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If the dimensions of a rectangle ABCD are 15 x 12, what is the area of rectangle BEFD?
Answers
Answer:
The area of rectangle BEFD is 180 square units.
Step-by-step explanation:
After checking the figure given, we have the following information:
[tex]AD = 15[/tex], [tex]AB = 12[/tex], [tex]BC = 15[/tex], [tex]CD = 12[/tex]
By Pythagorean Theorem, we determine the length of the line segment BD:
[tex]BD = \sqrt{AB^{2}+AD^{2}}[/tex] (1)
[tex]BD = \sqrt{12^{2}+15^{2}}[/tex]
[tex]BD = 3\sqrt{41}[/tex]
In addition, we know the following characteristics of the rectangle BEFD:
[tex]BD = EF[/tex], [tex]EF = EC + CF[/tex], [tex]BE = FD[/tex] (2), (3), (4)
By Pythagorean Theorem:
[tex]BC^{2} = BE^{2}+EC^{2}[/tex] (5)
[tex]CD^{2} = CF^{2}+DF^{2}[/tex] (6)
By (3), (4), (5) and (6):
[tex]BC^{2} = BE^{2} + EC^{2}[/tex] (7)
[tex]CD^{2} = (EF-EC)^{2} + BE^{2}[/tex] (8)
By (7) in (8):
[tex]CD^{2} = (EF-EC)^{2}+ (BC^{2}-EC^{2})[/tex]
[tex]CD^{2} = EF^{2}-2\cdot EF\cdot EC + EC^{2}+BC^{2}-EC^{2}[/tex]
[tex]CD^{2} = EF^{2}-2\cdot EF\cdot EC +BC^{2}[/tex]
Then, we clear [tex]EC[/tex]:
[tex]2\cdot EF\cdot EC = EF^{2} + BC^{2} - CD^{2}[/tex]
[tex]EC = \frac{EF^{2}+BC^{2}-CD^{2}}{2\cdot EF}[/tex]
If we know that [tex]EF = 3\sqrt{41}[/tex], [tex]BC = 15[/tex] and [tex]CD = 12[/tex], then the length of the segment [tex]EC[/tex] is:
[tex]EC = \frac{75\sqrt{41}}{41}[/tex]
And the length of the line segment [tex]CF[/tex] is:
[tex]CF = EF - EC[/tex]
[tex]CF = 3\sqrt{41}-\frac{75\sqrt{41}}{41}[/tex]
[tex]CF = \frac{48\sqrt{41}}{41}[/tex]
And the length of the line segment [tex]DF[/tex] is determined by Pythagorean Theorem:
[tex]FD = \sqrt{CD^{2}-CF^{2}}[/tex]
[tex]FD = \sqrt{12^{2}-\left(\frac{48\sqrt{41}}{41} \right)^{2}}[/tex]
[tex]FD = \frac{60\sqrt{41}}{41}[/tex]
And the area of the rectangle is determined by the following formula:
[tex]A = FD\cdot EF[/tex]
[tex]A = \left(\frac{60\sqrt{41}}{41} \right)\cdot (3\sqrt{41})[/tex]
[tex]A = 180[/tex]
The area of rectangle BEFD is 180 square units.
Related Questions
John read the first 144 pages of a novel, which was 3 pages less than 1/3 of the novel. Write an equation to determine the total number of pages (p in the novel.
Find the total number of pages in the novel.
Answers
Answer: 441 pages
Step-by-step explanation:
[tex]\frac{1}{3}p-3=144\\\frac{1}{3}p=147\\3(\frac{1}{3})p=147(3)\\p=441[/tex]
what is 13.5/10 simplified
Answers
Answer:
27/20
Step-by-step explanation:
[tex]\frac{13.5}{10} = \frac{13.5 * 2}{10 * 2} = \frac{27}{20}[/tex]
Check if -2 is the solution of equation 2 – x = 4x + 3
Answers
Answer:
7x the answer i think
Step-by-step explanation:
Answer:
[tex]\boxed {\boxed {\sf -2 \ is \ not \ a \ solution}}[/tex]
Step-by-step explanation:
We are asked to check is -2 is the solution of the following equation.
