The pair of lines are parallel.
What is line?A line is a one-dimensional figure, which has length but no width.
Given:
lines passes through (-3, -5) and (1, 3)
and, line passes through (0, 1) and (2, 0)
equation of line
y + 5 = -1/2 (x + 3)
-2y - 10 = x + 3
x + 2y + 13 = 0
and, equation of line
y - 1 = -1/2 (x - 0)
-2y + 2 = x
x + 2y -2 = 0
m1= -1/2 and m2 = -1/2
Hence, the lines are parallel.
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Copy the figure below onto a separate sheet of paper. Find the image of the figure under reflections in line m and then line t. In the box below, describe the location of the new image of point G. Use words like above, below, left, or right of line m and t.
The image of the figure under reflections in line m and then line t is shown below.
What is a transformation of geometry?A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.
Reflection does not change the size and shape of the geometry.
The image of the figure under reflections in line m and then line t.
The reflection of the rectangle DEFG will be given in the figure.
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Jack wants to pack three different colored shirts for a trip. If he has seven colors to choose from, how many different selections of shirts can he make
In the context of probability, an experiment is a process:
First, he has to decide on a pair of shirts and he has 7 different colors to choices.
A value between 0 and 1, inclusive, describes the relative possibility (chance or likelihood) that an event will occur.
For each of those choices he has a choice of 7 different shirts, so that gives him 3 times 7 = 21 different shirts.
For each of those 21 possibilities, he has 21 times 3 = 63 different outfits, and some of them may be acceptable to wear in public.
It is simply,3*3*7=64 ways.
The number of favorable outcomes is divided by the number of possible outcomes.
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What is the missing number in this sequence: 1 , 3, ___ , 10 , 15 , 21 ?
Please explain it step-by-step
Answer:
6
Step-by-step explanation:
the sequence increases by 1,2,3,4,5,6 each time, thus it is 6
help me please im in a rush
Answer: 390 m².
Step-by-step explanation:
[tex]Surface \ area = 11*13+11*12+11*5+2*\frac{12*5}{2}=11*(13+12)+11*5+12*5=\\ =11*25+5*(11+12)=275+5*23=275+115=390\ (m^2).[/tex]
he equation represents Function A, and the graph represents Function B:
Function A
f(x) = 6x - 1
Function B
graph of line going through ordered pairs 1, 4 and negative 1, negative 2 and negative 2, negative 5
Which equation best compares the slopes of the two functions?
Slope of Function B = 2 x Slope of Function A
Slope of Function A = Slope of Function B
Slope of Function A = 2 x Slope of Function B
Slope of Function B = − Slope of Function A
The slope of function A is 2 times the slope of function B.
Slope of a functionThe slope of a function is defined as the rate of change of the function. Given the equation
F(x) = 6x - 1
The slope of the equation is 6
For the line passing through the points (4, -1) and (-1, -2) and (-2, -5) the slope is expressed as:
Slope = -5+2/-2+1
Slope =-3/-1
Slope = 3
This shows that the slope of function A is 2 times the slope of function B.
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e
7 cm
Find the value of x to 3
significant figures.
x
12 cm
8 cm
Answer:
12.0 to 3 dig digs You must include the 0 to get 3 significant figures.
Step-by-step explanation:
Comment
This is a Pythagorean Problem. Use the formula
c ^2 = a^2 + b^2
Givens
a = 8 - 7 = 1 cm
b = 12 cm
c = ?
solution
c^2 = 1^2 + 12^2
c^2 = 1 + 144
c^2 = 145 Take the square root of both sides
√c^2 = √145
c = 12.04
c = 12.0 to 3 sig digs.
Here is a prism.
Its face is made from 6 identical squares
with side length 2 cm.
Work out the volume of the prism.
Height 2cm
Width 12 cm
Answer:
The required volume of the prism is 48 cubic centimeters
Volume of a prism.The formula for calculating the volume of a prism is expressed as:
V = lwh
where l is the side length
w is the width
h is the height
Given the following
l = 2 cm.
