Answers
The length οf the perpendicular is 2√2.
What is Trigοnοmetry?Trigοnοmetry is a branch οf mathematics that deals with the study οf relatiοnships between the sides and angles οf triangles. It includes the study οf trigοnοmetric functiοns such as sine, cοsine, and tangent, which are used tο sοlve prοblems in fields such as engineering, physics, and navigatiοn.
Step 1:
Let's call the length οf the perpendicular "p".
Frοm the given infοrmatiοn, we knοw that the hypοtenuse is 8√2 and the angle at the base is 30 degrees. We can use trigοnοmetry tο find the length οf the perpendicular.
In a right triangle, the sine οf an angle is defined as the length οf the side οppοsite the angle divided by the length οf the hypοtenuse. Sο we have:
sin(30°) = p/8√2
We can simplify this expressiοn by nοting that sin(30°) = 1/2 and 8√2 = 8√(2/2) = 8√(1/√2) = 8/√2. Substituting these values, we get:
1/2 = p/(8/√2)
Simplifying further, we can multiply bοth sides by 8/√2:
4/√2 = p
Tο express the result in simplest radical fοrm, we can ratiοnalize the denοminatοr by multiplying the numeratοr and denοminatοr by √2:
p = 4/√2 * √2/√2 = 4√2
Therefοre, the length οf the perpendicular is 4√2.
Step 2:
Let's call the length οf the perpendicular "p".
Frοm the given infοrmatiοn, we knοw that the hypοtenuse is 4√2 and the angle at the base is 45 degrees. We can use trigοnοmetry tο find the length οf the perpendicular.
In a right triangle, the sine οf an angle is defined as the length οf the side οppοsite the angle divided by the length οf the hypοtenuse. Sο we have:
sin(45°) = p/4√2
We can simplify this expressiοn by nοting that sin(45°) = √2/2 and 4√2 = 4√(2/2) = 4√(1/√2) = 4/√2. Substituting these values, we get:
√2/2 = p/(4/√2)
Simplifying further, we can multiply bοth sides by 4/√2:
2√2 = p
Therefοre, the length οf the perpendicular is 2√2.
To learn more about Trigonometry from the given link
https://brainly.com/question/24349828
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Related Questions
a newspaper editor hired a writer for jokes cartoons. the cost for 8 jokes and 6 cartoons is 610usd. the cost of 6 jokes and 8 cartoons is 510usd how much do a joke and a cartoon together cost
Answers
Answer:
a joke and a cartoon together cost $80
c=$15 j=$65
Step-by-step explanation:
j=joke
c=cartoon
8j +6c = 610
6j+8c = 510
Multiply the first by 8
Multiply the second by -6
64j +48c = 4880
-36j -48c = -3060
ADD both (c will cancel)
28j = 1820
j= 65
PLUG j
8(65) + 6c = 610
520+6c = 610
6c= 90
c = 15
j + c = 65+15 = 80
An amount of R351 is made up with 114 coins (R2 coins and R5 coins only). How many R2 coins are there? How many R5 coin are there?
Answers
Answer:
41
Step-by-step explanation:
For this, you have to make two equations;
One that calculates the amount of coins
and one that calculates the amount of R
I'm going to set
R2 = x
R5 = y
To make this a bit easier to look at
So to do the number of coins, you want to do this:
x + y = 114
This is saying that the total amount of R2 coins plus the total amount of R5 coins will add up to 114
Then, you want to calculate the worth of them.
2(x) + 5(y) = 351
This is saying that for ever R2 coin there is, it will increase the total by 2, and every R5, it will increase the total by 5. When you add these together, it will come out to 351.
Then you have to solve the system of equations:
x + y = 114
2x + 5y = 351
-2 * (x + y = 114)
2x + 5y = 351
-2x + -2y = -228
2x + 5y = 351
3y = 123
y = 41
Since y is the amount of R5 coins, we know we have 41 R5 coins.
