The students in a first-grade class were all asked to time how long (in seconds) they could hold their breath. The resultswere tallied and are presented in the following histogram.How many of those students held their breath greater than 12.5 and less than 15.5 seconds?
Answers
ANSWER:
13 students
STEP-BY-STEP EXPLANATION:
To find the answer we must add the number of students between the values 12.5 and 15.5, just like this:
[tex]\begin{gathered} 12.5-13.5=2\text{ students} \\ 13.5-14.5=5\text{ students} \\ 15.5-15.5=6\text{ students} \\ \text{Total}=\text{ }12.5-15.5=2+5+6=\text{ 13 students} \end{gathered}[/tex]Related Questions
does this represent exponential growth or exponential decay and identify the percent rate of changedetermine whether y= 500(1.08)t represents exponential growth or exponential decay and identify the rate of change.
Answers
Given:
[tex]500\mleft(1.08\mright)^t[/tex]To determine whether it represents exponential growth or exponential decay:
Since, the general exponential growth formula is,
[tex]f\mleft(x\mright)=a\mleft(1+r\mright)^x[/tex]Hence, the given represents exponential growth.
Comparing we get,
1+r=1.08
r=0.08
That is, r=8%
Therefore, the percentage rate of change is 8%.
Consider the following word problem:Two planes, which are 1180 miles apart, fly toward each other. Their speeds differ by 40 mph. If they pass each other in 2 hours, what isthe speed of each?Step 2 of 2: Solve the equation found in Step 1.
Answers
To answer this question, we can state the problem as follows:
1. The two planes are 1180 miles apart.
2. They fly toward each other.
3. Their speed differs by 40 mph: that is one of the planes is faster than the other 40 mph, or the other plane is slower than the other plane.
4. The time they encounter each other is 2 hours.
Then, we need to remember the formula for a constant speed:
[tex]V=\frac{d}{t}[/tex]Where
• d is the distance
,• t is the time
Then, we have that the speeds for each of the planes are:
[tex]V_{p1}=V_{p2}+40[/tex]We also have that the sum of the distance for both planes is 1180 miles:
[tex]d_{p1}+d_{p2}=1180[/tex]And we have that:
[tex]V=\frac{d}{t}\Rightarrow d=V\cdot t[/tex][tex]d_{p1}=V_{p1}\cdot t[/tex][tex]d_{p2}=V_{p2}\cdot t[/tex]But
[tex]V_{p1}=V_{p2}+40[/tex]Then, we have that:
[tex]d_{p1}+d_{p2}=1180[/tex][tex]V_{p1}\cdot t+V_{p2}\cdot t=1180\Rightarrow V_{p1}=V_{p2}+40[/tex][tex](V_{p2}+40)\cdot t+V_{p2}\cdot t=1180[/tex]Since t = 2, we have:
[tex](V_{p2}+40)\cdot2+V_{p2}\cdot2=1180[/tex][tex]2V_{p2}+80+2V_{p2}=1180\Rightarrow4V_{p2}+80=1180[/tex]Subtracting 80 from both sides of the equation:
[tex]4V_{p2}+80-80=1180-80\Rightarrow4V_{p2}=1100[/tex]Dividing both sides of the equation by 4, we have:
[tex]V_{p2}=\frac{1100}{4}\Rightarrow V_{p2}=275\text{mph}[/tex]Since we know that:
[tex]V_{p1}=V_{p2}+40[/tex]Then, we have:
[tex]V_{p1}=275\text{mph}+40\text{mph}\Rightarrow V_{p1}=315\text{mph}[/tex]In summary, therefore, the speed of each plane is:
• Speed of Plane 1 = 315 mph
,• Speed of Plane 2 = 275 mph
What’s the mid point of AB in the picture below
Answers
From the given linear graph, we would write out the co-ordinates of the points A and B first in the form of (x,y).
