If
θ
θ
is an acute angle of a right triangle and
tan θ=
3
5
tan θ=35
, what is the value of
cosθ
cosθ
?
Given:
In a right angle triangle θ is an acute angle and [tex]\tan\theta =\dfrac{3}{5}[/tex].
To find:
The value of [tex]\cos \theta[/tex].
Solution:
In a right angle triangle,
[tex]\tan \theta=\dfrac{Perpendicular}{Base}[/tex]
We have,
[tex]\tan\theta =\dfrac{3}{5}[/tex]
It means the ratio of perpendicular to base is 3:5. Let 3x be the perpendicular and 5x be the base.
By using Pythagoras theorem,
[tex]Hypotenuse=\sqrt{Perpendicular^2+base^2}[/tex]
[tex]Hypotenuse=\sqrt{(3x)^2+(5x)^2}[/tex]
[tex]Hypotenuse=\sqrt{9x^2+25x^2}[/tex]
[tex]Hypotenuse=\sqrt{34x^2}[/tex]
[tex]Hypotenuse=x\sqrt{34}[/tex]
In a right angle triangle,
[tex]\cos \theta=\dfrac{Base}{Hypotenuse}[/tex]
[tex]\cos \theta=\dfrac{5x}{x\sqrt{34}}[/tex]
[tex]\cos \theta=\dfrac{5}{\sqrt{34}}[/tex]
Therefore, the value of [tex]\cos \theta[/tex] is [tex]\dfrac{5}{\sqrt{34}}[/tex].
Find the missing angle.
Answer:
[tex]x=80[/tex]°
Step-by-step explanation:
[tex]sum ~of ~3~angles ~of ~a~ triangle ~is ~180[/tex]
[tex]80+20+x=180[/tex]
[tex]x=missing ~angle[/tex]
[tex]100+x=180[/tex]
[tex]x=180-100=80[/tex]
[tex]So, x=80[/tex]
-------------------------
hope it helps...
have a great day!!
Solve the following system of equations using the elimination method.
6x - 5y= -1
-6x – 4y = 10
A) (-1,-1)
B) (5,-5)
C) (-2,2)
D) (1,1)
Answer:D
Step-by-step explanation:
Below. What is m∠1?
m∠1 =
Answer:
m∠1 = 70
Step-by-step explanation:
A line is 180 degrees
The angles of a triangle total to 180 degrees
180 - 101 = 79
79 + 31 = 110
180 - 110 = 70
Nevaeh invested $1,200 in an account paying an interest rate of 2⅞ % compounded quarterly. Paisley invested $1,200 in an account paying an interest rate of 2⅝ % compounded continuously. To the nearest dollar, how much money would Nevaeh have in her account when Paisley's money has tripled in value?
Answer:
[tex]Nevaeh \ will \ have \ 1224.33 \ and \ Paisley \ will \ have \ 1275.[/tex]
Which equations have 8 as a solution?
15-n=7 n + 3 = 12 4n = 32
64 : n = 8
Select all the equations that have 8 as a solution.
A. 15-n=7
B. n + 3 = 12
C. 4n = 32
D. 64:n = 8
Answer:
The equations 15 - n = 7, 4n = 32, and 64 : n = 8 have 8 as a solution.
Step-by-step explanation:
Each equation will have work shown below :
15 - n = 7
For this equation, we would need to isolate the variables by doing the inverse operation to both sides of the equation. Here in this equation, the operation is to subtract and the inverse operation of that is addition. Since the original operation is subtraction, we need to add it by a negative sign to each side. In order to isolate the variables, we have to add -7 to both sides.
15 - n = 7
+ -7 + -7
8 = n
The right side has a sum of 0 so it doesn't require any value to the equation. As you can see in the equation, n equals to 8.
4n = 32
For this equation, we would need to isolate the variables by doing the inverse operation to both sides of the equation. Here in this equation, the operation is to multiply and the inverse operation of that is division. In order to isolate the variables, we have to divide 8 to both sides.
4n = 32
/4 /4
n = 8
The left side has a quotient of 0 so it doesn't require any value to the equation. As you can see in the equation, n equals to 8.
This is a ratio which is basically just the operation of division. For this equation, we would need to isolate the variables by doing the inverse operation to both sides of the equation. Here in this equation, the operation is to divide and the inverse operation of that is multiplication. Since the original operation is division, we need to multiply it by the reciprocal to each side. In order to isolate the variables, we have to multiply 1/8 to both sides.
64 : n = 8
* 1/8 * 1/8
8 = n
The right side has a product of 0 so it doesn't require any value to the equation. As you can see in the equation, n equals to 8.
CAN YOU GUYS AND GIRLS PLEASE HELP!!
Answer:
I have no idea
Step-by-step explanation:
two numbers are in the ratio 2:5. If 6 is subtracted from their sum, the result is 50. what is the larger number
Answer:
(2x+5x)-6=50
7x =56
x=8
5>2, so 5 is the bigger one
5*8=40
the answer is 40
My teacher took off points because I puter meters per second and not meters/second. Are these not the same thing?