So the answer is
41
Mark rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total that is a factor of 18.
Answers
Answer:
1/3
Step-by-step explanation:
Factors of 18 are 1,2,3,6,9
The side of a goal in soccer is the shape of a right trapezoid. The dimensions are shown below. What is the area of the net needed for both sides of the goal? Чft 8 ft 10 ft
Answers
Answer:
[tex]61^{2}[/tex]
Step-by-step explanation:
So area equals {(B+b) x h} / 2 the two bases are 4 and 10 which is 14 the height is 8 so 14 times 8 is 112. 112 divided by 2 is 61. I hope this helps.
Re write the quadratic function in standard form y=(x+5)(x-2)
Answers
Answer:
y = x^2 + 3x - 10
Step-by-step explanation:
x*x + 5*x + -2*x + 5*-2
= x^2 + 3x + -10
PLEASE RATE!! I hope this helps!!
This is a spinner for a game board. color the spinner to show 20% chance of black and 80% chance of red.
Answers
Answer:
Step-by-step explanation:
Divide the circle into 10 parts and color 2 parts black and 8 parts red.
How to illistrate 1/3×1/2
Answers
Answer:
=1/6
Step-by-step explanation:
thats the answer
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5 A bag of tiles contains 6 green, 4 yellow, and 5 blue tiles. If one tile is pulled at random what is the probability of NOT choosing a green tile.
Make sure to give your probability as a fraction in simplest form.
Answers
Answer:
3/5
Step-by-step explanation:
6+4+5 = 15
5+4 = 9
9/15 = 3/5
Answer:
3/5
Step-by-step explanation:
Since it given that a bag of tiles contains:
6 green
4 yellow
5 blue
To Find:
If one tile is pulled at random what is the probability of NOT choosing a green tile.
Solve:
knowing that there are a total of 15 tiles {6+5+4=15}
And there is 6 green tiles
Thus, 15 - 6 = 9
Hence, the probability of Not Choosing a green tiles before simplest form is 9/15
GCD - 3
Divide both the numerator and denominator by the GCD
9 ÷ 3/15 ÷ 3
Reduced fraction = 3/5
Therefore, the probability of Not choosing a green tiles is 3/5
~Lenvy~
Evaluate the function when x= -3, 0, and 1.
f(x) = 5 + 5x - 7
Answers
Answer:
f(-3) = -17
f(0) = -2
f(1) = 3
Step-by-step explanation:
f(-3) = 5 + 5(-3) - 7
5 -15 - 7
-10 - 7
=-17
f(0) = 5 + 5(0) -7
5 + 0 - 7
5 - 7
=-2
f(1) = 5 + 5(1) - 7
5 + 5 - 7
10 - 7
=3
PU
The data set below represents the different costs of a refrigerator at a local home improvement store.
$777, $498, $619. $379. $895, $1,256, $1,052
b. What is the median of the second half of the data? (third quartile) 379
T
Answers
Using the median concept, it is found that the third quartile is of is of $1,052.
What is the median of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.
In this problem, the ordered data-set is:
$379, $498, $619, $777, $895, $1,052, $1,256.
Hence, the median of $777 divides the data-set into two halfs:
The first half is: $379, $498, $619.The second half is: $895, $1,052, $1,256.Hence, the third quartile, which is the median of the second half, is of $1,052.
More can be learned about the median concept at https://brainly.com/question/25215461
Are the ratios 5:4 and 20:16 equivalent?
Answers
Answer:
yes
Step-by-step explanation:
If you take 20 and divide by 4 you get 5. if you take 16 and also divide by 4, you will get 4.
Please help!! I will give brainliest :)
Answers
Answer: I think its 75 percent
Step-by-step explanation:
Answer:
75%
Step-by-step explanation:
The shaded is part of the poster 9/12
To convert 9/12 into a percent
100 ÷ 12 = 8.3333333333333
[tex]\frac{9*8.3333333333}{12*8.3333333333} = \frac{75}{100}[/tex]
MATHEMATICS
NEED
SOME
HELP
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TY<3
Answers
Answer:
The answer is 157 mm.