Thus, we have:
[tex]\begin{gathered} A(-6,-4) \\ B(-3,3) \end{gathered}[/tex]The mid-point of a line segment;
[tex]\begin{gathered} A(x_1,y_1)\text{ and} \\ B(x_2,y_2) \end{gathered}[/tex]is given as:
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Thus, we have:
[tex]\begin{gathered} (\frac{-6+(-3)}{2},\frac{-4+3}{2}) \\ (\frac{-6-3}{2},-\frac{1}{2}) \\ (\frac{-9}{2},-\frac{1}{2}) \\ (-4.5,-0.5) \end{gathered}[/tex]Hence, the midpoint of the line segment AB is: ( -4.5, -0.5)
Evan is going to the 50th state fair this weekend. It costs $10 to enterand each ride is $2. How much will it cost Evan to go to the fair and ride 5rides? **Don't forget the initial cost.**( hint: determine the equation first y =X + and then plug in 5 for x) *
Answers
From the question, we are given the following;
Cost of entering the state fair = $10
Amount of each ride = $2
For us to determine the amount it will cost Evan to go to the fair and ride 5 rides, the equation y = $10 + 2x will be used where;
x is the total ride taken = 5 rides
y is the amount it cost evan to enter the state fair and ride 5 rides
Substitute x = 5 into the equation and get y;
y = $10 + 2x
y = $10 + $2(5)
y = $10 + $10
y = $20
Hence it will cost Evans $20 to go to the fair and ride 5 rides
jenelle and hadiya went to lunch,the bill,before sales before sales tax and tip,was 37.50.a sales tax of 8% was added.they added an 18% tip on the amount after the tax was added.a)what was the amount,in dollars,of the sales tax.b)what was the total amount they paid,including tax and tip.
Answers
$37.50
tax = 8%
tip = 18%
a) 37.5 ------------------ 100%
x ------------------- 8%
x = (8 x 37.5) / 100
x = 3
Tax = $3
b) Money of lunch plus tax = $40.5
40.5 -------------------- 100
x --------------------- 18
x = (18 x 40.5) / 100
x = 7.29
Total amount paid = 7.29 + 40.5
= $ 47.79
10. Find f(-3) + 1 using the following equation f(x) = 5x – 4
Answers
We are to find the value of f(-3) + 1
using the following expression for f(x):
f(x) = 5 x - 4
Then f(-3) = 5 (-3) - 4 = -15 - 4 = - 19
since we need to add 1 to this result, we get:
f(-3) + 1 = -19 + 1 = - 18
The length of a rectangle is 1m more than twice the width, the area of the rectangle is 45m^2
Answers
Let l and w be the length and width of the rectangle, respectively; therefore, according to the question
[tex]\begin{gathered} l=2w+1 \\ and \\ l*w=45 \end{gathered}[/tex]Where l and w are in meters.
Substitute the first equation into the second one, as shown below
[tex]\begin{gathered} l=2w+1 \\ \Rightarrow(2w+1)*w=45 \\ \Rightarrow2w^2+w=45 \\ \Rightarrow2w^2+w-45=0 \end{gathered}[/tex]Solve for w using the quadratic formula,
[tex]\begin{gathered} \Rightarrow w=\frac{-1\pm\sqrt{1+4*2*45}}{2*2}=\frac{-1\pm\sqrt{361}}{4}=\frac{-1\pm19}{4} \\ \Rightarrow w=\frac{9}{2},-5 \end{gathered}[/tex]But w has to be positive since it is a measurement; therefore, w=9/2.
Finding l given the value of w=9/2,
[tex]\begin{gathered} w=\frac{9}{2} \\ \Rightarrow l=2(\frac{9}{2})+1=10 \\ \Rightarrow l=10 \end{gathered}[/tex]Thus, the answers are length=10 m, width=4.5m
you are trying to upload a photo for your school picture,but you need to reduce the size of the photo by a quarter of its original size. Which is the correct power that will reduce the picture by a quarter?A: 2^2B: 2^4C: 2^-2D: 2^-4
Answers
the scale factor is 1/4, which is equivalent to:
[tex]\frac{1}{4}=\text{ }\frac{1}{2^2}=2^{-2}[/tex]If x is perpendicular to a and X is perpendicular to b then____X is perpendicular to a A // BA is perpendicular to YX // Y
Answers
Use the figures below. What is the ratio of AD to JM? A.2/3B.6/5C.3/2
Answers
Given:
Rectangle ABCD is similar to rectangle JKLM
From the first rectangle, we have:
AB = 15
DC = 6
From the second rectangle, we have:
JM = 10
ML = 5
We know that,
AD ~ JM
DC ~ ML
Thus, we have the ratio as:
[tex]\frac{AD}{JM}=\frac{DC}{ML}[/tex][tex]\begin{gathered} \frac{AD}{JM}=\frac{15}{10}=\frac{3}{2} \\ \end{gathered}[/tex]Therefore the ratio of AD to JM is:
[tex]\frac{3}{2}[/tex]ANSWER:
[tex]C\text{. }\frac{3}{2}[/tex]A house is worth $350,000 when purchased. It was worth $335,000 after the firstyear and $320,000 after the 2ndyear.1. Geometric or Arithmetic and Why?2. Complete a table that shows the value of the house for 5 years.3. Write an explicit and recursive formula for the sequence.4. What is the value of the house after you have lived in it for 10 years?
