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].
A cylinder has radius 3 meters. Its volume is 141.3 cubic meters. Find its height to the nearest tenth
of a meter.
Answer:
Height = 5meters
Step-by-step explanation:
Using the formula h= v over 3.14r^2 = 141.3 over 3.14 times 3^2 gives us 4.99747 meters.
Help plzzzz I need the correct answers ASAP and that's my last marking period 4 and I'm in grade 12th
It's homework: Comprehension Questions - 3.1 Credit Basics:
Question 10: it's part 1 multiple choice questions and Part II: Analyze: Understanding Amortization
Janet just graduated from college, has a job she’s scheduled to begin in 3 months, and has decided to treat herself to 6 weeks of travel across South America before she buckles down and starts working full-time. To do the trip, she’s thinking of applying for a personal loan of $3500, and the bank she uses for her checking and savings account has offered her an interest rate of 24%. She has a goal of paying off the trip within two years, so she uses a Bankrate.com loan calculator and gets the following amortization schedule:
4) How many months does it take Janet to pay off her loan?
5) What is the total amount of interest Janet will pay at the end of the loan?
Answer:
try c
Step-by-step explanation:
If Joe earns $38,000 a year:
1. How much does he make a month?
2. If his budget per month is $3,200, can he afford that on his salary?
What are the measures of ∠1 and ∠2?
Answer:
Angle 1 = 102
Angle 2 = 40.9
Step-by-step explanation:
[tex]1)\ 180 - 121.8 = 58.2[/tex]
[tex]2)\ angle\ 2 = 58.2 - 17.3 = 40.9[/tex]
[tex]3)\ angle\ 1 = 180 - 40.9 - 37.1 = 102[/tex]
Answer:
m∠1 = 67.4° m∠2 = 104.5°
Step-by-step explanation:
17.3 + m∠2 = 121.8
m∠2 = 104.5°
m∠1 + 37.1 = m∠2 = 104.5
m∠1 = 67.4°
what is the value of x?
Mrs. McClure's famous peanut butter cookies call for 1 cup of peanut butter for every 1 2 of a cup of oil. Today, she wants to make a huge batch with 1 cup of oil. How much peanut butter should she use?
Answer:
Amount of butter need for 1 cup of oil = 2 cup of butter
Step-by-step explanation:
Given:
Amount of butter need for 1/2 cup of oil = 1 cup
Find:
Amount of butter need for 1 cup of oil
Computation:
Amount of butter need for 1/2 cup of oil = 1 cup
1 cup butter = 1/2 cup oil
So,
Amount of butter need for 1 cup of oil = 1 / [1/2]
Amount of butter need for 1 cup of oil = 1 / [0.5]
Amount of butter need for 1 cup of oil = 2 cup of butter
What percent of the data is between 30 and 50 on the number line?
Answer:
20 percent
Step-by-step explanation:
50 - 30 = 20 percent
a centre seat costs 25£ less than an aisle or window seat. A window or aisle seat costs a and a centre seat costs £271.complete the equation that describes this. how much does an aisle or window costs?
Answer:
246
Step-by-step explanation:
271-25=246
Find the area of the figure.
Answer:
132
Explanation:
All you need to do is separately find the area of the shapes that are part of the figure (in this case the trapezoid and rectangle), and then add them all up.
1.(7x4) + (1/2x8[7+19])
2. 28 + 104
3. 132
~Hope this helps you~
A marble started with 0.0018 J of Potential Energy and at some point later it has only 0.0011 J of Potential Energy. How much Kinetic Energy does the marble have?
Answer:
the Kinetic Energy of the marble at the later point is 0.0007 J
Step-by-step explanation:
Given;
initial potential energy of the marble, P.E₁ = 0.0018 J
final potential energy of the marble, P.E₂ = 0.0011 J
At the initial starting point, the total mechanical energy is;
M.E = K.E + P.E
at the initial starting point, velocity = 0
M.E = 0 + P.E
M.E = P.E = 0.0018 J
At some point later, the total mechanical energy is;
M.E = P.E + K.E
0.0018 J = 0.0011 J + K.E
0.0018 J - 0.0011 J = K.E
0.0007 J = K.E
Therefore, the Kinetic Energy of the marble at the later point is 0.0007 J
Hello! Would appreciate help!!
Find the value of x. Round to the
nearest tenth.
