Question 3(Multiple Choice Worth 2 points)
(01.06 MC)
Simplify √√-72-
--6√√2
6√-2
6√√2i
061√2
Answers
Answer:
[tex]6i\sqrt{2}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sqrt{-72}[/tex]
Rewrite -72 as the product of 6 · -1 · 2:
[tex]\implies \sqrt{36 \cdot -1 \cdot 2}[/tex]
Apply the radical rule [tex]\sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]
[tex]\implies \sqrt{36} \sqrt{-1} \sqrt{2}[/tex]
Carry out the square root of 36:
[tex]\implies 6\sqrt{-1}\sqrt{2}[/tex]
Apply the imaginary number rule [tex]\sqrt{-1}=i[/tex] :
[tex]\implies 6i\sqrt{2}[/tex]
Related Questions
Mr. Edmonds is packing school lunches for a field trip for the 6th graders of Apollo Middle school. He has 50 apples and 40 bananas chips. Each group of students will be given one bag containing all of their lunches for the day. Mr. Edmonds wants to put the same number of apples and the same number of bananas in each bag of lunches. What is the greatest number of bags of lunches Mr. Edmonds can make? How many apples and bananas will be in each bag?
Answers
The greatest number of bags of lunches Mr. Edmonds can make = 40, And , in each bag there will be one apple and one banana chips bag.
In the above question, the following information is given :
Mr. Edmonds wants to pack lunches for the schools field trip where he wants to put the same number of apples and the same number of bananas in each bag of lunches
We are given that,
Number of available bananas chips packs = 40
Number of available apples = 50
We need to find the greatest number of bags of lunches Mr. Edmonds can make
As the pair should be an even number and we have less number of banana chips bags than apples. So the number of lunches which can be packed with equal number of apples and banana chips bags depend on banana chips bags
Therefore, the greatest number of bags of lunches Mr. Edmonds can make = 40
And , in each bag there will be one apple and one banana chips bag.
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Household Income
Under $50,000
$50,000 under $75,000
$75,000 under $150,000
$150,000 or above
Percentage
27.2
27.3
37.2
8.3
Event
ABCD
Suppose that a household with home Internet access only is selected at random. Apply the
special addition rule to find the probability that the household obtained has an income
a. under $75,000.
b. $50,000 or above.
c. between $50,000 and (under) $150,000
d. Interpret each of your answers in parts (a) - (c) in terms of percentages
e. Use the complement rule to answer part (b) in this exercise.
Answers
The probability for household with income under $75,000 is 54.5/100. the probability for household with income $50,000 or above is 72.8 /100, and the probability for household with income between $50,000 and (under) $150,000 is 64.5/100.
What is probability?
Probability describes potential. This area of mathematics examines how random events happen. The value might be between 0 and 1. Mathematicians have used probability to forecast the likelihood of certain events. In general, probability relates to how likely something is to happen. You can better understand the potential results of a random experiment by using this fundamental theory of probability, which also holds true for the probability distribution. To calculate the likelihood that an event will occur, we first need to know how many possible possibilities there are.
As given in the question,
Household with Income $50,000 are 27.2%
$50,000 - $75,000 are 27.3%
$75,000 - $150,000 are 37.2%
$150,000 or above are 8.3%
a) we have to find the probability for household with income under $75,000
So, Households having income under $75,000 are equal to:
(27.3 + 27.2)% = 54.5%
Therefore, probability = 54.5/100
b) we have to find the probability for household with income $50,000 or above,
So, household with income $50,000 or above are equal to:
(27.3 + 37.2 + 8.3)% = 72.8%
Therefore, probability = 72.8 /100
c) we have to find probability for household with income between $50,000 and (under) $150,000.
so, household with income between $50,000 and (under) $150,000 are equal to:
(27.3 + 37.2)% = 64.5%
Therefore, probability = 64.5/100
d) answer a can be interpret in percentage as 54.5%
answer b can be interpret in percentage as 72.8%
answer c can be interpret in percentage as 64.5%
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Which of the following statements about the table is true?
Select all that apply.
The table shows a proportional relationship.
All the ratios for related pairs of x and y are equivalent to 7.5.
When x is 13.5, y is 4.5.
When y is 12, x is 4.
