The owners want to hire a contractor to build a porch along side the parlor. The parlor is rectangular with width Of 32 feet and length of 50 feet. The porch will have the same width that on each side of the house. See design plans.
Answers
a) Basically, you are adding the length of porch to the original length of the parlor.
Let's say that the newly added porch is x.
(50 + x)(32 + x)
1600 + 50x + 32x + x²
x² + 82x + 1600
b) Just make the polynomial x² + 82x + 1600 equal to 2320.
x² + 82x + 1600 = 2320
subtract 2320 on both sides to make the polynomial equal to 0.
x² + 82x - 720 = 0
factor this
(x - 8)(x + 90) = 0
(x - 8) =0 (x + 90) = 0
x = 8 x = - 90
(-90ft doesn't make sense. So don't mind about this.)
So the porch should be 8ft.
Hope this helped!
The width of the porch will be 32 feet, the same as the parlor. However, to calculate the amount of building materials needed, additional specifics are required such as the porch's length, location of posts, and number of boards.
Explanation:To answer the question related to designing a porch that matches the width of the parlor, we first understand that the parlor is of a rectangular shape with a width of 32 feet. Considering that the porch will have the same width, it means the porch will also have a width of 32 feet.
From this point, specifics such as the desired length of the porch, location of posts, number of boards or rails, and other related factors would come into play in the calculating of building materials needed for the construction. There may also be the need to consider factors like the ratio of width to length in the design, akin to the mathematical relation mentioned in the statement 'X = Y x 2 + 1'.
So, while we know the width of the porch because it matches the parlor, the exact amount of materials that will be required would depend on further specifics of the porch design, similar to the steps in a stoichiometry problem in chemistry where one calculates the amount of reactants or products in a chemical reaction based on known ratios.
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Related Questions
If y represents total earnings in dollars and x represents hours worked, then which equation models the wages of someone who makes $9.50 an hour?
A. x = 950x
B. y = 950x
C. x = 9.50x
D. y = 9.50x
Answers
Answer:
Option D is correct
[tex]y = 9.50x[/tex]
Step-by-step explanation:
Here, y represents total earnings in dollars and x represents hours worked.
As per the statement:
To find which equation models the wages of someone who makes $9.50 an hour.
[tex]\text{"\$9.50 an hour"}[/tex] translated to 9.50x
then;
the total earning in dollars we get;
[tex]y = 9.50x[/tex]
Therefore, an equation [tex]y = 9.50x[/tex] models the wages of someone who makes $9.50 an hour
Which equation has a slope of 3 and a y intercept of 4?
A.y = 3x - 4
B.y = 3x + 4
C.y = 4x - 3
D.y = 4x + 3
Answers
The general equation in slope intercept form is given by:
[tex] y=mx+b [/tex]
where m is the slope and b is the y intercept.
Now we are given slope as 3 and y intercept as 4, plugging these values in the slope intercept form, we get
[tex] y=3x+4 [/tex]
Now if we compare the two equations, we see that option (b) y=3x+4 matches our requirement.
So answer is the equation with slope 3 and y intercept 4 is y=3x+4.
Answer each question (5 points each). the sample space of a probability experiment is ???? = {????, ????, ????,????, ????, ????, ????, ????} and three events are ???? = {????, ????, ????,????} ???? = {????,????, ????, ????} ???? = {????, ????, ????, ????} (a) what are the outcomes in the event ???? ???????? ????? (b) what are the outcomes in the event ???? ???????? ???? ???????? ????? (c) what are the outcomes in the event ???? ???????????? ????? (d) what are the outcomes in the event ???? ???????????? ?????
Answers
Hope this helps!!!!