Height 2cm
Width 12 cm
Substitute
V = 2(2)(12)
V = 48 cubic centimeters
Hence the required volume of the prism is 48 cubic centimeters
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In the figure below, ⎯⎯⎯⎯⎯⎯⎯⎯,⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯, and ⎯⎯⎯⎯⎯⎯⎯⎯⎯ are medians of △. If KC = 108 and OC = 2n+10, then n=
The question was incomplete. Below you will find the missing content.
In the figure below, BL, AM, and CK are medians of △ABC. If KC = 108 and OC = 2n + 10, then n=
The picture is attached below.
The value of n is 31.
The median is the line connecting the vertex and its midpoint on the opposite side of the triangle.
The intersection of all 3 medians of the triangle is called the centroid.
As we know centroid divides the median in the ratio of 2:1.
In the given picture,
Medians of triangle △ABC are AM, BL, and CK.
So the centroid of the triangle is O.
Given that KC= 108
As the centroid O divides the line KC in 2:1.
Let OC=2x
KO= X
As KC= KO+OC
⇒ 108= x+2x
⇒ 3x=108
⇒ x=108/3
⇒ x=36
Then OC= 2x= 2*36= 72
As given in the question OC= 2n+10
putting the value of OC in above equation
⇒ 72= 2n+10
⇒ 2n= 72-10
⇒ 2n=62
⇒ n=62/2
⇒n=31
Therefore the value of n is 31.
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The doubling period of a bacteria population is 10 minutes. At time t = 110 minutes, the bacterial population was 800.
What was the initial population at time t = 0? Round to the nearest whole number and give an un-rounded decimal.
Find the size of the bacteria population after 4 hours. Round to the nearest whole number and give an un-rounded decimal.
The initial population at time t = 0 was 0.39 while the size of the bacteria population after 4 hours was 6553600
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the bacteria population at time t. a represent the initial population at t = 0. Since the doubling period of a bacteria population is 10 minutes, hence:
[tex]y=a(2)^\frac{t}{10}[/tex]
At time t = 110 minutes, the bacterial population was 800. Hence:
[tex]800=a(2)^\frac{110}{10} \\\\a = 0.39[/tex]
At 4 hours (240 minutes):
[tex]y=0.39(2)^\frac{240}{10} =6553600[/tex]
The initial population at time t = 0 was 0.39 while the size of the bacteria population after 4 hours was 6553600
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A real estate office wants to make a survey in a certain town, which has 50,000 households, to determine how far the head of household has to commute to work. A simple random sample of 1,000 households is chosen, the occupants are interviewed, and it is found that on average, the heads of the sample households commuted 8.7 miles to work; the SD of the distances was 9.0 miles. (All distances are one-way; if someone isn't working, the commute distance is defined to be 0.)
a) The average commute distance of all 50,000 heads of households in the town is estimated as ____, and this estimate is likely to be off by ___ or so.
b) If possible, find a 90% confidence interval for the average commute distance of all heads of households in the town. If this isn't possible, explain why not.
The average commute distance of all 50,000 heads of households in the town is estimated as 8.7, and this estimate is likely to be off by 0.28 or so.
a. How to solve for the estimation and the standard deviationThe population mean = 8.7
population standard deviation = s/√n
s = 9
n = 1000
= 9/√1000
= 0.28
The conclusion is that the estimate is 8.7 and it is off by 0.28.
b. The 90 % confidence interval calculationCI = bar X ± Z∝/2(s/√n)
= 8.7±1.645(0.28)
= 8.7 ± 0. 47
Confidence interval = 8.23, 9.17
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Find the missing value.
Answer:
The correct answer is 6
Step-by-step explanation:
x/10=3/5
then cross multiply
it will now give
5x=30
x=6
A pupil scored 17/50 on a test. What percentage is this?
Answer:
34%
Step-by-step explanation:
hope I helped
have a nice day
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
If a pupil scored 17/50 on a test, then what percentage is this?
