Rooney drew a different line on the same coordinate plane that does not have a common point with the original line.
3. Draw a line on the same coordinate plane that does not have a common point with the original line. Write an equation of the new different line you drew.
Answers
The equation of the parallel line to the given line is, [tex]y=-\frac{2}{3}x+4[/tex].
What is coordinate plane?
The intersection of two number lines creates a two-dimensional plane known as a coordinate plane. The x-axis, a horizontal number line, and the y-axis, a vertical number line, are two examples of these number lines.
Let the equation of line is given.
We have to draw a new line which does not have a common point with the given line.
Since, if the lines does not have a common point then the lines are parallel.
So, we have to find the equation of parallel line to the given line.
First to find the equation of given line.
The line passes through the points (0, 2) and (3, 0).
So,
[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{0-2}{3-0} = -\frac{2}{3}[/tex]
Now consider, the point slope form of the line.
[tex]y-y_1=m(x-x_1)[/tex]
Plug [tex]m = -\frac{2}{3} , (x_1, y_1) = (0, 2)[/tex]
⇒
[tex]y-2=-\frac{2}{3}(x-0)\\ y=-\frac{2}{3}+2[/tex]
Hence, the equation of given line is [tex]y=-\frac{2}{3}+2[/tex].
Now to find the equation of parallel line.
Since, the slope of the parallel lines is same.
Suppose the parallel line passes through the point (0, 4) and (5, 0).
Consider, the point slope form
[tex]y-y_1=m(x-x_1)[/tex]
Plug [tex]m =- \frac{2}{3} , (x_1, y_1) = (0, 4)[/tex]
⇒
[tex]y-4=-\frac{2}{3}(x-0)\\ y=-\frac{2}{3}x+4[/tex]
Hence, equation of the parallel line to the given line is, [tex]y=-\frac{2}{3}x+4[/tex].
The graph of the both parallel lines is attached below.
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Related Questions
In kite wxyz , m∠zwy=43° and m∠xyw=12° . what is m∠wxy ? enter your answer in the box. m∠wxy = °
Answers
In kite wxyz where m∠zwy=43° and m∠xyw=12°, m∠wxy = 125°
Therefore the answer is 125.
A kite is a quadrilateral with pair of two adjacent equal sides. In the given kite wxyz, adjacent sides wx = wz and zy = xy
Here, from the figure it is evident that Δwyz is congruent to Δwyx as wx = wz, xy = zy and wy as common side by SSS congruent criteria. Thus
m∠xwy = m∠zwy = 43°
Now considering Δxwy, m∠xwy + m∠xyw + m∠wxy = 180° by angle sum property of triangle. Angle sum property of triangle states that the sum of interior angles of a triangle is 180°. Therefore,
m∠wxy = 180° - m∠xwy - m∠xyw
= 180° - 43° - 12°
= 125°
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5 divided by 4.75 i need help
Answers
Answer:
1.05
Step-by-step explanation:
5/4.75
1 1/20
You want to take out a loan for a car. Initially you are presented with a 4-year loan that has a $350 monthly payment. Another bank presents you with a 5-year loan that has the same interest rate as the 4-year loan
a. How would the monthly payment of the new 5-year loan compare to the monthly payment of the 4 year loan?
b. How would the total interest paid of the new 5-year loan compare to the total interest paid of the 4 year loan?
Answers
Answer:
i think its b
Step-by-step explanation:
4. Which of the following expressions has a
leading coefficient of -2
a. -2x^2+4x-8x^3
b. X-2
c. 3x^-2+6x+1
d. -2x^4+3x-10
e. -2x-3x^2
Answers
Answer:
Step-by-step explanation:
d
of the guests at a charity fundraiser, 180 own both a house in the hamptons and a house in palm beach. if not every guest at the fundraiser owns a house in either the hamptons or palm beach, what is the ratio of the number of people who own a house in palm beach but not in the hamptons to the number of people who own a house in the hamptons but not in palm beach? (1) one-half of the guests own a house in palm beach. (2) two-thirds of the guests own a house in the hamptons.
Answers
"NOT EVERYONE who attended ratio the fundraiser owned a home in the Hamptons or Palm Beach."