The unit rate of for related pairs of x and y is .
26
22 Undertond Proportional Relationships: Fouivalent Ratios
C
C
y
10.5 3.5
15.9 5.3
22.5 7.5
27
9
3
Answers
Answer:
there is a lot of ratios here, but I will try my best. A proportional relationship is the relationship that is proportional obviously. and if the ratio is related, pairs are equivalent to 7.5 then that must mean that the proportional relationship is fuevalent
4) At a fundraising event, there is a raffle. A total of 165people bought a raffle ticket. The ratio of losing ticketsto winning tickets is 12:3. How many people wonsomething in the raffle?
Answers
In order to determine the number of people which won something, it is necessary to write the following system of equations:
x + y = 165
y/x = 12/3
x is the people won and y the people lost.
The first equation represents tha total number of people in the event.
The second equation represents the ratio of losing tickets to winning people.
First, solve the second equation for y, and then replace the expression for y into the first equation:
y = 12/3 x
x + 12/3 x = 165
next, solve the last equation for x:
(3+12)/3 x = 165
15/3 x = 165
5x = 165
x = 165/5
x = 33
x is the number of people who won something in the event.
Hence, the number of people was 33
I just need to know the answer quick because I have to go somewhere
Answers
From the given graph, it is seen that f(x) is not defined for x<-4. The function g(x) is not defined for x>2
But the function p(x) represents a straight line which is defined for all real x.
Hence, the function p(x) has all real numbers as its domain.
Thus, the correct option is (D)
A union voted on whether to go on strike 120 people vote the ratio of yes and no votes is 2:3 how many people vote no
Answers
Answer:
80
Step-by-step explanation:
This is a ratio and we can set it up as follows and solve for x:
[tex]\frac{2}{3} = \frac{x}{120}[/tex]
Multiply both sides by 120
80 = x
Divide 120 / 5 = 24
Then multiply the individual digits of ratio (2:3) by 24
2 x 24 = 48
3 x 24 = 72
Put these numbers together in a ratio, 48:72
Therefore 72 people voted no.
Hope this helps
if A/B and C/D are rational expressions,then which of the following is true?*PHOTO*
Answers
In general,
[tex]\begin{gathered} \frac{w}{x}*\frac{y}{z}=\frac{w*y}{x*z} \\ x,z\ne0 \end{gathered}[/tex]Therefore, in our case, (Notice that since A/B and C/D are rational expressions, B and D cannot be equal to zero)
[tex]\frac{A}{B}*\frac{C}{D}=\frac{A*C}{B*D}[/tex]Notice that the left side of each option includes the term
[tex]\frac{A}{B}*\frac{D}{C}[/tex]However, we cannot assure that C is different than zero because it is only stated that C/D is rational.
Furthermore,
[tex]\frac{A}{B}*\frac{D}{C}=\frac{A*D}{B*C}[/tex]And (A*D)/(B*C) is not included among the options.
Therefore, the answer has to be option D as it is the only one that correctly expresses the multiplication of two fractions.Remember that there is a mistake in each option, the left side has to be A/B*D/CLars created a painting with an area of 42 square inches and a length of 6 inches. They create a second painting with an area of 28 square inches. It has the same width as the first painting. What is the length of the second painting?
Answers
The length of the second painting is 4 in.
What is Area of Rectangle?
Area of rectangle is length times of breadth.
Given that :
Lars created a painting with an area of 42 square inches and a length of 6 inches. now, calculating B of painting using formula :
Area of Rectangle=Length × Width
42 = 6 x b
b = 42/6
b = 8 in.
it is given that :
area of second painting = 28 square inches
and having same width as the first painting that is b = 8 in.
Now, calculating length second of painting using formula :
Area of Rectangle=Length × Width
28 = l x 8
l = 28/8
l = 4 in.
Therefore, the length of the second painting is 4 in.
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what are the equations of the asysyoptes of the rational function
Answers
To find the asymptotes, we have to solve the following.
[tex]x^2-4x+3=0[/tex]We have to find two numbers whose product is 3 and whose sum is 4. Those numbers are 3 and 1.
[tex](x-3)(x-1)=0[/tex]So, the solutions are x = 3 and x = 1.
