The eccentricity for r=5/2+1sin theta and the equation of the directrix of r=26. 4/4+4. 4 cos theta is 0.5 and x=6
To find the eccentricity of the polar equation r = 5/2 + 1sin(θ), we first need to convert it to rectangular form:
r = 5/2 + 1sin(θ)
r = 5/2 + 1y/r
r^2 = (5/2)r + y
x^2 + y^2 = (5/2)r + y
x^2 + y^2 = (5/2)√(x^2 + y^2) + y
x^2 - (5/2)√(x^2 + y^2) + y^2 = 0
We can see that this is the equation of a conic section, specifically an ellipse, since the signs of the x^2 and y^2 terms are the same. The standard form of an ellipse centered at the origin is:
x^2/a^2 + y^2/b^2 = 1
Comparing this to our equation, we can see that a^2 = (5/2) and b^2 = 1. The eccentricity of an ellipse is given by:
e = √(1 - b^2/a^2)
Plugging in our values, we get:
e = √(1 - 1/(5/2))
e = √(3/5)
e ≈ 0.5
Therefore, the answer is (A) 0.5.
To find the equation of the directrix for the polar equation r = 26.4/4 + 4.4cos(θ), we first need to convert it to rectangular form:
r = 26.4/4 + 4.4cos(θ)
r = 6.6 + 4.4x/r
r^2 = 6.6r + 4.4x
x = (r^2 - 6.6r)/4.4
We can see that this is the equation of a parabola, since the highest degree of the variable r is 2. The standard form of a parabola with its focus at (0, p) is:
y = (1/4p)x^2
Comparing this to our equation, we can see that p = -6.6/4 = -1.65. The directrix of a parabola is a line perpendicular to the axis of symmetry and located at a distance of |p| from the focus. Since the axis of symmetry is the x-axis, the equation of the directrix is:
y = 1.65
However, since the question asks for the equation of the directrix in terms of x, we can rewrite this as:
x = 0
Therefore, the answer is (C) x = 6.
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assuming the difference shown in the table remains constant over a 40 year career, approximately how much more does a man with a bachelors degree earn more than a man with a highschool education
high school degree, associates degree, bachelors degree, professional degree
women: $21,113 hs, $39,286 associates, $49,108 bachelor
$80,718 professional
men $40,447 hs, $ 50,928 associates, $ 66,196 bachelors
$119,474 professional
Assuming the difference shown in the table remains constant over a 40 year career difference approximately how much less does a women with a bachelors degree earn than a women with a professional degree?
As a percentage how much more does a man with a bachelors degree earn than a women with a bachelors degree? Assuming that the difference remains the same over a 40 year career, how. much more does the man earn than the women?
1. A man with a bachelοr's degree earns apprοximately $25,749 mοre per year than a man with a high schοοl educatiοn.
2. A wοman with a prοfessiοnal degree earns apprοximately $31,610 mοre per year than a wοman with a bachelοr's degree.
3. A man with a bachelοr's degree earns apprοximately 34.8% mοre than a wοman with a bachelοr's degree.
What is Percentage?Percentage can be calculated by dividing the value by the tοtal value, and then multiplying the result by 100. Percentage is a number οr ratiο expressed as a fractiοn οf 100. It is οften denοted using the percent sign, "%".
Bachelοr's degree: $66,196
High schοοl educatiοn: $40,447
Difference: $25,749
Therefοre, a man with a bachelοr's degree earns apprοximately $25,749 mοre per year than a man with a high schοοl educatiοn.
Prοfessiοnal degree: $80,718
Bachelοr's degree: $49,108
Difference: $31,610
Therefοre, a wοman with a prοfessiοnal degree earns apprοximately $31,610 mοre per year than a wοman with a bachelοr's degree.
Difference in average earnings fοr men and wοmen with a bachelοr's degree: $66,196 - $49,108 = $17,088
Average earnings fοr wοmen with a bachelοr's degree: $49,108
Percentage difference: ($17,088 / $49,108) x 100 = 34.8%
Therefοre, a man with a bachelοr's degree earns apprοximately 34.8% mοre than a wοman with a bachelοr's degree. Over a 40-year career, this translates tο a difference οf apprοximately $683,520 in earnings ($17,088 x 40).