Step-by-step explanation:
Given;Diameter (d) = 50 mmπ = 3.14To Find;The circumference of the circle.Formula;C = πdNow,
C = πd
C = 3.14 × 50 mm
C = 157 mm
Thus, The circumference of the circle is 157 mm.
A school band sold 432 tickets for their upcoming spring concert. This represents about 85.5% of the number of tickets sold last year. How many tickets were sold last year? (Round to the nearest whole number)
Answers
I got chu bro
How many more quarters does
Tommy need before he has $3.00
in quarters?
Answers
8 out of 9 people in a class of 360 people are right handed, what is the percentage or right handed people and left. Then how many people out of the class of 360 is left and right handed.
Answers
Answer:
88.889% are right handed, 11.111% are left handed, ~320 people are right handed in a class of 360, ~40 people are right handed.
Step-by-step explanation:
The fraction 8/9 is equal to .88889, or 88.889%
Likewise, the fraction 1/9 (remainder) is equal to .11111, or 11.111%
By multiplying 360 by these fractions to get the number of people who fit these criteria in the sample, you get:
360*8/9 = 320 people right handed.
360*1/9 = 40 people left handed.
Cheers!
In 1994, the moose population in a park was measured to be 4180. By 1999, the population was measured again to be 3480. If the population continues to change linearly: Find a formula for the moose population, P, in terms of t, the years since 1990. P(t)=? What does your model predict the moose population to be in 2002?
Answers
"If the population continues to change linearly", meaning the pattern or equation is the equation of a straight line.
[tex](\stackrel{x_1}{1994}~,~\stackrel{y_1}{4180})\qquad (\stackrel{x_2}{1999}~,~\stackrel{y_2}{3480}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3480}-\stackrel{y1}{4180}}}{\underset{run} {\underset{x_2}{1999}-\underset{x_1}{1994}}}\implies \cfrac{-700}{5}\implies -140[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4180}=\stackrel{m}{-140}(x-\stackrel{x_1}{1994}) \\\\\\ y-4180 = -140x + 279160 \\\\\\ y = -140x+283340~\hfill \boxed{P(t)=-140t+283340}[/tex]
what if t = 2002?
[tex]P(2002)=-140(2002)+283340\implies P(2002)= 3060[/tex]
how many integers from 100 to 999, inclusive, don't include the numbers 2,4,6,8? PLS HELP I WILL MARK BRAINLIEST
Answers
Answer:
243
Step-by-step explanation:
999-100= 899 integers
200s 400s 600s 800s excluded so 400 numbers excluded
899 - 400 = 499
20s 40s 60s 80s which are 40 integers x 4 = 160
499 - 160 = 339
2s 4s 6s 8s which are 4 integers x 6 x 4 ( 4 from each 100 ) = 96
339 - 96 = 243 integers
In a town of 117 000 people, 14000 like to
Watch hockey. What percent of the town's
Populations like to watch hockey?
Answers
Divide number that like hockey by population then multiply by 100:
14,000 / 117,000 = 0.11965
0.11965 x 100 = 11.965%
Round up to 12%
Did i do this right?
Answers
Answer:
yes
Step-by-step explanation:
Urgente!!! Doy 20 puntos
Answers
Answer:
74-7, 0, +9Step-by-step explanation:
Hope this helps
Which of the following is equivalent to 1 and
5/8
Answers
Use rounding to estimate the product of 5, 555 and 4, 444. Round both numbers to the nearest thousand to find your answer.
The solution is
Answers
Step-by-step explanation:
5,555 can be rounded up to 6,000 because the 5 next to the five thousand will make it go up. while the 4,444 will round to 4,000 . I don't have a clear answer but I hope this helps.
Help me please, thank you
Answers
Answer:
Option D is your correct answer
I think it will help.
three subtracted from five times a number is -39. what number is?