Hence, the asymptotes x = 1 and y = 1/2.The graph below shows the function.
The price of a notebook has risen to $3.35 today. Yesterday's price was $3.10. Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answers
The percent of increasing = amount of increasing/original amount x 100%
Since the price of the notebook on one day is $3.10
Since it is increased to $3.35
Then the amount of increasing = 3.35 - 3.10 = 0.25 dollars
Since the original price is 3.10
By using the rule above
[tex]\text{Percent}=\frac{0.25}{3.10}\times100[/tex]The percent of increasing = 8.064516%
Round it to the nearest tenth
The percent of the increase is 8.1%
Use the given scale factor and the side lengths of the scale drawing to determine the side lengths of the real object. Scale factor. 4:1 10 in 10 in A C 12 in Scale drawing Object A. Side a is 6 inches long, side bis 6 inches long, and side cis 8 inches long. B. Side a is 14 inches long, side bis 14 inches long, and side cis 16 inches long. C. Side a is 40 inches long, side bis 40 inches long, and side c is 48 inches long D. Side a is 2.5 inches long, side bis 2.5 inches long, and side cis 3
Answers
As the scale factor is 4:1 it means that for each 4inches in scale drawing correspond to 1 inch in the object.
Then, to find the side lengths in the object you multiply the measure of each side in the scale drawing by 1/4:
[tex]\begin{gathered} 10in\cdot\frac{1}{4}=2.5in \\ \\ 10in\cdot\frac{1}{4}=2.5in \\ \\ 12in\cdot\frac{1}{4}=3in \end{gathered}[/tex]Then, side a is 2.5 inches, side b is 2.5in and side c is 3inchesNot sure how to approach this question whether to use the factor theorem or to use the synthetic division
Answers
EXPLANATION
If x+2 is a factor, we need to equal the factor to zero, isolate x and substitute the value into the function:
[tex]x+2=0\text{ --> x=-2}[/tex]Plugging in x=-2 into the function:
[tex]P(-2)=(-2)^4-2(-2)^2+3m(-2)+64[/tex]Computing the powers:
[tex]P(-2)=16-2*4-6m+64[/tex]Multiplying numbers:
[tex]P(-2)=16-8-6m+64[/tex]Adding numbers:
[tex]P(-2)=72-6m=0[/tex]Adding +6m to both sides:
[tex]72=6m[/tex]Dividing both sides by 6:
[tex]\frac{72}{6}=m[/tex]Simplifying:
[tex]12=m[/tex]In conclusion, the value of m is 12
In the picture below, angle 2 = 130 degrees, what is the measurement of angle 1?
Answers
Answer:
50°
Step-by-step explanation:
[tex]\angle 1[/tex] and [tex]\angle 2[/tex] form a linear pair, and are thus supplementary (meaning they add to 180°).
Graph the parabola. I have a picture of the problem
Answers
Let's begin by listing out the given information
[tex]\begin{gathered} y=(x-3)^2+4 \\ y=(x-3)(x-3)+4 \\ y=x(x-3)-3(x-3)+4 \\ y=x^2-3x-3x+9+4 \\ y=x^2-6x+13 \\ \\ a=1,b=-6,c=13 \end{gathered}[/tex]The vertex of the function is calculated using the formula:
[tex]\begin{gathered} x=-\frac{b}{2a} \\ x=-\frac{-6}{2(1)}=\frac{6}{2}=3 \\ x=3 \\ \\ y=(x-3)^2+4 \\ y=(3-3)^2+4=0^2+4=0+4 \\ y=4 \\ \\ (x,y)=(h,k)=(3,4) \end{gathered}[/tex]For the function, we assume values for x to solve. We have:
[tex]\begin{gathered} y=(x-3)^2+4 \\ x=1 \\ y=(1-3)^2+4=-2^2+4=4+4 \\ y=8 \\ x=2 \\ y=(2-3)^2+4=-1^2+4=1+4 \\ y=5 \\ x=3 \\ y=(3-3)^2+4=0^2+4=0+4 \\ y=4 \\ x=4 \\ y=(4-3)^2+4=1^2+4=1+4 \\ y=5 \\ x=5 \\ y=(5-3)^2+4=2^2+4=4+4 \\ y=8 \\ \\ (x,y)=(1,8),(2,5),(3,4),(4,5),(5,8) \end{gathered}[/tex]We then plot the graph of the function:
sjsvsjsowbdjdbsosbwybwiw
Answers
Given 4 h + 6 = 30
4 h = 30 - 6
4 h = 24
Divide both sides by 4, we have:
h = 24 /4
h = 6
Find the missing quantity with the information given. Round rates to the nearest whole percent and dollar amounts to the nearest cent% markdown = 40Reduced price = $144$ markdown = ?
