Kira is using the figure shown to prove the Pythagorean theorem. She starts by writing the
equation (a+b)' - C = 4(ab) because she knows two equal ways to represent the area
of the shaded region. Which best describes the next steps Kira should take to complete her
proof?
Answers
Question:
Kira is using the figure shown to prove the Pythagorean theorem. She starts by writing the
equation [tex](a+b)^2 - c^2 = 4(\frac{1}{2}ab )[/tex] because she knows two equal ways to represent the area
of the shaded region. Which best describes the next steps Kira should take to complete her
proof?
Answer:
The correct option is;
d. Simplify both sides of the equation to get a² + 2·a·b + b² - c² = 2·a·b then subtract 2·a·b and add c² to both sides of the equation
Step-by-step explanation:
Here we have
The area of the larger square = (a + b)²
The area of the middle plain shaded square = c²
∴ Area of the shaded region = (a + b)² - c²
The shaded region consists of for right triangles of base, a and height, b therefore, the area of the shaded region is also the area of the four right triangles = 4 × (1/2 × base × height)
= 4×1/2×a×b = 4(1/2·a·b)
Hence area of the shaded region also = 4(1/2·a·b)
Therefore, (a + b)² - c² = 4(1/2·a·b)
Which is a² + 2·a·b + b² - c² = 4 × 1/2 × a·b = 2·a·b
∴ a² + 2·a·b + b² - c² = 2·a·b
Hence a² + 2·a·b + b² - c² + c² = 2·a·b + c² gives
a² + 2·a·b + b² = 2·a·b + c² gives
Also a² + 2·a·b + b² - 2·a·b = 2·a·b + c² - 2·a·b gives
a² + b² = c² which is Pythagoras theorem
Answer:
the last
Step-by-step explanation:
Related Questions
Roger currently makes $11 per hour after taxes. He works 34 hours per week. If Roger works 45 weeks out of the year, how much money will he earn during that time?
Answers
Answer:
$16,830 for the year
Step-by-step explanation:
34 hours per week at $11 per hour comes to $374 total per week.
Multiplying this by 45 weeks yields $16,830 for the year.
Laura has set out 60 m of a kite string which makes an angle of 68° with the ground what is the height of the kite
please help
Answers
Selecting which seven players will be in the batting order on a 11 person team.
A) Permutation
B) Combination
C) Circular permutation
Answers
Answer:
a:) combination
b:) permutation
c:) combination
Step-by-step explanation:
There are 330 ways the coach can select a batting order of seven players from an 11 person team. Therefore, option B is the correct answer.
What is a combination?Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by nCr and it is given by, nCr=n!/r!(n−r)!,where 0 ≤ r ≤ n.
To determine the number of ways the coach can select a batting order of seven players from an 11 person team, we can use the combination formula, which is given by:
nCr = n! / r!(n-r)!
where n is the total number of players on the team, and r is the number of players in the batting order. In this case, n = 11 and r = 7.
So, the number of ways the coach can select a batting order of seven players from an 11 person team can be calculated as follows:
11C₇ = 11! / (7!(11-7)!)
= (11 x 10 x 9 x 8) / (4 x 3 x 2 x 1)
= 330
Therefore, option B is the correct answer.
To learn more about combination here:
brainly.com/question/17196495.
#SPJ2
The number of cameras produces since May at a plant can be modeled by the function N(m)=50m+600 and the cost per camera can be modeled by C(m)=4m^2-15m+45, where m is the number of months since May. According to this model, what is the total amount of revenue generated by the plant's camera production on September?
Answers
Answer:
39200
Step-by-step explanation:
Revenue = number of cameras * cost
R(m) = N(m) * C(m)
= (50m+600) * (4m^2-15m+45)
The months since may is June July August September = 4 months
R(4) = (50*4+600) * (4*4^2-15*4+45)
(200+600) * (64-60+45)
800*49
39200
Answer:
39,200
Step-by-step explanation:
September is 4 months after may, so m = 4
No. of cameras:
N(4)=50(4)+600 = 800
Cost per camera:
C(4)=4(4²)-15(4)+45 = 49
Total cost:
N × C
800 × 49
39200
What is the product of (-a + 3)(a + 4)?
