Use the Pythagorean Theorem to find the length of the sides "d" and "f." Explain your answer.
Answers
Answer:
f = 10·√3/3 ≈ 5.774
d = 5·√3/3 ≈ 2.887
Step-by-step explanation:
The given parameters are;
The angles opposite the 90°, right angle, = 60° and 30°
The length of the leg opposite the 60° angle = 5
Therefore, by Pythagorean Theorem, we have;
f² = d² + 5²
However, by trigonometry, we have;
sin(θ) = Opposite/Hypotenuse
For the angle of the triangle, θ = 30°, we have;
sin(30°) = d/f = 0.5
∴ d = f × 0.5 = 0.5·f
Substituting the value of d in the equation given by Pythagorean Theorem, we have;
f² = (0.5·f)² + 5² = 0.25·f² + 5²
f² = 0.25·f² + 5²
f² - 0.25·f² = 5²
0.75·f² = 5²
f² = 5²/0.75 = 100/3
f = 10/√3 = 10·√3/3
f = 10·√3/3
d = f × 0.5 = 10·√3/3 × 0.5 = 5·√3/3
d = 5·√3/3.
Related Questions
This is the problem that I need help with please. :)
Answers
Answer:
umm I think it 186
Step-by-step explanation:
Add a researcher compared the Heights and shoe sizes for 50 men, selected at random. The equation shown describes a line of best fit for the data, where X is the shoe size and why is the height, in inches (y=1.6x + 58)
Answers
Complete question :
a researcher compared the Heights and shoe sizes for 50 men, selected at random. The equation shown describes a line of best fit for the data, where X is the shoe size and y is the height, in inches (y=1.6x + 58)
Based on the equation, what is the approximate shoe size for a man having a height of 60 inches
Answer:
1.25
Step-by-step explanation:
Given the regression equation :
y=1.6x + 58
X = shoe size ; y = height
Using the equation, the approximate shoe size of a man with a height of 60 will be ;
60 = 1.6x + 58
60 - 58 = 1.6x
2 = 1.6x
2/1.6 = 1.6x / 1.6
x = 2 / 1.6
x = 1.25
Hence, approximate shoe size of a man with a height of 60 will be 1.25
geometry of straight lines
Answers
I do geometry
Step-by-step explanation:
In geometry, the notion of line or straight line was introduced by ancient mathematicians to represent straight objects with negligible width and depth. Lines are an idealization of such objects, which are often described in terms of two points or referred to using a single letter.
Types of Lines:Vertical lines: are straight up and down and perpendicular to horizontal lines.Horizontal lines: are straight up and down and perpendicular to vertical lines.Diagonal lines: are lines that straight in any direction except vertical or horizontal.The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept. If you know two points that a line passes through, this page will show you how to find the equation of the line.
I hope it helps you!
Mr. Au went to eat at McDonald's this week. On Monday, he ate some hamburgers. On Tuesday, he ate nothing at McDonald's. On Wednesday, he ate four more hamburgers than the number that he ate on Monday. On Thursday, he ate nothing at McDonald's. On Friday, Mr. Au ate three times as many hamburgers as he ate on Wednesday. Mr. Au ate a total of 26 hamburgers that week. How many hamburgers did he eat each day?
Answers
Answer: See explanation
Step-by-step explanation:
Let the number of hamburger he ate on Monday be represented by x.
Monday = x
Tuesday = 0
Wednesday = x + 4
Thursday = 0
Friday = 3(x + 4)
Total hamburgers ate = 26
To find the amount of hamburger ate each day we add the number of hamburger ate per day all together. This will be:
= x + 0 + x + 4 + 0 + 3(x+4) = 26
2x + 4 + 3x + 12 = 26
5x + 16 = 26
5x = 26 - 16
5x = 10
x = 10/5
x = 2
Monday = x = 2 hamburgers
Tuesday = 0
Wednesday = x + 4 = 2 + 4 = 6 hamburgers
Thursday = 0
Friday = 3(x + 4) = 3(2 + 4) = 18 hamburgers
what is the x variable and y variable?
