = (0,1)U(3,4).
(c) Find the open interval(s) on which fis concave upward. (Enter your answer using interval notation.) = (0,2).
(d) Find the interval(s) on which fis concave downward. (Enter your answer using interval notation.) = (2,4)U(4,6).
(e) Find the coordinates of the point(s) of inflection. (x,y)
= (2, 3), (4, 1)
The graph of the derivative f' of a function fis shown.
(a) on what intervals is f increasing? (Enter your answer using interval notation.) = (0,1)U(3,5)
(b) On what intervals is f decreasing? (Enter your answer using interval notation.) = (1,3)U(5,6)
(c) At what values of x does f have a local maximum or local minimum? (Enter your answers as a comma-separated list.) = 1,3,5
how healthy are the employees at direct marketing industry? a random sample of 12 employees was taken, and the number of days each was absent for sickness was recorded (for a 1-year period). use these data to create a 95% confidence interval for the population mean days absent for sickness.
The sample mean is 5.0833 and the standard deviation is 3.476 and the confidence interval is (2.87, 7.29).
In the given question, a random sample of 12 employees was taken, and the number of days each was absent for sickness was recorded (for a 1-year period).
Using these data to create a 95% confidence interval for the population mean days absent for sickness
2 5 3 7 10 0 6 8 5 11 3 1
a) We have to find the sample mean and the standard deviation (round to two decimal places).
The sample mean;
X = 2+5+3+7+10+0+6+8+5+11+3+1/12
X = 61/12
X = 5.0833
Now the standard deviation
SD = √[{x(1)-X)^2+(x(2)-X)^2…………….(x(12)-X)^2}/N]
After solving using that formula;
SD = 3.476
b) 95% confidence in interval for the population mean days absent for sickness.
Lower Bound = X - t(α/2)*s/√n
Upper Bound = X + t(α /2)*s/√n
where
α /2 = (1 - confidence level)/2 = 0.025
X = sample mean = 5.083333333
t(α/2) = critical t for the confidence interval = 2.20098516
s = sample standard deviation = 3.476108936
n = sample size = 12
df = n - 1 = 11
Thus,
Lower bound = 2.874719086
Upper bound = 7.291947581
Thus, the confidence interval is (2.87, 7.29).
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The right question is:
How healthy are the employees at direct marketing industry? A random sample of 12 employees was taken, and the number of days each was absent for sickness was recorded (for a 1-year period). Use these data to create a 95% confidence interval for the population mean days absent for sickness.
2 5 3 7 10 0 6 8 5 11 3 1
a) Find the sample mean and the standard deviation (round to two decimal places)
b) 95% confidence in interval for the population mean days absent for sickness.
pls help with this homework
The solution of the system of equation 2x + 4y = 16, 2x - 4y = 0 is (4, 2). The correct option is A.
How to solve the system of equation?System of equations can be solved using different method such as substitution method, elimination method and graphical method. The system of equation can be solved with the elimination method as follows:
2x + 4y = 162x - 4y = 0
add equation(ii) to equation(i)
2x + 2x = 16 + 04x = 16
divide both sides by 4x = 16
x = 4
Let's find y
2x - 4y = 0-4
y = -2x-4y = -2(4)
-4y = -8
divide both sides by -4y = -8 / -4y = 2
Therefore, the solution is (4, 2)
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Solve this and I give you brain crown and points please quickly
Answer:
one solution
Step-by-step explanation:
because it has diffrent slopes
The present age of the father is three times the age of his son. If the age of the son after 10 years is equal to the age of the father before 20 years, find the present ages of father and the son.
Answer:
Hi
Step-by-step explanation:
I am just reply to see if i really understand that problem
Let's assume s the present age of the son, and f the present age of the father.
The age of the son After 10 years is equal to the age of the father before 20 years:
s+10=f+10-20
f=3s
=> s+10=f-10
=> s+10=3s-10
=> 2s=20
=> s=10 and f=30
I RLLY NEED HELP ASAP
solve each of the following problems by realizing it as a binomial experiment. a fair six-sided die is rolled four times. what is the probability that an odd number is thrown twice?
The probability of getting two odd numbers is 1/2*1/2 = 1/4.