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
First let's turn 17/50 into a decimal.
[tex]\bf{17/50=0.34}[/tex]
Now move the decimal point two places to the right to convert to percentages.
[tex]\bf{34\%}[/tex] .Uh-oh, better luck next time, student!
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=34\%}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]
The average daily temperature, t, in degrees fahrenheit for a city as a function of the month of the year, m, can be modeled by the equation t = 35 cosine (startfraction pi over 6 endfraction (m 3) 55, where m = 0 represents january 1, m = 1 represents february 1, m = 2 represents march 1, and so on. which equation also models this situation?
The answer will be t = [tex]sin((m.\frac{\pi}{6})+55)[/tex] average daily temperature, t, in degrees Fahrenheit for a city as a function of the month of the year.
What is temperature?Temperature is the degree or intensity of heat present in a substance or object, especially as expressed according to a comparative scale and shown by a thermometer or perceived by touch.
TO SOLVE:[tex]35cos(\frac{\pi}{6(m+3)}+55)\\\\35 cos(\frac{\pi m}{6} + 55 + \frac{\pi}{2})\\[/tex]
suppose [tex]x = m.\frac{\pi}{6}+55[/tex] and [tex]\frac{\pi}{2} = 90[/tex] degree
We know, cos(x+90°) = - sin(X)
⇒ [tex]cos((m.\frac{\pi}{6})+55+90degree)[/tex]degree = -[tex]sin((m.\frac{\pi}{6})+55)[/tex]
⇒ t = [tex]sin((m.\frac{\pi}{6})+55)[/tex]
Hence the answer will be t = [tex]sin((m.\frac{\pi}{6})+55)[/tex] average daily temperature, t, in degrees Fahrenheit for a city as a function of the month of the year.
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A cell phone company offers two plans to its subscribers. At the time new subscribers sign up, they are asked to provide some demographic information. The mean yearly income for a sample of 40 subscribers to Plan A is $57,000 with a standard deviation of $9,200. For a sample of 30 subscribers to Plan B, the mean income is $61,000 with a standard deviation of $7,100. At the .05 significance level, is it reasonable to conclude the mean income of those selecting Plan B is larger
Yes at 0.05 significance level we can conclude that mean income of those selecting plan B is bigger.
Given mean yearly income for sample of 40 subscribers is $57000 with standard deviation of $9200, mean yearly income for sample of 30 subscribers with standard deviation of $7100.
First we have been given significance level (α) of 0.05. So (1-α)=1-0.05=0.95 and we have to find Z score for this significance level. (1+0.95)/2=0.425
Z=1.44
Now we have to calculate margin of error which will be calculated as under:
[tex]M_{A} =Z*st/\sqrt{n}[/tex]
=[tex]1.44*9200/\sqrt{40}[/tex]
=1.44*9200/6.32
=1869.10
[tex]M_{B}=Z*st/\sqrt{n}[/tex]
=[tex]1.44*7100/\sqrt{30}[/tex]
=1.44*7100/3.47=2096.2
We know that margin of error shows the difference between real and calculated values. So if we increase mean of both plans by margin of error of respective plans then mean of plan A becomes=57000+1869.10=58869.10 and mean of plan B becomes =61000+2096.2=630622.2. We can clearly notice that mean of plan B is greater.
Hence it is reasonable to say that the mean of plan B is greater at the significance level of 0.05.
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An initial population of 910 quail increases at an annual rate of 20%. Write an exponential function to model the quail population.
The exponential function to model the quail population is 910*(1.2)^t
Concept: An exponential function is a mathematical function denoted f(x)=\exp or e^{x}. Unless otherwise stated, the term generally refers to a positive function of a real variable, although it may be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras.
