Find the area of the triangle. Round the answer to the nearest tenth.
A.
68.4 square units
B.
75.3 square units
C.
84.5 square units
D.
136.7 square units
Answers
Answer:
Option A. 68.4 square units.
Step-by-step explanation:
Since sides ED = EF = 13 units
So the given triangle is an isosceles triangle and in an isosceles triangle EFD, perpendicular drawn from E to DF, will be perpendicular bisector of DF.
Moreover, to this perpendicular bisector to DF will be the height of the triangle.
Now Area of a triangle of [tex]\frac{1}{2}[/tex] × base × height.
Sin 63 = [tex]\frac{Height}{Hypotenuse}[/tex] = [tex]\frac{h}{13}[/tex]
h = 13 sin 63 = 13 ( 0.891) = 11.583 units
Cos 63 = [tex]\frac{Base}{Hypotenuse}[/tex] = [tex]\frac{Base}{13}[/tex]
Base = 13 cos 63 = 13 × (0.454)
= 5.90 units
Since DF = 2 × base = 2 × 5.90
= 11.80 units
Now area of EDF = [tex]\frac{1}{2}[/tex] × 11.80 × 11.583
= 68.86 ≈ 68.40 square units.
Option A. 68.4 square units.
Related Questions
Match the corresponding function formula with each function when h(x) = 3x + 2 and g(x) = 2 x .
1. k(x) = 2x + 3x + 2 k(x) = g(x) ∘ h(x)
2. k(x) = 2x - 3x - 2 k(x) = g(x) + h(x)
3. k(x) = (3x)2-x + 2-x + 1 k(x) = h(x) ÷ g(x)
4. k(x) = 23x + 2 k(x) = g(x) - h(x)
5. k(x) = 2x(3x + 2) k(x) = g(x) × h(x)
6. k(x) = 3(2x) + 2 k(x) = h(x) ∘ g(x)
Answers
h(x) = 3x + 2
g(x) = 2^x
I proceed to calculate the different values of K (x)
case 1) k(x) = g(x) ∘ h(x)
g(x) ∘ h(x)=g(h(x))
k(x) = [2]^[3x + 2]-----------> is the option 4. k(x) = 2^(3x + 2 )
case 2) k(x) = g(x) + h(x)
k(x) = [2^x]+[3x + 2]=2^x+3x+2--------> is the option 1.) k(x) = 2^x + 3x + 2
case 3)k(x) = h(x) ÷ g(x)
k(x) = [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)
is the option 3.) k(x) = (3x)2^(-x) + 2^(-x + 1 )
case 4)k(x) = g(x) - h(x)
k(x) = [2^x]-[3x + 2]=2^x-3x-2--------> is the option 2.) k(x) = 2^x - 3x - 2
case 5) k(x) = g(x) × h(x)
k(x) = [2^x]*[3x + 2]-----------> is the option 5.) k(x) = 2^x(3x + 2)
case 6)k(x) = h(x) ∘ g(x)
h(x) ∘ g(x)=h(g(x))
k(x)=3*[2^x]+2---------------> is the option 6. k(x) = 3(2^x) + 2
To simplify the other user's answer (which is correct):
1 = B
2 = D
3 = C
4 = A
5 = E
6 = F
Alternatively, your right boxes should look like:
4
1
3
2
5
6
Which linear function has the greatest y-intercept?
A) x + 6y = 36
B) y = 15x + 5
C) 3x + 8y = 24
D) y = 4x + 7
Answers
Answer:
the answer is y=4x+7
Step-by-step explanation:
Please help me it's homework.
Answers
=======
2 faces of 2 * 8 = 32
2 faces of 2 * 7 = 28
2 faces of 7 * 8 = 112
Total = 172
Right Side Prism
=========
2 faces of triangles 1/2 * 7.2 * 4.8 = 34.56
1 bottom face of 7.2 * 10 = 72
2 slanted faces 6 * 10 = 120
Total 34.56 + 72 + 120 = 226.56
I'm in need of Brainlys. If this answer suits you can you award one if it is possible for you to do.