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Find the slope of the line that contains the points (10, 0) and (-20, -18)
The slope of the line that contains the points (10, 0) and (-20, -18) is: slope = (change in y)/(change in x) = 3/5.
The slope of a line is the measure of its steepness, and it's found by dividing the change in the y-coordinates by the change in the x-coordinates between two points on the line. In this case, the slope of the line that passes through the points (10, 0) and (-20, -18) can be calculated as follows:
slope = (change in y-coordinates) / (change in x-coordinates)
slope = (-18 - 0) / (-20 - 10)
slope = -18 / -30
slope = 3/5
Therefore, the slope of the line is 3/5.
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The computer lab at school has a new computer system. The system had a total cost of $1895. There is a special printer that can be added to the system. The printer can be purchased separately for $649. Writ an equation and solve to determine the cost of the system with the printer.
Consider the difference below.
x-3/x^2-x-5 - 5/8x
Place the steps require to simplify the given difference of two expressions into one, simplified rational expression in the correct order.
Answer:
x=3/8
Step-by-step explanation:
^2×5×3÷5/8=×3/8
Write an equation of the line that passes through the points. 13. (2,5), (0,5) 14. (-3,0), (0,0) 15. (0,-2), (4,-2)
The line that goes through the points (0, -2) and (4, -2) can be represented by the equation y = (-1/2)x - 2.
Since both points have the same y-coordinate of 5, the line must be a horizontal line passing through y = 5. Therefore, the equation of the line is y = 5.
Since both points have the same y-coordinate of 0, the line must also be a horizontal line passing through y = 0. Therefore, the equation of the line is y = 0.
The slope of the line passing through the two points can be found using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Substituting the given values, we get:
m = (-2 - 0) / (4 - 0) = -1/2
Using the point-slope form of the equation of a line, we can write the equation of the line as:
y - y₁ = m(x - x₁)
Substituting one of the given points, such as (0, -2), we get:
y - (-2) = (-1/2)(x - 0)
Simplifying, we get:
y + 2 = (-1/2)x
Therefore, the equation of the line passing through the points (0, -2) and (4, -2) is y = (-1/2)x - 2.
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What are the domain and range for the function f(x)=2x?
The domain and range for the function f(x) = 2x include the following:
Domain = (-∞, ∞).
Range = (-∞, ∞).
What is a domain?In Mathematics, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-∞, ∞} or {x|x ∈ R}.
Range = {-∞, ∞} or {y|y ∈ R}.
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You and a friend play a game where you each toss a balanced coin. If the upper faces on the coins are both tails, you win $1; if the faces are both heads, you win $2; if one shows a head and the other a tail, you lose $1.a) Give the probability distribution for X=your winnings on a single play of this game.b) What are your expected winnings?c) Suppose you change the rules so that if both coins are heads you win $100; if both coins are tails you win $5; if the coins do not match, you lose $52. What are your expected winnings?d) Find Var(X) for both games.e) Which game would you rather play? (Use the variance to help make this decision).
According to the probability distribution, you should rather play the second game than the first one.
a) The probability distribution for your winnings on a single play of this game is given by:
P(X=1) = 1/4
P(X=2) = 1/4
P(X=-1) = 1/2
b) Your expected winnings in this game is 0, since the expected value of X = 1*(1/4) + 2*(1/4) - 1*(1/2) = 0.
c) The probability distribution for your winnings in this game is given by:
P(X=100) = 1/4
P(X=5) = 1/4
P(X=-52) = 1/2
d) Your expected winnings in this game is 22, since the expected value of X = 100*(1/4) + 5*(1/4) - 52*(1/2) = 22.
e) The variance of X for the first game is
Var(X) = (1-0)2*(1/4) + (2-0)2*(1/4) + (-1-0)2*(1/2) = 0.75.
