Answers
The perimeter and area of each of the composite figure is:
a. Area: 138.6 mm²; Perimeter = 50.27 mm.
b. Area: 120.5 cm²; Perimeter = 42.7 cm
c. Area: 521.1 mm²; Perimeter: 95.8 mm
What is the Area of a Circle, Triangle, and a Rectangle?Area of a circle = πr²
Area of a triangle = 1/2(base)(height).
Area of a rectangle = (length)(width).
What is the Perimeter of a Composite Figure?The perimeter of a composite figure = the sum of all lengths of the sides surrounding the composite figure.
a. The area of the composite figure = area of rectangle + area of two semicircles
Two semicircles = 1 circle
Area of the rectangle = (15)(5) = 75 mm²
Area of the two semicircles = πr² = π(4.5²) = 63.6 mm²
The area of the composite figure = 75 + 63.6 = 138.6 mm².
Perimeter = 5(2) + 4(3) + (perimeter of 1 circle)
Perimeter = 5(2) + 4(3) + (2πr)
Perimeter = 5(2) + 4(3) + (2π(4.5))
Perimeter = 50.27 mm.
b. Area = area of triangle + area of square + area of half circle
Area = 1/2(base)(height) + s² + 1/2(πr²)
Base = 5 cm
Height = 7 cm
s = √(7² + 5²) = 8.6 cm [Pythagorean theorem]
r = 8.6/2 = 4.3 cm
Area = 1/2(5)(7) + 8.6² + 1/2(π(4.3²))
Area = 120.5 cm²
Perimeter = 5 + 7 + 8.6 + 8.6 + (perimeter of half circle)
Perimeter = 5 + 7 + 8.6 + 8.6 + 1/2(2πr)
Perimeter = 5 + 7 + 8.6 + 8.6 + (2π(4.3))
Perimeter = 42.7 cm
c. Area = area of triangle + area of rectangle + area of half circle
Area = 1/2(base)(height) + (length)(width) + 1/2(πr²)
Base = 32 - 20 = 12 mm
Height = 14 mm
Length = 20 mm
Width = 14 mm
r = 1/2(20) = 10 mm
Area = 1/2(12)(14) + (20)(14) + 1/2(π(10²))
Area = 521.1 mm²
Perimeter = 14 + 32 + hypotenuse of the triangle + (perimeter of half circle)
Hypotenuse = √(12² + 14²) = 18.4 mm
Perimeter of half circle = 1/2(2πr) = 1/2(2π(10)) = 31.4
Perimeter of the composite figure = 14 + 32 + 18.4 + 31.4
Perimeter of the composite figure = 95.8 mm
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Related Questions
Captionless Image
A. 9
B. 8
C. 6
D. 5
Answers
Answer: we need the immage
Step-by-step explanation:
Hi, can somebody help me.
In two or more complete sentences, describe the transformation(s) that take place on the parent function to achieve the graph of g(x)=log(-3x-9)+1.
Answers
Answer:
Logarithmic functions are the inverses of exponential functions. The logarithmic function y=log(x) is called the logarithmic function with base a .
When a constant c is added to the input of the parent function f(x)=loga(x), the result is a horizontal shift c units in the opposite direction of the sign on c. Our function is shifted 3 units to the right.
It is shifted 2 units vertical.(2 units down).
or
First, multiply the x by -3 and shift it 9 units to the right. Then, shift the function 1 unit down.
hope this was helpful
witch ones greater 52 4/9 or 211/4
Answers
Answer:
211/4 is bigger number cause if you look at it right 52 4/9 is smaller than 211/4
allie is making 8 dozen chocolate chip muffins for the food fair at school. the recipe she is using makes 3 dozen muffins. if the original recipe calls for 16 ounces of chocolate chips, how many ounces of chocolate chips does she need for her new amount? (allie buys her chocolate chips in bulk and can measure them to the nearest ounce.)
Answers
With the help of the ratio, we can conclude that Allie needs 42.72 ounces of chocolate chips for her new recipe.
