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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
if y varies directly as x, and y = 10 when x = 9, find y when x = 1/9
Answers
Answer:
10/81
Step-by-step explanation:
let,
y=kx
y=10 when x=9
so,
10=k×9
or, k=10/9
when x=1/9
y=kx
or, y=(10/9)×(1/9)
or, y=10/81
Given AB= CD, and mAB = 134 find mCD
Answers
Answer:
arc CD = 134°
Step-by-step explanation:
Given 2 equal chords in a circle then the minor arcs are equal, that is
arc CD = arc AB = 134°
The value of mCD is 134°.
What is an arc?The arc is a portion of the circumference of a circle.
Given data as :
chord AB = chord CD, and
mAB = 134°
The minor arcs are equal if there are two similar chords in a circle.
So, arc CD = arc AB
Substitute the value of mAB = 134° in the above equation,
⇒ mCD = 134°
Hence, the value of mCD is 134°.
Learn more about arc of circle here:
brainly.com/question/1577784
#SPJ2
Are 5-x=y and x-5=y the same ?
Answers
Answer:
not really
Step-by-step explanation:
because on the first equation you subtract 5and take to y as a negative and in the second equation 5 goes as a positive at least that is what i think
Answer:
no cause
5-x=y
5 is positive , x is negative
BUT
x-5=y
5 is negative, and x is positive
Someone please answer B for me 15 Points marking brainliest
Answers
Step-by-step explanation:
since you have figured out A already, what is the problem with B ? you "only" need to calculate the perimeter of the shape.
basically the same assumptions as for the area calculations :
the "inner" sides are truly parallel to the line outer sides, so that they are both 12-4=8 m long.
and I assume here in addition that the side with the tiles in front contains a door, which is usually 1 m wide. and for that length we don't need trim of the baseboards (as there are none, where there is a door).
so the needed trim is
12+12+4+8+8+(4-1) = 24+4+16+3 = 47 m
but if my assumption about the door is wrong, then you need to add an additional meter. = 48 m.
and if the side with the tiles does not need any baseboards and corresponding trim at all (for whatever reason), you need to subtract that side completely. = 44 m
x^2-4x^2y^2+y^2+2*x*y
Answers
Answer:
(x + y - 2xy)*(x + y + 2xy)
Step-by-step explanation:
x^2-4x^2y^2+y^2+2*x*y
=x^2 + 2xy + y^2 - (2xy)^2
=(x + y)^2 - (2xy)^2
=(x + y - 2xy)*(x + y + 2xy)
A rock is dropped from a height of 100 feet calculate the time between when the rock was strong and when he landed if we choose down as positive and ignore air friction the function is h(t)=16t^2-100
Answers
Answer:
[tex]2.5s[/tex]
Step-by-step explanation:
We are given a function which tells us at what time the rock is at a certain height. What should be the height of this function when the rock hits the ground? 0, because it has no height, it's on the ground!
So let's plug in 0, and see what value we get for the time.
[tex]0 = 16t^2-100\\100 = 16t^2\\\frac{100}{16} = t^2\\[/tex]
To solve for t we need to take the square root of both sides.
[tex]t = \sqrt{\frac{100}{16} } = \frac{10}{4} = 2.5s[/tex]
what is the measure of angle A
Answers
Answer:
a = 53
Step-by-step explanation:
Start with d
The ends of d + 53 are diameter ends. That means that d + 53 is a right angle
d + 53 = 90
d = 90 - 53
d = 37
Next, find b. The end points of b are the same end points as for 53 degrees. B is the central angle of 53 which means b = 2 * 53
b = 106
c is the supplement of b
c + b = 180
b = 106
c + 106 = 180
c = 180 - 106
c = 74
The triangle containing a and c is isosceles because 2 of the 3 angles are opposite radii. The lowest angle is also a because it is opposite one of the radii.
a + a + 74 = 180
2a = 180 - 74
2a = 106
a = 106/2
a = 53
Hard to believe, but there it is.
What is the estimated value of 2v12 . 3V5 / V30 . V36
Answers
Answer:
the correct answer is b and I know this because I just had it
Given the following coordinates complete the glide reflection transformation.
Answers
hopefully this answer can help you to answer the next question.
[tex]\sqrt{x - 5} - \sqrt{3 - 2.x} = 0[/tex]
Answers
Answer:
x = 8/3
Step-by-step explanation:
Copy the right side of the given to the right side of the equation.
sqrt(x - 5) = sqrt(3 - 2x) Square both sides.
x - 5 = 3 - 2x Add 2x to both sides
2x + x - 5 = 3 Combine
3x - 5 = 3 Add 5 to both sides.
3x = 3 + 5 Combine
3x = 8 Divide by 3
x = 8/3
Solve the compound inequality. Graph your solution. 2x – 2 < –12 or 2x + 3 > 7
Answers
Answer:
09
Step-by-step explanation:
Can somebody help me please!!!!!
Answers
Answer:
0
Step-by-step explanation:
g[f(x)] = x^2 - 3
= 3x^2
if gf(0) = 3(0)^2
= 0
The formula p=nc-e gives the profit p when a number of items n are each sold at a cost c and expenses e are subtracted. If p = 3750, n = 3000, and e = 900, what is the value of c?
Answers
Answer:
1.55
Step-by-step explanation:
p =nc-e
p=3750, n=3000, e=900, c=?
