Answers
Answer:
[tex]\frac{(a-b)^2+b^2}{a^2}[/tex]
which agrees with the first choice (A) in your list of possible answers
Step-by-step explanation:
Notice that the area of the outer square is given by the square of it side [tex](a)[/tex].Then the outer area is given by: [tex]a^2[/tex]
Now, the inner square's area we calculate by subtracting from the outer area four equal right angle triangles (those shaded in grey in the figure provided). Each of such right angle triangles have an area given by the general formula of a triangle's area:
[tex]Area_{triangle}= \frac{base\,*\,height}{2} =\frac{(a-b)\,b}{2} =\frac{ab-b^2}{2}[/tex]
Therefore the internal square's area is:
[tex]a^2-4\frac{ab-b^2}{2} =a^2-2ab+2b^2[/tex]
And then the quotient of this are over the larger square area becomes:
[tex]\frac{a^2-2ab+2b^2}{a^2} =\frac{a^2-2ab+b^2+b^2}{a^2}=\frac{(a-b)^2+b^2}{a^2}[/tex]
Related Questions
A recipe calls for 3 cups of flour for every 8 ounces of water. How many cups of
flour are needed if the baker uses 96 ounces of water?
Answers
Answer:
you need 36cups of flour
Step-by-step explanation:
3 cups of flour = 8 ounces of water
x cups of flour = 96 ounces of water
96*3 =8x
288 =8x
288/8=36
x=36
Make a copy of this document for yourself. Solve each problem. Remember to combine like terms and use inverse operations when necessary. Get the variable by itself.
Answers
Answer:
the answer is 5.
given, 2c-7c+8=-17
or, -5c=-17-5
or, c=-25/-5
therefore the value of c is 5...
Step-by-step explanation:
[tex]2c -7c +8 =-17\\Collect- like- terms\\2c-7c=-17-8\\Simplify\\-5c = -25\\Divide-both-sides-of-the-equation-by -5\\\frac{-5c}{-5} = \frac{-25}{-5} \\\\c = 5[/tex]
Select the graph for the solution of the open sentence. Click until the correct graph appears |x| < 3
Answers
|x| < 3 turns into -3 < x < 3
This says that x is between -3 and 3, but cannot equal either endpoint.
The graph will be a number line with open circles at -3 and 3. Then you shade in between those open circles.
It's the graph below vvv/ Have a good day! xx
ASAP FUNCTIONS HELP ASAP
Answers
Answer: B
Step-by-step explanation:
The range of a function is every valid y value, in this case represented by B
Please answer this question now in two minutes
Answers
Answer:
p = 100
Step-by-step explanation:
If Q and T are midpoints, then the triangles URS and UQT are similar triangles and verify the following proportions:
[tex]\frac{QT}{RS} =\frac{UQ}{UR} =\frac{UT}{US} =\frac{1}{2}[/tex]
and all should equal 1/2 because Q and T are midpoints.
Then we study in particular the proportion:
[tex]\frac{QT}{RS} =\frac{1}{2}[/tex]
since we know both segments can be expressed in terms of "p" as indicated in the problem:
[tex]\frac{QT}{RS} =\frac{1}{2}\\\frac{p-87}{p-74} =\frac{1}{2}\\2(p-87)=p-74\\2p-174=p-74\\2p-p=174-74\\p=100[/tex]
what is the point-slop of a line with slope 3/2 that contains the point (-1,2)?