Answers
A house is worth $350,000 when purchased. It was worth $335,000 after the first year and $320,000 after the 2nd year.
So, the difference between initial cost and the cost after one year =
335,000 - 350,000 = -15,000
The difference between the cost after one year and after 2 years =
320,000 - 335,000 = -15,000
As the common difference is constant
so, the cost represents Arithmetic sequence
the first term is 330,000 and the common difference is -15,000
The general form of the sequence is a + d(n - 1)
where a is the first term and d is the common difference and n the number of term
so, a = 335,000 and d = -15,000
so, the general form will be = 335,000 - 15,000(n-1)
So, the value of the house after 5 years = 335,000 - 15,000 * (5-1) = 275,000
-------------------------------------------------------------------------------------------------
1. Geometric or Arithmetic and Why?
Arithmetic
2. Complete a table that shows the value of the house for 5 years.
For 5 years:
first year = $335,000
second year = $320,000
third year = $305,000
fourth year = $290,000
fifth year = $275,000
3. Write an explicit and recursive formula for the sequence.
The formula will be : 335,000 - 15,000(n-1)
4. What is the value of the house after you have lived in it for 10 years?
After 10 years;
the value of the house = 335,000 - 15,000 * (10-1)
= 335,000 - 15,000 * 9 = $200,000
====================================================================
what is x^3 - 2x^2 - 4x - 1 divided by x + 1 ?
Answers
To answer this question we will use the long division.
Using long division we get:
Therefore:
[tex]\frac{x^3-2x^2-4x-1}{x+1}=x^2-3x-1.[/tex]Answer: Option A.
I need help with this question can you please help me ?
Answers
Answer:
Given that,
The product of a number and 6 equals twice the result of the sum of the number and 6.
Let the number be x,
product of a number and 6 is 6x.
sum of the number and 6 is x+6.
we get,
[tex]6x=2(x+6)[/tex]a) The equation could be used to find the number is,
[tex]6x=2(x+6)[/tex]b) On solving the above equation we get,
[tex]6x=2x+12[/tex][tex]6x-2x=12[/tex][tex]4x=12[/tex][tex]x=3[/tex]The number is 3.
Answer is: 3
What is the lateral surface area of the prism shown below? 9 m 6m 6 m 10 m
Answers
we are asked to find the surface area of a prism. To do that, we will find the areas of each lateral rectangle and the areas of the top and bottom triangles.
The areas of the rectangles are:
[tex]\begin{gathered} A_1=(10)(6)=60 \\ A_2=(10)(6)=60 \\ A_3=(10)(50)=50 \end{gathered}[/tex]To determine the ara of the top triangle we will use the following formula:
[tex]undefined[/tex]Which situation is best modeled by the graph? a.) the cost of buying muffinsb.) the distance between the train and the station as the train travels towards the stationc.) the amount of money left in the roll of quarters after paying a roll each dayd.) the distance a runner covers traveling at a steady paste
Answers
Notice that the graph plots points that as we move along the horizontal axis, go down in value. The Horizontal axis is most likely representing the time elapsed in each description.
Then, we DISCARD the first answer, since the cost of muffins don't go down as time goes by.
Answer b is a POSSIBLE answer, since the distance as the train approaches the station, is reducing (going down in value) as time goes by.
Answer C is not a good answer (we discard it) since after paying a roll each day, the number of quarters in each roll doesn't go down because we pay with the entire roll.
Answer d is also discarded, since the distance covered by the runner, should be going UP (increasing) as time goes by
Therefore, answer b) is the selected answer.