Answers
The given information:
% mark up = 40
Reduced = $144
Markdown = ?
The formula for percentage markup is given as
[tex]\text{ \%markup }=\frac{markup}{actual\text{ price}}\times100[/tex]Let the actual price be x
Hence,
Reduced price = 60% of actual price
[tex]60\text{\% of x = 144}[/tex]Solving for x
[tex]\begin{gathered} \frac{60x}{100}=144 \\ x=\frac{144\times100}{60} \\ x=240 \end{gathered}[/tex]Therefore, actual price = $240
Inserting these values into the %markup formula gives
[tex]40=\frac{\text{markup}}{240}\times100[/tex]Solve for markup
[tex]\begin{gathered} 40=\frac{100\times\text{markup}}{240} \\ 40\times240=100\times\text{markup} \\ \text{markup}=\frac{40\times240}{100} \\ \text{markup}=96 \end{gathered}[/tex]Threefore, markup = $96
Segment AC has a midpoint B. If AB = 2x - x - 42 andBCI_x+11x +21, find the length of Ac.
Answers
The equation for the segment AB is;
[tex]2x^2-x-42[/tex]The equation for the segment BC is ;
[tex]x^2+11x+21[/tex]If segment AC has midpoint at B , this means ;
AC = AB + BC
To get AC we add the equation for AB and BC
Performing addition as;
[tex]2x^2-x-42+x^2+11x+21[/tex]Collect like terms as;
[tex]2x^2+x^2+11x-x-42+21=AC[/tex][tex]3x^2+10x-21=AC[/tex]Answer
[tex]AC=3x^2+10x-21[/tex]
how much must be deposited at the beginning of every six months in account that pays 6% compounded semi-annually so that account will contain 21,000 at the end of three years
Answers
The formula for Final Amount, A after compounding for n period of times is given by
[tex]A=p(1+\frac{r}{100})^n[/tex]Where A = amount
p= principal
r = rate (in %)
n = number of compounding periods
From the question.
A=21,000, p = ?, r=6, n = 3 x 2 = 6
[tex]\begin{gathered} 21000=p(1+\frac{6}{100})6 \\ \\ 21000=p(1+0.06)^6 \\ 21000=p(1.06)6 \\ 21000=p(1.41852) \\ 21000=1.41852p \\ p=\frac{21000}{1.41852} \\ p=14,804.17 \end{gathered}[/tex]The amount that must be deposited at the beginning is 14,804.17
Over which interval(s) is the function decreasing?A) -4 < x < 3B) -0.5 < x < ∞C) -∞ < x < -0.5D) -∞ < x < -4
Answers
In the interval where the function is decreasingcreasing, the input or x values increase as the output or y values decrease. Looking at the graph, moving from the left to the right, the values of x are increasing whie the values of y are decreasing. This trend continued till we got to x = 0.5. Thus, in the interval from negative infinity to x = - 0.5, the function was decreasing.
The correct option is C
I wondered if you could teach me how to do this so I can do these problems independently.
Answers
Answer
a)
A' (-2, 6)
B' (7, 3)
C' (4, 0)
b)
D' (3, 3)
E' (-5, 0)
F' (2, 2)
c)
G' (3, 1)
H' (0, 4)
P' (-2, -3)
Explanation
For the coordinate (x, y)
A transformation to the right adds that number of units to the x-coordinate.
A transformation to the left subtracts that number of units from the x-coordinate.
A transformation up adds that number of units to the y-coordinate.
A transformation down subtracts that number of units from the y-coordinate.