O A. y 2 = 3/2(x-1)
O B. y+2 = 3/2(x-1)
O C. y-2 = 3/2(x + 1)
O D. y + 2 = 3/2(x + 1)
Answers
Answer:
The answer is option C.Step-by-step explanation:
Equation of a line is y = mx + c
where m is the slope
c is the y intercept
Equation of the line using point ( -1 , 2) and slope 3/2 is
y - 2 = 3/2(x + 1)Hope this helps you
Find the equation of the plane passing through the points
(-1,1,-4) and is perpendicular to each of the planes
-2x+y+z+2=0;x+y-3z+1=0
Answers
Extract the normal vectors from the given planes:
[tex]-2x+y+z+2=0\implies\vec n_1=(-2,1,1)[/tex]
[tex]x+y-3z+1=0\implies\vec n_2=(1,1,-3)[/tex]
(which are unique up to their signs, meaning either [tex]\vec n_1[/tex] or [tex]-\vec n_1[/tex] are valid choices for the normal vector)
The third plane must be perpendicular to both these given planes, which means it would be parallel to both [tex]\vec n_1[/tex] and [tex]\vec n_2[/tex], which in turn means its own normal vector [tex]\vec n_3[/tex] should be perpendicular to both [tex]\vec n_1[/tex] and [tex]\vec n_2[/tex].
Enter the cross product:
[tex]\vec n_3=\vec n_1\times\vec n_2=(-4,-5,-3)[/tex]
or (4, 5, 3), which also works.
The given plane passes through (-1, 1, 4), so its equation is
[tex](x+1,y-1,z-4)\cdot\vec n_3=0[/tex]
Simplify:
[tex](x+1,y-1,z-4)\cdot(4,5,3)=0[/tex]
[tex]4(x+1)+5(y-1)+3(z-4)=0[/tex]
[tex]\boxed{4x+5y+3z=13}[/tex]
A sphere fits perfectly into the cylinder as shown, touching the top and bottom of the
cylinder. If the height of the cylinder is 32 inches, what is the approximate volume of
the sphere?
A 2,7317 cu in.
B 4,0961 cu in.
C 8,192n cu in.
D 5,4611 cu in.
Answers
Answer:
Step-by-step explanation:
we khow that the height of the cylinder is 32 inches
divide it by 2 to get the radius 32/2= 16
let V be the volume :
V= (4/3)*16³*π = 17157.28 in³ this really close to the volume of this sphereThe volume of the sphere will be 5461.3 π cubic inches. Then the correct option is D.
What is the volume of the sphere?Let r be the radius of the sphere.
Then the volume of the sphere will be
V = 4/3 πr³ cubic units
A sphere fits perfectly into the cylinder as shown, touching the top and bottom of the cylinder.
If the height of the cylinder is 32 inches.
The height of the cylinder and sphere are same.
Then the radius of the sphere will be
r = 32 / 2
r = 16 inches
Then the volume of the sphere will be
V = 4/3 π(16)³ cubic units
V = 5461.3 π cubic inches
Then the correct option is D.
More about the volume of the sphere link is given below.
https://brainly.com/question/9994313
#SPJ2
In the parallelogram below,
z = [ ?
Answers
Explanation:
2z+16 + 124 = 180 degree
2z + 140 = 180
2z = 40
z = 40/2 = 20
Below is the work a student completed with an error. Identify the step where the error occurred and give the correct solution. Step 1:(12-20)-3(8-3)+13 Step 2:-8-24-9+13 Step 3:-32-9+13 Step 4:-41+13
Answers
Answer:
The error is in Step 2. The student distributed -3 incorrectly; it should have been 9, not -9. The correct solution is -8 - 24 + 9 + 13 = -32 + 9 + 13 = -32 + 22 = -10.
The perimeter of the rectangle above is:
Answers
Answer:
A. 8x² + 2y²
Step-by-step explanation:
There is a formula for the perimeter.
2l + 2w
2(4x²) + 2(y²)
8x² + 2y²
The perimeter of the rectangle is 8x² + 2y².
The equation yˆ=−6.2x2+41.5x−5.6 approximates the average number of cars that pass through an intersection x hours after 3:00 p.m. What is the best estimate for the average number of cars that pass through the intersection at 5:30 p.m.?
Answers
Answer:
59
Step-by-step explanation:
5: 30 pm is 2.5 hours after 3 : 00 pm
Substitute x = 2.5 into the equation
y = - 6.2(2.5)² + 41.5(2.5) - 5.6
= - 38.75 + 103.75 - 5.6
= 59.4
The average number of cars is 59
Find the value of this expression if x = 3.
x2 + 3
Express your answer as a fraction or integer.
