how to find the theta with side lengths of a triangle
Answers
Step-by-step explanation:
Hello, there!!!
I hope you mean the question is like the above problem in picture.
so, let's simply work with it.
here, we may use cosine rule,
so, according to cosine rule,
[tex] {c}^{2} = {a}^{2} + {b}^{2} - 2ab.cosc[/tex]
so, just put value of formulae here,
we get;
5^2 = 3^2 + 4^2 - (2×3×4) . cos thita
or, 25 = 9 + 16 -24 cos thita.
or, 24 cos thita = 0
or, cos thita = 0/25
or, cos thita = 0
now, taking cos to right side we get,
[tex] {cos}^{ - 1 } (0)[/tex]
now, after typing cos ^-1 (0) we get angle as 90°.
(note: in step {cos thita = 0} you couold directly write like; cos thita = cos 90°. and cos would be cancelled in it as cos 90°=0. but it is only applied in particular angle like 0°,30°,60°,..... which are identified or if you don't know you must use the method above using calculator and remember to put inverse {cos^-1}).
so, In this way we find angle.
I hope it helps....
Related Questions
Given: AB tangent at D, AD = OD = 4 Find: Area of the shaded region
Answers
Answer:
1.72
Step-by-step explanation:
AB tangent at D, AD = OD = 4
so triangle OAD is right angle with side of 4 and 4.
area of OAD = 1/2 * 4 * 4 = 8
Angle AOD = DAO = 45 deg.
so circular sector OCD area = area of circle O * 45/360
= pi * 4 * 4 * 45/360
= 2pi
Shade area ACD = trigangle OAD - circular sector OCD
= 8 - 2pi
= 1.72
PLEASE help!!!
Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations). The figures below are based on semicircles or quarter circles and problems b), c), and d) are involving portions of a square.
Answers
Answer:
Step-by-step explanation:
The shaded regions consist of a triangle and a semicircle
Area of shaded regions = Area of Triangle + Area of semicircle
Area of Triangle = (h x b) ÷ 2
Height, h = 10 cm
Base, b = 8 cm
Are of the triangle component = (10 x 8) ÷ 2
= 80 ÷ 2
= 40 cm^2
Area of semicircle = πr^2 ÷ 2
Diameter, D = 8 cm
Radius, r = 8 cm ÷ 2 = 4 cm
Are of the semicircle component = [π(4^2) ÷ 2)
= 16π ÷ 2
= 16π cm^2
Total area of shaded regions
= (40+16π) cm^2
= 8 (5 +2π) cm^2
Answer:
[tex]\boxed{\sf Area = 8\pi + 40\ cm^2}[/tex]
[tex]\boxed{\sf Perimeter = 4\pi + 22\ cm}[/tex]
Step-by-step explanation:
Area of the figure:
Firstly: Area of semicircle:
[tex]\sf \frac{\pi r^2}{2} \\Where\ r = 4 \ cm\\\frac{\pi (4)^2}{2} \\\frac{16 \pi}{2}\\8 \pi \ cm^2[/tex]
Then Area of Triangle
[tex]\sf 1/2 (Base)(Height)\\1/2(10)(4)\\10*2\\20\ cm^2[/tex]
Area of Figure = Area of Semicircle + 2(Area of triangle)
=> 8π + 2(20)
=> 8π + 40 cm²
Perimeter of Semicircle:
Firstly, we'll have to find the hypotenuse
[tex]\sf c^2 = a^2+b^2\\c^2 = 4^2+10^2\\c^2 = 16+100\\c^2 = 116\\c = 11\ cm[/tex]
Then, Perimeter of the semi-circle:
=> πr
Where r = 4 cm
=> 4π
Now, the perimeter of the whole figure:
=> 4π + 2(11)
=> 4π + 22 cm
1/2x-(x-2/3a)+1/4a please help me im so confused!
Answers
I need domain and range
Answers
Answer:
-3 and infinity
Step-by-step explanation:
Clarissa and Shawna, working together, can paint the exterior of a house in 6 days. Clarissa by herself can complete this in 5 days less than Shawna. how long will it take Clarissa to complete the job by herself?