What is statement type questions?
In research, a statement of the problem is used as a claim that outlines the problem addressed by a study. The problem statement answers the question briefly: What is the problem that the research will address? What are the objectives of a problem statement?
Consider the following diagram in the attachment (12) for both statement
H = the number of people who owned a home in the Hamptons but did not own a home in Palm Beach.
P = the number of people who owned a home in Palm Beach but did not own a home in the Hamptons.
N = the number of people who did not own a home in Palm Beach or the Hamptons.
Union = H+P+180 Universal = H+P+180 + N P/H =??
Statement 1: (P+180) / (H + P + 180 + N) = 1/2 Inadequate
Statement 2: (H+180) / (H + P + 180 + N) = 2/3 Inadequate
1 and 2 statements
Solve for H and P to find P/H; however, N cannot be eliminated.
This is insufficient.
We should find the ratio of red boxes, however with the information provided, this is impossible.
"NOT EVERYONE who attended the fundraiser owned a house in the Hamptons or Palm Beach.".
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What is life? Ok answer me that I'm okay just answer the question
Answers
The required life is any living thing that has the property to be born, grow and end of the life cycle is life.
What are living beings?Any object that has characteristics of life is called living a being.
Here,
Life can be defined as the ability for growth, response to encouragements, metabolism, energy vitality and reproduction are characteristics that set life apart from matter that lacks biological activities, such as signaling and self-sustaining processes.
Thus, the required life is any living thing that has the property to be born, grow and end the life cycle is life.
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3y= -6x+1. Find the value of y.
Answers
[tex]3y= -6x+1[/tex] for y
Divide both sides by 3:
[tex]\dfrac{3y}{3} =\dfrac{-6x+1}{3}[/tex]
[tex]\fbox{y = $-2x+\dfrac{1}{3} $}[/tex]
What is the average rate of change for the function over the interval [-6,-4]
Answers
Answer:20
Step-by-step explanation:
What is the range of f(x) = -3x + 7 for the domain {-8, -6, -3, -2, 2}?
Answers
Answer:
10
Step-by-step explanation:
Population size:5
Lowest value: -8
Highest value: 2
Oscar drove 3 hours in 105 miles. How many miles did he drive per minute?
Answers
Answer:
35
Step-by-step explanation:
1.divide the miles that Oscar drove to get 105÷3=35
Find the area of sector FIJ. Round to
the nearest tenth.
Answers
The area of sector FIJ is 233.4cm².
What is the area of the sector?
The quantity of space included within the sector's perimeter is referred to as the sector's area in a circle. A sector always starts at the circle's center. The area of a circle encompassed between its two radii and the arc next to them is known as the sector of a circle.
Here, we have
Given: FI = 13cm and angle = 160°
The area of a sector is given as
= (θ/360)×π×r²
= (160/360)×π×13²
= 0.44×3.14×13²
= 233.4cm²
Hence, the area of sector FIJ is 233.4cm².
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Please help! Multiple GEO post
Answers
The exterior angle y of the triangle is 60 degrees.
How to find the angle of a triangle?The sum of angles in a triangle is 180 degrees. The external angle y of the triangle can be found using exterior angle theorem.
Therefore, the exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
Hence, using the exterior angle theorem,
y = 35 + 25
y = 60 degrees.
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PLEASE HELP!
P(x)=x^3 - 4x^2 - 1
Where P is in hundreds of dollars and x is the number of years elapsed since the start up year
Answers
Answer:
Yes, the company will break even at some point in time
Step-by-step explanation:
I am not sure what methodology your teacher has been using. I am going to provide a simple methodology
The polynomial function for profit is[tex]p(x) = x^3 - 4x^2 - 1[/tex]If [tex]p(x)[/tex]has at least one zero then that means it will intersect the x-axis and the company will break even(Revenue = Costs)
The zeros of [tex]p(x)[/tex] are the values of x where [tex]p(x) = 0[/tex]
So if we can find out if [tex]p(x)[/tex] ever crosses the x-axis then that would indicate that the company will break-even at some value of [tex]x[/tex] years. If not, the company will never break even.
There is a rule to determine how many zeros a polynomial will have or in other words how many times it crosses the x-axis. This is known as Descartes' Rule of Signs.