:) :) :)
Solve the system of equations and choose the correct ordered pair. 2x + 6y = 6 3x – 2y = 20
Answers
Multiply each equation by the value that makes the coefficients of xx opposite.(−3)⋅(2x+6y)=(−3)(6)(-3)⋅(2x+6y)=(-3)(6)(2)⋅(3x−2y)=(2)(20)(2)⋅(3x-2y)=(2)(20)Simplify.−6x−18y=−18-6x-18y=-186x−4y=406x-4y=40Add the two equations together to eliminate xx from the system.Divide each term by −22-22 and simplify.Tap for more steps...y=−1y=-1Substitute the value found for yy into one of the original equations, then solve for xx.Tap for more steps...x=6x=6The solution to the independent system of equations can be represented as a point.(6,−1)
Answer:
solution is (6,-1)
Step-by-step explanation:
[tex]2x + 6y = 6[/tex]
[tex]3x – 2y = 20[/tex]
WE use elimination method to solve for x and y
Multiply the second equation by 3
[tex]3x – 2y = 20[/tex] times 3
[tex]9x – 6y = 60[/tex]
[tex]2x + 6y = 6[/tex] , add both equations
------------------------------
[tex]11x = 66[/tex]
Divide both sides by 11
[tex]x=6[/tex]
Plug in 6 for x in first equation
[tex]2x + 6y = 6[/tex]
[tex]2(6) + 6y = 6[/tex]
[tex]12 + 6y = 6[/tex], subtract 12 on both sides
[tex]6y = -6[/tex]
divide both sides by 6
[tex]y=-1[/tex]
[tex]x=6 \ and \ y= -1[/tex]
Riya is applying to her garden.She applies it at a rate of 25 ,000 cm^3 of mulch for every m^2 of garden space. At what rate is ray applying mulch in m^3/m^2
Answers
Riya is applying mulch at a rate of 0.025 m^3/m^2 after converting the original rate of 25,000 cm^3/m^2 to cubic meters per square meters.
Explanation:To find out the rate at which Riya is applying mulch in m^3/m^2, you first need to convert the given value from cubic centimeters (cm^3) to cubic meters (m^3). We know that 1 m = 100 cm, so 1 m^3 = 100 cm * 100 cm * 100 cm = 1,000,000 cm^3. Therefore, we need to divide the given value by 1,000,000 to convert it from cm^3 to m^3. So, if Riya applies 25,000 cm^3 of mulch for every m^2 of garden space, this is equivalent to 25,000/1,000,000 = 0.025 m^3/m^2.
In conclusion, Riya is applying mulch at a rate of 0.025 m^3/m^2.
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Carlos’s credit card has an APR of 14.78% and a grace period of 18 days, and Carlos pays his balance in full every month. If his last billing cycle ended on March 28, 2010, and he made his payment on April 13, 2010, Did he owe any interest on his last statements balance?
Answers
A ball made out of a special material is inflated such that its diameter changes from 12inches to 15 inches. What is the approximate change in the volume of the ball?
Answers
V = (4/3) • π • r^3
The initial radius is 6 inches (radius is half of diameter)
Plug in to get its volume:
V = (4/3) • π • (6)^3
V is about 904.7787 in^3
Now do the same for the enlarged sphere, with radius 7.5 inches
V = (4/3) • π • (7.5)^3
V is about 1767.1459 in^3
To find the change, get the difference between the two volumes:
(New Volume) - (Old Volume)
1767.1459 - 904.7787
The change is around 862.3672 in^3
15 4/5% of 50
A. .79 B. 79
C. 790 D. 7.9
Answers
"The correct answer is B. 79.
To solve the given problem, we need to calculate 15 4/5 percent of 50. First, let's convert the mixed number to an improper fraction to make the calculation easier.
15 4/5% as a fraction is 15 + 4/5, which can be written as 75/5 + 4/5 = 79/5.
Now, to find the percentage of 50, we multiply 50 by the fraction representing the percentage:
[tex]\[ \frac{79}{5} \times 50 = \frac{79 \times 50}{5} \][/tex]
Next, we simplify the multiplication:
[tex]\[ \frac{79 \times 50}{5} = \frac{3950}{5} \][/tex]
Now, we divide 3950 by 5:
[tex]\[ \frac{3950}{5} = 790 \][/tex]
However, since we are looking for 15 4/5 percent and not 15 4/5 times 50, we need to adjust our calculation by dividing by 100 to get the correct percentage:
[tex]\[ \frac{790}{100} = 79 \][/tex]
Therefore, the final answer is B. 79."
if (1+sina)(1+sinb)(1+sinc)=(1-sina)(1-sinb)(1-sinc)=k then value of k=?
a. (cosacosbcosc)
b.(sinasinbsinc)
c. (3sinasinbsinc),
Answers
Raj is 3 years older than Zia. The sum of the squares of their ages is 369. How old are they?