A) Translate the statement above into an equation that you can solve to answer this question, Do not solve it yet. Use x as your variable.
The equation is _____
B) Solve your equation in part {A} for x
.Answer x=
Answers
Answer:
A) 5x - 3= -39
B) 5x = -39 + 3
5x = -36
x = -36/ 5
x= -7.2
What is the probbability of flipping a coin 15 times and getting heads 6 times?
Answers
Answer:
if I'm wrong let me know 25
Dylan purchased a new car in 1993 for $26,300. The value of the car has been depreciating exponentially at a constant rate. If the value of the car was $2,700 in the year 2001, then what would be the predicted value of the car in the year 2006, to the nearest dollar?
Answers
The predicted value of the car in the year 2006 to the nearest dollar would be $651.
What is the predicted value of the car?The first step is to determine the rate of depreciation
g = (FV/PV)^(1/n) - 1
Where:
FV = value of the car in 2001
PV = value of the car in 1993
n = number ofyears = 8
(2700/26,300)^(1/8) - 1 = -24.76%
Now determine the value of the car in 2006
2700x ( 1 - 0.2476)^5 = $651
To learn more about depreciation, please check: https://brainly.com/question/25552427
please solve for x please use statement reason
Answers
AE || BC
===》 DCB angle = DAE angle
AC /
__________________________________
Thus :
DCB angle = x
And also we know that the submission of interior angles of any triangle must equals to 180 degrees so :
In BCD triangle :
B + C + D = 180
x + x + D = 180
D = 180 - 2x
__________________________________
In the other hand we know that :
BDC angle + BDA angle = 180
because they make a straight line together so ;
180 - 2x + 50 = 180
- 2x = 180 - 230
- 2x = - 50
x = 25
And we're done...
Have a great time ♡
(NEED HELP ASAP)An urn contains three red marbles, and six blue marbles. What is the probability of selecting at random, without replacement, two blue marbles?
Answers
Answer:
6/9 or 1/3
Step-by-step explanation:
There is a total of 9 marbles of both colors in the bag.
(3 red marbles + 6 blue marble = 9 marbles)
This means the denominator of your probability will be 9. There are 6 blue marbles in the bag so, in conclusion, the probability that you will take a blue marble out of the bag is 6/9. Also, 6/9 when simplified, is 1/3.
Have a great rest of your day
#TheWizzer
Abby is shooting a rocket off the top of a 128 foot tall building at a velocity of 96 feet per second. The equation to represent this is h(t) = -16t? +960 + 128 where h(t) represents the height of the rocket and t is the time after takeoff.
What is the maximum height of the rocket?
How many seconds does ot take to get to the maximum height?
Find the time it takes (in seconds) for the rocket to crash to the ground.
Answers
Answer:
a) 272 feet
b) 3 seconds
c) 7.123 seconds
Step-by-step explanation:
A graphing calculator provides an easy way to answer questions about the parameters of a quadratic function. Here the graph shows ...
a) the maximum height is 272 feet
b) it takes 3 seconds to get there
c) the rocket crashes after about 7.123 seconds
__
You can solve this algebraically by rewriting the equation in vertex form.
h(t) = -16t² +96t +128 . . . . . . given
h(t) = -16(t² -6t) +128 . . . . . . . factor out leading coefficient
h(t) = -16(t² -6t +9) +128 -(-16)(9) . . . . complete the square
h(t) = -16(t -3)² +272 . . . . . . write in vertex form
The vertex of the height function is (3, 272) meaning the rocket reaches a maximum height of 272 feet after 3 seconds.
__
The zero of the function can be found to be ...
0 = -16(t -3)² +272
0 = (t -3)² -17 . . . . . . divide by -16
t -3 = ±√17 . . . . . . add 17, take the square root
t = 3 +√17 ≈ 7.123106 . . . . . positive time value for h(t) = 0
It takes about 7.12 seconds for the rocket to crash.