Answers
Answer:
Pythagoras's theorem
Step-by-step explanation:
In the given drawing, there are three right triangles (two smaller triangles formed inside one right triangle), which are;
1) The smallest right triangle with side lengths 'b', 'f', and 'd'
2) The intermediate right triangle with side lengths 'f', 'a' and 'c - d'
3) The right triangle ΔABC containing the other two with side lengths, 'a', 'b', 'c'
By trigonometric ratio we have;
1/cos(B) = a/(c - d) = c/a
By cross multiplication, we get
a² = c² - c·d
Similarly, we have;
The vertex angle for the small right triangle at C = ∠B
1/sin(B) = b/d = c/b
∴ b² = c·d
Therefore, adding the values of 'a²', and 'b²' together, we get;
a² + b² = c² - c·d + c·d = c²
Therefore;
a² + b² = c² which is Pythagoras's theorem.
Related Questions
I have 3 red markers, 3 blue markers, and 3 green markers. I take the caps off and put on the caps randomly. Find the expected number of markers that have the same color cap and marker.
Answers
Answer:
The expected number of markers that have the same color cap and marker is 3.
Step-by-step explanation:
Every marker has a [tex]\frac{1}{3}[/tex] chance to get the same color cap, because there are always 3 same caps, and 9 total caps. By linearity of expectation, the expected number of markers that have the same color cap and marker is equal to the sum of all marker's individual 'contribution' to the same color cap count. So the expected value is [tex]9 \cdot \frac{1}{3} = 3[/tex], precisely what we were after.
Answer:
3
Step-by-step explanation:
By running the following Python code, we can safely assume the answer to be 3:
---------------------
import random
def cap_throw():
cap_list = ['R', 'R', 'R', 'G', 'G', 'G', 'B', 'B', 'B']
random_cap_list = cap_list[:]
random.shuffle(random_cap_list)
counter = 0
for i in range(len((cap_list))):
if cap_list[i] == random_cap_list[i]:
counter += 1
return counter
results_list = []
for i in range(10 ** 6):
results_list.append(cap_throw())
print(sum(results_list) / len(results_list))
---------------------
Which gave 2.998795.
PRACTISE NOW 11
Ex
15
Mr Lee drove from City P to City Q, which are 600 km apart. During his return journey,
his average speed was increased by 7 km/h and the time taken was 15 minutes less.
() If he drove at an average speed of x km/h on his journey from City P to City Q,
formulate an equation in x and show that it reduces to x2 + 7x – 16 800 = 0.
(ii
) Solve the equation x² + 7x - 16 800 = 0, giving both your answers correct to
2 decimal places.
(iii) Find the time taken for the return journey.
Answers
Answer:
i. x² + 7x - 16800 = 0 ii. x = 126.16 km/h or -133.16 km/h iii. 5.01 h
Step-by-step explanation:
i. If he drove at an average speed of x km/h on his journey from City P to City Q formulate an equation in x and show that it reduces to x2 + 7x – 16 800 = 0.
For the first journey from City P to City Q, with Mr Lee moving at an average speed of x km/h, he reaches there in time, t and covers the distance, d = 600 km
So, xt = 600 (1)
On his return journey from City Q to CIty P, his average speed increases by 7 km/h, so it is (x + 7)km/h and his time is 15 minutes less than his first journey. 15 min = 15/60 h = 0.25 h, we have that his time for the journey is (t - 0.25) h. Since the distance covered is the same d = 600 km,
We have (x + 7)(t - 0.25) = 600 (2)
Expanding the brackets, we have
xt - 0.25x + 7t - 0.25(7) = 600
xt - 0.25x + 7t - 1.75 = 600
From (1) t = 600/x and xt = 600
Substituting these into the equation, we have
600 - 0.25x + 7(600/x) - 1.75 = 600
simplifying
-0.25x + 4200/x - 1.75 = 600 - 600
-0.25x + 4200/x - 1.75 = 0
multiplying through by x, we have
-0.25x² + 4200 - 1.75x = 0
dividing through by -0.25, we have
-0.25x²/-0.25 + 4200/-0.25 - 1.75x/-0.25 = 0
x² - 16800 + 7x = 0
re-arranging, we have
x² + 7x - 16800 = 0
ii. Solve the equation x² + 7x - 16 800 = 0, giving both your answers correct to 2 decimal places.