[tex]2-x= 4x+3[/tex]
We must substitute -2 in for x and solve both sides of the equation. If the two sides are equal, then -2 is the solution.
[tex]2- (-2) = 4(-2)+3[/tex]
Solve both sides of the equation according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Let's start with the left side.
[tex]2+2= 4(-2)+3 \\[/tex]
[tex]4= 4(-2)+3[/tex]
Now solve the right side. Remember to multiply first.
[tex]4= -8+3[/tex]
[tex]4= -5[/tex]
[tex]4\neq -5[/tex]
4 is not equal to -5, so -2 is not the solution for this equation.
need some help with this
Answers
Answer:
A horizontal line has a slope of zero
Step-by-step explanation:
Let’s start by some examples!
We’re going to use two points that identify that a horizontal line has a slope of zero
Two points will be: (7, 4) & (7, -6)
Then use the Slope-Formula to identify the slope
Slope = change in y/change in x
Slope = (y2 - y1)/(x2 - x1)
Slope = (-6 - 4)/(7 - 7)
Slope = -10/0
Slope = 0
Therefore, a horizontal line has a slope of zero
Answer:
Zero (0)Step-by-step explanation:
Horizontal lines have no steepness at all because any calculation the slope of line means dividing zero by another number to the answer is always zero
A table is made using the following two patterns.
Pattern 2: Starting number: 5, Rule: Multiply by 3
1
Pattern y: Starting number: 20, Rule: Multiply by
2
Complete the table for the given patterns.
C
y
5
20
Answers
Answer:
x y
5 20
15 10
45 5
Step-by-step explanation:
Pattern x:
Start with 5.
Multiply by 3: 5 * 3 = 15
Multiply by 3: 15 * 3 = 45
Pattern x:
Start with 20.
Multiply by 1/2: 20 * 1/2 = 10
Multiply by 1/2: 10 * 1/2 = 5
x y
5 20
15 10
45 5
30 points please help
Find the volume of the pyramid.
76.34 ft3
458.06 ft3
916.11 ft3
305.37 ft3
Answers
Answer:
With the formula of lwh/3 the answer is 305.37
Step-by-step explanation:
l×w×h /3 =305.37
Answer:
916.11 ft³
Step-by-step explanation:
(9×6)×7.83/2×13/3
= 211.41×13/3
= 916.11 ft³
Answered by GAUTHMATH
what is the decrease of a right angle pls help i suck at math NVM ITS 90
Answers
Answer: 90 degrees
Step-by-step explanation:
Viết phương trình đường thẳng biết
a) vuông góc với đường thẳng x+2y=1 và đi qua A(1;2)
b) đi qua gốc toạ độ và đi qua điểm M (-1;3)
Answers
Answer:
Step-by-step explanation:
a) 2x - y = 0
True or False:
4x and 4x2 are like terms
Answers
Actually its false
In algebra 4x and 4x² are two different terms and are not like terms.
Must click thanks and mark brainliest
This is the recursive formula for a geometric sequence:
f(1)=8,000
f(n)=1/2(n − 1), for n > 2
What is the fifth term in the sequence?
Answers
Answer:
Step-by-step explanation:
f(1) = 8000
f(2) = 1/2(n - 1)
f(2) = 1/2(2 - 1)
f(2) = 1/2 Note: this really does not make sense. I think what you mean is 1/2*f(n-1). If this is true, leave a note within the next hour.
Answer:
f(5) = 500
Step-by-step explanation:
Using the recursive rule and f(1) = 8000 , then
f(2) = [tex]\frac{1}{2}[/tex] f(1) = [tex]\frac{1}{2}[/tex] × 8000 = 4000
f(3) = [tex]\frac{1}{2}[/tex] f(2) = [tex]\frac{1}{2}[/tex] × 4000 = 2000
f(4) = [tex]\frac{1}{2}[/tex] f(3) = [tex]\frac{1}{2}[/tex] × 2000 = 1000
f(5) = [tex]\frac{1}{2}[/tex] f(4) = [tex]\frac{1}{2}[/tex] × 1000 = 500
Given the arithmetic sequence 2, -7, -16, -25, ..., determine the
general term tn.
