Graph the image of △IJK after the following sequence of transformations:
Translation 17 units left and 5 units up
Reflection across the line y=1
Answers
Please find attached the graph of the image of ΔIJK following a translation transformation of (-17, 5), and a reflection across the line y = 5
What is a transformation in geometry?A transformation is an operation that changes the location, size and shape of geometric figures.
The coordinates of the vertex of ΔIJK are; I(14, 8), J(8, 5), K(14, 2)
The translation transformation is 17 units left and 5 units up = T₍₋₁₇, ₅₎
The location of the vertices of the image of ΔIJK following the translation transformation are;
[tex]I(14,\, 8)\ \underset{\longrightarrow}{T_{(-17,\, 5)}}\ I'(-3,\, 13)[/tex]
[tex]J(8, 5)\ \underset{\longrightarrow}{T_{(-17,\, 5)}}\ j'(-9,\, 10)[/tex]
[tex]K(14, 2)\ \underset{\longrightarrow}{T_{(-17,\, 5)}}\ K'(-3,\, 7)[/tex]
The coordinates of a point following a reflection across the line y = 1 are as follows;
The coordinates of the vertices of the image I'J'K' relative to the line y = 1 are;
I'(-3, 13), Relative point I'(-3, 12)
J'(-9, 10) has a relative point at (-9, 9)
K'(-3, 7) has a relative point (-3, 6)
The coordinates of the vertices of the reflected image are therefore;
(x, y) [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex] (x, -(y - 1))
Which gives;
I'(-3, 12) [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex] I''(-3, -12 + 1) = I''(-3, -11)
J'(-9, 9) [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex] I''(-9, -9 + 1) = I''(-9, -8)
k'(-3, 6) [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex] k''(-3, -6 + 1) = k''(-3, -5)
Please find attached the image of the ΔIJK following the translation and reflection transformation
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Related Questions
List all factors of the numerator and denominator. Use gcf method to simplify Creduce) each fraction. You must show work
Answers
The reduced fraction is 6/7 using GCF method.
What is GCF method?
The largest number, which is the factor of two or more number is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors which are common in both. The largest number that is found in the common factors is called the greatest common factor. The GCF is also known as the Highest Common Factor (HCF)
Given,
the fraction = 24/28.
the factors of 24 = 2×2×2×3
The factors of 28 = 2×2×7
The gcf is 2 × 2 = 4
divide the denominator and numerator by 4
24 ÷ 4 = 6
28÷ 4 = 7
We get,
the fraction = 6/7.
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consider performing a partial f test to test for the inclusion of pctrush in the model. either in words or formula, what are the null and alternative hypotheses for this test?
Answers
The null and alternative hypothesis of the pctrush are explained below.
Given that;
By performing a partial F-test;
In hypothesis testing, the F test is a statistical test that is used to determine whether or not the variances of two populations or two samples are equal. The data in a f test follows a f distribution. In this test, two variances are divided and compared using the f statistic. Depending on the problem's characteristics, a f test can be either one- or two-tailed.
The one-way ANOVA (analysis of variance) test is run using the f value discovered after running the f test. More information on a f test, the f statistic, its critical value, formula, and how to perform a f test for hypothesis testing will be provided in this article.
The f test statistic is used in a test called the f test to determine if the variances of two samples (or populations) are equal. An f test needs a f distribution in the population and independent events for the samples in order to be valid. The null hypothesis can be rejected after conducting the hypothesis test if the f test results are statistically significant; otherwise, it cannot be rejected.
Null hypothesis:
The idea that there is no influence on the population is known as the null hypothesis.
We can reject the null hypothesis if the sample contains sufficient data to refute the assertion that there is no effect in the population (p). If not, we are unable to rule out the null hypothesis.
Although it may sound odd, statisticians only accept the phrase "fail to reject." Avoid using words like "prove" or "accept" when referring to the null hypothesis.
Alternative hypothesis:
The alternate response to your research question is the alternative hypothesis (Ha). It asserts that the populace is affected.
Your research hypothesis and your alternate hypothesis are frequently identical. It is, in other words, the assertion that you anticipate, or hope will be accurate.
The complement of the null hypothesis is the alternative hypothesis. The exhaustive nature of null and alternative hypotheses ensures that they account for all potential outcomes. Additionally, they are mutually exclusive, so only one of them can be true at once.
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In a two-digit number, the unit digit is 5 more than the tens digit. The number itself is three times the sum of the digits. What is the number?
Answers
Answer:
27
Step-by-step explanation:
You want a 2-digit number that is 3 times the sum of its digits, where the units digit is 5 more than the tens digit.