What is the ratio?A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.So, first, we will take the ratio of a new recipe to the old recipe:
8:3 = 8/3 = 2.67Now, the chocolate chips she needs for the new recipe:
16 × 2.67 = 42.72Chocolate chips for new recipe = 42.72 ouncesTherefore, with the help of the ratio, we can conclude that Allie needs 42.72 ounces of chocolate chips for her new recipe.
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water flows at a constant rate. Kian measures 8 cups in 6 seconds. whats the constant of proportionality of cups of water to minutes
Answers
The constant of proportionality in cups of water to minute is 80 cups/min
What is the constant of proportionality in cups per minute?Here we have the proportional relation:
y = k*x
Where y is the number of cups and x the time in seconds, then:
y/x = k
Replacing the values we know:
y = 8 cups.
x = 6 seconds.
We can get the value of k, the constant of proportionality, but first, let's write the time in minutes.
x = 6 seconds
remember that 1 min = 60 sec, then:
6 sec = (6/60) min = 0.1 min
So the constant of proportionality is:
k = 8cups/0.1 min = 80 cups/min
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Give the coordinates and quadrant of Point C.
Answers
The coordinates is (-4,5) and the quadrant is ii
What is coordinate plane ?A coordinate plane, often referred to as a rectangular coordinate plane grid, is a two-dimensional plane created by the intersection of the Y-axis, a vertical line, and the X-axis, a horizontal line. An area of two dimensions made up of two number lines is known as a coordinate plane. It is created when a point termed the origin, where the X-axis and Y-axis cross, is reached. You may find points by using the numbers on a coordinate grid. Graphing points, lines, and many other things may all be done using a coordinate plane. It serves as a map and provides exact driving instructions.
The coordinates is (-4,5) and the quadrant is ii
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bryce orders the following items from catalog what is the total price he charges to his credit card if the sales tax is 6 percent and nontaxable shipping cost 5$ for the order round to the nearest cent if necessary `
Answers
The total price that Bryce got charged to his credit card is $120.54 .
In the question ,
it is given that the
price for Shorts = $14.00
price for Soccer Ball = $25.00
price for Shin guard = $10.00
price for Cleats = $60.00
the total price for all the items = 14+25+10+60 = $109
Given that the sales tax is 6% of the total price .
So , the sales tax = 6% of 109 = 0.06×109 = $6.54
According to the question
total price = price + sales tax + shipping cost
= 109 + 6.54 + 5
= 120.54
Therefore , the total price that Bryce got charged to his credit card is $120.54 , the correct option is (D) $120.54 .
The given question is incomplete , the complete question is
Bryce orders the following items from a catalog. What is the total price he charges to his credit card if the sales tax is 6 percent and nontaxable shipping costs $5 for the order? Round to the nearest cent if necessary. Shorts=$14.00 ,Soccer ball=$25.00 ,Shin guards=$10.00 ,Cleats=$60.00 .
(A) $104.94
(B) $109.94
(C) $115.54
(D) $120.54
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Mai biked 6\frac{3}{4} miles today, and Noah biked 4\frac{1}{2} miles.
How many times the length of Noah’s bike ride was Mai’s bike ride?
Answers
It was 1.5 times the length of Noah's bike ride as Mai’s bike ride.
The problem we dealing with is related to mixed numbers which are referred to as mixed numbers and could be the whole number, and a proper division spoke together. It for the most part speaks to a number between any two whole numbers.
Since we are providing mai's rate which is 6 3/4 miles and Noah's rate of 4 1/2 miles, So in order to find the time the length of Noah's ride is compared to Mal's, we just need to divide the given rates by each other
=> 6 3/4 divided by 4 1/2,
=> 27/4 divided by 9/2, (The result is an improper fractions)
=> 27/4 X 2/9
=>3/2
=> 1.5
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the value of y varies directly with x. if x = 4, then y = -6. what is the constant of variation
Answers
Solve 7x + 6<3(x - 2).