.can you please help me thank you you will be given brainley
Answers
Fiecare dintre cei 25 de elevi ai clasei a |||-a a realizat un jurnal al luni . Stiind ca pentru fiecare zi s-a folosit o pagina si ca luna are 31 de zile,afla cate pagini au jurnalele tuturor elevilor.
Answers
Each of the 25 students in the class has made a journal on Monday. Knowing that every day a page was used and that the month is 31 days, find out how many pages the logs of all students.
Let
x--------------> total students
y--------------> total days in a month
z--------------> total page used per one student in 1 day
T--------------> total page used per total students in 1 month
we know that
x=25 students
y=31 pages
z=1 page
T=[x]*[y]*[z]------------> T=[25]*[31]*[1]------------> T=775 pages
the answer is 775 pages
the answer in Romanian
lăsa
x--------------> numărul total de elevi
y--------------> total zile într-o lună
z--------------> pagina totală utilizată pentru un student în 1 zi
T--------------> pagina totală utilizată pentru toți elevii în 1 lună
noi stim aia
x=25 elevi
y=31pagini
z=1 pagină
T=[x]*[y]*[z]------------> T=[25]*[31]*[1]------------> T=775 pagini
răspunsul este de 775 de pagini
The image of a figure is shown. What are the coordinates of X in the pre-image of the figure if the rule that created the image was T–5.2, 1.4(x, y)? PLEASE ANSWER
X =
a. (-7.2, 3.4)
b. (1.2, 6.6)
c. (3.2, 0.6)
b. (9.2,-0.4)
Answers
Hope this somewhat helped! :)
Solve the following system of equations using matrices.
4x – 2y = -6
3x – 6y = -18
(40, 90)
(3, 0)
(0, 3)
(-6, 18)
Answers
.. (x, y) = (0, 3) . . . . . your 3rd selection
_____
I prefer using the RREF function to put the augmented matrix into reduced row-echelon form. If the equations are dependent or inconsistent, using that method tells you so without giving a matrix inversion error.
Number of security staff = a over 100 if a audience, is 10500, how many security staff are needed for the event
Answers
.. Number of security staff = 10500/100 = 105
A 10-foot ladder is leaning against a tree. The bottom of the ladder is 4 feet away from the bottom of the tree. Approximately how high up the tree does the top of the ladder reach?
A.2.4
B.6.0
C. 9.2
D. 10.8
Answers
Find the exact value of sin ( 2
a. if cos a = 3 /5 . assume a is a quadrant i angle in standard position.
Answers
From Pythagoras theorem the third side will be 4
cos a =3/5
sin a =4/5
sin 2a =2 x 4/5
sin 2a= 8/5
Select the correct factor from the presentation and calculate how many calories used. (Round to the hundredths.) A person weighing 165 lbs. jogs 1 mile in 8 minutes. How many calories used?
A. 102.30
B. 107.25
C. 253.85
D. 266.13
Answers
Answer:
the answer is 107.25
Step-by-step explanation:
Answer:
B. 107.25
Step-by-step explanation:
Let x be the calories burnt by the man,
Since, when a person runs 1 miles in 8 minutes,
Then,
[tex]\frac{\text{Calories used by him}}{\text{His weight in lb}}=65\%[/tex],
Given,
Weight of the person = 165 lb,
Thus,
[tex]\frac{x}{165}=\frac{65}{100}[/tex],
[tex]x = \frac{165\times 65}{100}[/tex]
[tex]x=\frac{10725}{100}[/tex]
[tex]\implies x=107.25[/tex]
Hence, 107.25 calories will be used.
HELP! ASAP!
What is the measure of ∠A?
What is the measure of ∠B?