For this question,
a) The coordinates are translated to the right by 4 units and upwards by 1 unit
That is,
(x, y) = (x + 4, y + 1)
A (-6, 5) = A' (-6 + 4, 5 + 1) = A' (-2, 6)
B (3, 2) = B' (3 + 4, 2 + 1) = B' (7, 3)
C (0, -1) = C' (0 + 4, -1 + 1) = C' (4, 0)
When a given point with coordinates P (x, y) is reflected over the y-axis, the y-coordinate remains the same and the x-coordinate takes up a negative in front of it. That is, P (x, y) changes after being reflected across the y-axis in this way
P (x, y) = P' (-x, y)
For this question,
b) The coordinates are reflected over the y-axis
D (-3, 3) = D' (3, 3)
E (5, 0) = E' (-5, 0)
F (-2, 2) = F' (2, 2)
In transforming a point (x, y) by rotating it 90 degrees clockwise, the new coordinates are given as (y, -x). That is, we change the coordinates and then add minus to the x, which is now the y-coordinate.
P (x, y) = P' (y, -x)
For this question,
c) The coordinates are rotated about (0, 0) 90 degrees clockwise.
G (-1, 3) = G' (3, 1)
H (-4, 0) = H' (0, 4)
I (3, -2) = P' (-2, -3)
Hope this Helps!!!
What is the sign of when x > 0 and y < 0 ?
Answers
The number line always goes from negative to positive :
It increases from left to right
SInce negative is always on the left side of the zero
Snumber greater than zero are always positive
i.e. x > o
5|x +1| + 7 = 38
Solve for x
Answers
Answer: No solutions
Step-by-step explanation:
[tex]5|x+1|+7=-38\\\\5|x+1|=-45\\\\|x+1|=-9[/tex]
However, as absolute value is non-negative, there are no solutions.
during happy hour appetizers are at 30% off how much would each appetize your cost show the original price your math and discounted price
Answers
EXPLANATION
Let's see the facts:
Appetizers = 30%
The discount price is given by the following equation:
Discount percentage=
Could you send me a screenshot of the question for better understanding, please?
Write an equation of the line that passes through (-4,-5) and is parallel to the line defined by 4x +y = -5. Write the answer inslope-intercept form (if possible) and in standard form (Ax+By=C) with smallest integer coefficients. Use the "Cannot bewritten" button, if applicable.The equation of the line in slope-intercept form:
Answers
Answer: y = -4x - 21 OR 4x + y = -21
The given line is 4x + y = -5
Given point = (-4, -5)
Step 1: find the slope of the line
The slope intercept form of equation is given as
y = mx + b
Re -arrange the above equation to slope - intercept form
4x + y = -5
Isolate y
y = -5 - 4x
y = -4x - 5, where m = -4
Since the point is parallel to the equation
Therefore, m1 = m2
m2 = -4
For a given point
(y - y1) = m(x - x1)
Let x1 = -4, and y1 = -5
[(y - (-5)] = -4[(x - (-4)]
[y + 5] = -4[x + 4]
Open the parentheses
y + 5 = -4x - 16
y = -4x - 16 - 5
y = -4x - 21
The equation is y = -4x - 21 or 4x + y = -21
A
Westway Company pays Suzie Chan a weekly pay of:
Social Security tax on salary up to $142,800:
Medicare tax:
The state unemployment rate (SUTA):
FUTA rate:
Required:
Using the information given above, answer the following question:
Note: Use cells A2 to 86 from the given information to complete this question.
1. What is Suzie Chan's yearly salary?
2. How much did Westway deduct for Suzie's Social Security for the year?
3. How much did Westway deduct for Suzie's Medicare for the year?
4. What state unemployment taxes does Westway pay on Suzie's yearly
salary?
5. What federal unemployment taxes does Westway pay on Suzie's yearly
salary?
Graded Worksheet
B
$3,000.00
6.20%
1.45%
5.10%
0.60%
Answers
The Suzie Chan's yearly salary is 156,426 .
The Westway deduct $9,698.412 for Suzie's social security for the year.
The Westway deduct $2268.177 for Suzie's Medicare for the year.
The state unemployment taxes worth $7977.726 deducted from Suzie's salary.
The FUTA taxes worth $938.556 deducted from Suzie's salary.
What is tax?
A tax is a mandatory financial charge or other sort of levy placed on a taxpayer (an individual or legal entity) by an administrative body to pay for certain public expenditures and administrative costs (regional, local, or national).