The variance of X for the second game is Var(X) = (100-22)2*(1/4) + (5-22)2*(1/4) + (-52-22)2*(1/2) = 1344.5.
You would rather play the second game, since its variance is much larger, which means there is a greater potential for large gains.
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PLEASE SHOW WORK!!!!!!!!!
1) The equal expressions are I and III
2) The value of the expression is 3 41/80
What is an absolute value expression?An absolute value expression is a mathematical expression that represents the distance of a number from zero, regardless of the sign of the number. The absolute value of a number is always positive, so an absolute value expression represents a positive number or zero.
The absolute value of a number x is denoted by |x| and is defined as follows:
|x| = x, if x is positive or zero
|x| = -x, if x is negative
Since -/x/ = -x then this are the equal expressions.
[tex]a^2/a + 1 + a + 1/a^2[/tex]
Then;
[tex]4^2/4 + 1 + 4 +1/4^2[/tex]
16/5 + 5/16
= 3 41/80
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melanie spent half of her allowance going to the movies. Then, she washed the family car and warned $10. what is her weekly allowance is she ended up with $22.50.
The weekly allowance of Melanie that she ended up is $65 by solving the equation formed according to the question.
What is an equation?An equation is a mathematical statement that shows that two expressions are equal. It typically contains one or more variables and can be written using mathematical symbols such as addition, subtraction, multiplication, division, and exponentiation. An equation can also contain mathematical functions, constants, and other mathematical operations.
What are mathematical functions?In mathematics, a function is a rule that assigns each element in one set, called the domain, to a unique element in another set, called the range or codomain. In other words, a function is a relation between two sets where each element in the domain is mapped to a unique element in the range.
Let's assume that Melanie's weekly allowance is "x".
According to the problem, Melanie spent half of her allowance going to the movies. So, she spent (1/2)x dollars at the movies.
Then, she earned $10 by washing the family car.
Therefore, her total spending is (1/2)x + $10.
Since she ended up with $22.50, we can set up an equation:
x - [(1/2)x + $10] = $22.50
Simplifying this equation, we get:
(1/2)x = $32.50
Multiplying both sides by 2, we get:
x = $65
Therefore, Melanie's weekly allowance is $65.
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Please I need help with quiz corrections should be easy if you are good at geometry!!
A right triangle, also known as a right-angled triangle, is a triangle that has one angle measuring 90 degrees.
What is a right angle triangle?Right triangles have some unique properties that make them useful in various applications, such as in geometry and trigonometry. For example, the Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
We know that;
Tan 45 = 14/x
x = 14
Sin 45 = 14/y
y = 20
Again;
Tan 60 = 16√3/x
x = 16√3 * 1/√3
x = 16
Sin 60 = 16√3/y
y = 16√3 ^ 2/√3
y = 32
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the population of a community is known to increase at a rate proportional to the number of people present at time t. if an initial population p0 has doubled in 4 years, how long will it take to triple? (round your answer to one decimal place.) 4.8 incorrect: your answer is incorrect. yr how long will it take to quadruple? (round your answer to one decimal place.)
The population will take around 6.9 years to triple and 9.2 years to quadruple.
Let P(t) be the population at time t. According to the problem, the rate of increase of the population is proportional to the population itself, which means: dP/dt = kP
where k is the proportionality constant. This is a separable differential equation that can be solved by separating the variables and integrating both sides:
∫ dP/P = ∫ k dt
ln|P| = kt + C
where C is the constant of integration. Applying the initial condition that the population doubles in 4 years, we get:
ln|2p0| = k(4) + C
ln|p0| + ln|2| = 4k + C
ln|p0| + ln|2| - 4k = C
Substituting C into the previous equation and using it for the new population level, we get:
ln|3p0| = kt + ln|p0| + ln|2| - 4k
ln|3p0|/|p0| = kt - 4k + ln|2|
ln|3/2| = (k/ln2)t - 4k/ln2
ln|3/2|/(k/ln2) = t - 4/ln2
t = ln|3/2|/(k/ln2) + 4/ln2
Therefore, it will take approximately 6.9 years for the population to triple and 9.2 years to quadruple.