Answers
Answer:
a² - a + 12
Step-by-step explanation:
(see attached)
using the Foil Method :
(-a + 3)(a + 4)
= (-a)(a) + (-a)(4) + (3)(a) + (3)(4)
= -a² - 4a + 3a + 12
= -a² - a + 12
The base of a triangle is 3cm and the height is 5cm. What mathematical operations described must be performed in order to find the area of this triangle
Answers
a boys buys 9 apples for Rs 9.60 and sells them at 11 for rs 12 find his gain or loss percent
Answers
What is the measure of mop
Answers
Please help! This is Quadratic Formula and the discriminant. The answer is -3+3 square root symbol 5 over 2. Every time i try to get that answer I get a different one. Please help asap
Answers
Answer:
See explanation
Step-by-step explanation:
[tex]n^2+3n-7=2[/tex]
Subtract 2 from both sides:
[tex]n^2+3n-9=0[/tex]
Using the quadratic formula:
[tex]n=\dfrac{-3\pm\sqrt{9+36}}{2}=\dfrac{-3\pm \sqrt{45}}{2}=\dfrac{-3\pm 3\sqrt{5}}{2}[/tex]
I agree with you on the answer, have you tried both adding and subtracting the root? That is important, because there are two solutions to this problem. Feel free to discuss more and I can try to help!
What is the quotient?
(-3)^0 / (-3)^2 = ?
A: -9
B: -1/9
C: 1/9
D: 9
Answers
Answer:
Step-by-step explanation:
Quotient means result of division
anything raised to 0 is 1
(-3)^0 = 1
(-3)^2 = -3 * -3 = 9
Quotient = 1/9
Answer:
1/9
Step-by-step explanation:
What is the range of the function y= e^4x
Answers
Answer:
The answer would be {y|y>0}
Step-by-step explanation:
hope this helps
Question is in the photo above
Need the number of units.
Answers
Answer:
Step-by-step explanation:
rectangle and triangle is here
area of triangle = 1/2 * 5 * 12 = 30
area of rectangle = 1 * 12 = 12
total is 12 + 30 = 42
Zugo delivers muffins for the Pastry-and-Muffin company. Each muffin is packed in its own
little box. An individual muffin box has the shape of a cube, measuring three inches on
each side. Zugo packs the individual muffin boxes into a larger box. The larger box is also
in the shape of a cube, measuring two feet on each side. How many of the individual
muffin boxes can fit into the larger box?
Answers
Answer:
512
Step-by-step explanation:
You can figure this a couple of ways.
1) Figure the number of muffin boxes that goes into each dimension of the larger box:
(2 ft)/(3 in) = (24 in)/(3 in) = 8 . . . . muffin boxes in each direction.
Then the total number of muffin boxes that will fit in a larger box is ...
8×8×8 = 512
512 muffin boxes can fit into the larger box.
__
2) The volume of a muffin box in cubic feet is ...
((3 in)/(12 in/ft))^3 = (1/4 ft)^3 = 1/64 ft^3
The volume of a larger box in cubic feet is ...
(2 ft)^3 = 8 ft^3
Then the number of smaller boxes that will fit in the larger box is ...
(8 ft^3)/(1/64 ft^3) = 8×64 = 512
512 muffin boxes can fit into the larger box.
A torch and a battery cost £2.50 altogether.
The torch costs £1.50 more than the battery.
What fraction of the total price is the torch?
Give your answer in its simplest form.
PLEASE CHECK UR ANSWER
Answers
Answer:
1 1/2 i think
Step-by-step explanation: to find out the batteries price you subtract 2.50 from 1.50 and get 1 then convert to fractions so 1 1/2 and 1 and when you add them together you get the total price so the torch accounts for 1 1/2 of the total price.
Which equation is true for x= -6 and x=2
Answers
Answer:
What are you options
Step-by-step explanation:
What is the value of x in this equation 9 + 9 = 3(x - 6)?
Answers
Answer: [tex]x=12[/tex]
Step-by-step explanation:
[tex]9+9=3(x-6)[/tex]
simplify: add the 9's together and distribute the 3
[tex]18=3x-18[/tex]
add 18 to both sides
[tex]36=3x[/tex]
divide by 3
[tex]12=x[/tex]
[tex]x=12[/tex]
A bag contains six red marbles and three
blue marbles. You randomly pick a
marble and then pick a second marble
without returning the marbles to the bag.
Both marbles are red.
Answers
answer: the answer is
1/72
Calculate (full working out)
5.16 x 2.93 =
Answers
helpppppp pros only helppppppp me plzzzzzzzzzzz ill reporte you if you do bad qweshtones
Answers
Answer:
We are looking for 2 numbers that have a product of 72 and a sum of 17. These 2 numbers are 9 and 8. Therefore, the factored version would be (z + 9)(z + 8), or A.
Hope this helps!
what is the domain and range of this graph?
Answers
Answer:
Domain- {-2,2}
Range-{-3,2}
Step-by-step explanation:
Find each boundary of the line and make the corresponding points because its a continuous line.