Answers
Answer:
x is the hours worked and y is the money earned
Step-by-step explanation:
Usually the x variable is the independent variable
The independent variable is the variable that does not rely on anything
The y variable is the dependent variable
The dependent variable is the variable that relies on the independent variable
In this case the money earned depends on how many hours you work for
I hope this helps :)
Answer:
I believe that it would be x is hours worked and y is dollars earned but I could be wrong I skipped a year of math because I completed it so quickly now I cant remember some stuff
Solve the following functions:
f(x) = 20x - 90 find f (x) = 10
Answers
Answer:
x=5
Step-by-step explanation:
Graph the line
y=-2x=2
please hurry!
Answers
Answer:
-1,0
0,-2
slope is -2/1
Answer:
View the Screenshot that I have sent.
Ishaan is 3 times as old as Christopher and is also 14 years older than Christopher.
How old is Ishaan?
Answers
Answer:
Ishaan is 21. Christopher is 7.
Answer: Ishann is 21 years old.
Step-by-step explanation:
In this situation, we will represent Ishaan age by the variable y and we will represent Christopher's age by x.
Ishaan is 3 times as old as Christopher and that can be represented by the equation, y = 3x
He is also 14 years older, and it can also be represented by the equation,
y = x + 14.
y= 3x
y = x + 14
Using both equations, substitute the value of y in one of the equations into the other.
x + 14 = 3x Solve for x .
-x -x
14 = 2x
x = 7
This means that Christopher is 7 years old.
To solve for Ishaan's age , input the value of x into one of the equations.
y = 3(7)
y = 21.
subtract (7x^5-12x^2y+33y^2) from (5x^5-5x^2y+9y^2) simplify your results:
Answers
Answer:
- 2 [tex]x^{5}[/tex] + 7x²y - 24y²
Step-by-step explanation:
( 5 [tex]x^{5}[/tex] - 5x²y + 9y² ) - ( 7 [tex]x^{5}[/tex] - 12x²y + 33y² ) =
5 [tex]x^{5}[/tex] - 5x²y + 9y² - 7 [tex]x^{5}[/tex] + 12x²y - 33y² =
( 5 [tex]x^{5}[/tex] - 7 [tex]x^{5}[/tex] ) + ( - 5x²y + 12x²y ) + ( 9y² - 33y² ) =
- 2 [tex]x^{5}[/tex] + 7x²y - 24y²
the sum of 1 and 3 times a number is 22. write and solve and equation to determine the number. select the solution and graph that represents the number
a) x=4
b) x=6
c) x=7
d) x=9
Answers
Answer:
b
Step-by-step explanation:
If the sum of 1 and 3 times a number is 22, then x=7 is the solution and graph that represents the number
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
The sum of 1 and 3 times a number is 22.
Let the unknown number be x
1+3x=22
Now subtract 1 from both the sides
1+3x-1=22-1
3x=21
Divide both sides by 3
x=7
So the solution of sentence sum of 1 and 3 times a number is 22 is 7.
x=7 is the equation of graph that represents the number
Hence x=7 is the equation of graph that represents the number
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ2
cual es la respuesta de 1000+25
Answers
Answer:
1025
Step-by-step explanation:
1 0 0 0
+ 2 5
---------------
1 0 2 5
----------------
HOPE THIS HELPS
PLZ MARK AS BRAINLIEST!!!!!!
Which statement correctly compares the angles?
Angle G is congruent to angle P.
Angle G is smaller than angle P.
Angle G is larger than angle P.
Angle G is congruent to angle N.
Answers
Answer:
its B
Step-by-step explanation:
well...you can see it XD
Answer:
Yepp B is correct on Edge
Step-by-step explanation:
There are 1 × 1014 good bacteria in the human body. There are 2.6 × 1018 good bacteria among the spectators in a soccer stadium. About how many spectators are in the stadium? Express your answer in scientific notation.
Answers
Answer:
There are [tex]2.6\times 10^{4}[/tex] spectators in the soccer stadium.
