Answers
Answer:
[tex]x =6[/tex]
[tex]y=6\cdot \sqrt{2}[/tex]
Step-by-step explanation:
Trigonometric Ratios
The ratios of the sides of a right triangle are called trigonometric ratios. There are six trigonometric ratios: sine, cosine, tangent, cosecant, secant, and cotangent.
The longest side of the right triangle is called the hypotenuse and the other two sides are the legs.
Choosing any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.
The image shows a right triangle where the angle of 45° has x as the opposite leg, 6 as the adjacent leg, and y as the hypotenuse. The trigonometric ratio that applies here is the cosine ratio, defined as:
[tex]\displaystyle \cos\theta=\frac{\text{adjacent leg}}{\text{hypotenuse}}[/tex]
[tex]\displaystyle \cos 45^\circ=\frac{6}{y}[/tex]
Solving for y:
[tex]\displaystyle y=\frac{6}{\cos 45^\circ}[/tex]
[tex]\cos 45^\circ=\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}[/tex]
Substituting:
[tex]\displaystyle y=\frac{6}{\frac{1}{\sqrt{2}}}[/tex]
[tex]y=6\cdot \sqrt{2}[/tex]
Now use the tangent ratio:
[tex]\displaystyle \tan\theta=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]
[tex]\displaystyle \tan 45^\circ=\frac{x}{6}[/tex]
Solving for x:
[tex]x=6\cdot\tan 45^\circ[/tex]
[tex]\tan 45^\circ=1[/tex]
Substituting:
[tex]x=6\cdot 1[/tex]
[tex]x =6[/tex]
Answer:
[tex]x =6[/tex]
[tex]y=6\cdot \sqrt{2}[/tex]
Related Questions
PLEASE ANSWER ASAP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
and answer like
answer 1. ___________________
answer 2.___________________
answer 3.___________________
answer 4.___________________
answer 5.___________________
Answers
Answer:
answer 1: proportinal
answer 2:proportinal
answer 3:not proportinal
answer 4:proportinal
answer 5:not proportinal
Step-by-step explanation:
btw im in k12 too i hope this helps
Answer:
1) proportional
2) proportional
3) not proportional
4) proportional
5) not proportional
Step-by-step explanation:
What is the solution to the equation below? Round your answer to two
decimal places.
6 • e^x = 25
Answers
x = 1.43 is the solution to the equation 6 • e^x = 25, rounded to two decimal places
3x+4y=-36, -2x+4y=-16
Answers
Answer:
3x+4y=-36
x= -4/3y-12
-2x+4y=-16
x= 2y+8
Evaluate 4x-(y + 2) + 6 when x = 2 and y = 3
Answers
Answer:
answer is 3
Step-by-step explanation:
8-5
4(2)=8
3+2=5
8-5=3
Answer:
46
Step-by-step explanation:
Suppose you earned $15 from your job last week. You want to save $3 and buy
some books that cost $4 each. To find how many books you can buy, solve the
equation.
plz help
Answers
SOME ONE HELP ITS DUE IN 3 HRS ITS ONLY ONE QUESTION PLS
The measures of two of the angles are 50° and 30° what is the last angle?
Answers
Answer: The answer would be 100 degrees.
Step-by-step explanation:
180 - (50+30) = 100
Hope this helps :)
x^2+6x-19=0 pls helpppp
Answers
Answer:
Step-by-step explanation:
Since this is not factorable, let's just complete the square:
[tex]x^2+6x=19\\x^2+6x+9=28\\(x+3)^2=28\\x+3=\sqrt{28}\\x=2\sqrt{7}-3[/tex]
A car manufacturer produced 5,000 cars for a limited edition model. Dealers sold all of these cars at mean price
of $36,000 with a standard deviation of $3,000. Suppose we were to take random samples of 9 of these cars
and calculate the sample mean price x for each sample.