Answers
x--------------> ages of Raj
y--------------> age of Zia
we know that
x=y+3-------------> equation 1
x²+y²=369-----------> equation 2
I substitute 1 in 2
(y+3)²+y²=369----------> y²+6y+9+y²=369---------> 2y²+6y-360=0
2y²+6y-360=0
using a graph tool-----------> to calculate the quadratic equation
see the attached figure
the solution is
y=12
x=y+3--------> x=12+3--------> x=15
the answer is
Raj is 15 years old
Zia is 12 years old
Final answer:
Zia's age is 12 and Raj's age is 15
Explanation:
To solve this problem, we can set up two equations using the given information. Let's assume Zia's age is x. Since Raj is 3 years older than Zia, Raj's age can be represented as x + 3.
The first equation is [tex]x^2 + (x + 3)^2 = 369.[/tex]
Simplifying this equation, we get [tex]x^2 + x^2 + 6x + 9 = 369.[/tex]
Combining like terms, we have [tex]2x^2 + 6x + 9 = 369.[/tex]
Next, we can rearrange the equation by subtracting 369 from both sides and combining like terms to get [tex]2x^2 + 6x - 360 = 0.[/tex]
Now, we can solve this quadratic equation for x using factoring, completing the square, or the quadratic formula. The solutions are x = -15 and x = 12.
Since age cannot be negative, Zia's age is 12 and Raj's age is 12 + 3 = 15.
Is the product of 2/5 and 5 greater or less than 2/5? Is it greater or less than 5? explain your reasoning.
Answers
5 = 5/1 as a fraction
2/5 × 5/1 = 2
ANSWER:
The product of 2/5 and 5 is greater than 2/5, and less than 5.
Another way you could find out if it's greater or less is by converting the fraction to a decimal and then multiplying it.
You must divide the numerator by the denominator to convert a fraction to a decimal.
2 ÷ 5 = 0.4
0.4 × 5 = 2
In P.E class, Janie ran 5 kilometers in 19 minutes 15 seconds. Based on this information, what was the constant of proportionality?
Answers
Multiple Choice
You can model the population of a certain city between 1945-2000 by the radical function P(x)=55,000 sqrt x-1945. Using this model, in which year was the population of that city 165,000?
A)1948
B)1951
C)1954
D)1957,
Answers
Solution:
If P(x) = 165,000
Then
165,000 = 55,000(x - 1945)^(1/2)
x= 1954
to check it, substitute x
165,000 = 55,000(1954 - 1945)^(1/2)
165,000 =165,000
The graph is supposed to show f(x)=3sin(x/4+1)-1/2. Which of the following are correctly represented in the graph? Select all that apply. (2 answers)
a. the amplitude
b. the vertical shift
c. the horizontal shift
d. the period
e. the horizontal expansion or compression
Answers
The vertical shift is correct
and the horizontal shift is correct
Answer:
a , b, c are only applicable in graph.
Step-by-step explanation:
Given : The function [tex]f(x)=3sin(\frac{x}{4}+1)-\frac{1}{2}[/tex]
To find : Which of the following are correctly represented in the graph?
Solution :
General form of sin function is [tex]y=A sin(B(x-C)+D[/tex]
Where A is the amplitude
[tex]B=\frac{2\pi}{\text{Period}}[/tex]
D is the vertical shift.
C is the horizontal shift or phase shift.
Comparing with the general form:
[tex]f(x)=3sin(\frac{x}{4}+1)-\frac{1}{2}[/tex]
Transform little bit we get,
[tex]f(x)=3sin(\frac{1}{4}(x-(-4)))-\frac{1}{2}[/tex]
a. Amplitude is [tex]A=3[/tex]
It is correct.
b. Vertical shift is [tex]D= -\frac{1}{2}[/tex]
it is correct.
c. Horizontal shift [tex]C=-4[/tex]
It is correct.
d. Period is [tex]P=\frac{2\pi}{B}[/tex]
[tex]P=\frac{2\pi}{\frac{1}{4}}[/tex]
[tex]P=8\pi[/tex]
It is not correct .