Given data
Initial population= 910 quail
Rate= 20%
Now using the model below:
A= P(1+r)^t
r= 0.2
A= 910(1+0.2)^t
A= 910*(1.2)^t
Hence the expression to model the population is 910*(1.2)^t
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Describe the transformations necessary to transform f(x) into g(x)
a) f(x)= √x; g(x)= √3x -1
b) f(x)=[tex]x^4[/tex]; g(x)= [tex]2(x-3)^4[/tex]
Using translation concepts, the transformations are given as follows:
a) The function is horizontally compressed by a factor of 3 and shifted down one unit.
b) The function is shifted right 3 units and vertically stretched by a factor of 2.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Item a:
The transformations are:
x -> 3x, hence the function is horizontally compressed by a factor of 3.y -> y - 1, hence the function is shifted down one unit.Item b:
The transformations are:
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Suppose a circle has a radius of 13 inches. How far would a 24 inch chord be from the center of the circle? (Hint: Draw a diagram)
PLEASE PLEASE HELPPPP
Answer:
24 Inches
Step-by-step explanation:
Its 24 Inches away from the centre lol
Answer:
Step-by-step explanation:
Directions
Draw a circleDear a chord with a length of 24 inside the circle. You just have to label it as 24Draw a radius that is perpendicular and a bisector through the chordDraw a radius that is from the center of the circle to one end of the chord.Label where the perpendicular radius to the chord intersect. Call it E.You should get something that looks like the diagram below. The only thing you have to do is put in the point E which is the midpoint of CB.Givens
AC = 13 inches Given
CB = 24 inches Given
CE = 12 inches Construction and property of a midpoint.
So what we have now is a right triangle (ACE) with the right angle at E.
What we seek is AE
Formula
AC^2 = CE^2 + AE^2
13^2 = 12^2 + AE^2
169 = 144 + AE^2 Subtract 144 from both sides.
169 - 144 = 144-144 + AE^2 Combine
25 = AE^2 Take the square root of both sides
√25 = √AE^2
5 = AE
Answer
The 24 inch chord is 5 inches from the center of the circle.
Which of the following best describes a parabola?
A.The locus points equidistant from a given line of symmetry and focus.
B.The locus of points equidistant from two given points.
C.The locus of points equidistant from a given directrix and focus.
D.The locus of points equidistant from a center.
The Parabola is a locus of points equidistant from a single point called focus and a line called Directrix. The correct option is C.
What is a Parabola?A parabola is a U-shaped figure, all the point on the parabola is equidistant from the focus, and a line called Directrix.
The Parabola is a locus of points equidistant from a single point called focus and a line called Directrix.
Therefore, The correct option is C.
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Henry buys
2 sandwiches at £1.85 each
2 Drinks at 72p each
1 bag of sweets at £1.05
Hey pays with a £10 note.
Work out how much change Henry should get.
First we have to change rupees into paise .
[Rupees = 100paise]
Sandwiches = 1.85+1.85=370paise
Drinks = 72p+72p=144paise
Sweets = 105paise
Adding the total payment:-
370+144+105=619paise
619 paise means 6.19rupess
Hence 10-6.19=3.81rupess.
factorise fully
-x-10
The factorized expression of -x - 10 is -(x + 10)
How to factorize the expression?The expression is given as:
-x - 10
Factor out -1 from the expression
-1(x + 10)
Rewrite as:
-(x + 10)
Hence, the factorized expression of -x - 10 is -(x + 10)
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Find the total cost of 2.5kg of chicken at $6.10 per kg and 0.5 kg of cheese at $10.60 per kg?
Answer:
$20.55
Step-by-step explanation:
2.5 x 6.1 + 0.5 x 10.6 = 15.25 + 5.3 = 20.55
5) find the mean of the following sets of numbers, 7, 3, 5, 2,9,10
Answer:
The mean is ^6
Step-by-step explanation: To figure out the mean, add up the numbers, 7+3+5+2+9+10=36 then divide it by how many numbers you have 36/6=6
Turn 12 ¾= to a decimal
Answer:
12.75
Step-by-step explanation:
Turn 12 ¾ = to a decimal
¾ = 0.75
12 + 0.75
12.75
Please help me out i will mark you brainlest
The appropriate values are; [tex]sin \theta = \frac{3\sqrt{10} }{10 }[/tex], [tex]cos\theta = -\frac{\sqrt{10} }{10}[/tex], [tex]cot\theta= -\frac{1}{3}[/tex], [tex]sec\theta=-\sqrt{10}[/tex] and [tex]csc\theta= \frac{\sqrt{10} }{3}[/tex].