O [XIX<-3]
O {XIX < 0}
O {XIX<-2}
O [xlx>-3]
Answers
Step-by-step explanation:
X<-3 Inequality form , [XIX <-3]
The coordinate pairs of a function are given.
{(-2, 0), (0, 1), (4, 3), (6, -3)}
What is the domain of the function?
Answers
D = {-2, 0, 4, 6}
I NEED HELP
Graph the image of the given triangle after the transformation that has the rule (x, y)→(x, −y).
Answers
The image of the given triangle after transformation that has the rule (x,y)→(x,−y) is graphed below .
In the question
the triangle is given ,
From the figure , we can see that the coordinates of the triangle are
(2,7) , (4,-3) , (-5,-2)
let us name the coordinates of the triangle as A(2,7) , B(4,-3) , C(-5,-2) .
applying the transformation , that has rule (x,y)→(x,−y)
Using this rule to find the new coordinates of the triangle A'B'C' .
when A= (2,7)
A' = (2,-7)
When B = (4,-3)
B' = (4,-(-3))
B' = (4,3)
When C = (-5,-2)
C' = (-5,-(-2))
C' = (-5,2)
So the coordinates of the triangle A'B'C' is A' = (2,-7) , B' = (4,3) , C' = (-5,2) .
the image triangle A'B'C' is shown below
Therefore , The image of the given triangle after transformation of the rule (x,y)→(x,−y) is graphed below .
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Let the function P be defined by p(x)=6n^2-4n-16 where (n-2) is a factor. To rewrite the function as a product of two factors, long devision was used.
Answers
The relation of the function as a product are found for the long division as: (n-2)×(6n - 16) + 0 = 6n² - 4n - 16
What is referred as the long division?Long Division is a technique for dividing large numbers that divides the problem into several steps that follow a sequence. Just like in frequent division problems, a dividend is divided by divisor, yielding the quotient and, in some cases, a remainder.Each component of a division equation has its own name.Dividend: The dividend is really the number divided during the division process.Divisor: The divisor is the number whereby the dividend is divided.Quotient: A quotient is an outcome of the division process.Remainder: We can't always divide things exactly. There could be an extra number. The leftover number is known as the remainder.The following describes the relationship between such four parts:
Divisor x Quotient + Remainder = Dividend
From the given pictures write the value of each part;
Dividend = 6n² - 4n - 16
Divisor = (n-2)
Quotient = 6n - 16
Remainder = 0
Thus, the relation becomes;
(n-2)×(6n - 16) + 0 = 6n² - 4n - 16
Thus, the relation of the function as a product are found for the long division.
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What are the rules of PERFECT SQUARE TRINOMIAL
Answers
The rules of Perfect Square Trinomial are, an expression obtained from the square of the binomial equation is a perfect square trinomial. If a trinomial is in the form [tex]ax^{2} +bx+c[/tex] is said to be a perfect square, if and only if it satisfies the condition [tex]b^{2} = 4ac[/tex].
What is Perfect Square Trinomial :Perfect square trinomials are algebraic expressions with three terms that are obtained by multiplying a binomial with the same binomial. A perfect square is a number that is obtained by multiplying a number by itself. Binomials are algebraic expressions consisting of just two terms that are either separated by a positive (+) or a negative (-) sign. Similarly, trinomials are algebraic expressions consisting of three terms. When a binomial consisting of a variable and a constant is multiplied by itself, it results in a perfect square trinomial having three terms. The terms of a perfect square trinomial are separated by either a positive or a negative sign.
A perfect square trinomial is defined as an algebraic expression that is obtained by squaring a binomial expression. It is of the form [tex]ax^{2} +bx+c[/tex]. Here a, b, and c are real numbers and a ≠ 0. For example, let us take a binomial (x+4) and multiply it to (x+4). The result obtained is [tex]x^{2} +8x+16[/tex]. A perfect square trinomial can be decomposed into two binomials and the binomials when multiplied with each other gives the perfect square trinomial.