SetupLet t represent the tens digit. Then the units digit is (t+5) and the sum of digits is ...
t +(t +5) = 2t+5
The value of the number is ...
10t +(t+5) = 11t +5
The value is 3 times the sum of digits, so we have ...
11t +5 = 3(2t +5)
Solution11t +5 = 6t +15
5t = 10 . . . . . . . . . . subtract (6t+5)
t = 2
(t+5) = 7
The number is 27.
The scatter graph shows the maximum temperature and the numbers of hours of sunshine in 13 British towns in one day.
A line of best fit has also been drawn.
One of the points in an outliner.
a) Write down the coordinates of this point. (1)
b) For all the other points write down the type of correlation in just one word. (1)
On the same day, in another British town, the maximum temperature was 17.4C.
c) Estimate the number of hours of sunshine in this town on this day. (2)
You must use the drawing tool to show how the line of best fit has been used to get your answer.
A weatherman says that temperatures are lower on days when there is less sunshine.
d) Does the scatter graph support this? (1)
A yes B no C can't say
Total marks: 5
Answers
Answer:
See attached worksheet.
Step-by-step explanation:
The worksheet summarizes the steps for analyzing the data on the graph. Note that a "line of best fit" was drawn to help illustrate the linear behavior of the data, and to better the question concerning hours of sunshine in another British town. There are techniques for ensuring a line such as this fits the actual data as closely as possible. These techniques draw a line that has the least overall deviation from the actual data. For our purposes, a hand-drawn line appears to match the data reasonably well, so we are able to concule that the relationship is liner: There is a proportional change in y for every set change in x. That change is known as the slope. The slope of this liner would represent the direct relationship between hours of sun and maximum temperature.
Find g(x), where g(x) is the translation 2
units left of f(x)= -5x + 5.
Answers
Answer:
g(x)=(-5x+2)+5
Step-by-step explanation:
how many ways are there to seat four of a group of ten people around a circular table where two seatings are considered the same when everyone has the same immediate left and immediate right neighbor?
Answers
The number of ways which are there to seat four of a group of ten people around a circular table is 1260.
To choose 4 people from a group of ten we need to count such people, which can be found using 10! / 4! × (10-4)! , after solving this we need to multiply 3! by this to get the desired answer. This is done because for that 4 people to sit in a circle, the possibilities for n people to sit around a circle is (n-1)! , and since n here is 4 the possibilities will also be (4-1)! which is 3! here.
Hence the final answer: 3! × 10! / 4! × (10-4)! = 1260
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Decrease 330 km by 54%.
Answers
Answer: 151.8
Step-by-step explanation:
330/100 x 54 = 178.2
330- 178.2 = 151.8
3b(2x-z^3)=2h-7gx change the subject to x
Answers
Answer:
Step-by-step explanation:
3b(2x - z^3) = 2h - 7gx Distribute 3b
6bx - 3bz^3 = 2h - 7gx Add 3bz^3 to both sides
6bx = 3bz^3 + 2h - 7gx Add 7gx to both sides
6bx + 7gx = 3bz^3 + 2h Factor left side, factor out a gcf of x
x(6b + 7g) = 3bz^3 + 2h Divide both sides by (6b + 7g) to isolate x
x = (3bz^3 + 2h)/ (6b + 7g)
a physics professor wants to know what percent of physics majors will spend the next several years doing post-graduate research. he has the following probability distribution. x p (x) 1 0.35 2 0.2 3 0.15 4 ? 5 0.10 6 0.05 (a) on average, how many years would you expect a physics major to spend doing post-graduate research?
Answers
It can take 3 years that a physics major to spend doing post-graduate research
Given that,
A physics professor is curious about the proportion of physics majors who will pursue post-graduate study during the coming years. He has the probability distribution shown below. x P(x) x*P (x) 1 0.35 2 0.20 3 0.15 4 5 0.10 6 0.05
To find P(X<=3)
P(X<=3)=P(X=0,1,2,3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)
= 0.35+0.20+0.15
= 0.7
P(X<=3)=0.7
Hence, A physics major may need to spend three years conducting post-graduate research. and the probability that a physics major will spend no more than three years conducting post-graduate research is 70% or 0.7
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What is the equation of the line that passes through the point (6,-5) and has a slope of -{1}{3}?