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Express sin A as a fraction in simplest terms.
Answer:
7/25
Step-by-step explanation:
Sin = [tex]\frac{opposite}{Hypotenuse}[/tex]
Hypotenuse = 50
Adjacent = 48
Pythagorean Theorem: a² + b² = c²
48² + b² = 50²
2304 + b² = 2500
b² = 196
b = 14
Opposite = 14
Sin A = 14/50 = 7/25
cory and quentin went bowling on friday night corey has his own bowling shoes but quentin had to rent his at the alley shoes rent for a flat fee of $4 plus $2 per hour the equation y=2x+4 describes the cost of renting the shoes if quentin only had $11 how many hours can he rent the bowling shoes.
Therefore , the solution of the given problem of equation comes out to be he can hire the shoes for three hours with his meagre $11 budget.
Equation : What is it?Complex algorithms frequently employ a variable term to guarantee congruence with the two opposing assertions. Equations, which are academic expressions, are used to demonstrate the equality of different academic figures. In this instance, the normalise method provides b + 6 rather than merely expression separating 12 into two pieces for using the data from y + 6.
Here,
To begin, we can construct an expression to symbolise the circumstance:
=> y = 2x + 4
where x represents the number of hours that Quentin rents the shoes for and y represents the overall cost of the rental.
We can put y equal to 11 because we know that Quentin only has $11 to spend:
=> 11 = 2x + 4
We can now determine x:
=> 2x = 11 - 4
=> 2x = 7
=> x = 7/2
Quentin can therefore spend $11 to hire the shoes for 3.5 hours (7/2 hours).
He would have to pay either $10 or $12 to hire the shoes for either three or four hours. He can hire the shoes for three hours with his meagre $11 budget.
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i have to use the information given to create an equation then create a table to find points to graph the expressions.
Answer:
A) Missing Table Values. See the attached worksheet
B) The car will be worth less than $8,000 in 9.8 years
Step-by-step explanation:
Part B: Years until car is less than $8,000
The new $25,000 car depreciates by 11% each year. Expressed another way, it retains 89% of its value each year. The value, y, after x years can be calculated from:
y = ($25,000)*(0.89)^x
This function is graphed on the attached worksheet. The line intersets the $800 on the y axis at 9.8 years. The car will be worth less than $8,000 after 9.8 years.
One can also calculate the value of x:
$,8000 = ($25,000)*(0.89)^x
x = 9.77, mathematically
Part A: Table of values
See the attached worksheet. The values are not exactly a straight line, but come close to f(x) = 8x+50, from which the missing values may be calculated. Legally, however, this is a slightly more complex line, for which I'm unclear about the best approach for its derivation.
Please ASAP Help
Will mark brainlest due at 12:00
Answer:
12 units
Step-by-step explanation:
solve 6x^2+1≥5x graphically
Answer:
[tex]x \leq \frac{1}{3}[/tex] or [tex]x \geq \frac{1}{2}[/tex]
Answer:
Below
Step-by-step explanation:
From the graph below you can see that
x < = .33 3 and x >= .5
combined
.333 ≥ x ≥ .5
Help me plsssssssssssssssssssss
Answer:
157°
Step-by-step explanation:
We can see that the angle here is an alternate angle, this means it is an opposite angle that has the same value as each other.
Knowing this, we can see that if the angles are alternated the missing angle should be 157 as well.
Hope this helps have a lovely day! :)
5. Just before the presidential election in November 2016, a local newspaper conducted a poll of registered voters in a large city and found that 120 out of a random sample of 250 men intended to vote for Donald Trump and 132 out of a random sample of 240 women intended to vote for Donald Trump. (a) Is there convincing evidence that there is a difference in the proportion of all men and the proportion of all women in this city who intended to vote for Trump at the a = 0. 05 significance level? (b) Based on your conclusion in part (a), which mistake, a Type I error or a Type Il error, could you have made? Interpret this error in context
A Type I error that could have been made in this case would be concluding that there is no difference between the proportions of men and women who intended to vote for Trump when in reality there was a difference.