What are the trig values?Given the equation and interval.
tanθ = -3, [ π/2 < θ < π ]
First, we use the definition of tangent to determine the known sides of the unit circle right triangle.
Note that; the quadrant determines the sign of each values.
tanθ = opposite / hypotenuse
We can use Pythagoras theorem to find the hypotenuse of the unit circle right triangle as the opposite and adjacent sides are known.
Hypotenuse = √( opposite² + adjacent² )
Hence, we have;
Hypotenuse = √( [3]² + [-1]² )
Hypotenuse = √( 9 + 1 )
Hypotenuse = √10
1) To find sinθ
sinθ = opposite / hypotenuse
sinθ = 3/√10
We simplify
sinθ = 3/√10 × √10/√10
sinθ = 3√10 / 10
[tex]sin \theta = \frac{3\sqrt{10} }{10 }[/tex]
2) cosθ
cosθ = adjacent / hypotenuse
cosθ = -1 / √10
Simplify
cosθ = -1 / √10 × √10/√10
cosθ = -√10 / 10
[tex]cos\theta = -\frac{\sqrt{10} }{10}[/tex]
3) cotθ
cotθ = adjacent / opposite
cotθ = -1 / 3
[tex]cot\theta= -\frac{1}{3}[/tex]
4) secθ
secθ = hypotenuse / adjacent
secθ = √10 / -1
[tex]sec\theta=-\sqrt{10}[/tex]
5) cscθ
cscθ = hypotenuse / opposite
cscθ = √10 / 3
[tex]csc\theta= \frac{\sqrt{10} }{3}[/tex]
Therefore, the appropriate values are; [tex]sin \theta = \frac{3\sqrt{10} }{10 }[/tex], [tex]cos\theta = -\frac{\sqrt{10} }{10}[/tex], [tex]cot\theta= -\frac{1}{3}[/tex], [tex]sec\theta=-\sqrt{10}[/tex] and [tex]csc\theta= \frac{\sqrt{10} }{3}[/tex].
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A scatter plot is shown. A scatter plot is shown with numbers from 1 to 10 at increments of 1 on the x axis and numbers from 0 to 10 at increments of 1 on the y axis. The ordered pairs 0, 2 and 1, 3 and 1, 9 and 1.2, 4 and 1.9, 4 and 2.6, 4.2 and 3, 5 and 4, 5 and 4, 6 and 4.8, 6.1 and 5, 7 and 5, 7.9 and 6.9, 7.1 and 6, 8 and 7, 3.8 and 7, 8.2 and 7, 9.1 and 7.1, 9.8 and 8, 10 and 10, 7. How many outliers does the graph show? 1 2 3 4
There is only 2 outliers in a scatter plot. And the graph is attached below
A scatter plot is shown. In the form of (x, y) coordinates. The ordered pairs 0, 2 and 1, 3 and 1, 9 and 1.2, 4 and 1.9, 4 and 2.6, 4.2 and 3, 5 and 4, 5 and 4, 6 and 4.8, 6.1 and 5, 7 and 5, 7.9 and 6.9, 7.1 and 6, 8 and 7, 3.8 and 7, 8.2 and 7, 9.1 and 7.1, 9.8 and 8, 10 and 10, 7.
Coordinate, is represented as the values on x axis and y axis of graph
Clearly every preceding coordinate is close to each other and follow a close patter of line or continuous curve. except only two points are far from the curve are (1, 9) and (10, 7).