Briefly the rule states that the number of zeros can be determined by the number of sign changes in the polynomial for consecutive termsp(x) can be re-written as:
+x³ - 4x² - 1If we look at the signs we see + - -Therefore there is one sign change from + to -This means p(x) will have one zero
Therefore the company will break-even at some point
Other Notes
You can also solve for the roots of the polynomial and see how many real roots are there. In this case there is one real root at [tex]x\approx \:4.0606[/tex]. But that is a lot of workAnother way to approach this problem is to simply graph the function and see if it crosses the x axis. I have provided the graph of this function and you can see that it does cross the x-axis at [tex]x = 4.06[/tex]I hope that helps you
20 POINTS!
Given the equations 2x-3y=-6 and x+3y+-12, solve for x and y by substitution, elimination, and graphing.
Answers
The solution of the set of equation 2x-3y=-6 and x+3y+-12 is (-6,-2).
What is Substitution, Elimination and Graphing methord of solving Equation?By Substitution Method:
1. Resolve ONE of the x or y equations. If one of the equations has previously been solved for x or y, this step can be avoided.
2. Substitute the outcome for that variable in the other equation.
3. Either all x terms or all y terms will now make up the new equation. Fix the variable's place in the equation.
4. To obtain the alternative answer, plug the solution back into the beginning equation (the one you used to solve for x or y).
When using the Elimination method,
start by aligning the x- and y-coordinates on the same side of the equation.
2. Whichever you decide to remove, find a common multiple for the Xs OR the Ys.
3. To enable the addition of the equations, make one of those multiples negative.
4. One of the variables will be removed when the equations are combined. Give the variable that is still present its final solution.
5. To determine the other number, enter your response from step four into either of the equations.
Graphing a solution:
1. Rewrite the initial y equation in the form y = mx + b a. Step 2 can be immediately followed if the line has previously been solved for y.
2. Draw a line to represent the first equation.
3. Apply the second equation to steps 1 and 2 as before.
4. The intersection of the two lines represents the system's solution. There are infinitely many solutions if the lines match. There are no solutions if the lines are parallel and do not intersect.
Substitution methord,
The equations are
2x -3y = -6
⇒ x = 3/2y - 3.
Putting this value in the second equation we get,
(3/2)y - 3 + 3y = -12
⇒(9/2)y = -9
⇒y = -2.
Therefore,
x = (3/2)y - 3 = (3/2)(-2) - 3 = -6
x = -6, y = -2.
By Elimination Methord ,
2x- 3y = -6
x + 3y =-12
simply adding both equation we get,
3x = -18
x = -6.
and y = -2
For graphical methord plot both lines in the graph then find the point where they intersect it will be (-6,-2).
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how to simpify 2,400/100
Answers
Answer:
24/1
Step-by-step explanation:
[tex] \frac{2400}{ \\ 100} [/tex]
and u get 24/1
When it comes to creditors and
debtors, which of the following
occurs?
A. Creditors and debtors receive loans from
consumers as capital.
B. Every debtor is guaranteed a loan.
C. Debtors receive loans as capital from creditors.
D. All creditors have the same interest rates for
debtors.
Answers
The only true given statement about debtors and creditors is; C. Debtors receive loans as capital from creditors.
How to identify creditors and debtors?Debtors are defined as the party from whom we have to receive the payment in the form of cash or any negotiable instrument.This means an asset for the firm.
Meanwhile, the creditors are defined as the party to which we will pay in the future agreed date in the form of cash or any negotiable instrument. This means liability for a firm.
A) This is not true because creditors don't receive loans from consumers as capital. This is the role of debtors.
B) This is not correct because it is not true that every debtor is guaranteed a loan.
C) This is true as defined earlier on the role of debtors and creditors.
D) This is not true because different creditors have different lending rates as the case may be.
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1. Square the binomial (p + q). What is the result?