(a) Yes, there is convincing evidence that there is a difference in the proportion of all men and the proportion of all women in this city who intended to vote for Trump at the a = 0. 05 significance level. The p-value of this test is 0.023, which is less than the significance level of 0.05, suggesting that the difference between the proportions of men and women who intended to vote for Trump is statistically significant.
(b) If we had concluded that there was no difference in the proportions of men and women who intended to vote for Trump when there actually was a difference, we would have made a Type I error. This error refers to rejecting the null hypothesis when it is actually true. In this context, a Type I error would mean concluding that there is no difference between the proportions of men and women who intended to vote for Trump when in reality there was a difference.
This answer concludes that there is convincing evidence that there is a difference in the proportion of all men and the proportion of all women in this city who intended to vote for Trump at the a = 0.05 significance level.
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Write the following as a radical expression.
7^{\frac{7}{8}}
Answer: $\sqrt[8]{7^7}$
Step-by-step explanation:
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In a sequence of numbers, a4=12, a5=14, a6=16, a7=18, and a8=20.
Which equation can be used to find the nth term of the sequence, an?
an=2n+12
an=3n+12
an=3n
an=2n+4
The correct equation to find the nth term of the given sequence is an=2n+12, which can be demonstrated by calculating the 4th to 8th terms and verifying that they match the given values.
The formula an=2n+12 can be used to find the nth term of the sequence. This formula states that the nth term is equal to twice the value of n (2n) plus 12 (2n + 12). To demonstrate, for the 4th term of the sequence (a4), we can use the formula and calculate a4 = 2(4) + 12 = 20, which is equal to the given value of a4 = 12. Similarly, we can calculate the other values of the sequence using the same formula: a5 = 2(5) + 12 = 22 (which is equal to the given value of a5 = 14), a6 = 2(6) + 12 = 24 (which is equal to the given value of a6 = 16), a7 = 2(7) + 12 = 26 (which is equal to the given value of a7 = 18), and a8 = 2(8) + 12 = 28 (which is equal to the given value of a8 = 20). Therefore, we can conclude that an=2n+12 is the correct equation to find the nth term of the sequence.
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A person invested $ 790 in an account growing at a rate allowing the money to double
every 13 years. How much money would be in the account after 30 years, to the
nearest dollar?
Answer:
Submit Answer
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A doubling equation in exponential growth can be used to solve the question. The amount after 30 years will be $3911.22
The growth rate is governed by exponential equation. Doubling equation means to the time needed to make the initial amount double. If the number of years and doubling time given, then the doubling equation is,
P = P₀[tex](2)^{t/d}[/tex]
P is the final amount
P₀ is the initial amount
t is the time in years
d is the doubling time
P₀ = 790 t= 30 d= 13
P = 790 [tex](2)^{30/13}[/tex]
= 3911.21506157
So the amount after 30 years will be $3911.22
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There’s a spinner with 12 equal areas numbered one through 12 if the spinner is one one time what is the probability that the result is a multiple of five and a multiple of two
The probability that the result is a multiple of five and a multiple of two is 1/3, since there are only three multiples of five and two that can be produced on the spinner: 10, 6, and 2.
The spinner has 12 equal areas, numbered one through 12. The probability of getting a multiple of five and a multiple of two on one spin is 1/3, since there are only three multiples of five and two that can be produced: 10, 6, and 2. To calculate this probability, we need to look at the total number of possible outcomes and divide it by the number of outcomes that are multiples of five and a multiple of two. In this case, the total number of outcomes would be 12, and the number of outcomes that are multiples of five and a multiple of two is three (10, 6, and 2). Dividing 12 by 3 gives us the probability of 1/3.
Total number of outcomes = 12
Number of outcomes that are multiples of five and two = 3 (10, 6, and 2)
Probability = 3/12 = 1/3
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The answer to the question please
Answer:
2/9
Step-by-step explanation:
Answer:2/9
Step-by-step explanation:
The surface area of the cone is 376.8 square yards. What is the slant height of this cone ? use pie= 3.14 and round your answer to the nearest hundredth.