Answers
Answer:
μₓ = 36,000 dollarsσ ₓ= 1,000 dollarsShow work:to find μₓ = 36,000 dollars:
Look in the question, it states that the mean is $36,000.
to find σ ₓ= 1,000 dollars:
[tex]\frac{3000}{\sqrt{9} } = 1000[/tex]The height, x, of a model built with toy blocks is proportional to the number of blocks, y, that is used. The table below shows this relationship. Which of the following is the missing value for the table?
Answers
Write the equation of the line, in point-slope form. Identify (x1, y1) as the point (-2, 2). Use the box provided to submit all of your calculations and final answers.
Answers
Answer:
Slope: -1
Point-Slope Form: y - 2 = -1 (x - (-2))
Step-by-step explanation:
Answer: y-2=-1(x+2)
Step-by-step explanation: use whichever points you want I’m using (-2,2)
Find slope: y2-y1/x2-x1 so 2+2/-2-2 = 4/-4 = -1
Plug in these into y-y1= m(x-x1)
y-2= -1(x+2)
Debby had 928 quarters. If it costs 8 quarters for each coke from a coke machine, how many could she buy
Answers
Answer: 116
Step-by-step explanation: simply divide 8 into 928
Answer:
116 coke
Step-by-step explanation:
992/8
=116
Debby would be able to buy 116 cokes from the coke machine.
I need help with this please help????
Answers
Answer:
D.29
Step-by-step explanation:
all you have to do is replace the x's with -2
4(-2)^2-3(-2)+7=4*4+6+7=16+6+7=22+7=29
How many solutions are in the graph
A. One solution
B. Two solutions
C. No solutions
D. Infinitely many solutions
Answers
Answer:
Infinite Many Solutions
Step-by-step explanation:
If I am correct the two lines are overlapping each other in more than one place so that means there are infinitely many solutions. Also, there can be no " two solutions" for this type of equation. There can only be one solution, no solution, or infinitely many solutions.
Keisha is reading a 310 page book at a rate of 23 pages per day.Use a point-slope equation to determine how many pages she will have left to read after reading the book for 10 days. She will still have [ ] pages left to read after 10 days.
Answers
Answer:
80 pages
Step-by-step explanation:
Point slope Equation is :
y = mx + c
In the above question
y = 310 pages
x = number of days = 10 days
m= 23 pages per day
c = ?? Unknown
c = y - mx
c = 310 - 23 × 10
c = 310 - 230
c = 80 pages
She will still have 80 pages left to read after 10 days
Determine the GCF of 3x^3,6x^2 and 15x
Answers
Answer:
3x
Step-by-step explanation:
The GCF would be 3x, if you took out 3x from those numbers you'd be left with x^2, 2x, and 5, which can't be reduced any further.
A wheel with a diameter of 12 inches will move 377 inches when rolled five times. How far will the same wheel move to the nearest inch in 16 rolls?
HELP ME I BEG YOU SMART PEOPLE
Answers
Answer:
1, 206 inches
Step-by-step explanation:
Solve for x by factoring sqrt{x+7}=x+5
Answers
Answer:x=-3
Step-by-step explanation:
Factor and set each factor equal to zero.
Hellllllllllllllllllllllllllllllllllllllllllllllllllllllllppppppppppppppp
Answers
Answer:
144 calories
Step-by-step explanation:
12%(1200)=
0.12(1200)=144
Find the volume of a cylinder with a height of 6cm and a radius of 3cm
Answers
Answer:
a) 54π cm³
Step-by-step explanation:
area of circle=πr²
9π
π9*6=54π
Answer:
b
Step-by-step explanation:
Solve for x for the equation 5x+2=12
Answers
Answer:
x=12
Step-by-step explanation:
Subtract 2 from both sides
Subtract 2 from 12 to get 10
Divide both side by 5
Finally,divide 10 by 5 to get 2
5(2)+2=12
please help and show work
Answers
Answer:
1. a=20
2. a=17
3. x=12 y=4
Step-by-step explanation:
set them equal to each other for each figure, the first one is 6a+10=130 therefore 6a=120 if you subtract 10 from each side. then you divide by 6 to get a=20.