Answers
Therefore
m∠A = m∠C, so that
5y - 3 = 3y + 27
Subtract 3y from each side.
5y - 3y - 3 = 3y - 3y + 27
2y - 3 = 27
Add 3 to each side.
2y - 3 + 3 = 27 + 3
2y = 30
y = 30/2 = 15
Therefore
m∠A = 5*15 - 3 = 72°
m∠C = 72°
Let x = m∠B
Then x = , m∠B = m∠C
Because the sum of the angles in the parallelogram is 360°, therefore
x + x + 72 + 72 = 360
2x = 360-144 = 216
x = 216/2 = 108
Answer:
m∠A = 72°
m∠B = 108°
Answer:
What is the measure of ∠A?
72°
What is the measure of ∠B?
108°
Step-by-step explanation:
I literally copied and pasted from edge
What is the denominator of the fraction 1/9?
Answers
any number below the bar is the denominator, any number above the bar is the numerator
Find all real values of $v$ that satisfy the equation $(v+6)^2 = 324$. If you find more than one, then list your values in increasing order, separated by commas.
Answers
(v+6)^2 = 324-----> I raise to 1/2 both members----> [(v+6)^2]^(1/2)=(324)^(1/2)[(v+6)]=(324)^(1/2)-------------> v+6=√324
v=√324-6---------> 18-6=12
v=12
the answer is v=12
Answer:
The values of v in increasing order are, -24, 12
Step-by-step explanation:
Given equation is,
[tex](v+6)^2=324[/tex]
[tex]v+6=\pm 18[/tex]
[tex]v=-6\pm 18[/tex]
[tex]\implies v=-6-18\text{ or }v=-6+18[/tex]
[tex]\implies v = -24\text{ or }v=12[/tex]
Since, -24 < 12
Thus, the values of v in increasing order are,
-24, 12
Ava bought a rectangular rug for her hallway. The rug is 2\3 yards wide and 2 3\4 yards long. What is the area of the rug as a mixed number in simplest form?
Answers
Answer:
1 5/6
Step-by-step explanation:
You are preparing to tile the floor of a rectangular room that is 15.5 feet by 18 feet in size. The tiles you plan to use are squares, measure 12 inches on each side, and are sold in boxes that contain enough tiles to cover 25 square feet. Each box costs $30.
To determine the cost of materials you multiply 15.5 by 18, divide by 25, round up to the next whole number, and multiply by 30. Is this correct?
A) Yes.
B) No, you need to round down and then multiply by 30.
C) No, you need to round down and then multiply by 144.
D) No, you need to divide by 144, round up, and then multiply by 30.
E) No, you need to divide by 144, round down, and then multiply by 30.
Answers
To find the cost of tiling the room, you have to calculate the area in square feet, convert tile size to the same units, calculate how many boxes needed and round up, then multiply by the cost per box. The correct answer is D).
Explanation:The correct answer is D). The process to determine the cost of the tiles needed to cover the room starts with calculating the area of the room in square feet. This is done by multiplying the room's length and width, so 15.5 feet * 18 feet which equals 279 square feet.
The tiles are 12 inches in size on each side, but the dimensions of the room are in feet. Therefore, we need to convert the tile size to square feet. Since 1 foot = 12 inches, 1 square foot = 144 square inches. Our tile is 12 inches * 12 inches = 144 square inches, which equals 1 square foot.
However, the tiles are sold in boxes that cover 25 square feet. So, we will divide the total room area by the area covered by one box of tiles. 279 square feet / 25 = 11.16 boxes needed, approximately.
It's important to round up at this stage, as you can't buy a fraction of a box. So, you'd need 12 boxes.
The last step is to calculate the total cost, which is done by multiplying the number of boxes by the cost of each box. So, 12 * $30 equals $360.
