Answer:
y = 6(sq rt 3)
x = 18
Step-by-step explanation:
y = (0.5)(12)(sq rt 3) = 6(sq rt 3)
x = (0.866)(12)(sq rt 3) = (10.392)(sq rt 3) = sq rt 324
reduced
x = 18
The trigonometric function gives the ratio of different sides of a right-angle triangle. The value of x and y is 18 and 6√3 units respectively.
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
Let the side with label x be the base of the triangle and y be the perpendicular.
As the length of the base is x while the angle is 30°, and the length of the hypotenuse is 12√3, therefore, the value of x can be written as,
[tex]Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Cos (30^o)=\dfrac{x}{12\sqrt3}\\\\\\Cos (30^o) \times {12\sqrt3}={x}\\\\x = {12\sqrt3} \times \dfrac{{\sqrt3}}{2}\\\\x = 18[/tex]
Now, as we know that the length of the perpendicular side is y, therefore, the value of y can be written as,
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Sin (30^o)=\dfrac{y}{12\sqrt3}\\\\\\Sin (30^o) \times {12\sqrt3} ={y}\\\\\\y = \dfrac{1}{2} \times 12\sqrt3\\\\\\y = 6\sqrt3[/tex]
Hence, the value of x and y is 18 and 6√3 units respectively.
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Find x, to the nearest hundredth.
Answer: 13.99
Step-by-step explanation:
Using sine rule
((sin 90)/18)= ((sin (180-(90+39)))/x)
((sin 90)/18)=((sin 51)/x)
(1/18)=(0.7771/x)
Cross multiply
x= 0.7771*18
x= 13.99
Sharon is buying candy. she buys 5 type on the menu if she splits the price equality with four friends how mich do they each pay
Answer:
D. 0.65
Step-by-step explanation:
0.05 x 5=0.25
0.01 x 5=0.05
0.07 x 5=0.35
0.25+0.05+0.35=0.65
they all must pay 0.65 each
Answer:
0.65
Step-by-step explanation:
Plz need an answer fast
Answer:
Not a function becuase one input value corresponds with multiple output values.
Step-by-step explanation:
Hope it helps
Solve for x.
4(5x−20)=−20
Enter your answer in the box.
x =?
Answer:
4(5x-20)=-20 should be x=3
Answer:
x = 3
Step-by-step explanation:
4(5x−20)=−20 | Given
20x - 80 = -20 | Distribute the number on the outside (multiply all numbers on the inside by the number on the outside, 4×5x and 4×-20)
20x = 60 | Add 80 to both sides (do the opposite operation, if its a negative number add it to both sides)
x = 3 | Divide both sides by 20x (20x turns into x and 60 turns into 3 via 60÷20)
how do I solve for x?
Step-by-step explanation:
(5x + 1 ) + 14x + (4x + 5)= 180 [ sum of all angles of a triangle is 180]
Solve the equation 7^{2x}+7^{x+1}+4=0. Correct to 4 decimal places.
Answer:
Step-by-step explanation:
Here is the exact form and decimal form!
HELP ASAP I WILL MARK BRAINLIEST
Answer:
It's the first one...!!!
Simplifly 25 : 15:30
Answer:
5:3:6
Step-by-step explanation:
because I took math
The end points of cd are given.find the coordinates of the midpoint M. C(-8,-6) and D(-4,10)
Answer:
i dont know this is ut of my slybos
Step-by-step explanation:
The end points of cd are given.find the coordinates of the midpoint M. C(-8,-6) and D(-4,10)
Breyelle is planning on purchasing a new sports-utility vehicle. The list price of the one she is most interested in buying is $32,000. This vehicle is expected to depreciate in value by 8.5% per year.
Which model could be used to calculate the daily depreciation for this vehicle?
V(t)=32,000(0.0233)^t
V(t)=32,000(0.9150)^t
V(t)=32,000(0.9767)t^t
V(t)=32,000(0.9998)^t
Answer:
V(t)=32,000(0.9767)t^t
Step-by-step explanation:
The correct model which could be used to calculate the daily depreciation for this vehicle is,
⇒ V (n) = 32,000 (0.915)ⁿ
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
We have to given that;
Breyelle is planning on purchasing a new sports-utility vehicle.
Here, The list price of the one she is most interested in buying is $32,000.
And, This vehicle is expected to depreciate in value by 8.5% per year.
Hence, the daily depreciation for this vehicle is,
V (n) = 32,000 (1 - 8.5%)ⁿ
V (n) = 32,000 (1 - 0.085)ⁿ
V (n) = 32,000 (0.915)ⁿ
Thus, The correct model which could be used to calculate the daily depreciation for this vehicle is,
⇒ V (n) = 32,000 (0.915)ⁿ
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Answer pls. question in photo
One afternoon, a student who is 5 feet 4 inches tall measured shadows to find the height of a telephone pole. The student's shadow was 5 feet long. At the same time, the shadow of the telephone pole was 18 feet 9 inches long. How tall is the telephone pole?