Thus, The required outliers is given by (1, 9) (10, 7)
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if 251 base x =100, find x
If [tex]251_x\equiv100_{10}[/tex], then this translates to the equation
[tex]251_x = 2x^2 + 5x + 1 = 100[/tex]
Solve for [tex]x[/tex].
[tex]2x^2 + 5x = 99[/tex]
[tex]2\left(x^2 + \dfrac52 x\right) = 99[/tex]
[tex]2 \left(x^2 + \dfrac52 x + \dfrac{25}{16}\right) - \dfrac{25}8 = 99[/tex]
[tex]2 \left(x + \dfrac54\right)^2 = \dfrac{817}8[/tex]
[tex]\left(x + \dfrac54\right)^2 = \dfrac{817}{16}[/tex]
[tex]x + \dfrac54 = \pm \dfrac{\sqrt{817}}4[/tex]
[tex]x = \dfrac{-5\pm\sqrt{817}}4[/tex]
though it is a bit unusual (but not entirely out of the question) to have an irrational base number system.
In case you meant [tex]100_2[/tex] on the right side, then [tex]100_2 = 2^2 = 4_{10}[/tex], so that
[tex]2x^2 + 5x + 1 = 4 \\\\ 2x^2 + 5x - 3 = 0 \\\\ (x+3) (2x-1) = 0 \\\\ x=-3 \text{ or } x = \dfrac12[/tex]
which at first glance seem like more reasonable choices of base.
Phillip flips an unfair coin eight times. This coin is twice as likely to come up heads as tails. How many times as likely is Phillip to get exactly three heads than exactly two heads
4 times as likely is Phillip to get exactly three heads than exactly two heads
A chance that something might exist, happen, or be true : the state or fact of being possible is called possibilities.
Possibility is the universal set whereas probability is the subset. Possibility is surer to occur than probability. Possibility has its opposite in the word impossibility whereas probability has its opposite in the word improbability.
How to solve?We can find;
P (three heads) = C(8,3)(2/3)^3(1/3)^5 = 448 / 6561
P (two heads) = C(8,2)(2/3)^2(1/3)^6 = 112 / 6561
So...... 448 / 112 = 4 times more likely to get 3 heads than 2 heads
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Please help ASAP
Please help ASAP
Please help ASAP
Using proportions, it is found that:
Unit price for the 11.3 ounce package: $0.33 per ounce.Unit price for the 29.3 ounce package: $0.31 per ounce.The 29.3 ounce package is the better deal.What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The unit price is given by the cost divided by the number of ounces, and the better deal is given by the deal with the lowest unit price.
Hence, for the 11.3 ounce package:
u = 3.68/11.3 = $0.33 per ounce.
For the 29.3 ounce package:
u = 8.98/29.3 = $0.31 per ounce.
Due to the lower unit cost, the 29.3 ounce package is the better deal.
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Check all that are Solutions are there inequality
The solutions of the inequality x>-2 is 0, 4 2/5, 1.999, 347.595
Number line is a arrangements of numbers on a straight line A number line has zero on its centerAll the numbers lie on the left-hand side of 0 are negative numbersAll the numbers lie on right-hand side of 0 are positive numbersWhen we move from left to right, the numbers are increasing When we move from right to left, the numbers are decreasingGiven the inequality is x>-2
Solution of the inequality is greater than -2
0, 4 2/5, 1.999, 347.595 are the solutions of given inequality.
Hence, the solutions of the inequality x>-2 is 0, 4 2/5, 1.999, 347.595
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Write an algebraic expression for this statement.
A stick [tex]l[/tex] feet long is broken into two parts, one of which is twice as long as the other. How long is the shorter piece?
**Please Help, Respond soon....Will mark brainliest for correct answer**
The algebraic expression is 2/3(2y + y)
How to determine the expressionThe length of the 2/3 feet long
It is broken into two parts x and y
If x is twice the length of y, we have
x = 2y
The algebraic expression is 2/3/x + y , if x = 2y
We have that,
2/3(2y + y)
Thus, the algebraic expression is 2/3(2y + y)
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