Op²+q²
Op²+2pq+q²
Op² + pq+q²
2p+2q
Answers
Answer: p²+2pq+q²
Step-by-step explanation:
squaring a binomial works like this:
(p+q)² = (p+q)(p+q)
try the FOIL method: multiply the first, outside, inside, and last numbers/variables to distribute properly
F: (p)(p) = p²
O: (p)(q) = pq
I: (q)(p) = pq
L: (q)(q) = q²
then add them all together
q²+pq+pq+q²
and combine like (identical) terms
q²+2pq+q²
it's 2pq because they're being added, not multiplied.
hope this helps!
scientific notation is used to keep track of very small and vary large numbers during mathematical calculations. truefalse
Answers
It is true that very small and very large and small numbers can be expressed in terms of scientific notation.
What is Scientific Notation ?Scientific notation is a method of expressing numbers in terms of a decimal number between 1 and 10, but not 10 itself multiplied by a power of 10.
The general for of scientific notation is
In scientific notation, all numbers are written in the general form as
N × [tex]10^{m}[/tex]
N times ten raised to the power of m, where the exponent m is an integer, and the coefficient N is any real number. The integer m is called the order of magnitude and the real number N is called the significand.
The digit term in the scientific notation indicates the number of significant figures in the number. The exponential term only places the decimal point. As an example,
4660000 = 4.66 x 106
This number only has 3 significant figures. The zeros are not important, they are just placeholders. As another example,
0.00053 = 5.3 x 10-4
This number has 2 significant figures. The zeros are only placeholders.
Scientific Notation Rules:
While writing the numbers in the scientific notation we have to follow certain rules they are as follows:
The scientific notations are written in two parts one is the just the digits, with the decimal point placed after the first digit, followed by multiplication with 10 to a power number of decimal point that puts the decimal point where it should be.
If the given number is greater than 1 and multiples of 10 then the decimal point has to move to the left, and the power of 10 will be positive
Example: Scientific notation for 8000 will be 8 × 103.
If the given number is smaller than 1 means in the form of decimal numbers, then the decimal point has to move to the right, and the power of 10 will be negative.
Example: Scientific notation for 0.008 will be 8 × 0.001 or 8 × 10-3.
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Kyra walks 4m East, 2 meters South, 4 meters West, and finally 2 meters North.
Answers
Answer:
I think she is forming a letter but not so sure. I don't understand your question. Sorry
7
a-4
a - 4
||
|
14
6
Are these 2 equivalent.
Answers
The equations a + 4 = 14 and a = 6 - 4 are not equivalent.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
From the information, a - 4 = 14
Therefore a = 14 + 4
a = 18.
a + 4 = 6
a = 6 - 4.
a = 2
They are not equivalent.
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a - 4 = 14
a + 4 = 6
Are these 2 equivalent.
Your team wins 66 of 82 games. Is this proportional to 99 wins in 125 games?
Answers
If you think about this, we can figure out that 66 is 2/3 of 99. To find out what 2/3 of 125 is, we can divide 125 by 3.
So, no. This is not proportional.
If one amount is proportional to another, the two amounts increase and decrease at the same rate so there is always the same relationship between them.
The formula for a proportional equation is y = kx. The letters y and x are the variables in the equation. The letter k represents the constant of proportionality, which remains the same.
What is a proportional relationship example?
Now, we're going to consider an example of proportional relationship in our everyday life: When we put gas in our car, there is a relationship between the number of gallons of fuel that we put in the tank and the amount of money we will have to pay. In other words, the more gas we put in, the more money we'll pay.
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what is the slope of 0,70 and 20,80
Answers
Answer:
What is the slope of 0,70 and 20,80
Step-by-step explanation:
What is the slope of 0,70 and 20,80
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Usually Cassandra tap dances 1 7/8 hours a day. Today she reduced this time by half. For how long did she tap dance today?
Answers
Answer: 15/16 hour
Step-by-step explanation:
Please match the formula and definition with the correct word. = W/t = F/d = (v₂-V₁)/t = m/v = d/t = ma 1. Speed 2. Acceleration 3. Force 4. Work 5. Power 6. Density plsss fast
Answers
Matching the formulas and their respective definitions are;
W/t = Power
F/d = Work
(v₂-V₁)/t = Acceleration
m/v = Density
d/t = Speed
ma = Force
How to identify mathematical formulas?A) W/t
This means work done divided by the time taken. This results in an expression called Power.