Please help
Answer:
19.9875 feet
Step-by-step explanation:
The formula is given as:
Shadow of the student/Height of the student = Shadow of the telephone pole/Height of the telephone pole.
1 inch = 0.0833 feet
Shadow of the student = 5ft
Height of the student = 5 feet 4 inches
4 inches to feet
= 4 × 0.0833 feet
= 0.33 feet
Hence: Height of the student = 5 + 0.33 = 5.33 feet
Shadow of the telephone pole = 18 feet 9 inches long
9 inches to feet
= 9 × 0.0833 feet
= 0.75 feet
Hence: Shadow of the telephone pole = 18 + 0.75 = 18.75 feet
Height of the telephone pole= x
Therefore:
5/5.33 = 18.75/x
Cross Multiply
5x = 5.33 × 18.75
x = 5.33 × 18.75/5
x = 19.9875 feet
The height of the telephone pole = 19.9875 feet
What is the area of the following circle?
Either enter an exact answer in terms of pie or use 3.14 for pie and enter your answer as a decimal.
r=1
(20 points)
Answer:
3.14
Step-by-step explanation:
A= 3.14 x r to the power of 2
pls help me answer this (multiple choice)
Answer:
Option 3, 18.0
Step-by-step explanation:
To find the Hypotenuse of a right triangle, use the Pythagoras theorem:
[tex]a^{2} +b^{2} =c^{2}[/tex]
(see image below)
(the longest side of any right △ is always C)
In this equation, we know A is 10 and B is 15, so plug in these numbers and solve for C
[tex]10^{2} +15^{2} =c^{2}[/tex]
[tex]100 + 225 =c^{2}[/tex]
[tex]325 = c^{2}[/tex]
Now that the equation is simplified, we find the square root of 325 to solve for C.
[tex]\sqrt{325 = c^{2}}[/tex]
[tex]18.0 = c[/tex]
The final answer is C = 18.0
Hope this helps you understand :)
A boy arrived at school at 8:15am if he stayed in the school for 4 hours 20 minutes when did he leave
Answer:
12:35
Step-by-step explanation:
The boy left school at time 12:15 pm.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Examples:
1 hour = 60 minutes
1 minute = 60 seconds
1 km = 1000 m
We have,
To find out when the boy left school, we need to add 4 hours and 20 minutes to the time he arrived at school.
To add minutes, we need to make sure both times are in the same format. Let's convert the arrival time of 8:15 am to minutes:
So,
8:15am = 8 x 60 + 15 = 495 minutes
Now we can add 4 hours and 20 minutes:
495 + 4 x 60 + 20 = 735 minutes
So the boy left school at 735 minutes after midnight.
To convert this back to a time, we can divide by 60 to get the number of hours and minutes:
735 minutes / 60
= 12 hours (with 15 minutes remaining)
Therefore,
The boy left school at time 12:15 pm.
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A pound of popcorn is popped for a class party. The popped corn is put into small popcorn boxes that each holds 120 popped kernels. There are 1,600 kernels in a pound of unpopped popcorn. If all the boxes are filled except for the last box, how many boxes are needed, and how many popped kernels are in the last partially filled box?
Answer:
14 ; 40
Step-by-step explanation:
Number of unpopped popcorn = 1600 kernels
Kernel per popped corn = 120
Number of boxes needed :
Number of unpopped / kernel per popped corn
1600 / 120
= 13.3333
Hence, number of boxes needed = 14
Number of popped kernel. In partially filled box :
1600 - (120 * 13)
1600 - 1560
= 40
The diameter of a spherical basketball is 10 inches. What is the volume of the basketball? Give the exact solution.
Step-by-step explanation:
Volume of sphere =4/3pir3
=4/3 X pie X rXrXr
R=diameter /2=10/2=5 inches
V=4/3 X 22/7 X 5 X 5 X 5
= 11000/21=523.8in3
Hey! please help me out.. I would really appreciate it!
With step by step explanation!
question
3)
[tex]y = 2x[/tex]
answer
[tex] \frac{y}{2 } = x[/tex]
question
[tex]5 - y = 3x[/tex]
answer
[tex] x= \frac{5 - y}{3} [/tex]
question
4)
[tex]y = 5x + 20[/tex]
answer
[tex]x = \frac{y - 20}{5} [/tex]
question
[tex]y = x + 4 [/tex]
answer
[tex]x = y - 4[/tex]
question
5)
[tex] - 3x - 2y = - 12[/tex]
answer
[tex]x = - \frac{2(y - 6)}{3} [/tex]
question
[tex]y = 5x - 7[/tex]
answer
[tex]x = \frac{y + 7}{5} [/tex]
question
6)
[tex]y = 3x - 22[/tex]
answer
[tex]x = \frac{y + 22}{3} [/tex]
question
[tex]y = 2x - 15[/tex]
answer
[tex]x = \frac{y + 15}{2} [/tex]
all you have to do is plus, subtract and divide
HOPE IT WORKS!