Find the missing dimension of the figure shown to the right round to the nearest tenth.
Answers
On the right triangle, we know the measure of the hypotenuse and one of its sides, then, using the pythagorean theorem, we get:
[tex]x=\sqrt[]{(29)^2-(14)^2}=\sqrt[]{841-196}=\sqrt[]{645}=25.4[/tex]therefore, the missing dimension is 25.4''
Please I need help finding the equation of the parallel line and the perpendicular line.
Answers
The equation parallel to the given equation and passing through the point (8, 3) is:
[tex]y\text{ = }\frac{5}{2}x\text{ - 17}[/tex]The equation perpendicular to the given equation and passing through the point (8, 3) is:
[tex]y\text{ = }\frac{-2}{5}x\text{ + }\frac{31}{5}[/tex]Explanations:The equation of the line parallel to the line y = mx + c and passing through the point (x₁, y₁) is given as:
[tex]y-y_1=m(x-x_1)[/tex]The equation of the line perpendicular to the line y = mx + c and passing through the point (x₁, y₁) is given as:
[tex]y-y_1\text{ = }\frac{-1}{m}(x-x_1)[/tex]Now, for the equation:
[tex]\begin{gathered} y\text{ = }\frac{5}{2}x\text{ - 7} \\ m\text{ = }\frac{5}{2} \end{gathered}[/tex]The line parallel to the equation and passing through the point (8, 3) will be:
[tex]\begin{gathered} y\text{ - 3 = }\frac{5}{2}(x\text{ - 8)} \\ y\text{ - 3 = }\frac{5}{2}x\text{ - 20} \\ y\text{ = }\frac{5}{2}x\text{ - 20 + 3} \\ y\text{ = }\frac{5}{2}x\text{ - 17} \end{gathered}[/tex]The line perpendicular to the given equation and passing through the point (8, 3) will be:
[tex]\begin{gathered} y\text{ - 3 = }\frac{-2}{5}(x\text{ - 8)} \\ y\text{ - 3 = }\frac{-2}{5}x\text{ + }\frac{16}{5} \\ y\text{ = }\frac{-2}{5}x\text{ + }\frac{16}{5}+3 \\ y\text{ = }\frac{-2}{5}x\text{ + }\frac{31}{5} \end{gathered}[/tex]Find the volume of thetriangular prism.24 m7 m3.6 mThe volume of the triangular prism ism3
Answers
The volume of a triangle prism formula is shown below.
[tex]\text{Volume of a triangular prism = Base area x Lenght}[/tex]From the figure,
The triangle of base 3.6m and height 24m is the base of the prism.
Therefore, the base area is the area of the triangle.
Area of the triangle = 1/2 x base x height
Area = 1/2 x 24 x 3.6
= 12 x 3.6
= 43.2
The volume = Base area x Length
Length = 7m
Base area = 43.2 meter square
Therefore,
The violume = 43.2 x 7
= 302.4
Final amswer
[tex]\text{Volume = 302.4 m}^3[/tex]Hello, I need some assistance with this homework question please for precalculusHW Q15
Answers
Solution
The remainder theorems state that when a polynomial a(x) is divided by a linear polynomial b(x) whose zero is x = k, the remainder is given by r = a(k).
Given
[tex]f(x)=4x^3-10x^2+10x-4[/tex]since f(x) is divided by x - 2, the remainder is
[tex]f(2)=4(2)^3-10(2)^2+10(2)-4=4(8)-10(4)+20-4=32-40+20-4=8[/tex]Therefore, the remainder is 8
Which answers describe the shape below? Check all that apply.A. SquareB. RhombusC. QuadrilateralD. TrapezoidE. RectangleF. Parallelogram
Answers
Recall the following definitions:
A square is a shape that has 4 sides. All of them with the same length. It has 2 pairs of parallel sides and has 4 right angles. Based on this definition, the given shape is a square.
A rhombus is a shape that has 4 sides. It has two pairs of parallel sides and each par has the same length. Based on this definition, it is also a rhombus.
A quadrilateral is closed shape that has 4 sides. Based on this definition, this shape is also a quadrilateral.
A trapezoid is a quadrilateral that has exactly one pair of parallel sides. As in this case we have two pairs of parallel sides, it is not a trapezoid.