Answer:
No
Step-by-step explanation:
Meters per second is how many meters in one second
meters/second is meters divided by one second
Hope this helps you understand better!
It is the same but the teacher may be trying to get you to put it that way for future math problems.
Help in class ez rly ez
Answer:
The slope is 4x
The y-intercept is -5
Slope-intercept form = y = 4x - 5
Step-by-step explanation:
I hope this helps.
Answer:
mark lazyboss330 as brainliest :D
why havent u been active for like a month? :c
Which of the following are possible rational roots of the polynomial function? Check all that apply. F(x) = 5 x2-3x+3
A. ±3
B. ±1
C. ±1/3
D. ±5
E. ±1/5
The possible rational roots are (a) ±3, (b) ±1, (e) ±5
How to determine the possible roots?The polynomial function is given as:
f(x) = 5x^2 - 3x + 3
Take the factors of the first term and the last term
5 = 1, 5
3 = 1, 3
The rational root is then calculated using:
Roots =±(Factors of 3)/(Factors of 5)
This gives
Roots =±(1, 3)/(1, 5)
Solve the expression
Roots = ±1, ±3/5, ±1/5, ±3
Hence, the possible rational roots are (a) ±3, (b) ±1, (e) ±5
Read more about rational roots at:
https://brainly.com/question/17754398
#SPJ1
Write an equation where x = 8.
Answer:
x (23+12)= 280
Step-by-step explanation:
X=8
add 23 plus 12 which equals 35
then multiply 35 by 8
Hope it helps
Answer:
-x + 39 = 31
Step-by-step explanation:
You would subtract 39 which would make -8. Then you would divide by -1 (x) and your answer is:
x = 8
Please help ASAP!!!! Will give brainliest!!!
Answer: 0
Step-by-step explanation: it said round to the nearest hundredth when you just need 0.21 so 0.21 rounded to the nearest hundredth is going to be 0.
where do i put the thing at chile hempp me out
Answer:
for just chile id put it at 30 or 20
Step-by-step explanation:
Which equation describes the line that passes through the
point (1, 6) and is parallel to the line 2x + y = 3?
A 2x-y=13
B 2x + y = 13
C 2x - y = 8
D 2x + y = 8
At a fixed interest rate, an investment of $4000 earns $210. How much do you need to invest at the same rate to earn $336?
Answer:
what they said^
Step-by-step explanation:
What is the volume of a cylinder that has a radius of 2 meters and height of 10 meters? Use 3.14 for π
Answer:
125.66
Step-by-step explanation:
The formula for the volume of a cylinder is V=Bh, V=πr2h, or πr2h
==
π π
r 2
2 2 ≈
Vh 10125.66371
I'm not good at explaining it but this should be the answer
PLEASE HELP AS SOON AS POSSIBLE SHOW WORK PLZ I NEED HELP
Answer:
D. (8.2, 24.3)
The table shows the relationship between the number of cups and total volume of lemonade served.
Cups of Total. Volume Lemonade Served
2 (ounces)
3 16
4 24
32
How many ounces is served per cup of lemonade?
Enter the answer in the box.
ounces per cup=
Answer: 8
Step-by-step explanation:
2 cups = 16
Half of the 16 is 8
What is the GCF of 36x^2y and 18xy ^2?
Please i really need the answers
is 8 yard, 9 yards, and 12 yards right triangle
Answer:
No
Step-by-step explanation:
you can check with the pythagorean theory
[tex]8^{2}+9^{2} =12^{2}[/tex]
64 + 81 = 144
145 = 144
this is not true, therefore those side lengths do not make a right triangle.
Seth bought a 15 ounce jar of peanut butter for $3.15. what is the unit price?
Lyndsay visited the beach with her friend. Her beach towel is in the shape of a rectangle. Which is the perimeter of the towel? (1 point)
Answer:
8 meters
Step-by-step explanation:
To find the perimeter follow these steps:
1. add the lengths together (the longe sides) so add 3 meters and 3 meters you get 6 meters
2. add the widths together (the short sides) so add 1 meter and 1 meter you get 2 meters
3. add the total lengths and widths together (6 meters plus 2 meters) you get 8 meters
Have a fantastical day!
PLEASE HELP ME ASAP
ITS IN SQUARE FEET NO GUESSES
Answer:
d should be correct
Step-by-step explanation:
why my answer beacuse i see 4in in the painted area
I'm thinking of a number. If you multiply it by four and then add 13 you will get 37. What is my number?
Answer: 6
Step-by-step explanation: subtract 13 from 37, you get 24. divide 24 by 4.
Help please please no links
Answer:
I think B
Step-by-step explanation:
plz let me know if i'm wrong tho
Answer:
Y || Z
Step-by-step explanation:
Perpendicular Transversal Theorem
If two lines are perpendicular to the same line, then the two perpendicular lines are parallel.
pls help hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Answer:
Step-by-step explanation:
d
whoever gets it right gets 10 points and brainliest!
Answer:
92 in
Step-by-step explanation:
just break it down into parts
Answer: 92in²
Step-by-step explanation: area of shaded region=9×12-4×4=92in²
What is the measure of
Which functions have a vertex with a x-value of 0? Select three options