What are binomial experiments used for?When there are only two possible outcomes for an experiment, binomial probability may be used to estimate the likelihood of each result (success and failure).There are just two outcomes that can happen on each try in a binomial situation. You may label one of the alternatives Fail and the other Succes, depending on what you desire. A 6 on a dice is a success, whereas anything other than a 6 is a failure.A statistical experiment with the following characteristics is called a binomial experiment: There are n repeated trials in the experiment. There are only two potential results for each experiment. One of these results is referred to be a success, and the other as a failure.Making the standard assumptions (unbiased die, faces numbered 1-6), there are three odd numbers per die (1, 3 and 5), so the probability of getting an odd number on a die is 3/6 = 1/2, and the probability of getting two odd numbers is 1/2*1/2 = 1/4.
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1/2*1/2 = 1/4 is the likelihood of receiving two odd numbers.
What are the purposes of binomial experiments ?When an experiment has just two possible results, binomial probability can be used to calculate the likelihood of each outcome (success and failure).
In a binomial circumstance, there are only two outcomes that can occur on each try. Depending on what you want, you may declare one of the possibilities a failure and the other a success. Anything less than a 6 is a failure, whereas a 6 is a triumph.
A binomial experiment is a statistical test that has the following features: The experiment consists of n repeated repetitions. Each experiment has only two possible outcomes. One of these outcomes is known as a success, while the other is known as a failure.
According to the given information
The probability of receiving an odd number on a die is 3/6 = 1/2 and the likelihood of getting two odd numbers is 1/2*1/2 = 1/4 under the usual assumptions (unbiased die, faces numbered 1-6). There are three odd numbers per die (1, 3 and 5).
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the manager of a clothing factory checks a random sample 500 shirts for defects he finds that 8 are defective the factory produces 2625 shirts on friday
The expected number of defective shirts produced by the factory on Friday is of:
42 shirts.
How to obtain the expected amount?The expected number of defective shirts produced by the factory on Friday is obtained as the multiplication of the sample proportion by the total number of shirts produced on Friday.
The manager of a clothing factory checks a random sample 500 shirts for defects he finds that 8 are defective, hence the sample proportion is given as follows:
p = 8/500 = 0.016.
The factory produces 2625 shirts on Friday, hence the expected number of defective shirts is given as follows:
E(X) = 0.016 x 2625 = 42 shirts.
Missing InformationThe problem is incomplete and could not be found on any search engine, hence we suppose that it asks for the expected number of defective shirts produced by the factory on Friday.
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The rate of change of the line represented by each table
Answer: m = 3
Step-by-step explanation:
Let pick 2 points ( 0,3) ( 2,9)
Y increased by 6, x increase by 2
Slope is 6/2 = 3
As shown in the diagram below, ABC is parallel to EFG and BF is congruent to EF. SCBF equals 42. 5° then EBF is...
Considering the figure angle EBF is calculated to 68.75 degrees
How to find the < EBFExamining the figure and noting the parallel lines
< CBF = < BFE (alternate angels postulates)
< CBF = 42.5
< BFE = 42.5
Triangle BFE is an isosceles triangle given that the two sides are equal the base angles are also equal
Therefore, applying sum of angels of a triangle = 180 we have
< BFE + < FEB + < EBF = 180 (sum of angles of a triangle)
< FEB = < EBF (base angles of isosceles triangle)
let < FEB = x
42.5 + x + x = 180
42.5 + 2x = 180
2x = 180 - 42.5
2x = 137.5
x = 68.75
angle < EBF is solved to be 68.75
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writ an expression that finds the sum of x and y
On solving the provided question, An expression that finds the sum of x and y => X + Y
What is an expression?a collection of numbers, symbols, and operators (like + and ) that represent a value. Examples - 2 + 3 is a formula and there is also the statement 3 x/2. The equals symbol does not appear in expressions. Actually, none of these = ≠ < > ≤ ≥
How do you write a mathematical expression?We frequently have to understand a written phrase in order to write an expression. For instance, the notation x + 6 can be used to represent the phrase "6 added to some number," where x stands for the unknown value.
An expression that finds the sum of x and y -
=> X + Y
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Car A travels 702 miles on 12 gallons of gasoline. Car B travels 873 miles on 15 gallons of gasoline. Hugo wants to buy a car with lower fuel consumption. Find out the distance each car could travel per gallon of gasoline. Then, tell which of the two cars (A or B) Hugo should buy.
Hugo will buy car B.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Car A travels 702 miles on 12 gallons of gasoline.