Write an algebraic expression for each situation.
a. 7 more than a number
b. Twice a number
Step-by-step explanation:
a- 7 + X
b- 2x is the equation for these terms I think so
Please help out with this geometry homework I was assigned. And what formula do I use?
Answer:
[tex] V_{cone} \approx 1,178.97 \: {in}^{3} [/tex]
Step-by-step explanation:
Diameter of cone = 16 in
Radius of cone r = 16/2 = 8 in
Height of cone h = 17.6 in
[tex]V_{cone} = \frac{1}{3} \pi {r}^{2}h \\ \\ V_{cone} = \frac{1}{3} \times 3.14 \times {(8)}^{2} \times 17.6 \\ \\ V_{cone} = \frac{1}{3} \times 3,536.896 \\ \\ V_{cone} = 1,178.96533 \\ \\ V_{cone} \approx 1,178.97 \: {in}^{3} \\[/tex]
Which is the correct algebraic expression for each phrase? 13 times the cost of one ticket *
A. t ÷ 13
B. t - 13
C. 13 + t
D. 13t
Can someone help me answer this question
Answer: (C) 25 lawns
Step-by-step explanation: he has 15 cars so his you follow the line from the graph it will end at 25 lawns
sorry this is a bad explanation but C is correct-
Find the indicated side of the right triangle x=
9514 1404 393
Answer:
x = 9y = 9√2Step-by-step explanation:
Side lengths in an isosceles right triangle have the reduced ratios ...
1 : 1 : √2
Yours have the ratios ...
9 : x : y
If you multiply the reduced ratios by 9, you can find the values of x and y.
9 : 9 : 9√2 = 9 : x : y
x = 9
y = 9√2
Help Please :)
I'm not sure if I'm correct.
Answer:
You are correct!
For the triangle it is given that AE2 + EB2 = 9 and BE2 + EC2 = 16
Find AC =
Answer:
Step-by-step explanation:Given : right triangle ABC , AE^2 + EB^2 =9 and BE^2 + EC^2 = 16
To find : AC
Solution:
BE ⊥ AC
∠AEB = 90°
=> ΔAEB is right angled
=> AB² = AE² + EB²
=> AB² = 9
∠BEC = 90°
=> ΔBEC is right angled
=> BC² = BE² + EC²
=> BC² = 16
∠ABC = 90°
=> AC² = AB² + BC²
=> AC² = 9 + 16
=> AC² = 25
=> AC = 5
AC = 5
The length of AC is 5 units.
What is a Triangle?Any three-sided polygon having three edges and three vertices is referred to as a triangle in geometry. The most important attribute of a triangle is that its internal angles sum to 180 degrees. The triangle's angle sum attribute is what is known as.
As per the given data:
We are given the diagram of ΔABC which is right-angled.
BE is perpendicular to AC.
AE² + EB² = 9 ...(i)
BE² + EC² = 16 ..(ii)
By using the Pythagoras theorem in ΔABE:
AE² + EB² = AB²
From comparing with eq (i)
AB² = 9
AB = √9 = 3 units
By using the Pythagoras theorem in ΔCBE:
BE² + EC² = BC²
From comparing with eq (ii)
BC² = 16
BC = √16 = 4 units
By using the Pythagoras theorem in ΔABC:
AB² + BC² = AC²
AC² = 3² + 4²
AC² = 9 + 16 = 25
AC = 5 units.
The length of AC is 5 units.
Hence, The length of AC is 5 units.
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10/2
20/2
50/2
100/2
Answer:
10/2 =5
20/2=10
50/2=25
100/2=50
What is the value of n^-4 w^0 for n=-2 and w=5?
Answer:
1/16
Step-by-step explanation:
-2^-4 = 1/(-2)^4
5^0 = 1
1/(-2)^4 = 1/16
Please help, math isn’t my strong suit.
An art class charges each student $15 to attend, plus a fee for supplies. The instructor hopes to collect $240 total from the 12 students who attend the class.
2.1) Write a question that you could figure out using this information and whose answer is not already given.
Answer:
Find the cost of supplies charged by the instructor for each student.
What are the four things
that make up
galaxy ? I need a answer quickly and I need it to be correct! I need a answer ASAP! Thanks