Answer:
17.14
Step-by-step explanation:
tan 35 = 12/x
x = 12/ tan 35
= 17.14
can someone teach me how to solve for surface area of a rectangular prism or something that looks like this i have a huge test tmr and i have so much anxiety….
Answer:
52 meters squared
Step-by-step explanation:
Hey, don't worry you'll do great on the test. Just relax before it and you'll be fine.
Basically, you need to find the area of each rectangle which isn't too hard. AS you can see, the first one 4 m x 5m = 12 m which is your first number. Then you can see another red rectangle. Since it's a net, the 4m side length would be the same and the other one is labeled 3 m. So, 4x3 = 12m. That's your second one. Then you see a yellow rectangle on the far left. Since we know the red rectangle has one side length of 3m, we can apply that to the yellow ones as well since it's a net. So 2x3=6 and same for the other yellow rectangle. Then, we see the purple rectangle on the top which has one length of 2m. But, the red rectangle below it had a length of 4m so we can bring that to this as well. so 2x4 = 8m (another number). Then, finally, the last rectangle below has one side of 4m and the yellow rectangle (remember) above has one side length of 2m (which we would bring down). So, 4x2=8m. So, we add them all together. 12+12+8+8+6+6 = 52 meters squared (dont forget units!)
Sorry if this was too long, but an edit: if you notice all the same colored rectangles have the same area, since it's a rectangular prism. so if you find one of the same color, you basically have the other one as well.
Good luck on your test, hope you do well!!
I need to turn this in ASAP please help!-
In the last three years, Frederico's basketball team won 50 more games than they lost. If they won 130 games, what was the ratio of wins to losses? Write the ratio in all three forms. 13/8, 13 to 8, 13:8 13/18. 13 to 18. 13:18 5/13, 5 to 13, 5:13 13/5. 13 to 5, 13:5
Answer:
13/8, 13 to 8, 13:8
Step-by-step explanation:
if they won 50 more than they lost and won a total of 130 games, this means they lost 80 games (130-50=80). we can then write this as 130:80, which simplifies to 13:8
Answer:
The answers are 13/8, 13 to 8, 13:8.
Step-by-step explanation:
Since Frederico's team won 50 more games than they lost, and the won 130 games, then you would subtract the two numbers to find their losses:
130 - 50 = 80
The ratio of there wins to losses is 130 to 80.
Then you need to simplify this answer, which would make the ratio 13 to 8.
Three ways to write this are 13/8, 13 to 8, 13:8.
It would be ABSOLUTLEY FANTABULOUS if I could get brainliest!!!!
= 1 cubic ft
What is the volume of the solid figure? Enter the answer in the box.
Answer:
800
hope this helps
PLEASE HELP ASAP I have no idea how to solve this pls pls pls
Answer:
Step-by-step explanation:
you have to use trigonometric functions
cos 30 = adj. /hyp.
cos 30 = 12 / y
y = 12/cos 30 ≅13.86
tan 30 = opp./adj
tan30 = x / 12
x = 12 tan30 ≅6.93
3.2x4.9-1.5 simplify
Answer:
14.18
Step-by-step explanation:
3.2*4.9= 15.68
15.68 -1.5 = 14.18
I need help!!!!!!!!!?
What is the value of x in the equation 2x + 3y = 36, when y = 6? A. 8 B. 9 C. 27 D. 36
Answer:
x = 9
Step-by-step explanation:
When y = 6 :
2x + 3y = 36
2x + 3(6) = 36
2x + 18 = 36
2x = 36 - 18
2x = 18
x = 9
its math algebra 1 i need help
Answer:
The 3rd one which is C
Step-by-step explanation:
It's the 3rd one because if you look at the orange like where the 2 and the 4 is you will see the orange line is between them two which that's where the 3 will go and the others don't have that, so it C hope this helps you!
h(x) = 18.75 - 4.53x What is the value of h(−11)?
Answer:
h(-11) = 68.57
Step-by-step explanation:
h(x) = 18.75 - 4.53x
h(-11) = 18.75 - 4.53(-11)
h(-11) = 18.74 + 49.83
h(-11) =:68.57
What is the volume of hemisphere with a radius of 8 ft rounded to the nearest tenth of cubic foot
Answer:
1072.3[tex]ft^{3}[/tex]
Step-by-step explanation:
A hemisphere is half of a sphere, so the volume V of the hemisphere is the volume of the sphere divided by 2.