3750 = 3000c - 900
3750 + 900 = 3000c
4650 = 3000c
3000c = 4650
c = 4650/3000
c = 1.55
volume of a cuboid whose edges are 4 cm, 5 cm and 6 cm
Answers
Answer:
120
Step-by-step explanation:
Formula for cuboid: L × W × H
Plug in:
L × W × H
4 × 5 × 6
^ ^
20 × 6
^ ^
120
Hope this helps.
A right triangle has a 12in base and an 8in height. What is the area of the triangle, in in??
Answers
Answer:
48
Step-by-step explanation:
using the formula 1/2 b*h
8*12=96
96/2=48
Please help explanation if possible
Answers
Which linear inequality is represented by the graph?
Answers
Answer:
D
Step-by-step explanation:
The correct answer is D
Answer:
D
Step-by-step explanation:
y<2/3 x-1 is the answer
How to do this question
Answers
Answer:
Step-by-step explanation:
Answered by G a u t h m a t h
Please mark it as brainliest & thank it if it helped you
Please help explanation if possible
Answers
[tex] \Large \colorbox{red}{ \sf\color{white}{Aиswεr : }}[/tex]
Sudden uncontrollable fear or anxiety, often causing wildly unthinking behaviour.
Answer:
y = 0.45x
Step-by-step explanation:
After 2 secs can ring 2 × 0.45
After 3 secs can ring 3 × 0.45
After 4 secs can ring 4 × 0.45 , then
After x secs can ring y = x × 0.45 = 0.45x , that is
y = 0.45x
Find the area of a regular pentagon
with a side length of 10 cm. Round to
the nearest tenth.
10 cm
[? ] cm2
Answers
Step-by-step explanation:
here~~~~~~~~~~~~~~~~~~~~~~~
What is the volume of this figure?
Answers
Answer:
156.25
Step-by-step explanation:
1/2 × b ×h =12.5
12.5 ×9 =156.25 hope you ace it
Arrange in descending order.
10,-5,-1, 12, 0, -13
Answers
Answer:
12, 10, 0, -1, -5, -13
Step-by-step explanation:
Find the length of the segment indicated. Round to the nearest tenth
Answers
Answer:
x=5
Step-by-step explanation:
x is the length of the line segment from the center to the boderline of circle. So x=5
How many significant digits are there in the number 1.00250? OA) 7 OB) 6 OC) 5 OD) 4
Answers
Answer:
OB
Step-by-step explanation:
start counting from 1
Then your significant digit is 6
What is the value of x in the equation -5/4x=-160
Answers
[tex] \\ \sf \longmapsto \: - \frac{ 5}{4} x = - 160 \\ \\ \sf \longmapsto \: \frac{5}{4} x = 160 \\ \\ \sf \longmapsto \: x = 160 \times \frac{4}{5} \\ \\ \sf \longmapsto \: x = 32 \times 4 \\ \\ \sf \longmapsto \: x = 128[/tex]
Step-by-step explanation:
-5/4x=-160
5/4x=160
x=160×4/5
x=640/5
x=128
Which transformation gives the same result as a reflection over the x-axis followed b
a reflection over the y-axis?
Answers
Answer:
filtration system is not working
filtration
A trapezoid has two basses that measure 11 cm and 8 cm. The height of the figure is 5 cm. What is the area of the trapezoid? A) 95 cm2. B) 64 cm2. C) 47.5 cm2. D) 24 cm2
Answers
Answer:
C.47,5cm²
Step-by-step explanation:
HELP ITS DUE IN THE MORNING AND ITS 3:57
Answers
Answer:
A " (1,-2)
B " (4,0)
C " (6,-3)
Step-by-step explanation:
Hope it helped.
° ° °
PLEASE HELP! ASAP
Sarah is five years old. When she asked her father about his age, he gave her this answer. "When you are my age, I will be 67." How old is her dad?
Answers
Her dad = 36
Sarah = 5
After 31 years sarah = 36
And her dad = 67
Answered by Gauthmath must click thanks and mark brainliest
Can anyone help me with this answer?
Answers
Answer: B. 1.5 × 10⁻¹⁸
Step-by-step explanation:
Concept:
When multiplying exponents, add the exponents together.
When dividing exponents, subtract the exponents.
When converting scientific notation to an integer:
If the exponent is negative, move the decimal to the left with the same amount of units as the exponents. For example: If converting 5 × 10⁻³, since the exponent is -3, we move the decimal to the left 3 unitsIf the exponent is positive, move the decimal to the right with the same amount of units as the exponentsFor example: If converting 2 × 10⁴, since the exponent is 4, we move the decimal to the right 4 unitsWhen converting an integer to scientific notation:
If the number is ≥1, then count the moves of decimal point until the integer is 0<integer<10. The number of moves will be the exponent that is positive.For example: If converting 300, since there are two moves until it is left with 0<3<10. Thus, the scientific notation will be 3 × 10²If the number is <1, then count the moves of decimal point until the integer is 0<integer<10. The number of moves will be the exponent that is negative.For example: If converting 0.004, since there are three moves until it is left with 0<4<10. Thus, the scientific notation will be 4 × 10⁻³Given:
Mass of one water molecule = 3.0 × 10⁻²³
Total number of molecules (required by the question) = 50,000
Solve:
Formula
Total mass = Mass of one water molecule × Total number of molecules
Substitute the values into the formula
Total mass = 3.0 × 10⁻²³ × 50,000
Convert 50,000 into scientific notation
Total mass = 3.0 × 10⁻²³ × 5 × 10⁴
Multiply numbers together/ Multiply exponents together
Total mass = 15 × 10⁻¹⁹ = 1.5 × 10⁻¹⁸
Hope this helps!! :)
Please let me know if you have any questions