Step-by-step explanation:
From this statement, we can calculate the number of spectators in a soccer stadium by dividing the amount of bacteria among the spectators in a soccer stadium by the amount of bacteria in the human body. That is:
[tex]x = \frac{2.6\times 10^{18}\,bacteria}{1\times 10^{14}\,bacteria}[/tex]
[tex]x = \frac{2.6}{1}\times \frac{10^{18}}{10^{14}}[/tex]
[tex]x = 2.6\times 10^{18-14}[/tex]
[tex]x = 2.6\times 10^{4}[/tex]
There are [tex]2.6\times 10^{4}[/tex] spectators in the soccer stadium.
I will give Brainlyest to the first person
A family gathered 12 seashells from the beach bringing the total number of seashells in their collection to 86
Which equation can be used to find, x, the number of seashells in the collection before the 12 were added?
Answers
Answer:
The first selection is the answer.
Step-by-step explanation:
x+12=86
The equation that can be used to find x is x + 12 = 86
A linear equation is of the form:
y = mx + b;
where y, x are variables, m is the slope of the line and b is the y intercept.
Let x represent the number of seashells in the collection before the 12 were added. Hence to find x, we use the equation:
x + 12 = 86
The equation that can be used to find x is x + 12 = 86
Find out more at: https://brainly.com/question/13911928
Is this true or false? Pls help a dumb person out
Answers
Solve (x + 2 -6).
{x | -6 1}
{x | x < 0}
Answers
Answer:
x^2 + x = 0
Step-by-step explanation:
Simplifying
x2 + x = 0
Reorder the terms:
x + x2 = 0
Solving
x + x2 = 0
Solving for variable 'x'.
Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + x) = 0
who good at math? , cuz i need help .
Answers
Answer:
what kind of math?
Step-by-step explanation:
Answer:
It depends your grade, but I might be able to help.
Step-by-step explanation:
What type of math?
Letters used in the word mathematics
Answers
Answer:
In this case, there are 11 letters in the word 'mathematics'; three letters appear twice: m, a, and t.
Step-by-step explanation:
I don't know why you want this but there you go
A particular computer takes 11 minutes to download a 33-minute TV show. How long will it take the computer to download a 2-hour movie?
Answers
Answer:
42 minutes because i add 33min and 1/2 hours together and got 42
Step-by-step explanation:
42 minutes because i add 33min and 1/2 hours together and got 42
Answer:
40 minutes
Step-by-step explanation:
120 minutes = 2 hrs
120/33 = 3.636363636363....
and 3.6363636363.... x 11 minutes = 40 minutes
%50 POINTZ Which set of statements explains how to plot a point at the location (Negative 2.5, 3.75)?
Start at the origin. Move 2.5 units left because the x-coordinate is -2.5. -2.5 is between -2 and -3. Move 3.75 units up because they-coordinate is 3.75. 3.75 is between 3 and 4.
Start at the origin. Move 2.5 units left because the x-coordinate is -2.5. -2.5 is between -2 and -3. Move 3.75 units down because they-coordinate is 3.75. 3.75 is between 3 and 4.
Start at the origin. Move 2.5 units up because the x-coordinate is -2.5. -2.5 is between -2 and -3. Move 3.75 units left because the y-coordinate is 3.75. 3.75 is between 3 and 4.
Start at the origin. Move 2.5 units right because the x-coordinate is -2.5. -2.5 is between -2 and -3. Move 3.75 units up because they-coordinate is 3.75. 3.75 is between 3 and 4.
Answers
Answer:
Move 2.5 units left because the x-coordinate is -2.5. -2.5 is between -2 and -3. Move 3.75 units up because they-coordinate is 3.75. 3.75 is between 3 and 4.
Step-by-step explanation:
Look at the picture.
(x ; y)
x < 0 - move x units left
x > 0 - move x units right
y < 0 - move y units down
y > 0 - move y units up
Answer:
answer is A
Step-by-step explanation:
your welcome :)
Marching Bands: In how many ways can four marching bands and three floats line up for a paradeif two bands cannot march next to one another?
Answers
Answer:
There's 6 ways the boats can line up for the parade.
Step-by-step explanation:
Feel free to give brainliest.
Have an outstanding day!
At the annual dog show, Chantel noticed that there were three more Scotties than Schnauzers. She also
realized that the number of Wirehaired Terriers was five less than twice the number of Schnauzers. If there
were 78 dogs in all (counting Schnauzers, Scotties, and Wirehaired Terriers), how many Schnauzers were
there? Write and solve an equation.