Answers
Answer:
Step-by-step explanation:
Common difference is -9.
t_1 = 2
t_n = t_1 - (n-1)9
= t_1 - (9n - 9)
= 2 - (9n - 9)
= 11 - 9n
find the missing side. Round it to the nearest tenth.
Answers
Answer:
19.1
Step-by-step explanation:
Answer:
x ≈ 19.1
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos33° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{16}{x}[/tex] ( multiply both sides by x )
x × cos33° = 16 ( divide both sides by cos33° )
x = [tex]\frac{16}{cos33}[/tex] ≈ 19.1 ( to the nearest tenth )
Answer problem below
Answers
9514 1404 393
Answer:
17.078 square units
Step-by-step explanation:
The area of a segment is given by the formula ...
A = 1/2r²(θ -sin(θ)) . . . . where θ is in radians
The angle θ is 48°, or π(48°/180°) radians = 4π/15 radians.
Then the segment area is ...
A = (1/2)(19²)(4π/15 -sin(48°)) = 17.078 . . . square units
divide 12by8 and 4by3
Answers
Ms. Dawson’s call did a science experiment. The class started out with 650 bacteria cells. The growth rate predicted was 4.5%. Sketch the graph that represents the situation. Label the y-intercept and the point that represents the projected bacteria population 30 h from the start of the experiment. Round to the nearest whole number.
Answers
Answer:
your slope would be 4.5.... so go up 4 and to the right 5. the y-intercept is 650 so that is where your line would start instead of at 0... hope this helped :)
Step-by-step explanation:
The exponential function gotten from the table is given by y = 650(1.045)ˣ
Exponential functionAn exponential function is in the form:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multipliers.
Let y represent the bacteria population after x hours.
The class started out with 650 bacteria cells.
a = 650Growth rate = 4.5%
b = 100% + 4.5% = 104.5% = 1.045The exponential function gotten from the table is given by y = 650(1.045)ˣ
After 30 hours:
y = 650(1.045)³⁰ = 2434Find out more on exponential function at: https://brainly.com/question/12940982
Find the total surface area of this square based
pyramid.
10 in
5 in
Answers
Answer:
125in
Step-by-step explanation:
Each triangular face has a base of 5 in and a height of 10 in. The area of it is given by the formula ...
A = (1/2)bh
A = (1/2)(5 in)(10 in) = 25 in²
The square base has an area given by the formula ...
A = s² . . . . . where s is the side length
A = (5 in)² = 25 in²
The total area is the sum of the areas of the 4 faces and the base:
total area = 4 × (area of 1 face) + (area of base)
total area = 4 × (25 in²) + 25 in²
total area = 125 in²
Justin is saving money to buy a stereo. He has $25 saved in the bank right now. He earns $40 each week delivering newspapers.
Let y = the total amount of money Justin has, and x is in weeks.
Answers
Insert the missing number.
4
6 9 14
23
40
?
138
266
Answers
Answer: The missing number is 73
Step-by-step explanation:
Given:
4, 6, 9, 14, 23, 40, ?, 138, 266
Solve:
First, we try arithmetic patterns.
6 - 4 = 2
9 - 6 = 3
14 - 9 = 5
23 - 14 = 9
40 - 23 = 17
Clearly, there aren't arithmetic patterns.
Then, try through multiplication, exponents, and combination.
Finally, the pattern is multiplied by 2 on each number, then subtract 2 starting with 4 and add 1 for each increasing number.
4×2-2=6
6×2-3=9
9×2-4=14
As it goes on, the missing number would be:
40×2-7=73
Hope this helps!! :)
Please let me know if you have any questions
the sum of the ages of a man and his wife is at least 104 years if the man is x years old and the wife is x - 4 years old find the possible values of x
Answers
Answer:
x + ×-4 > or =104
X> or =54
am I right please ?
the sum of the ages of a man and his wife is at least 104 years if the man is x years old and the wife is x - 4 years old find the possible values of x
Solution :x + x - 4 = 1042x - 4 = 1042x = 108x = 108/2 x = 54Hence, the possible value for x is 54
Find the midpoint of the segment with the following endpoints.