Actual period in graph is [tex]2\pi[/tex]
e. The horizontal expansion or compression
It also not correct because period is not correct.
The expansion and compression depends on the period.
Therefore, a , b, c are only applicable in the graph.
The sum of 3 consecutive even numbers of 78
Answers
3x+6=72
3x=72
x=72/3
x=24
Find the least common multiple of x² + x – 12 and x² + 2x – 15.
A) (x + 4)(x - 3)(x + 5)
B) (x – 3)(x + 5)(x – 4)
C) (x – 4)(x – 3)(x – 5)
D) (x + 4)(x – 5)(x – 3),
Answers
2. w+4/w-5
3.b-10/b-1
The least common multiple of x² + x – 12 and x² + 2x – 15 is (x + 4)(x – 3)(x + 5), Option A is correct.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .
We need to find the least common multiple of x² + x – 12 and x² + 2x – 15.
Let us find the factor of x² + x – 12
x² + 4x -3x – 12
x(x+4)+3(x+4)
(x + 4)(x – 3)
Now let us factorize x² + 2x – 15.
x² + 5x-3x – 15.
x(x+5)-3(x+5)
(x-3)(x+5)
So, the least common multiple of x² + x – 12 and x² + 2x – 15 is (x + 4)(x – 3)(x + 5).
Hence, the least common multiple of x² + x – 12 and x² + 2x – 15 is (x + 4)(x – 3)(x + 5), Option A is correct.
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Which set of side lengths can form a triangle?
a. 6cm, 8cm, and 16cmB. 6cm, 8cm, and 10cmC. 6cm, 7cm, and 14cmD. 6cm, 7cm, and 20cm
Answers
If exy = 3, then what is dy/dx at the point (1, ln3)?
Answers
differentiating our expression implicitly we get:
(x(dy/dx)+y)e^(xy)=0
N/B
when differentiating e^(xy) we apply chain rule. When differentiating xy, we use product rule.
next, we substitute (1, ln(3)) and solve for dy/dx
(1(dy/dx)+ln(3))^(1ln(3))=0
((dy/dx)+ln(3))e^(ln(3))=0
but
e^(ln3)=3, this is because e and ln are inverse of each other.
3((dy/dx)+ln(3))=0
dy/dx+ln (3)=0
dy/dx=-ln(3)
The answer is :
dy/dx=-ln(3)
What do you ask about if you want to know the price of an item?
A. el dependiente
B. el vestido
C. el precio
D. la tienda
Please help thank you
Answers
Answer:
1. C el precio
2. C mil
3. C El abrigo y las botas cuestan doscientos dolares
4. A maya
5. C blouse
Step-by-step explanation:
HELP!! ASAP!!!!! Which system of equations below has infinitely many solutions?
a) y = –3x + 4 and y = –3x – 4
b) y = –3x + 4 and 3y = –9x + 12
c) y = –3x + 4 and y = -1/3+ 4
d) y = –3x + 4 and y = –6x + 8
Answers
Answer B since
(y=-3x+4)* 3==> 3y=-9x+12 which is the second equation ==>infinity many solutions.
Answer:
The correct option is B. [tex]y=-3x+4 \ \text{and}\ \ 3y=-9x+12[/tex]
Step-by-step explanation:
Consider the two linear equation:
[tex]a_1x+b_1y+c_1=0\ \text{and}\ \ a_2x+b_2y+c_2=0[/tex]
The pair of linear equation has infinitely many solutions when:
[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]
Now consider the option.
Option a) [tex]y=-3x+4 \ \text{and}\ \ y=-3x-4[/tex]
The above equation can be written as:
[tex]y+3x-4=0 \ \text{and}\ \ y+3x+4=0[/tex]
Therefore,
[tex]\frac{1}{1}=\frac{3}{3}\neq\frac{-4}{4}[/tex]
Thus, this pair has no solution.
Now consider the option B. [tex]y=-3x+4 \ \text{and}\ \ 3y=-9x+12[/tex]
The above equation can be written as:
[tex]y+3x-4=0 \ \text{and}\ \ 3y+9x-12=0[/tex]
Therefore,
[tex]\frac{1}{3}=\frac{3}{9}=\frac{-4}{-12}[/tex]
Thus, this pair has infinitely many solution.