Answers
9514 1404 393
Answer:
(s+3) +s +(2s-5) = 7820 SchnauzersStep-by-step explanation:
Each of the quantities is described in terms of the number of Schnauzers, and that is the number we are asked for. It is convenient to write an equation for the number of Schnauzers. We choose to use s for the variable representing that number.
s = # of Schnauzers
s+3 = # of Scotties, 3 more than the number of Schnauzers
2s-5 = # of Wire-haired Terriers, 5 less than twice the number of Schnauzers
The total number of dogs is then ...
(s+3) +(s) +(2s-5) = 78
4s -2 = 78 . . . . simplify
4s = 80 . . . . . . add 2
s = 20 . . . . . . . divide by 4
There were 20 Schnauzers at the dog show.
Mikaila collected 27 pounds of glass bottles to bring to the recycling center. she also collected 400 ounces of newspapers and 160 ounces of aluminum cans. what is the total weight of the items Mikaila brought to the recycling center? write your answer in ounces. think you❤!
Answers
The Ride-It Store rents bicycles.The cost is $8.50 for 1 hour, $13.65 for 2 hours,$18.80 for 3 hours, and $23.95 for 4 hours.If the pattern continues, how much will it cost Nate to rent a bike for 6 hours?
Answers
Answer:
in six hours it would be $34.25
Step-by-step explanation:
The computation of the total cost for 6 hours is shown below:
For one hour it would be $8.50
For two hours
= $13.65 - $8.50
= $5.15
For three hours
= $18.80 - $13.65
= $5.15
For four hours
= $23.95 - $18.80
= $5.15
For five hours
= $23.95 + $5.15
= $29.10
For six hours
= $29.10 + $5.15
= $34.25
Hence, in six hours it would be $34.25
Solve: 4-(9g-5)=-27 please help
Answers
Answer:
-2
Step-by-step explanation:
9g-4-5=-27
9g-9=-27
Add 9 to both sides
9g=-18
g=-2
Answer:
-18
if you need more info. just search up you question on Google and click the first link
Find the slope of the line. Explain or show your reasoning.
Write an equation for the line.
Find the values for and . Explain or show your reasoning.
Answers
Please help me with this question.... please...
Answers
Answer:
just plug in the x value into the equation and put it in ur calculator
y=(200 • .05)(5)+200, y= 250
y=(200 • .05)(20)+200, y=400
Marisa's car gets an average of 28 miles per gallon of gas. She plans to drive 200 miles today and 220 miles tomorrow. How many gallons of gas should she expect to use in all?
A) 15 gallons
B) 28 gallons
C) 56 gallons
D) 67 gallons
Answers
Answer:
15
Step-by-step explanation:
Add the total of miles Marisa is going to drive; 200 + 220 = 420
Next, divide the total miles by the average miles Marisa can travel on one gallon of gas; 420 / 28 = 15
(Hope this helps!)
Shoppers at a grand opening for a sporting goods store receive a gift bag when they make a purchase. How often will a bag contain both a T-shirt and socks? Items in the Gift Bag T-shirt Every 4th bag Socks Every 3rd bag
Answers
Answer:
Every 12th bag
Step-by-step explanation:
Given that:
Gift bag contains :
T - shirt = every 4th bag
Socks = Every 3rd bag
To obtain how often gift bag contains both T-shirt and socks , obtain the Lowest common multiple of 4 and 3
Multiples of :
4 : 4, 8, 12, 16, 20, 24,....
3 : 3, 6, 9, 12, 15, 18, 21, 24,....
Hence, the lowest common multiple of both 4 and 3 is 12.
The bag will contain both T-shirt and socks after every 12th bag
Natalia and her friends held a bake sale to benefit a local charity, friends sold 15 cakes on the first dayand 22 cakes on the second day of the bake saleThey collected $60 on the first day $88 on the second day Write an equation to represent the amount R Natalia and her friends raised after selling c cakes .
Please i need this asap it’s due in 15 minutes!! I will give brainliest to whoever gets it right first!!