Using the quadratic formula, we solve x² + 7x - 16800 = 0 for x
So, [tex]x = \frac{-7 +/-\sqrt{7^{2} - 4 X 1 X -16800} }{2 X 1}\\x = \frac{-7 +/-\sqrt{49 + 67200} }{2} \\x = \frac{-7 +/-\sqrt{67249} }{2} \\x = \frac{-7 +/- 259.32}{2} \\x = \frac{-7 + 259.32}{2} or x = \frac{-7 - 259.32}{2} \\x = 252.32/2 or x= -266.32/2\\x = 126.16 km/hor x = -133.16 km/h[/tex]
So, x = 126.16 km/h or -133.16 km/h
iii. Find the time taken for the return journey
The time taken for the return journey is t' = t + 0.25. Now. t = 600/x
Since x cannot be negative, we use x = 126.16 km/h.
So, t = 600/x = 600/126.16 = 4.76 h
t' = t + 0.25
t' = 4.76 + 0.25
t' = 5.01 h
19.- Según la gráfica ¿Cuál es la rapidez media entre 4 s y 8 s?
A. 8 m/s
B. 1 m/s
C. 0,5 m/s
Answers
Answer:
B. 1m/s es la respuesta correcta
the ratio of the measures of the sides of a triangle is 2:7:6. if the perimeter of the triangle is 345 yards, find the measure of the median side.
Answers
Answer:
the sides are 46, 161, 138 respectively to sides 2, 7, 6
Step-by-step explanation:
2+7+6=15
345/15=23 this is our factor
2x23=46
7x23=161
6x23=138
The mass of the particles that a river can transport is proportional to the fifth power of the speed of the river. A certain river normally flows at
a speed of 4 miles per hour. What must its speed be in order to transport particles that are 12 times as massive as usual? Round your
answer to the nearest hundredth.
Answers
Answer:
6.58 miles per hour
Step-by-step explanation:
Let the mass and speed be represented by m and s respectively. So that,
m [tex]\alpha[/tex] [tex]s^{5}[/tex]
m = k[tex]s^{5}[/tex]
where k is the constant of proportionality.
For a certain river, speed = 4 miles per hour.
m = k [tex](4)^{5}[/tex]
m = 1024k ............ 1
In order to transport particles that are 12 times as massive as usual;
12m = k[tex]s^{5}[/tex]
m = [tex]\frac{ks^{5} }{12}[/tex] ............. 2
Thus,
[tex]\frac{ks^{5} }{12}[/tex] = 1024 k
[tex]s^{5}[/tex] = 12 x 1024
= 12288
[tex]s^{5}[/tex] 12288
s = [tex]\sqrt[5]{12288}[/tex]
= 6.5750
s = 6.58 miles per hour
Therefore, its speed must be approximately 6.58 miles per hour.
Samantha wants to buy a house and plans to rent the apartment located in the basement for extra income. The house has a purchase price of $200,000 and she will make a 10% down payment. Samantha has qualified for a 30 year mortgage with a fixed rate of 5.875%. Approximately how much rent should she charge for the apartment in order to cover her monthly mortgage payment if she only wants to spend $500 a month of her own money?
Answers
Answer:
$567.07
Step-by-step explanation:
Given that :
Purchase price = $200,000
Number of years = 30
Rate = 5.875%
Down payment = 10%
Hence, mortgage amount :
Purchase price - down payment
200,000 - (0.1 * 200000)
200,000 - 20,000
= $180,000
Using a mortgage calculator :
Mortgage amount = 180,000
Mortgage term = 30 years
Interest = 5.875%
Monthly payment will be : $1067.07
Hence, if she only wants to $500 from her own money, A rent of ($1067.07 - $500) = $567.07 will need to be charged
A cheesecake recipe says:
Mix 12 ounces of cream cheese with 15 ounces of sugar.
1. What is the unit rate of cream cheese for sugar?
2. what is the unit rate of sugar for cream cheese?