Hence, the correct option is B. [tex]y=-3x+4 \ \text{and}\ \ 3y=-9x+12[/tex]
Triangle ABC is undergoing a series of transformations. Which of the following transformations will NOT cause the resulting triangle A'B'C' to maintain congruence with triangle ABC? A. reflection over the x-axis B. translation 6 units to the right C. dilation with a scale factor of 3 D. rotation of 180 degrees clockwise
Answers
dilation will change the shape and it will not be congruent
Answer:
The image triangle compare to the pre-image triangle will be similar due to dilation.
Step-by-step explanation:
sum of 2x 2 + 3x - 4, 8 - 3x, and -5x 2 + 2.
Answers
= 2x² + 3x - 4 + 8 - 3x - 5x² + 2
= -3x² + 6
= 3(-x² + 2)
Final answer:
To sum the given polynomials, you combine like terms, resulting in the final expression of -3x^2 + 6.
Explanation:
The sum of the polynomials 2x2 + 3x - 4, 8 - 3x, and -5x2 + 2 can be found by combining like terms. This process involves adding the coefficients of terms with the same power of x.
Step 1: Identify and arrange like terms.
Terms with x2: 2x2 and -5x2Terms with x: 3x and -3xConstant terms: -4, 8, and 2Step 2: Combine like terms.
For x2 terms: 2x2 + (-5x2) = -3x2For x terms: 3x - 3x = 0x (This term will cancel out)For constant terms: -4 + 8 + 2 = 6Step 3: Write the sum of the polynomials.
The sum is: -3x2 + 6.
50 POINTS!!!!!!! Soybean meal is 16% protein; cornmeal is 8% protein. How many pounds of each should be mixed together in order to get 320-lb mixture that is 14% protein?
How many pounds of cornmeal should be in the mixture?
How many pounds of soybean meal should be in the mixture?
Answers
Bars of soap come in packages of 6 and packages of 8. The 6-bar pack costs $7.86, and the 8-bar pack costs $8.88. Which is the better deal? What is the
price per bar of the better deal?
Answers
8.88 / 8 = 1.11 per unit
the 8-bar pack is the better deal
A customer buys an apple pie for $8.04, 6 cloves of garlic for $0./9 each, and a quarts of milk for $1.31. You are working the cash register. The customer gives you a $5 bill, six $1 bills, and a quarter. The register tells you that you ow the customer $0.16 . Round the price of each item to the nearest $0.10 to estimate how much the customer owes.
Answers
The customer gave you 5 + 6 + 0.25 or $11.25, which is very close (and slightly higher) than the total of your estimates. I'd guess the register is correct.
Actual value is $8.04 + 6*0.29 + 1.31 = 8.04 + 1.74 + 1.31 = $11.09. The register is definitely correct.
Final answer:
To estimate the total cost, round each item to the nearest $0.10, sum them up, and subtract from the amount given by the customer. The estimated total cost is $9.80, and the estimated change to be returned is $1.45.
Explanation:
To estimate the total amount the customer owes after rounding to the nearest $0.10, we need to perform the following calculations:
Apple pie: $8.04, rounded to $8.00
6 cloves of garlic: $0.09 each, so $0.09 x 6 = $0.54, rounded to $0.50
Quart of milk: $1.31, rounded to $1.30
The estimated total cost is $8.00 (apple pie) + $0.50 (garlic) + $1.30 (milk) = $9.80.
The customer gives a total of $5 + $6 + $0.25 = $11.25.
Subtracting the estimated total cost from the amount given by the customer:
$11.25 - $9.80 = $1.45, which is the estimated change to be returned to the customer.
A conservation determines that a particular beach is eroding at a rate of 1.1% each year. When writing an explicit formula to represent the amount of beach remaining each year, which value should she use as the common ratio?