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Which equivalent expression would you set up to verify the associative property of addition for (3x + 4) + ((5x2 – 1) + (2x + 6))
(3x + 4) + (5x2 – 1)
(5x2 – 1) + ((3x + 4) + (2x + 6))
((3x + 4) + (5x2 – 1)) + (2x + 6)
(3x + 4) + (5x2 – 1) + (2x + 6)
Answers
(3x + 4) + [(5x2 - 1) + (2x + 6)]
As given in the definition below, to make it an associative property, we can change the bracket
[(3x + 4) + (5x2 - 1)] + (2x +6)
Your answer will be the third option :)
It's C.
Trust me, I had trouble figuring out this answer...
Find the smallest value of k if 264k is a perfect square
Answers
264k = 132*2k = 11*12*k = 11*3*2*2*k
To get a perfect square, you are going to have to have an even number of prime factors.
You have one 11 and one 3. You are going to have to do something about those two.
k = 11 * 3 <<<<< ======= answer.
Now put that into 264k and you get 11 * 3 * 2 * 2 * 11 * 3 which is a perfect square. 11^2 * 3^2 * 2^2 = 4356
The square root of 4356 = 66
4356 is a perfect square when 33 = k.
Given that ∆MTW ≅ ∆CAD, which angles are corresponding parts of the congruent triangles?
∠M ≅ ∠A
∠M ≅ ∠D
∠M ≅ ∠C
Answers
Answer:
It is M = C
Step-by-step explanation:
The measure of the angle ∠WMT is congruent to the measure of the angle ∠DCA. Then the correct option is C.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The triangle ∆MTW is congruent to the triangle ∆CAD. Then we have
∠MTW ≅ ∠CAD
∠TWM ≅ ∠ADC
∠WMT ≅ ∠DCA
The proportion of the point ∠WMT is harmonious with the proportion of the point ∠DCA. Then, at that point, the right choice is C.
More about the triangle link is given below.
https://brainly.com/question/25813512
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Why would someone choose to use a graphing calculator to solve a system of linear equations instead of graphing by hand? Explain your reasoning.
Sample Response: A graphing calculator is more accurate than graphing by hand. If the slope and/or y-intercept is a fraction or decimal, it is more difficult to accurately graph by hand. Using a calculator might also be more time efficient because it might accept a line in any form. A calculator’s window can be adjusted quickly instead of having to redraw a graph by hand when adjusting the scale.
Answers
1) You can write the system of linear equations as big as you want. This is: systems 3 * 3, 4 * 4, 5 * 5.
2) The response to systems of equations greater than 2 * 2 can be complicated when you graph the solution, therefore, the graphing calculator can be much more efficient in these cases.
3) You can write the linear equations in any way. Resolving by hand you should probably rewrite the system of equations to find the solution.
Which graph shows the equation y = x + 2?
Answers
A employer, who started a new business, has promised his employees a minimum starting wage of $3, with an increase of $2 every 4 years. Sketch a graph of wage as a function of time for 16 years. Assume the wages take effect at the beginning of the year where the change is made. (HINT: use a step function to represent the function.)
Answers
To sketch the graph, use a step function to represent the wage as a function of time over 16 years. The minimum starting wage is $3, and it increases by $2 every 4 years.
Explanation:
To sketch a graph of wage as a function of time for 16 years, we can use a step function to represent the function.
The minimum starting wage is $3 and it increases by $2 every 4 years. For the first 4 years, the wage will be $3. At the start of the 5th year, the wage will increase to $5. This pattern continues, with the wage increasing by $2 every 4 years.So, the graph will have flat lines representing each 4-year interval, with a step up at the start of each interval.
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what do all similar circles have in common
a) congruent circumference value
b) congruent diameters
c) π
Answers
All the similar circles have π in common.
Thus, option (c) is correct.
When two circles are similar, it means they have the same shape but possibly different sizes.
However, the ratio of their corresponding lengths, including the circumference, remains constant.
Second, the ratio of the diameter will be constant but not congruent.