Answers
Answer:
y = - [tex]\frac{1}{3}[/tex] x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - [tex]\frac{1}{3}[/tex] , then
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
to find c substitute (6, - 5 ) into the partial equation
- 5 = - 2 + c ⇒ c = - 5 + 2 = - 3
y = - [tex]\frac{1}{3}[/tex] x - 3 ← equation of line
answer please will give 20 points
Answers
Answer:plot the point (2,5)
Step-by-step explanation:
Find x if AC= 17, BD = 2x - 6, AD= x + 16, and BC = 6
Answers
Answer:
Hey, hope it helps my friend
Step-by-step explanation:
In the image
For her final project, stacy plans on surveying a random sample of students on whether they plan to go to florida for spring break. From past years, she guesses that about % of the class goes. Is it reasonable for her to use a normal model for the sampling distribution of the sample proportion? why or why not?.
Answers
Yes, it is reasonable for her to use a normal model for the sampling distribution of the sample proportion. In this case, less than ten efforts have been successful. Since 5 is a lot less than 10, this is the case.
Because the data don't fit the success and failure criteria, it is not appropriate to adopt a normal model for a sampling of the sample distribution.
50 students make up the sample. The probability that she assumes 10% of the group will attend is 10%.
It will be demonstrated by:
1 - p = 1 - 10% = 1 - 0.10 = 0.90
np = 50 × 0.1 = 5. This suggests the number of victories.
Less than 10 attempts have succeeded in this instance. 5 is much less than 10, hence this case. As a result, the data does not satisfy the requirement.
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The question is -
For her final project, Stacy plans on surveying a random sample of 50 students on whether they plan to go to Florida for spring break. from past years, she guesses that about 10% of the class goes. is it reasonable for her to use a normal model for the sampling distribution of the sample proportion? why or why not?
Explain how the equations 2/3m=-4 and -4m=24 are equivalent?
Answers
Both 2/3m=-4 and -4m=24 have a solution of 1/6 and are equivalent
What are algebraic expressions?Algebraic expressions are described as expressions that contains terms, variables, coefficients, constants and factors.
They are also known to be made up of some arithmetic operations, such as;
AdditionSubtractionMultiplicationDivisionBracket ParenthesesWe have the equations;
2/3m=4 and -4m=24
Let's solve for m in the first equation
12m = 2
Divide both side by coefficient of m
m = 2/ 12 = 1/ 6
For the second equation
-4m = 24
Divide both sides by - 4
m = 24/-4
m = 6/ -1
Take inverse
m = 1/6
Hence, the equations are equivalent
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The red figure is congruent to the blue figure. Which choice describes a sequence of transformations in which the blue figure is the image of the red figure?
1. Rotate the triangle 90º counterclockwise about the origin and then translate it 7 units left and 1 unit up.
2. Rotate the triangle 90º clockwise about the origin and then translate it 7 units left and 1 unit up.
3. Rotate the triangle 90º counterclockwise about the origin and then translate it 1 unit left and 7 units down.
4. Rotate the triangle 90º clockwise about the origin and then translate it 1 unit left and 7 units down.
Answers
The choice which describes a sequence of transformations in which the blue figure is the image of the red figure is: 4. Rotate the triangle 90º clockwise about the origin and then translate it 1 unit left and 7 units down.
What is a rotation?In Mathematics, the rotation of a geometric figure 90° about the origin in a clockwise or counterclockwise direction would produce a geometric figure that has these coordinates (y, -x).
From the information provided in the graph about the transformation applied to the red triangle to create the blue triangle, we have the following ordered pairs that represents a rotation of 90º clockwise:
(x, y) → (y, -x)
Ordered pair A = (-5, 2) Ordered pair A' = (2, 5)
Ordered pair B = (-5, 6) Ordered pair B' = (6, 5)
Ordered pair C = (-1, 2) Ordered pair C' = (2, 1)
After a translation of 1 unit left and 7 units down, we have:
Ordered pair A' = (2, 5) → Ordered pair A' = (2 - 1, 5 - 7) = (-1, -2)
Ordered pair B' = (6, 5) → Ordered pair B' = (6 - 1, 5 - 7) = (.5, -2)
Ordered pair C' = (2, 1) → Ordered pair C' = (2 - 1, 1 - 7) = (-1, -6)
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A class of 25 children shares 600 beads.
On a day when 1 child is absent, what is the ratio of the number of children present to the number of beads?
Answers
Answer:
Step-by-step explanation:
The answer would be 24:600. One student is absent so there are 24 students present. The number of beads is still 600, so the ratio is 24:600 which simplifies to 1:25.
Examine the equation below used for determining the balance on a bank account. Look through this chapter and your notes to help you write a problem that could be modeled by the equation.
Answers
The balance on the bank account at the end of the third quarter of the year is 2,630.80
How to find the compound interest?
Compound interest is defined as the interest calculated on the principal and the interest accumulated over the previous period.