V = (2/3)*[tex]\pi[/tex][tex]r^{3}[/tex]
= (2/3)*[tex]\pi[/tex][tex](8ft)^{3}[/tex]
= (2/3)*[tex]\pi[/tex]*512[tex]ft^{3}[/tex]
= 1072.3[tex]ft^{3}[/tex]
Which expression shows the result of applying the distributive property to 9(2 + 5m)?
• 2 + 45m
O 18 + 45m
O 11 + 14m
18 + 5m
Answer:
18+45m
Step-by-step explanation:
You multiply when applying the distributative property:
9(2+5m)
18+45m multiply 9 by each value in parentheses
help asap pleaseeee !!!!!!
Answer:
C. ⅓ × (8 + 7) + 12
Step-by-step explanation:
Let's translate each statement given to numerals and symbols first:
Twelve => 12
One-third => ⅓
Sum of 8 and 7 => (8 + 7)
Representing this statement altogether will be:
⅓ of (8 + 7) = ⅓ × (8 + 7)
If 13 is added, we would get:
⅓ × (8 + 7) + 12
What is the length of leg s of the triangle below?
Answer:
E. 8
Step-by-step explanation:
It's a special right angle triangle. Hypotenuse is
[tex] \sqrt{2} x[/tex]
where x is the length of other legs. Also other two sides of triangle are always equal.
So to find the other leg divide by .
[tex] \sqrt{2} [/tex]
The length will be 8.
Janette measures the heights in inches of some of the flowers in her garden to see which ones are growing more. The heights are listed below. Which line plot represents the data correctly? 7 1 2 712 7 7 7 1 2 712 6 3 4 634 7 1 4 714 7 1 4 714 7 1 4 714 7 7 6 1 2 612 7 3 4 734 7 3 4 734 6 3 4 634 8 1 4 814 7 7 7 1 2 712 7 7 7 1 4 714 7 7 7 1 2 712 7 1 2 712
Answer:
Dot plot A
Step-by-step explanation:
In other obtain the solution to the question given, we obtain the frequency distribution of the data values given and compare to the box plots given to identify which boxplot correctly conveys the data.
___ Frequency
6 1/2 - 1
6 3/4 - 2
7 = 5
7 1/4 = 4
7 1/2 = 5
7 3/4 = 2
8 1/4 = 1
If /\PQR~/\SQT, find the value of x.
Answer:
[tex] \frac{x + 13}{8} = \frac{21}{x - 9} \\ {x}^{2} + 4x - 117 = 168 \\ {x}^{2} + 4x - 285 = 0 \\ (x - 15)(x + 19) = 0 \\ x = 15 \\ x = - 19[/tex]
Convert 100° to radians. Will mark brainlist if correct
the table describes some of the solutions of the inequality 3m>21. Which graph best describes the solutions of 3m>21?
Answer:
Option 3
Step-by-step explanation:
Given inequality is,
[tex]3m\geq 21[/tex]
To find the solutions of the given inequality solve this inequality first.
[tex]\frac{3m}{3}\geq \frac{21}{3}[/tex]
[tex]m\geq 7[/tex]
This inequality will be represented by an arrow starting from 7 and directing towards infinity.
Since, inequality is having a sign notation of greater than equal to, arrow will start with a dark circle located at 7.
Therefore, Option 3 (from the top) will be the answer.
The diameter of a circle measures 20 yd. What is the circumference of the circle?
Use 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.
20 yd
yd
Answer: 62.8 yd
Step-by-step explanation:
Circumference= diameter*pi
20*3.14= 62.8
Choose a number sentence is that illustrates distribute property of multiplication over addition 2×7+8 = 2+7×2+8
Answer:
[tex](b)\ 2 * (7 + 8) = (2 * 7) + (2 * 8)[/tex]
Step-by-step explanation:
Given
[tex](a)\ 2 * (7 + 8) = (2 + 7) * (2 + 8)[/tex]
[tex](b)\ 2 * (7 + 8) = (2 * 7) + (2 * 8)[/tex]
[tex](c)\ 2 * (7 + 8) = (2 * 7) + 8[/tex]
Required
Which illustrates distributive property of multiplication over addition
The property states that:
[tex]a(b + c) = a * b + a * c[/tex]
By comparison
[tex]a = 2\ b = 7\ c = 8[/tex]
So, we have"
[tex]2(7 + 8) = 2 * 7 + 2 * 8[/tex]
[tex]2(7 + 8) = (2 * 7) + (2 * 8)[/tex]