(CORRECT ANSWER GETS A GOOD 5 STARS AND BRAINLESST)
Answers
Number 1 answer :
Cream cheese = 12 Sugar= 15 12 divided by 15 = 0.8
There are 0.8 ounces of cream cheese for every ounce of sugar.
Number 2 answer:
Sugar= 15 Cream cheese = 12 15 divided by 12 = 1.25
There are 1.25 ounces of sugar for every ounce of cream cheese.
Write down a
12
Write down a different ratio equivalent to 9: 12
No
-
Answers
Answer:
3 : 4
18 : 24
I hope it helps
PLEASE HELP WITH I WILL GIVE FREE HUGS AND BRAINLIEST
Answers
Answer:
Step-by-step explanation:
a=1
b=-2
c=1.5
d=-20
B=-2
C=-3.5
D=-0.5
E=-20
If you solved the equation y=kx for k, what would k be equal to?
O k = xy
k = y/x
O k = x/y
O k = x+y
O k=y-X
Back
Nort
Answers
Answer:
k = [tex]\frac{y}{x}[/tex]
Step-by-step explanation:
y = kx
Divide by x on both sides to isolate k
k = [tex]\frac{y}{x}[/tex]
18 + x = 10 x=____ help
Answers
Answer:
X=-8
Step-by-step explanation:
18+x=10
-18 -18
x=-8
x = -8 i think I’m not sure.
Pleaseeee helppp answer correctly !!!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!
Answers
Krutika and Natasha win some money and share it in the ratio 4:3. Krutika gets £7 more than Natasha. How much did they get altogether?
Answers
Answer:
49
Step-by-step explanation:
The computation of the total amount is shown below:
Let us assume the natasha be 4x
And, the krutika be 3x
Now as per the situation
4x = 3x + £7
x = £7
For natasha = 4(7) = 28
For krutika = 3(7) = 21
So, the total amount is
= 28 + 21
= 49
Please triple check
Answers
Answer: The answer should be [tex]\frac{1}{6}[/tex] because that is the probability of that spinner
Step-by-step explanation:
Please help I will give brainliest
Answers
Answer:
c
Step-by-step explanation:
hope it helps if not sorry <3
5 pts! (Yall I really need help) How much does a video game cost per in:
America
Great Britain
Japan
Answers
Answer:
there are millions of video games, ranging from all different prices, so it all depends on what game.
Step-by-step explanation:
A total of $5000 is invested part of 6% and the remainder at 12% how much is invested at each rate if the annual interest is $480
Answers
Answer:
for 12% it would be $3,000
And, for 6% it would be $2,000
Step-by-step explanation:
The computation of the amount invested at each rate is shown below:
Let us assume the amount invested at 12% be x
So, the $5,000 - x be invested at 6%
The total interest earned is $480
So the equation would be
0.12x + 0.06($5,000 - x) = $480
0.12x + $300 - 0.06x = $480
0.06x = $80
x = $3,000
So for 12% it would be $3,000
And, for 6% it would be $2,000
The area, A, in square feet, of a rectangular storage bin in a warehouse is given by the function A(x) = x2 - 6x, where x is the width, in feet, of the storage bin.
Part A: Based upon this function, which statement would be true? Show your work or explain how you found the solution.
The x-intercepts of the function are 3 and -9, which are a lower bound and an upper bound for the possible values of the length of the storage bin.
The x-intercepts of the function are 3 and -9, which are a lower bound and an upper bound for the possible values of the width of the storage bin.
The x-intercepts of the function are 0 and 6, which are a lower bound and an upper bound for the possible values of the length of the storage bin.
The x-intercepts of the function are 0 and 6, which are a lower bound and an upper bound for the possible values of the width of the storage bin.
Answers
Answer:
The x-intercepts of the function are 0 and 6, which are a lower bound and an upper bound for the possible values of the width of the storage bin.
Step-by-step explanation:
Given
[tex]A(x) = x^2 - 6x[/tex]
Required
Which is true about the x intercept
To do this, we make A(x) = 0.