A rectangle is a quadrilateral that has a pair of parallel sides of equal length and has 4 right angles. Based on this definition, this shape is also a rectangle.
A parallelogram is a quadrilateral that has two pairs of parallel sides with the same length. Based on this definition, this shape is also a parallelogram
Find g′(4) given that f(4)=5, f′(4)=−1, and g(x)=(√x)*f(x).
Answers
Given that:
[tex]g(x)=\sqrt[]{x}f(x)[/tex]You need to find:
[tex]g^{\prime}(x)[/tex]In order to derivate the function, you need to apply the Product Rule
[tex]\frac{d}{dx}(u\cdot v)=u\cdot v^{\prime}+v\cdot u^{\prime}[/tex]Then, you get:
[tex]g^{\prime}(x)=\sqrt[]{x}\cdot f^{\prime}(x)+f(x)(\sqrt[]{x})^{\prime}[/tex]Since:
[tex]\sqrt[]{x}=x^{\frac{1}{2}}[/tex]You know that:
[tex]\frac{d}{dx}(\sqrt[]{x})=\frac{1}{2}x^{\frac{1}{2}-1}=\frac{1}{2}x^{-\frac{1}{2}}=\frac{1}{2\sqrt[]{x}}[/tex]Hence:
[tex]\begin{gathered} g^{\prime}(x)=\sqrt[]{x}\cdot f^{\prime}(x)+f(x)(\frac{1}{2\sqrt[]{x}}) \\ \\ g^{\prime}(x)=\sqrt[]{x}\cdot f^{\prime}(x)+\frac{1}{2\sqrt[]{x}}f(x) \end{gathered}[/tex]Knowing that you need to find:
[tex]g^{\prime}(4)[/tex]You can rewrite the function as follows:
[tex]g^{\prime}(4)=\sqrt[]{4}\cdot f^{\prime}(4)+\frac{1}{2\sqrt[]{4}}f(4)[/tex]Knowing that:
[tex]\begin{gathered} f\mleft(4\mright)=5 \\ f^{\prime}\mleft(4\mright)=-1 \end{gathered}[/tex]You can substitute values:
[tex]g^{\prime}(4)=(\sqrt[]{4})(-1)+(\frac{1}{2\sqrt[]{4}})(5)[/tex]Evaluating, you get:
[tex]\begin{gathered} g^{\prime}(4)=(2)(-1)+(\frac{1}{2\cdot2})(5) \\ \\ g^{\prime}(4)=-\frac{3}{4} \end{gathered}[/tex]Hence, the answer is:
[tex]g^{\prime}(4)=-\frac{3}{4}[/tex]
What type of model does the data suggest?х01234y2.55102040A ConstantB ExponentialCLinearD) Quadratic
Answers
The function for this data can be represented as:
[tex]y=5\times2^{n-2}[/tex]Therefore, it is exponential.
The figure below was made with a scale of 1 unit = 9 cm.Draw the figure with a new scale of 1 unit = 3 cm.You can place your figure anywhere on the grid on the right.9 cmCurrent scale1 unit = 9 cmExplanationCheck3 cmNew scale1 unit = 3 cmI need help with this math problem
Answers
We will draw the figure
In a new scale, the new scale is
[tex]1\text{ unit= 3 cm}[/tex]Note that the draw above is a square of side 18cm, therefore in the new scale the side of the square have to be drawn using
[tex]\frac{18cm}{3cm}=6\text{ }units[/tex]That is, if we change the units our new square have a side of 6 units as follows
Let c(t) be the number of customers in a restaurant t hours after 8 a.m. Explain the meaning of each statement.c(3)=c(3)
Answers
Given:
Here, c(t) be the number of customers in a restaurant t hours after 8 a.m.
The statement is,
[tex]c\left(3\right)=c\left(3\right)[/tex]To find:
The meaning of the given statement.
Explanation:
Since c(t) is the number of customers in a restaurant t hours after 8 a.m.
So, c(3) be the number of customers in a restaurant 3 hours after 8 a.m.
That is,
The number of customers in a restaurant 3 hours after 8 a.m is equal to the number of customers in a restaurant 3 hours after 8 a.m.
Final answer:
The number of customers in a restaurant 3 hours after 8 a.m is equal to the number of customers in a restaurant 3 hours after 8 a.m.