Compound interest is found using the formula
A=P(1+r/n)ⁿˣ where:
A= Amountr= interest raten= number of interest applied per period and x= number of time periodTherefore, the amount (A)=2630.80
The P=2500
interest rate is 0.17%
Number of interest applied per period is 365 periods and
number of time period is 3.
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Pls help/ A function (x) is graphed on the coordinate plane.
What is the function rule in slope-intercept form?
Enter your answer in the box.
f(x)=
Answers
The function rule in slope-intercept form is y = -4x - 2
How to calculate the slope-intercept form of this function?Mathematically, the slope-intercept form of a straight line can be calculated by using this equation:
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the intercept.From the graph of this line, we have the following data points:
Point (x, y) = (-1, 2)
Point (x, y) = (0, -2)
In Mathematics, the slope of any straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (-2 - 2)/(1 - 0)
Slope, m = -4/-1
Slope, m = -4
Note: The y-intercept occurs at the point where the x-value is equal to zero (0).
Now, we can write the function rule for this line in slope-intercept form as follows:
y = mx + c
y = -4x - 2
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The table of ordered pairs (x, y) gives an exponential function.
Write an equation for the function.
X
-1
0
1
2
y
1
3
2
12
72
Answers
The equation for the function of the ordered pair is y =10x+2.
What is equation for the function?
An equation that has one solution for y for each value of x is referred to be a function. For each input of a particular type, a function assigns precisely one output. The names f(x) or g(x) are frequently used in place of y when naming functions. If our function's value is f(2), then we should calculate its value when x=2. Each functional equation contains some information about a function or several functions. An illustration of a functional equation is f (x) f (y) = x y, f(x) f(y) = x y.
Here in given order pair , let us take any two points,
[tex](x_1,y_1)=(0,2)\\(x_2,y_2)=(1,12)[/tex]
Now using slope formula,
=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> slope m =10/1 = 10
Now using equation formula,
=> [tex]y-y_1=m(x-x_1)[/tex]
=> y-2 =10(x-0)
=> y-2 = 10x
=> y=10x+2.
Therefore equation of the following order pair is y = 10x+2.
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helppp PLSSSSSSSSSSSSS I NEEED HELPPPPPPPPPPPPPPPPP
Answers
Answer:
15c + 19d
Step-by-step explanation:
Here to simplify we have to add like-terms
3c + 14d + c + 11c + 5d = ( 3c + c + 11c) + ( 14d + 5d) = 15c + 19d
Glad to Help
1. Why is identifying
the domain and range important when
defining a function?
Answers
Identifying the domain and range is important when defining a function because domain gives all the input values and range gives all the output values a function can take. It is very essential to know domain and range of a function.
Domain are represented by independent variable and are graphed on x coordinate of the axis.
Range are dependent values and are graphed on y axis of the graph.
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Example of a slope intercept form equation with a negative slope and y-intercept of 0
Answers
Answer:
An example would be y = -x.
Step-by-step explanation:
Since the y-intercept is 0, we don't have to write it out. The slope has to be negative, so I chose -1 as the slope. We don't have to write 1 when we use it as a coefficient, so that is why I wrote it as -x. Now to put it all together in slope intercept form, we get y = -x.
Hope this helps.
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In ΔSTU, TU = 11, US = 17, and ST = 18. Which statement about the angles of ΔSTU must be true?
Answers
For the given triangle STU all the angles of ΔSTU are not equal to each other is the true statement .
As given in the question,
In the given triangle STU,
TU = 11
US = 17
ST = 18
we can see that
TU < US < ST
⇒ 11 < 17 < 18
⇒ 11 + 17 = 28
⇒ 28 > 18
All the sides of the triangle are not equal to each other.
This implies that all the angles opposite to the unequal sides are also not equal to other.
Therefore, for the given triangle STU all the angles of ΔSTU are not equal to each other is the true statement .
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Eva says
3
4
is equivalent to
15
20
. Check her work by completing the table of equivalent ratios.
Answers
The equivalent ratio table is:
3 4
6 8
9 12
12 16
15 20
What is a Ratio?A ratio indicates the number of times one number contains another.
To find the equivalent ratio of 3/4 write the table of 3 in one column of the table and write the table of 4 in another column of the table.
The equivalent ratio table is:
3 4
6 8
9 12
12 16
15 20
The above table indicates that 3/4 = 6/8 = 9/12 = 12/16 = 15/20.
Therefore, from the table, 3/4 is equivalent to 15/20.
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what is the value of m and n?