Answers
Answer:
0.989
Step-by-step explanation:
A conservationist determines that a particular beach is eroding at a rate of 1.1% each year. When writing an explicit formula to represent the amount of beach remaining each year, the common ratio is 0.989
The required explicit formula to represent the amount of beach remaining each year will be y = a(0.011)^x
Exponential functionsExponential functions are inverse of trigonometry functions. The standard form of exponential function is expressed as:
y = ab^x
b is the rate
Given;
Rate = 1.1% = 0.011
The required explicit formula to represent the amount of beach remaining each year will be y = a(0.011)^x
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If x = 12.8, what is the value of 2(z - 4)? [Type your answer as a number.]
need help
Answers
"Hope this is your question, if not I think you will, still be able to find an answer of your question based on this solution"
The expression is :
2(z-4)
so we may think that the given value is z = 12.8 instead of x=12.8, then only we can plug it in given expression.
so plugging z=12.8 in the expression:
2(12.8-4)
We will use PEMDAS rule here,
So simplifying parenthesis first,
12.8-4 = 8.8
Now multiplying the result 8.8 with 2 to get the answer,
8.8 *2 = 17.6
Answer : 2(z-4) = 17.6 for z=12.8
"hope this helps"
How to find the measure of an interior angle of an irregular polygon?
Answers
Exterior Angles of a Polygon Definition: the angle formed by any side of a polygon and the extension of its adjacent side Try this Adjust the polygon below by dragging any orange dot. Click on "make regular" and repeat. Note the behavior of the exterior angles and their sum. Regular polygons In the figure above check "regular". As you can see, for regular polygons all the exterior angles are the same, and like all polygons they add to 360° (see note below). So each exterior angle is 360 divided by the n, the number of sides. As a demonstration of this, drag any vertex towards the center of the polygon. You will see that the angles combine to a full 360° circle. Convex case In the case of convex polygons, where all the vertices point "outwards" away form the interior, the exterior angles are always on the outside of the polygon. In the figure above, check "regular" and notice that this is the case. Although there are two possible exterior angles at each vertex (see note below) we usually only consider one per vertex, selecting the ones that all go around in the same direction, clockwise in the figure above. Taken one per vertex in this manner, the exterior angles always add to 360° This is true no matter how many sides the polygon has, and regardless of whether it is regular or irregular, convex or concave. In the figure above, adjust the number of sides, switch to irregular and drag a vertex to see that this is true. In the figure above click on 'reset' and check "both". You will see that both angles at each vertex are always congruent (same measure). This is because they form a pair of vertical angles, which are always congruent. Drag the vertices around and convince yourself this is true. Concave case If the polygon is concave, things are a little trickier. A concave polygon has one or more vertices "pushed in" so they point towards the interior. In the figure above, uncheck "regular" and drag a vertex in towards the interior of the polygon. Notice that the exterior angle flips over into the inside of the polygon and becomes negative. If you add the exterior angles like before, they still add to 360°, you just have to remember to add the negative angles correctly. Exterior and Interior angles are supplementary At any given vertex, the interior angle is supplementary to an exterior angle. See Interior/Exterior angle relationship in a polygon. Walking the polygon In the figure above, imagine the polygon drawn on the ground. Stand on one of the sides and face along the line. Now if you walk around the polygon along each line in turn, you will eventually wind up back where you started, facing the same way. So you must have turned through a total of 360°, a full circle. This confirms that the exterior angles, taken one per vertex, add to 360° The sum of exterior angles - watch out! In most geometry textbooks they say flatly that the exterior angles of a polygon add to 360° This is only true if: You take only one per vertex, and Take all the angles that point in the same direction around the polygon. But in many cases they fail to state these conditions. In the figure at the top of the page, check the "Both" checkbox. You will see there are two per vertex and they actually add to 720° (360 times 2) So if you are asked "What is the sum of the exterior angles of a polygon?" without any conditions, you will have to guess which one they mean. Usually they mean taking one per vertex, and the answer is 360°, although strictly speaking this is wrong.
HELPP needed due today !!
Answers
f is between e and g, EF=7 and FG=6. find EG
Answers
------ (FG)
------ + ------- =
6 + 7 =
13
The measure of line segment EG is 13 cm.
Given that, F is between E and G, EF=7 and FG=6.
We need to find the measure of EG.
What is a line segment?A line segment is a part of a line that has two endpoints and a fixed length. It is different from a line that does not have a beginning or an end and which can be extended in both directions. In this lesson, we will learn more about a line segment, its symbol, and the way to measure a line segment.
Now, EG=EF+FG
⇒EG=7+6=13 cm
Therefore, the measure of line segment EG is 13 cm.
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