B) F/d
This means force divided by the distance. This results in an expression called Work.
C) (v₂-V₁)/t
This means change in velocity divided by time. This results in an expression known as acceleration.
D) m/v
This means mass divided by volume. This results in an expression known as density.
E) d/t
This means distance divided by time and this results in an expression called "speed"
F) ma
This means mass multiplied by the acceleration and this results in an expression called Force.
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Please help me. I don't want to get the answer wrong
Answers
Answer:
photo?
Step-by-step explanation:
n divided by 6 equals 42 please explain
Answers
The value of n when is divided by 6 and it gives 42 is 252
What is division?Division is the opposite of multiplication. If 3 groups of 4 make 12 in multiplication, 12 divided into 3 equal groups give 4 in each group in division and 12 divided by 4 gives 3 in each group. This means that 3 and 4 are factors of 12
When dividing a number by another number that is not it's factor, there will be remainder for example 12 divided by 5 . It will give 2 remainder 2. This is because 5 is not a factor of 12.
Similarly, n divided by 6 to give 42. This means that 42 and 6 are factors of n
Therefore to find n we multiply 42 and 6.
n = 42×6
n = 252
therefore the value of n is 252
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Determine whether AB¯¯¯¯¯¯¯¯ A B ¯ is congruent to CD¯¯¯¯¯¯¯¯ C D ¯ . Justify your answer. A(1, 5) A ( 1 , 5 ) , B(6, 1) B ( 6 , 1 ) C(−2, 8) C ( − 2 , 8 ) , D(−6, 3) D ( − 6 , 3 ) Which of the following best solves the problem? Show Hints
Answers
AB is congruent to CD.AB = CD =[tex]\sqrt{14} units[/tex] (proved)
What is the distance formula of coordinate geometry?In coordinate geometry, we use the distance formula to find the distance between two coordinates in a straight line. It represented D.
Let's consider two points on a coordinate plane given as A and B (x₂, y₂).
D = [tex]\sqrt{(x2 -x 1)^2 + (y2 - y1)^2}[/tex]
Given:
The coordinates of the given quadrilateral are,
A(1, 5), B(6, 1), C(−2, 8), D(−6, 3).
According to the question we need to determine AB = CD.
By using the distance formula of coordinate geometry.
[tex]\sqrt{(x2 -x 1)^2 + (y2 - y1)^2}[/tex]
Distance between A and B,
[tex]AB =\sqrt{(6 - 1)^2 + (5-1)^2 } \\AB = \sqrt{5^2 + 4^2} \\AB = \sqrt{25 + 16} \\AB = \sqrt{41} units[/tex] .......(1)
Distance between C and D,
[tex]CD =\sqrt{(-6 -(-2))^2 + (3-8)^2 } \\CD = \sqrt{(-4)^2 + (-5)^2} \\CD = \sqrt{16 + 25} \\CD = \sqrt{41} units[/tex].......(2)
From equation (1) and (2) we find that
AB = CD =[tex]\sqrt{14} units[/tex]
Hence, AB is congruent to CD.AB = CD =[tex]\sqrt{14} units[/tex] (proved).
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Write an expression to represent the perimeter of the figure below.
Answers
There are two ways to write the expression: one simplified, one in full form
Since there are 2 pairs of equal sides, that means each side has a double.
First way (simplified): 2(x+4) + 2(2x-8)
Second way (full form): 6x-8
Hope this helped :)
Given ab, and c is not parallel to a or b, which statements
must be true?
Select each correct answer.
O
□m/4=m/8
m/8=m/9
m/2=m/7
m/7=m/10
a
C
1/2
3/4
5/6
7/8
9/10
11/12
Answers
Proportions
Lily planted 8 zucchini plants and got 50
zucchinis. Next year she intends on planting
20 zucchini plants. How big will her harvest
be?
29
A 125
B 145
C 75
D 95
Answers
Answer:
a) 125
Step-by-step explanation:
[tex]\frac{8}{50}[/tex] = [tex]\frac{20}{x}[/tex] Cross multiply and solve for x
8x = 1000 Divide both sides by 8
[tex]\frac{8x}{8}[/tex] = [tex]\frac{1000}{8}[/tex]
x = 125