Enter the correct answer.
Answers
Answer:
9
Step-by-step explanation:
x2 + 3
(3)2 + 3
6 + 3
9
Answer:
12.
Step-by-step explanation:
x = 3; x^2 + 3.
(3)^2 + 3 = 3 * 3 + 3 = 9 + 3 = 12
Hope this helps!
what is this answer 4\5+2\10
Answers
Answer:
1
Step-by-step explanation:
To add fractions, we need to make the denominators the same. Luckily, we can simplify 2/10 to 1/5. Now that the denominators are both 5, we can add. When adding fractions, we only add the numerator, and the denominator remains the same, so we'd do 4+1/5, which equals 5/5, which simplifies to 1.
Answer:
1 or 10/10
Step-by-step explanation:
Step 1 make a common denominator
to make a common demoniator multiply the top and bottom number by the same number
so multiply the 4 and 5 by 2 to get 8/10
Step 2 now that you have 8/10 add it with 2/10
Step 3 solve to get 10/10 and then simplify it to 1
Ratio and Proportion problem
Please help meh
Answers
Answer:
hope its helpful to uh.......
What’s 10 to the power of 10 A.100,000 B.10,000,000 or C.1,000,000,000
Answers
Answer:
10,000,000,000
hopefully this helped :3
Answer:
C.10,000,000,000
Step-by-step explanation:
FUNCTIONS HELP ME ASAP
Answers
Hey there! :)
Answer:
f(-2) = 2.
Step-by-step explanation:
To find f(-2), we simply need to look at the y value at x = -2.
At x = -2, the y value is equal to 2.
Therefore:
f(-2) = 2.
Answer: b)2
Step-by-step explanation:
Visually, when x = -2, y = 2
Express your answer as a decimal. 606/15
Answers
Answer:
40.4 is the ANSWERExplanation:
606/15 = 600/15 + 6/15
40 + 0.4 = 40.4
a vertical flag pole TAD is supported by two wires AB and AC, given that angle ABD=67°,AB =2 m and AC =2.5m . find the length of AD
Answers
Answer:
a) 1.84m
b) 42.53°
Step-by-step explanation:
First, look though the diagram provided by the question.
And use the formula: [tex]\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}[/tex]
Based on Additional Mathematics Form 4 (Dual Language Programme) KSSM from Malaysia
To find the length of AD
[tex]\frac{AD}{sin 67}=\frac{2}{sin 90}[/tex]
[tex]AD=\frac{2}{sin 90} * sin 67[/tex]
AD= 1.84 m
Find the angle C
[tex]\frac{sin 90}{2.5}=\frac{sin C}{1.84}[/tex]
sin C=[tex]\frac{sin 90}{2.5} * 1.84[/tex]
= 0.736
[tex]sin^{-1} (0.736)=47.39[/tex] degree
So, we have the value of AD and the value of angle C. Now , we can solve the the angle of CAD.
Same as the first question use the formula of sine rule and you will get the answer.
[tex]\frac{sin 90}{2.5}=\frac{sin ACD}{1.69}[/tex]
[tex]sinA = \frac{sin90}{2.5} * 1.69[/tex]
=0.676
=42.53°
So, the answer of the angle of CAD is 42.53°
Check the answer:
90°+47.39°+42.53°
=179.92°
=180°(rounded off)(Proved)
That is all from me. I hope you will understand my solution.
What are the answers for each?
Answers
Answer:
7% of 33= 2.1
2% of 640= 12.8
15% of 470=70.5
7/9 of 51= 119/3
.52 of 62= 32.24
Answer:
1) 2.31
2) 12.8
3) 72
4) 44.625
5) 32.24
Step-by-step explanation:
7% of a number is simply 0.07*the number.