(-8, 7) and (0,1)
Answers
Answer:
(-4,4)
Step-by-step explanation:
To find the x coordinate of the midpoints, add the x coordinates of the endpoints and divide by 2
(-8+0)/2 = -8/2 = -4
To find the y coordinate of the midpoints, add the y coordinates of the endpoints and divide by 2
( 7+1)/2 = 8/2 =4
(-4,4)
2. Find 3 rational number between:
1) -5 and -6 2) ( -1/7) and (1/8)
i need steps
explanation also pls guys
Answers
Step-by-step explanation:
between -5 and -62
-7,-10,-60...so..on
between -1/7 and 1/8
Multiply any number by number with both the numbers but it should be multiplied by both the numbers:
for example:
-1/7×3/3= -3/21 ; 1/8×3/3= 3/24
So,
-2/21,2/24,1/24
hope it helps
This...ik what mean is I'm just trying to find what the original numbers would be?
Answers
Answer:
17.5
Step-by-step explanation:
all the 10 numbers added together equal 10*16 = 160
-this is because all of the numbers added, and then divided by 10 equals 16
so the numbers in total, added equal 160.
subtract 20 (7+13) from 160 = 140
divide by 8
140/8 = 17.5
17.5
Explanation 17×5 is five but 2×5 is seven so 7×10 is 10
Find the multiples of 7 which is greater than 56 but less than 77
Answers
Answer:
63,70
Step-by-step explanation:
7 x 8 = 56
7 x 11 = 77
multiples of 7 and 9, 7 x 10
63 and 70
7×9 = 63
7×10 = 70
Answered by Gauthmath must click thanks and mark brainliest
Instructions: Find the value of the trigonometric ratio. Make sure to
simplify the fraction if needed.
Х
40
32
N
24
Y
Tan Z
Answers
Answer:
tan Z = 4/3
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta= opp / adj
tan Z = 32/24
Divide top and bottom by 8
tan Z = 4/3
The circumference of a circle is 16πw⁴.
Derive an expression for the area in terms of pi and w
Answers
Answer:
A = Pi (8 w**4)**2
Step-by-step explanation:
C = 16 Pi w**4 (given)
C = 2 Pi R (stand forula)
So then find R in terms of w by settting C = C from above
2 Pi r = 16 Pi w**4
2R = 16 w**4
R = 8 w**4
SO
A = Pi R**2
A = Pi (8 w**4)**2
Add.
(-2+6x3 – 3x_) + (4x3 – 5 + x²)
Express the answer in standard form.
Enter your answer in the box.
Answers
14+x+x^2
Write an example of an equation for an exponential growth function
Answers
Answer:
f(x) = 2^x
Step-by-step explanation:
Find the value of the variable (x) to the nearest tenth.
Answers
Answer:
I think its ten
Step-by-step explanation:
Determining the Domain and Range from a Graph
Determine the domain and range of the given function.
The domain is
ty
4
The range is
2
-4
-2
4
Into
Answers
Answer:
Domain is all real numbers, and range is all numbers greater than or equal to -2. If thee was anything you didn't understand let me know.
Step-by-step explanation:
The domain is what x values work, or it may be better to say the horizontal axis. is there any number you cannot use? if you cannot tell, this is a parabola, like x^2. Is there any number you cannot plug into x^2. The answer is no, the domain for all parabolic functions is all real numbers.
The range you really want to look at visually here. Range is y values you can get, or values on the vertical axis. I would also compare it to x^2 again. You should know you can make it as high as you want, here is the same. but at -2, there is no point below that. so the range is -2 and up
The other options are just specific numbers. you can disprove those by choosing a number not on their lists. For the domain literally any other number. For range any number not on the list greater than -2
Please help me. Taylor pays $5.25 for 5 yard of frabric.Whats the cost per yard?
Thank you!
Answers
Answer:
$1.05 per yard
Step-by-step explanation:
5.25 ÷ 5 = 1.05
Answer:
$1.05 per yard.
Step-by-step explanation:
find unit rate; (cost / quantity)
5.25 / 5 = 1.05