Substitute 0 for A(x) in [tex]A(x) = x^2 - 6x[/tex]
[tex]0 = x^2 - 6x[/tex]
Rewrite as:
[tex]x^2 - 6x=0[/tex]
Factorize:
[tex]x(x - 6)=0[/tex]
Split:
[tex]x = 0\ or\ x - 6 = 0[/tex]
[tex]x = 0\ or\ x = 6[/tex]
Option D is correct
What does 0.9a - 2.7b =
Answers
1/6(x+6)=11 Solve the equation.
Answers
1/6(x+6)=11
distribute
1/6x+1=11
-1 on both sides
1/6x=10
×6 on both sides
1x=60
x=60
Because 10 lies between two consecutive perfect squares ___ and ___ square root of 10 is located between the square roots of these twi numbers. This means the square root of 10 is located between 3 and 4
Answers
Answer:
wut
Step-by-step explanation:
jack is paid $54 for working 9 hours how many dollars would he earn for working 6 hours
Answers
Answer:
$36
Step-by-step explanation:
54/9=6
6*6=36
$36
Help me please answer
Answers
Answer:
B.........................
Answer:
36 because 2 x 3 = 6 and 6 x 6 = 36
Step-by-step explanation:
The answer is D
heyy pls help with these math questions hurry!
Answers
Answer:
m=2/5, y=3x7, (7,0), y=x-2, (0,-2)
Step-by-step explanation:
A(n) is an expression that contains numbers, variable, and mathematical operations like addition, subtraction, multiplication and division and do not include equal signs.
Answers
Answer:
Variable Expression; Numeric Expression. A numeric expression consists of numbers and operations, but never include any variable. Some of the examples of numeric expressions are 10 + 5, 15 ÷ 2, etc. Variable Expression. A variable expression is an expression which contains variables along with numbers and operation to define an expression.
Step-by-step explanation:
Variable Expression; Numeric Expression.
What is an Expression?
An expression is a number, a variable, or a combination of numbers and variables and operation symbols.
Determining:Variable Expression; Numeric Expression. A numeric expression consists of numbers and operations, but never includes any variable. Some of the examples of numeric expressions are 10 + 5, 15 ÷ 2, etc. Variable Expression. A variable expression is an expression that contains variables along with numbers and operations to define an expression.
Learn more about Expressions:
https://brainly.com/question/1280754
#SPJ2
help plz i’ll give extra points
Answers
Explanation:
y = mx + b
b = 12.75 (it’s the point where the line crosses the y-axis)
m = ?
Find m(slope):
m = (y1 - y)/(x1 - x)
y1 = 35.75 and y2 = 12.75
x1 = 1 and x = 0
m = (35.75 - 12.75)/(1-0)
m = 23
Now we have both m and b:
y = 23x + 12.75
Which equation correctly describes photosynthesis?
water + sugar + oxygen
-
carbon dioxide + chlorophyll
O sunlight + water + carbon dioxide
oxygen + sugar
O sunlight + sugar – water + oxygen
carbon dioxide + oxygen
water + sugar + sunlight
Answers
Answer:
carbondioxide + oxygen
Answer:
carbon dioxide + oxygen → water + sugar + sunlight
Step-by-step explanation:
hope i helped
4/9 x 15/8 answer the question and give the simplest form.
Answers
Amy and Katie have between $125 and $200 dollars to spend on jewelry for Christmas presents for their friends. If they buy 8 bracelets at $3.50 each and 6 necklaces at $12 each, how many pairs of earrings can they buy if they cost $6.00 each?
Answers
Explanation:
budget_ 125 + 200 = 325 dollars
bracelets 8 units x $ 3.5 each = $ 28
necklaces 6 units x $ 12 each = $ 72
total spending $ 100
remanining $225
cost per earring $ 6
maximum amount of earring they can purchase: 225 / 6 = 37 units
What is the value of 0.1322 rounded to the nearest hundredth place?
Answers
Answer:
Step-by-step explanation:
0.1322 ≅ 0.13
Answer:
0.13
Step-by-step explanation:
First we need to find the given place value, which is the hundreds place.
0.1322
Next, we look at the next number over, which is two.
0.1322
0-4 stays the same. 5-9 round up one. Doing so, we keep the number three the same.
0.1300
get rid of the extras.
(not a Bakogou reference)
0.13
~Hope this helps~