Therefore,
An expression obtained from the square of the binomial equation is a perfect square trinomial. If a trinomial is in the form [tex]ax^{2} +bx+c[/tex] is said to be a perfect square, if and only if it satisfies the condition [tex]b^{2} = 4ac[/tex].
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Solve the triangle. Round the side length to the nearest tenth and the angle measures to the nearest degree.
Answers
Answer: 41, 54, 6.1
Step-by-step explanation:
By the law of Cosines,
[tex]b^2=4^2 +5^2 -2(4)(5)\cos 85^{\circ}\\\\b=\sqrt{4^2 +5^2 -2(4)(5)\cos 85^{\circ}} \\\\ =\sqrt{41-40 \cos 85^{\circ}}\\\\\approx 6.1[/tex]
By the law of sines,
[tex]\frac{\sin A}{a}=\frac{\sin C}{c}=\frac{\sin B}{b}\\\\\frac{\sin A}{4}=\frac{\sin C}{5}=\frac{\sin 85^{\circ}}{\sqrt{41-40 \cos (85^{\circ})}}\\\\\implies \sin A=\frac{4\sin 85^{\circ}}{\sqrt{41-40 \cos 85^{\circ}}} \implies \angle A \approx 41^{\circ}\\\\\implies \sin C=\frac{5\sin 85^{\circ}}{\sqrt{41-40 \cos 85^{\circ}}} \implies \angle C \approx 54^{\circ}[/tex]
1/8y= -3/4x-1 in standard form
Answers
Can somebody help me with this??? Emma helps her mother walk the dog 2 weeks per month. How many weeks per year does Emma walk the dog?
Answers
Answer: 24 weeks
Step-by-step explanation:
There are 12 months in a year
In each of those months, Emma walks the dog for 2 weeks
2 times 12 is 24
so Emma walks the dog 24 weeks per year
What initial investment must be made to accumulate $120000 in 12 years if the money is invested in a mutual fund that pays 14%annual interest, compounded monthly? Use the analytical solution to find the answer.
Answers
What initial investment must be made to accumulate $120000 in 12 years if the money is invested in a mutual fund that pays 14%
annual interest, compounded monthly?
Remember that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
A=$120,000
t=12 years
r=14%=14/100=0.14
n=12
substitute in the given formula
[tex]120,000=P(1+\frac{0.14}{12})^{12\cdot12}[/tex]Solve for P
P=$22,583.42If the value of the expression below is a perfect square, which could be the value of m?
expression is 10m
A: m= 2/5
B: m= 1/2
C: m=1
D: m=2
Answers
Answer:
A
Step-by-step explanation:
[tex]m=2/5 \implies 10(2/5)=4 \\ \\ m=1/2 \implies 10(1/2)=5 \\ \\ m=1 \implies 10(1)=10 \\ \\ m=2 \implies 10(2)=20[/tex]
Of these, only 4 is a perfect square.
Which property justifies the statement below?
7(mn) = (7m)n
Which property justifies the statement below?
7(mn) = (7m)n
Associative Property
Inverse Property
Identity Property
Commutative Property
Answers
Property justifies the given statement 7(mn)= (7m)n is :
Associative property of multiplication.
As given in the question,
Given statement :
7(mn) = (7m)n
Property justifies the given statement 7(mn)= (7m)n is :
Here three numbers are multiplying to each other.On left hand side 7 is multiplied to a group formed by mn.On right hand side 7m is group together and get multiplied to n.After regrouping result remain same as they equal to each other.Left hand side is equal to right hand side.This shows that it is associative property of multiplication.Therefore, property justifies the given statement 7(mn)= (7m)n is :
Associative property of multiplication.
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The graph of g(x) is a transformation of the graph of f(x) = 3ª.
Enter the equation for g(x) in the box.
g(x) =
Answers
The graph is as follows: f(x) = 3ˣ
The graph f (x) is transformed into the graph g(x)
The points (-2, 2) and (-2) on the curve g(x) are (-1,4).