Answer:
14
Step-by-step explanation:
The formula is
376.8 =
work out the value of 7a - 7b
when a-b=5
Answer:
35
Step-by-step explanation:
Simplification :
7(a-b) as 7 is common
as we know a-b is 5 ,
7 * 5 = 35 in the answer.
Please mark me as the brainliest TQ!
Answer: 35
Step-by-step explanation:
7a - 7b
= 7(a-b)
= 7(5)
= 35
Find the next term in the series.
240, 332, 118, 168, 57, 86, ? ,45
Answer:
32 or 24 or 13 or 21
Step-by-step explanation:
332-240=92
168-118 = 50
86-57 = 29
45-13= 32
or
45-21= 24
Solve for x to make A||B.
B
3x
A
X =
?
7x
Enter
Answer:
x = 18
Step-by-step explanation:
the angle vertically opposite 7x is 7x
making 3x and 7x same- side interior angles summing to 180° , that is
3x + 7x = 180
10x = 180 ( divide both sides by 10 )
x = 18
for A and B to be parallel then x = 18
It’s the average distance to the ____ also measures how far is the data spread apart in the population.
*
It’s the average distance to the Mean also measures how far is the data spread apart in the population.
What is Population?
In statistics, a population refers to the entire group or set of individuals, objects, or events that share a common characteristic or feature. The population can be any size, from a small group of people to an entire country or even the whole world.
In order to make statistical inferences about a population, it is often not practical or feasible to study the entire population. Instead, researchers typically take a sample from the population, which is a smaller subset of the population, and use the sample data to make predictions or draw conclusions about the population as a whole.
The average distance to the mean (or average) also measures how far the data is spread apart in the population.
This is commonly known as the standard deviation, which is a measure of the amount of variation or dispersion in a set of data values. A larger standard deviation indicates a greater amount of variability or spread in the data, while a smaller standard deviation indicates that the data points are closer to the mean.
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The equations of four lines are given. Identify which lines are parallel.
Line 1:
y = 8x - 3
Line 2: y-6=(x-4)
Line 3:
Line 4:
y = 3x + 4
1
x - 3y = -4
O All four lines are parallel.
O Lines 3 and 4 are parallel.
O Lines 1 and 3 are parallel.
O Lines 2 and 3 are parallel.
►
For the given equations, using slope formula option B: Lines 3 and 4 are parallel, is the correct option.
What is slope?
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
The four different equations are given.
To identify parallel lines, we need to compare their slopes.
If two lines have the same slope, they are parallel.
Line 1 is in slope-intercept form (y = mx + b) where the slope is m = 8.
Line 2 is in point-slope form (y - y1 = m(x - x1)) where the slope is m = 1/8.
Line 3 is in slope-intercept form where the slope is m = 3.
Line 4 is in slope-intercept form where the slope is m = 1/3.
Comparing the slopes, we see that -
Lines 1 and 2 have different slopes, so they are not parallel.
Lines 1 and 3 have different slopes, so they are not parallel.
Lines 1 and 4 have different slopes, so they are not parallel.
Lines 2 and 3 have different slopes, so they are not parallel.
Lines 2 and 4 have different slopes, so they are not parallel.
Lines 3 and 4 have the same slope (m = 3), so they are parallel.
Therefore, lines 3 and 4 are parallel.
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Elvis chooses three DIFFERENT numbers .
- The sum of the three numbers is 24.
- one of the numbers is a square number.
The other 2 numbers are factors of 20.
FIND THE 3 NUMBERS CHOSEN BY ELVIS..
To get the answer i need the full working out and the answer
Answer: 16+4+4
Step-by-step explanation: The answer is 16, 4, and 4.
Square values in 24 are 4,9, and 16.
You can take a look at this and see that a factor of 24 is 4.
You can do 16+4+4.
Hope this helps!
-You Brainly Helper!