For the next one set them equal again to get 4a-4=2a+30 first you add 4 to each side to get 4a=2a+34 then you subtract 2a from each side to get 2a= 34 then you divide by 2 to get a=17
Last one you have to set 6y+1 equal to 4y+9 because they are equal distance. you get 6y+1=4y+9 then you subtract 4y to get 2y+1=9 then you subtract 1 to get 2y=8 then you divide by two and get y=4
For the second variable of the last equation you set the remaining two equations equal to each other to get 2x-5=x+7 then you subtract x from both sides to get x-5=7 then you add five to each side to get x=12 so your final answer for the last question is x=12 y=4
Hope this helped ;)
can someone help me w this ?
Answers
Have a nice day!
Answer:
first choice
Step-by-step explanation:
a^2 + b^2 = c^2
a^2 + 10^2 = 15^2
a^2 + 100 = 225
- 100 -100
a^2 = 125
square 125
a = 11.18
Helpppp!!
Select all the functions whose graphs include the point (16,4).
y = 2x
y = x?
y = x + 12
y = x - 12
Answers
Answer:
it is the first one I am sure of it
A traveler is walking on a moving walkway in an airport. The traveler must walk back on the walkway to get a bag he forgot. The traveler's ground speed is 1 fts against the walkway and 5 ft/s with the walkway. What is the traveler's speed off the walkway? What is the speed of the moving walkway? The traveler's speed off the walkway is ft/s.
Answers
Answer: here is your answer
Step-by-step explanation:
You can put this solution on YOUR website!
+t+ = traveler's speed in ft/sec
+w+ = walkway's speed in ft/sec
given:
+t+-+w+=+2+
+t+%2B+w+=+6+
-------------
Add the equations
+2t+=+8+
+t+=+4+
and
+t+%2B+w+=+6+
+4+%2B+w+=+6+
+w+=+2+
The traveler's speed off the walkway is 4 ft/sec
The speed of the moving walkway is 2 ft/sec
PLZ HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!
Use the original price and the markup to find the retail price.
Original price: $64; Markup: 20%
The retail price is $ ___________
Answers
Answer:
$72 would be the retail price
Step-by-step explanation:
Anyone please help like I said I will Venmo you 5 dollars not joking but please help
Answers
Answer:
0 = 0 miles
1 = 1.5 miles
2 = 3 miles
3 = 4.5 miles
4 = 6 miles
5 = 7.5 miles
Step-by-step explanation:
multiply each hour by 1.5
If a garden snail travels 1.5 miles per hour, then when 0 hours pass, it would have travelled 0 miles (no time has passed).
After 1 hour, it would have travelled 1.5 miles.
After 2 hours, it would have travelled 3 miles (1.5 miles × 2 hours).
After 3 hours, it would have travelled 4.5 miles (1.5 miles × 3 hours).
After 4 hours, it would have travelled 6 miles (1.5 miles × 4 hours).
After 5 hours, it would have travelled 7.5 miles (1.5 miles × 5 hours).
I hope this helps!
HELP HELP HELP I REALLY NEED HELP PLEASE PLEASE PLEASE!!!!!
Answers
Answer:
i think 7 maybe?
How do i solve this?
Answers
Answer:
x=5
Step-by-step explanation:
the angle LMN is a 90 degree angle, so we need 11x+35 to equal 90.
11(5)+35=90
Valerie and her parents are going to her grandparents' house in Tennessee. It is a 3-hour drive. If they leave at 9:00 am and don't make any stops, what time will they be at Valerie's grandparents' house?
Answers
Answer: 12:00 pm
Step-by-step explanation:
Valerie and her parents are goig to see her grandparents.
The grandparents leave 3 hours away.
They leave at 9:00 am.
The rime they'll arrive is therefore:
= 9 + 3 hours
= 12:00 pm
F(x)= x^6 + 63x^3 -64