Let any point on f be (a,b) (x).
After translation, a brand-new curve, g(x), is obtained that is perpendicular to the line, asymptotically equal to y=1, or when y reaches 1, the graph is perpendicular to the x axis.
The graph of the translated curve is g(x)=y-1=3ˣ⁺² where g(x) = y = 3ˣ⁺² + 1.
The following graph shows the two.
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a cell phone battery is rated at 3.85 v and can store 10.78 watt-hours of energy. (a) how much average current can it deliver over a period of 3 hours if it is fully discharged at the end of that time? (b) how much average power is delivered in part (a)? (c) what is the ampere-hour rating of the battery?
Answers
The 10.78 watt–hour battery with a voltage rating of 3.85 V gives;
(a) The average current delivered in 3 hours is approximately 0.93 A
(b) The average power delivered at 0.93–A is approximately 3.593 watts
(c) The ampere hour rating of the battery is 2.8 Ah
What is the relationship between power and energy?Power is the rate at which energy is given out or expended.
The rating of the phone battery = 3.85–VThe power stored in the battery = 10.78 watt–hoursRequired;
(a) The amount of average current that can be delivered in 3 hours
Solution;
The power in the battery is given by the equation;
P = I²•R = I•V
10.78 watt–hour = 10.78 J/s × 60 × 60 s = 38,808 J
In 3 hours, the energy per second, which is the power is given by the equation;
P = 38,808 J/(3×60×60 s) ≈ 3.593 watts
I = P/V
Therefore;
I = 3.593 watts/(3.85 V) ≈ 0.93 A
The average current it can discharge in 3 hours is approximately 0.93 A(b) The average power delivered is given by the equation;
P = Energy/Time
Therefore;
P = 38,808 J/(3×60×60 s) ≈ 3.593 watts(c) An equation that can be used to find the ampere hour, Ah is as follows;
Ah = Watt hour ÷ Voltage
The ampere hour rating of the battery is therefore;
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find the equation of the line in form y=mx+c
please help giving brainliest
Answers
Answer:
Step-by-step explanation:
Equation of line in slope intercept form: y = mx +c
Pick any two points from the table and find the slope.
(-2 , 9) ; (-1,7)
[tex]\sf \boxed{\bf Slope= \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf = \dfrac{7-9}{-1-[-2]}\\\\=\dfrac{-2}{-1+2}\\\\=\dfrac{-2}{1}\\\\=-2[/tex]
y = -2x + c
Substitute (-2,9) in the above equation and find the y-intercept 'c'.
9 = -2*(-2) +c
9 = 4 + c
9 - 4 = c
c = 5
Equation of line:
y =-2x + 5
Luke runs the trail in the park near his home 5 days a week. How many miles does he run in a week if the trail is 3 1/3 miles?
Answers
Explanation: 5 x 3 1/3 = 16 2/3
Is my answer correct?
Answers
Using the concepts of the mean and of the mean absolute deviation, the correct option is given as follows:
Last month, the amount of rain that fell each day varied less than the month before.
What is the mean absolute deviation of a data-set and what does it represent?The mean of a data-set is given by the sum of all observations divided by the cardinality of the data-set, which is the number of observations in the data-set.The mean absolute deviation of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations, hence it basically is the mean of the deviations, given a degree of variability.The mean absolute deviation(MAD) represents the average by which the values differ from the mean.In this problem, we have that:
Two months ago, the measures were: Mean 9.4 cm, MAD 3.5 cm.Last month, the measures were: Mean 11.5 cm, MAD 1.6 cm.Due to the lower mean absolute deviation combined with the higher mean, the amount varied less than the month before, hence the last option is correct.
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During the experiment, the volume dropped to milliliters. Find the percent of decrease.
Answers
The percentage of decrease for the chemistry experiment is 25%.
How to calculate the percentage?The. percentage is defined as the number representing any number with respect to 100.