Third, the value of π is the universal constant whose value is 22/7 or 3.14.....
which is the same for every similar circle.
Thus, π has a common value.
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How could the relationship of the data be classified? (1 point)
scatter plot with points loosely scattered going down to the right
Answers
X divides into the line PQ in the ratio 2:3 P is (2,1) and Q is (12.5,7.5) work out the coordinates of point X
Answers
x = 2/5(Q) + 3/5(P)
= 2/5(12.5,7.5) + 3/5(2,1)
= 2( 2.5, 1.5) + 3( 0.4, 0.2)
= (5,3) + (1.2,0.6)
= (6.2, 3.6)
The Coordinates of X will be;
=(6.2, 3.6)
Answer: (6.2, 3.6)
Step-by-step explanation:
We know that if a point M (x,y) divide a line segment having endpoints [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in ratio m:n , then the coordiantes of M is given by :-
[tex]x=\dfrac{mx_2+nx_1}{m+n}\ ;\ y=\dfrac{my_2+ny_1}{m+n}[/tex]
Given : X divides into the line PQ in the ratio 2:3 P is (2,1) and Q is (12.5,7.5).
Then, coordinate of X is given by :-
[tex]x=\dfrac{2(12.5)+3(2)}{2+3}\ ;\ y=\dfrac{2(7.5)+3(1)}{2+3}\\\\\Rightarrow\ x=\dfrac{31}{5}\ ;\ y=\dfrac{18}{5}\\\\\Rightarrow\ x=6.2\ ;\ y=3.6[/tex]
Hence, the coordinate of X = (6.2, 3.6)
Question 11 options: you take a ride on a ferris wheel which has a diameter of 300 feet. if you ride for four revolutions, what linear distance did you travel? use 3.14 for pi when completing your calculations. round your answer to the nearest whole number, if necessary. the distance traveled is
Answers
Can someone please help me with 4?? I’m really struggling.
Answers
m<DAC=y
m<BAC=3x
ABCD is a square so m<DAB = 90° because each angle in a square is a right angle so 3x+y=90° (1) ;
AC is a diagonal in the square so m<DAC=m<BAC so 3x=y (2);
Find x by substituting y to 3x from (2) into (1)
3x+3x=90
6x=90
x=90/6=15°
Answer x=15°
Debra is on the swim team. Each week she swims a total of 7000 meters. How many kilometers does she swim each week?
Answers
this is a physics question that requires a lot of math. Hoping on of you genius could help me.
Q: You're driving down the highway late one night at 16m/s when a deer steps onto the road 44m in front of you. Your reaction time before stepping on the brakes is 0.50s , and the maximum deceleration of your car is 10m/s2 .
How much distance is between you and the deer. I solved this =23m
What is the maximum speed you could have and still not hit the deer?
The answer is 25 m/s. A lot of people had stated to use the quadratic formula. I just don't know where to begin.
Answers
If it takes 0.5 seconds before stepping on the breaks while going 16 m/s, then you travel 8 meters before anything happens. That means you are 44-8 = 36 meters away from the deer now.
v^2 = v_initial^2 + 2(acceleration)(distance)
0 = (16 m/s)^2 + 2(-10m/s^2)(distance)
256 m^2/s^2 / (2(10 m/s^2) = distance = 12.8 meters (13 meters after significant figures are taken into account).
The maximum speed would be:
0 = v_initial^2 + 2(-10m/s^2)(36m)
v_initial^2 = 720m^2/s^2
v_initial = 27 mph
How do you solve this inequality: 7 ≤ x+11
Answers
7 ≤ x + 11
subtract 11 from both sides
-4 ≤ x
From there on, any number greater than or equal to -4 will be a solution to the inequality
Hope this helps
[tex] 7 \leq x+11 \\ \\ 7 -11\leq x \\ \\ -4 \leq x\qquad\to\qquad x\in \left[-4; +\infty) [/tex]