7/8 is just .875*the number
Hope it helps <3
Find the lateral surface area in square kilometers, of the 3-dimensional figure shown below
Answers
Answer:
108
Step-by-step explanation:
Add the sides of the triangle
5+3+4 = 12 then look for the height
which is 9
12*9 is 108
x = [? ]°
117
124°
107
102
145
Answers
Answer:
x = 125°
Step-by-step explanation:
The sum of angles in an n-sided polygon is (180°)(n -2). For a hexagon, the sum of angles is ...
(180°)(6 -2) = 720°
We can use this to find x.
x +117° +124° +102° +145° +107° = 720°
x = 720° -595°
x = 125°
Trapezoid ABCD is rotated 180 degrees about the origin and then reflected over the x-axis, followed by a reflection over the y-axis. What is the location of point A after the transformations are complete?
Answers
Answer:
the location of point A after the transformations are complete is (-5, 1)
Step-by-step explanation:
Given the coordinate of the trapezoid at A(-5, 1), B(-4, 3), C(-1, 3) and D(-2, 1).
The location of point A is at (-5, 1) which is the second quadrant, when it is rotated 180 degrees about the origin, the point moves to the fourth quadrant and the new point is at (5, -1). If it is then reflected over the x axis, the x coordinate remain the same and the sign of the y coordinate changes making the new point (5, 1). If it is then reflected over the y axis, the y coordinate remain the same and the sign of the x coordinate changes making the new point (-5, 1).
the location of point A after the transformations are complete is (-5, 1)
Answer:
the location of point A after the transformations are complete is (-5, 1)
Step-by-step explanation:
Each ferry in the Sydney Harbour has a capacity of 230 people. If there are 9 ferries in operation today, how many people could travel using this service today?
Answers
Answer:
2070
Step-by-step explanation:
Multiply 230 people by 9 ferries, if each ferry is used once.
help i must get this correct i will make u brainllest
plzzz anyone
Answers
Answer:
22
Step-by-step explanation:
x-1 is a midsegment.
According to the Triangle midsegment theorem, x-1 is half of the third side (42)
x-1 = 42/2
x-1 = 21
x= 22
or
2x-2=42
2x=44
x=22
Hope this helps!
If you look at the top sides and bottom sides of both figures, this means that they are the same or similar.
In this figure, they are similar because one side is half of the other.
So... divide the longer length in half and solve for x.
42 / 2 = 21
x - 1 = 21
x - 1 + 1 = 21 + 1
x = 22
Therefore, the answer is C.
Best of Luck!
What is "5t + 76" if t = 6?
Answers
Answer:
106
Step-by-step explanation:
given: 5t + 76
If t = 6, we substitute t=6 into the equation and solve:
5t + 76
= 5(6) + 76
= 30 + 76
= 106
Hi there! Hopefully this helps!
---------------------------------------------------------------------------------------------------
Answer: 106.
First, we need to evaluate.
(Note: when a letter and a number are close to together [5t] it means to multiply)
So if "t" = 6 we rewrite the problem like this:
5(6) + 76.
5 x 6 = 30.
Now we rewrite the problem again.
30 + 76 = 106.
can someone help me with this question please.
Answers
Answer:
a) 280°
b) Ans - (D) P is North East of Q
You work as a health inspector and must visit each of the 15 restaurants in town once each week.
a) In how many different orders can you make these inspections?
b) If you were to work 50 weeks a year and use a different order every week, how long would it take you to try all of the different possible orders
Answers
Answer:
Step-by-step explanation:
The no of different ways in which these restaurants can be visited
= ¹⁵P₁₅
= 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 1.30 x 10¹²
b ) Each combination takes 1 week and 50 weeks in a year to work
No of years to take to try all the combination
= 1.30 x 10¹² / 50
= 2.615 x 10¹⁰ years .
Help me!!!!!!! Plzzzz
Answers
Answer:
Option 3
Step-by-step explanation:
Need hep with this question
Answers
Answer:
V= -2000t + 20000
Step-by-step explanation:
Let m be the slope of our function :
m=(20000-16000)/(0-2)= -2000so our function is V= -2000t + b b is the intitial price so b = 20000then : V= -2000t + 20000Let's check :
take the second year : V= -2000*2 +20000 = 16000 that's true !