In this case, at the begining, the experiment was 4 millimeters and the end had an experiment of 3 millimeters.
The decrease in the percentage will be:
= Change in value /Original value × 100
= (4 - 3)/4 × 100
= 1/4 × 100
= 25%
The percentage is 25%.
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Lines b and c are parallel. What is the measure of Angle6? Horizontal and parallel lines b and c are cut by transversal a. Where line b intersects line a, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: (13 x + 9) degrees, 2, 4, 3. Where line c intersects line a, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 5, 6, (5 x + 9) degrees, 8.
Answers
Using the angle theorems, the measure of angle 6, m ∠6, is 54°
Calculating the measure of anglesFrom the question, we are to determine the measure of angle 6
From the given diagram, we can write that
(13x + 9)° = m ∠5 (Corresponding angles theorem)
and
m ∠5 + (5x + 9)° = 180° (Linear pair theorem)
Thus,
(13x + 9)° + (5x + 9)° = 180°
Now, we will solve for x
13x + 9 + 5x + 9 = 180
18x + 18 = 180
Subtract 18 from both sides of the equation
18x + 18 - 18 = 180 - 18
18x = 162
x = 162/18
x = 9
Now, to determine the measure of angle 6
m ∠6 = (5x + 9)° (Vertical angles theorem)
Substitute the value of x
m ∠6 = (5(9) + 9)°
m ∠6 = (45 + 9)°
m ∠6 = 54°
Hence, measure of ∠6 is 54°
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m∠PQS=(3x−3)° and m∠RQS=(x+19)°. Find the value of x.
Answers
Since both angles are the same, x has a value of 11
What are angles?Angles are formed when two or more lines intersect. This in other words means that angles is the measure of space between the intersection of rays or lines
How to determine the value of x?The given parameters are
m∠PQS=(3x−3)° and m∠RQS=(x+19)°.
From the question, the measures of both angles are the same
This means that
m∠PQS=(3x−3)° = m∠RQS=(x+19)°.
So, we have the following equation
3x − 3 = x + 19
Collect the like terms in the equation
So, we have the following equation
3x - x = 3 + 19
Evaluate the like terms in the equation
So, we have the following equation
2x = 22
Divide both sides by 2
So, we have the following equation
x = 11
Hence, the value of x in the angles is 11
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Possible question
m∠PQS and m∠RQS are congruent angles
m∠PQS=(3x−3)° and m∠RQS=(x+19)°. Find the value of x.
Janice is offered medical and dental insurance through her company. Medical insurance costs $6,740 annually and dental costs $630
annually. Jessica's company pays 70% of medical insurance and 85% of dental insurance. How much does Jessica pay each biweekly pay
period for medical and dental insurance?
Answers
Medical insurance Jessica pays biweekly is $196.58 or 197 dollars.
Dental insurance Jessica pays biweekly is $22.3125 or 22 dollars.
How to find the biweekly pay?
Janice:
Medical insurance costs $6,740 annually
Dental costs $630
Solution:
Jessica:
70% of medical insurance = 70/100*6,740
= 674 * 7
= $4,718/annum.
85% of dental insurance = 85/100 * 630
= 63 * 8.5
= $535.5/annum
Medical insurance Jessica pays per month = 4,718/12 = $393.16
Medical insurance Jessica pays biweekly = 393.16/2 = $196.58 or $197
Dental insurance Jessica pays per month = 535.5/12= $44.625
Dental insurance Jessica pays biweekly = 44.625/2 = $22.3125 or $22.
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Which equation represents a line which is parallel to the line y-2x =7
Answers
The line which is parallel to the given line is 2x- y= 0 or y= 2x.
The given line y= 7+ 2x
this is written in the form y= mx +c where if we compare these two equations we get m= 2
Now consider a point which passes through the origin (0,0)
Thus y-y₁= m(x-x₁)
y- 0 = 2 ( x- 0)
y= 2x or 2x- y= 0
Thus, the line which is parallel to the given line is 2x- y= 0.
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