And, Car B travels 873 miles on 15 gallons of gasoline.
Now,
Since, Car A travels 702 miles on 12 gallons of gasoline.
And, Car B travels 873 miles on 15 gallons of gasoline.
Hence, The distance of car A for travels in per gasoline = 702 / 12
= 58.5 miles
And, The distance of car B for travels in per gasoline = 873 / 15
= 56.2 miles
Since, Hugo wants to buy a car with lower fuel consumption.
Clearly, The car B consume lower fuel.
Hence, Hugo will buy car B.
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Your average monthly expenditure for gasoline during the first quarter was $167.70. You spent $147.20
in April and $172.90 in May. How much can you spend in June to have the same average as in the first
quarter?
If you have to maintain the same average as in the first quarter of the year, you will have to spend $183 in the month of June.
What is a function? What is equation modelling? What is a mathematical equation and expression?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the functionEquation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given is that your average monthly expenditure for gasoline during the first quarter was $167.70. You spent $147.20 in April and $172.90 in May.
Assume that you can spend $x in the month of June. So, we can write -
(147.2 + 172.9 + x)/3 = 167.7
147.2 + 172.9 + x =503.1
x = 183
Therefore, you can spend $183 in the month of June to have the same average.
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(PLEASE HELP)
Consider circle O with diameter GB. Line AD is tangent to circle O at point A and line DB is tangent to circle O at point B. The measure of ∠GBA is 38°. Chord GC bisects ∠G. Determine each measure
The angles GBD, GBD and G measures 90 , 90, 52 degree respectively.
GB is the diameter given.
AD is the tangent given.
The tangent makes 90 degree angle with diameter.
hence the angle GBD will be : 90°
Similarly, GBA will also be 90°
The angle GBA is given as 38°
Hence the angle G will be = 90 - 38 =52
All points in a plane that are at a specific distance from a specific point, the centre, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant. The radius of a circle is the separation between any point on the circle and its centre.
The radius must typically be a positive integer. A degenerate situation is a circle with radius equal to zero (one point). Except when otherwise specified, this article discusses circles in Euclidean geometry, namely the Euclidean plane.
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A line crosses through the points (0, 1) and (-4, -1). What is the equation of the line in slope-intercept form? HURRY I NEED HELP
The equation of the line in slope-intercept form is y = 0.5x + 1
How to determine the equation of the line in slope-intercept form?From the question, we have the following parameters that can be used in our computation:
Points = (0, 1) and (-4, -1)
A linear equation is represented as
y = mx + c
Where
c = y when x = 0
m = slope
This means that
c = 1
So, we have the following representation
y = mx + 1
At (-4, -1), we have
-1 = -4m + 1
This gives
-4m = -2
Divide by -4
m = 0.5
So, we have
y = 0.5x + 1
Hence, the equation is y = 0.5x + 1
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Use Green's Theorem to calculate the circulation of G around the curve, oriented counterclockwise. G = 7yi + xyj around the circle of radius 6 centered at the origin. Close int C G. dr= [ ]
The circle's perimeter is determined by F = -9π, according to green's theorem.
What is Green's theorem?The simple formula for Green's theorem is the link between the total amount of microscopic circulation inside curve C and the macroscopic circulation revolving around it.
Remembering that we are talking about two dimensions, if C is a straightforward closed curve in the plane, it will enclose the region D (shown in red) in the plane.
So, knowing that this exercise should be solved using Green's theorem, then:
[tex]\begin{aligned}& \int 4 y d x+2 x y d y=\iint(d / d x)(2 x y)-(d / d y)(4 y) d A \\& =\iint 2 y-4 d A\end{aligned}[/tex]
You must convert in this manner to polar coordinates, and the result will be:
[tex]\begin{aligned}& \int_0^3 \int_0^{2 \pi}(2 r \sin (\theta)-4)(r) d \theta d r \\& =\int_0^3(-2 r \cos (\theta)-4 \theta)(-2 r \pi) d r \\& =-(\pi)\left(r^2\right)=-9 \pi\end{aligned}[/tex]
Therefore, the circle's perimeter is determined by F = -9π, according to green's theorem.
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Correct question;
Suppose F⃗ (x,y)=4yi⃗ +2xyj⃗ . Use Green's Theorem to calculate the circulation of F⃗ around the perimeter of a circle C of radius 3 centered at the origin and oriented counter-clockwise.