Please help with number 8Solve each equation by completing the square.simplify all irrational and complex situations
Answers
We're going to solve by completing the square the given equation:
5x²+14x=3 (divide both sides by 5)
x² +(14/5)x=3/
Three points are shown on the coordinate plane.What is the distance from point A to point B?
Answers
Answer:
The distance from point A to point B is;
[tex]5\text{ units}[/tex]Explanation:
Given the points A and B with coordinates as shown on the graph;
[tex]\begin{gathered} A(0,5) \\ B(3,1) \end{gathered}[/tex]Recall that the distance between two points can be calculated using the formula;
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]substituting the coordinates of point A and B. we have;
[tex]\begin{gathered} d=\sqrt[]{(3-0)^2+(1-5)^2} \\ d=\sqrt[]{3^2+4^2} \\ d=\sqrt[]{9+16} \\ d=\sqrt[]{25} \\ d=5 \end{gathered}[/tex]Therefore, the distance from point A to point B is;
[tex]5\text{ units}[/tex]Ravi had 119 dollars to begin with. He just spent b dollars.using. B, write expression for the number of dollars he has left
Answers
Given:
Total money Ravi has to begin with = 119 dollars.
He spent b dollars.
The number of dollars he has left is:
119 - b
The coordinates of three vertices of a rhombus are (-3, 0), (0, 5) and (3, 0). What are the coordinates of the fourth vertex?
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given coordinates
[tex]A(-3,0),B(0,5),C(3,0),D(x,y)[/tex]STEP 2: State the side properties of a rhombus
In a rhombus, all sides are equal. This means that the length of the sides are equal and therefore the distances of the vertices apart will be the same.
And also, Diagonals of rhombus bisect each other. This implies that:
Co-ordinates of mid-points of AC= Co-ordinates of mid-points of BD
STEP 3: Find the distances of the sides
Midpoints of AC will be calculated as:
[tex]\begin{gathered} \mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right) \\ \left(x_1,\:y_1\right)=\left(-3,\:0\right),\:\left(x_2,\:y_2\right)=\left(3,\:0\right) \\ =\left(\frac{3-3}{2},\:\frac{0+0}{2}\right) \\ =\left(0,\:0\right) \end{gathered}[/tex]Midpoints of BD will be calculated as:
[tex]\begin{gathered} \mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right) \\ \left(x_1,\:y_1\right)=\left(0,\:5\right),\:\left(x_2,\:y_2\right)=\left(x,\:y\right) \\ =\left(\frac{x+0}{2},\:\frac{y+5}{2}\right) \\ =\left(\frac{x}{2},\:\frac{y+5}{2}\right) \end{gathered}[/tex]Since midpoints are the same as mentioned above, this means that:
[tex]\begin{gathered} \left(\frac{x}{2},\:\frac{y+5}{2}\right)=(0,0) \\ \frac{x}{2}=0,x=0 \\ \frac{y+5}{2}=0,y+5=0,y=-5 \\ \\ \therefore(x,y)=(0,-5) \end{gathered}[/tex]Hence, the coordinates of the fourth vertex is given as:
[tex][/tex]Find the length of side x in simplest radical form with a rational denominator.30°х60°12
Answers
Ok, to find the lenght of side x we are going to use the sine function:
[tex]\sin (30)=\frac{12}{x}[/tex]Clearing x:
[tex]x=\frac{12}{\sin (30)}=\frac{12}{1/2}=24[/tex]Finally we get that x is equal to 24.
In this diagram, ABAC – AEDF. If thearea of ABAC = 6 in2, what is thearea of AEDF?DAE 2 inB3 inс=Area = [? ] in2Enter a decimal rounded to the tenths.a
Answers
Area of ΔBAC = 6 in^2
EF = 2 in
BC = 3 in
Both triangles are similar, so:
Area ΔBAC : Area of ΔEDF = BC^2 : EF^2
Replacing:
6 / Area of ΔEDF = 3^2 / 2^2
Cross multiply
6 * 2^2 = 3^2 * Area of ΔEDF
24 = 9 * Area of ΔEDF
24/9 = Area of ΔEDF
Area of ΔEDF = 8/3 in^2 = 2.7 in^2