Answers
The value of m is 36 degrees and the value of n is 27 degrees
Consider the triangle on right side
Two sides of the triangle is equal, therefore it is an isosceles triangle.
One angle of the triangle = 126 degrees
Other two angles of the triangle is equal
The sum of interior angles of the triangle is 180 degrees
Then, the equation will be
126 + n + n = 180
2n + 126 = 180
2n = 180 - 126
2n = 54
n = 54/2
n = 27 degrees
Consider the full triangle
The equation will be
(m +27) + 90 +27 = 180
m + 27 + 90 + 27 = 180
m + 144 = 180
m = 180 - 144
m = 36 degrees
Hence, the value of m is 36 degrees and the value of n is 27 degrees
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Write equivalent fractions for 8/9 and 5/8 using the least common denominator.
Type the fractions, using a slash ( / ) to separate the numerator and denominator.
8/9 =
5/8 =
Answers
The equivalent fractions for 8/9 and 5/8 using the least common denominator are 8/9 = 64/72 and 5/8 = 45/72.
What is the Least Common Denominator?
The smallest number that can serve as a common denominator for a group of fractions is known as the least common denominator (LCD). The smallest number that may be used as the denominator to produce a group of comparable fractions that all have the same denominator is known as the lowest common denominator.
The given fractions are 8/9 and 5/8.
The denominators of these fractions are 8 and 9.
so Least Common Divisor(LCD) of 8 and 9 will be = 8 × 9
= 72.
so the equivalent fraction can be calculated as
for 8/9 = [tex]\frac{8*8}{9*8}[/tex]
= 64/72
and for 5/8 = [tex]\frac{5*9}{8*9}[/tex]
= 45/72
Hence, the equivalent fractions are 64/72 and 45/72.
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Hey, I haven't been able to get any of these right, I wasn't a there the day we learned this and i'm needing help getting the rest of it done before 3:00. Could any of you please help me out on this, it'd mean a lot!
Answers
The correct graph for each of the equations are respectively;
5) Graph C
6) Graph A
7) Graph B
How to Interpret Linear Equation Graphs?The general form of equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
5) We are given the linear equation as;
-9x + 3y = 0
3y = 9x + 0
y = 3x + 0
The slope is 3 and y-intercept is zero. Thus, the correct graph for this function is; Graph C
6) We are given the linear equation as;
4x - 6y = 12
Rearranging we have;
6y = 4x - 12
y = ⁴/₆x - 2
y = ²/₃x - 2
Thus, slope is 2/3 and y-intercept is -2. The correct graph is graph A
7) The correct graph of the function 25x - 10y = -50 is the graph B.
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It take an ant farm 2 day to conume 1/2 of an apple. At that rate, in how many day will the ant farm conume 2 apple?
Answers
the ant will take 8 days to consume 2 apples.
Given, an ant takes 2 days to consume 1/2 of an apple.
We have to find the number of days ant will take to consume 2 apples.
So, ant takes 2 days = consumption of 1/2 apple
ant takes 4 days = consumption of 1 apple
Consumption of 1 apple = ant takes 4 days
Consumption of 2 apples = ant takes 4×2 days
Consumption of 2 apples = ant takes 8 days
Hence, the ant will take 8 days to consume 2 apples.
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Charis invested 140. She earned a simple interest of 3% per year on the initial investment. If no money was added or removed from the investment, what was the amount of interest Charis received at the end of two years?
Answers
The amount received by Charis on Simple interest in 2 years will be $8.4
What is Simple Interest?
The process of figuring out how much interest will accrue on a given principal sum of money is known as simple interest (S.I.).
It's formula is given by S.I. = PRT/100 where P = principle amount
R= rate and T = time.
Main Body:
P= $140
R= 3%
T= 2 years
so S.I. = 140*2*3/100
S.I. = $ 8.4
Hence total amount received by Charis at the end of 2 years will be $8.4
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I need this by tonight would be appreciated. :) I know this is basic stuff I'm in Middle School but when I signed up for this there wasn't a middle school option.
Answers
The area of the floor of the convenience store would be = 212.5 ft²
What is the area of an object?The area of an object is defined as the total space that is being occupied by that object.
To calculate the area of the convenience store is to find the area of the shaded part which would be = area of square - area of the triangle.
Area of square = l ×w = 15 × 15 = 225ft²
Area of triangle= 1/2 base ×height
= 1/2 × 5 × 5
(Note: 15 - 10 = 5 ft from the diagram used as base and height)
= 25/2
= 12.5 ft²
The area of the convenience store;
= 225 - 12.5
= 212.5 ft².
Therefore, the area that is covered by the convenience store should be = 212.5ft².
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