Please help me now please I promise I will mark you brainliest
Answers
Answer:
On the circle
Step-by-step explanation:
I dont know the exact way to do this, but i graphed them, then drew a circle, and it was in the line. So i think its on the line
Answer:inside
Step-by-step explanation:
The distance from A to M is sq rt of 41
The distance from A to V is sq rt of 40
please answer my question −4y−4+(−3)
Answers
Answer:
-4y - 7
Step-by-step explanation:
−4y−4+(−3)
Combine like terms
-4y - 7
Answer:
5
Step-by-step explanation:
y= 4+ 4 - 3
A chocolate factory made 708.6 pounds of dark chocolate in 6 days. How much dark chocolate, on average, did the factory make per day?
A) 116.76
B) 117.66
C) 118.10
D) 118.43
Answers
Answer: it’s answer C.
Step-by-step explanation: 708.6 ÷ 6 = 118.1(0)
Answer:
c
Step-by-step explanation:
What is the difference between a rectangular prism and a triangular prism?
The two bases of a rectangular prism are rectangles, while the two bases of a triangular prism are triangles.
A rectangular prism has two bases, while a triangular prism has one base,
A triangular prism has two bases, while a rectangular prism has one base.
A rectangular prism has two bases and three faces, while a triangular prism has two bases and four faces.
Dintro
Done
Answers
Answer:
The two bases of a rectangular prism are rectangles, while the two bases of a triangular prism are triangles.
Step-by-step explanation:
Any prism has two bases. Since we are talking about a rectangular prism and a triangular prism both must have two bases.
For example, a square prism has two bases and they are both square.
In this case a rectangular prism has two bases that are rectangles and a triangular prism also has two bases and both bases are triangles.
Note: For the figure to have only one base it must be called a pyramid.
Thus, the answer is:
The two bases of a rectangular prism are rectangles, while the two bases of a triangular prism are triangles
Answer:
a
Step-by-step explanation:
Charlie has a box that is In the shape of a rectangular prism its height is twice the length its length is three times the width in the word measures 4 inches what is the volume of the box the volume of the box is
Answers
Answer:
1152 in ^ 3
Step-by-step explanation:
We know that the width is:
w = 4 in
They also tell us that the length is three times the width, therefore:
l = 3 * w
l = 3 * 4 = 12
l = 12 in
and as for the height, they tell us that it is twice the length, so:
h = 2 * l
h = 2 * 12 = 24
h = 24 in
now the volume is w * l * h, replacing:
v = 4 * 12 * 24
v = 1152
volume equals 1152 in ^ 3
Brenda and Jasmine are selling cookie dough for a school fundraiser. Customers can buy packages of chocolate chip cookie dough and packages of double chocolate cookie dough. Brenda sold 6 packages of chocolate chip cookie dough and 4 packages of double chocolate cookie dough for a total of $86. Jasmine sold 3 packages of chocolate chip cookie dough and 5 packages of double chocolate cookie dough for a total of $85. What is the cost each of one package of chocolate chip cookie dough and one package of double chocolate cookie dough?
Answers
Answer:
one package = $5. / double package= $14
Step-by-step explanation:
Lets say x is a package and y a double package
6x + 4y = $86
2(3x + 5y = $85)
6x + 10y = $170
-6x -4y. -86
6y = $ 84
÷6. ÷6
y= $14
6x +4y = $86
6x + 4($14) = $86
6x + $56 = $86
-56. -56
6x = $30
÷6. ÷6
x = $5
Answer:
chocolate chip = 5
double chocolate chip=14
Step-by-step explanation:
c = chocolate chip
d = double chocolate chip
Brenda
6c+4d = 86
Jasmine
3c+ 5d = 85
Multiply the second equation by -2
-6c -10d = -170
Add this to the first equation
-6c -10d = -170
6c+4d = 86
--------------------
- 6d = -84
Divide by -6
-6d /-6 = -84/-6
d =14
Now we can find c
3c+ 5d = 85
3c+5*14 = 85
3c +70 = 85
Subtract 70
3c = 85-70
3c = 15
Divide by 3
3c/3 = 15/3
c = 5
A tablet manufacturer tested 125 tablets and found that 2 had broken screens. how many broken screens should the manufacturer expect out of 45000 tablets?
Answers
Answer:
720
Step-by-step explanation:
125tablets, 2 of which had broken screens.
multiply 45000 by 2, then divide 125=720
Answer:
720
Step-by-step explanation:
125 tablets, 2 of which had broken screens.
Multiply the 45,000 by 2, then divide by 125.
So therefore, the answer is 720.
Inequalities
Would this be correct?
Answers
Answer:yes
Step-by-step explanation: 20<_x-8 = 20 <_20 which is correct
If Quadrilateral JKLM is a square, where points J(0, 5), K(4, 7), L(?, ?) and M(2, 1) are known. Find the coordinates of point L
Group of answer choices
(7, 2)
(6, 3)
(5, 4)
(4, 4)
Answers
Answer:
THANKS FOR THE POINTS ^^^^
Step-by-step explanation:
(6,3)
Complete 5-8 for 15 points.