It is given in the question that weekly salary of Suzie is $3,000.
we know that, there are 365 days in a year and 7 days in a week.
Therefore, weeks in a year = 365/7 = 52.142
Yearly salary is equal weekly salary times weeks in a year.
Yearly Salary = (3000)52.142
yearly Salary = $156,426
Social security taxes are 6.20%
So, 6.20% of 156,426 is $9,698.412
Therefore, The Westway deduct $9,698.412 for Suzie's social security for the year.
Medicare taxes are 1.45%
So, 1.45% of 156,426 is $2268.177
Therefore, The Westway deduct $2268.177 for Suzie's Medicare for the year.
The state unemployment taxes are 5.10%
So, 5.10% of 156,426 is $7977.726
Therefore, The state unemployment taxes worth $7977.726 deducted from Suzie's salary.
The FUTA taxes are 0.60%
So, 0.60% of 156,426 is $938.556
Therefore, The FUTA taxes worth $938.556 deducted from Suzie's salary.
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Given the recursive formula for an arithmetic sequence,An = an-1 - Tt, where the first term of the sequence is 7. Which of the following could be explicitformulas for the sequence? Select all that apply.
Answers
From the recursive formula:
[tex]a_n=a_{n-1}-\pi[/tex]we notice that the common difference of the sequence is -pi. Now we know that the first term is 7, then the explicit formula is:
[tex]a_n=7-\pi(n-1)[/tex]when
[tex]n>0[/tex]We can relabel this sequence if we assume we start at zero, in this case the sequence will be:
[tex]a_n=7-\pi n[/tex]when:
[tex]n\ge0[/tex]What is the driving distance from the police station to an animal shelter
Answers
The coordinates of the Police station is (0, -4)
The coordinates of Animal shelter is (6,- 2)
The distance between the Police station and the Animal shelter is given by the formoula;
[tex]\begin{gathered} \text{Distance}=\sqrt[]{(x_2-x_1)^2+(y}_2_{}-y_1)^2_{} \\ \text{Distance}=\sqrt[]{(6-0)^2+(-2--4)^2}=\text{ }\sqrt[]{6^2+2^2} \end{gathered}[/tex][tex]\text{Distance}=\sqrt[]{36+4}\text{ = }\sqrt[]{40}=\text{ 6.325}\approx6.33[/tex]Section 5.2-10. Solve the following system of equations by substitution or elimination. Enter your answer as (x,y).-2x+3y = 15-x-3y = 12
Answers
1)-2x2)
[tex]-2x+3y-(-2x-6y)=15-2\times12\Rightarrow-2x+3y+2x+6y=15-24\Rightarrow9y=-9\Rightarrow y=-1[/tex]y=-1 implies
[tex]-2x+3\times(-1)=15\Rightarrow-2x-3=15\Rightarrow-2x=18\Rightarrow x=-9[/tex]Hence the solution is
[tex](-9,-1)[/tex]if a fraction product always l esser than the lesser factor
Answers
We have that whenever you multiply two positive fractions, the product will be smaller than both factors. For example, if we have the following:
[tex]\frac{1}{2}\cdot\frac{3}{4}=\frac{3}{8}[/tex]notice that both factors are fractions and the product is less than both factors.
find the measure of a triangle if the vertices of triangle EFG are E(-3,3), F(1,-1), and G(-3,-5). then classify the triangle by its sides
Answers
EFG is a triangle with vertices
E(-3,3), F(1,-1) and G(-3,-5).
First, let us evaluate the length of each side of the triangle using the distanec formula.
[tex]\begin{gathered} EF=\sqrt[]{(1+3)^2+(-1-3)^2} \\ =\sqrt[]{16+16} \\ =\sqrt[]{32} \\ =4\sqrt[]{2} \\ FG=\sqrt[]{(-3-1)^2+(-5+1)^2} \\ =\sqrt[]{16+16} \\ =4\sqrt[]{2} \\ EG=\sqrt[]{(-3+3)^2+(-5-3)^2} \\ =\sqrt[]{8^2} \\ =8 \end{gathered}[/tex]Since two sides of the triangle are equal, therefore, EFG is an isoscele triangle.