Answers
Answer:
Clarissa will take 10 hours by herself
Step-by-step explanation:
Let s = time for shawna
s-5 = time for clarissa
The formula for determining the time is
1/a + 1/b = 1/c where a and b are the times alone and c is the time together
1/s + 1/(s-5) = 1/6
Multiply each side by 6s(s-5) to clear the fractions
6s(s-5) ( 1/s + 1/(s-5)) = 1/6 *6s(s-5)
Distribute
6(s-5) + 6s = s(s-5)
Distribute
6s -30 +6s = s^2 -5s
Combine like terms
12s -30 = s^2 -5s
Move everything to the right
0 = s^2 -5s -12s +30
0 = s^2 -17s +30
Factor
0 = ( s-15) (s-2)
Using the zero product property
s-15 =0 s-2 =0
s =15 s=2 ( This is not a reasonable answer since it is less than the time together)
s=15
s-5 = 10
Clarissa will take 10 hours by herself
The lengths of two sides of an isosceles triangle are 5 and 9. The length of the third side could be
Answers
The length of the side can be both 5 and 9.
What is an Isosceles Triangle?An Isosceles Triangle is a triangle that has two equal sides.
The length of the sides of an isosceles triangle is given as 5 and 9
To determine the third side, the property of Triangle Inequality will be used
According to the property, the sum of any pair of a triangle’s sides is always greater than the third side.
If the third side is 5 then
5+5 > 9
10 >9
true
if the third side is 9 then
5+9 > 9
14>9
Therefore, the length of the side can be both 5 and 9.
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what is the value of x ?
Answers
Answer:
35
Step-by-step explanation:
it's the same value each side
the function f(x)=-(x5+)(x+1) is shown. what is the range of the function
Answers
Answer:
all real numbers less than or equals to 4
PLZ HELP I WILL MARK YOU AS BRAINLIEST
The ages of two groups of karate students are shown in the following dot plots: The mean absolute deviation (MAD) for group A is 2.07 and the MAD for group B is 5.51. Which of the following observations can be made using these data? Group A has greater variability in the data. Group A has less variability in the data. Group B has a lower range. Group B has a lower mean.
Answers
Answer:
Group A has less variability in the data.
Step-by-step explanation:
Examining the data for both groups virtually as represented on the dot plot, we can easily tell that the data in group A are less spread compared to group B data.
Group A has a range value of 10 (14 - 4), while group B has a range value of 19 (26 - 7).
Therefore, "Group A has less variability in the data."
30 times the square of a nonzero number is equal to eight times the number what is the number
Answers
Answer: 4/15
Step-by-step explanation:
Answer:
[tex]\frac{4}{15}[/tex]
Step-by-step explanation:
Number sentence: [tex]30x^{2}[/tex] = [tex]8x[/tex]
You can start by applying algebra to the left side of the equation by dividing each side by x. This should be how it looks now: 30x = 8
Now divide each side by 30 to keep reducing it: [tex]x = \frac{8}{30}[/tex]
Now that we have [tex]\frac{8}{30}[/tex], we can reduce that by dividing the top and bottom by 2:
[tex]\frac{8}{30} = \frac{4}{15}[/tex].
Therefore, the number is [tex]\frac{4}{15}[/tex].
Hi how do I solve this simultaneous equation
Answers
Answer:
M (-3, -5/2)
N (3, -1)
Step-by-step explanation:
Solve the first equation for x.
4y = x − 7
x = 4y + 7
Substitute into the second equation.
x² + xy = 4 + 2y²
(4y + 7)² + (4y + 7)y = 4 + 2y²
Simplify.
16y² + 56y + 49 + 4y² + 7y = 4 + 2y²
18y² + 63y + 45 = 0
2y² + 7y + 5 = 0
Factor.
(y + 1) (2y + 5) = 0
y = -1 or -5/2
Plug back into the first equation to find x.
x = 4(-1) + 7 = 3
x = 4(-5/2) + 7 = -3
M (-3, -5/2)
N (3, -1)
A white-tailed deer can sprint at speeds up to 30 miles per hour. American bison can run at speeds up to 3,520 feet per minute. Which animal is faster and by how many miles per hour? There are 5,280 feet in one mile. A deer is 10 miles per hour faster than a bison.
Answers
3520/5280 = 2/3 of a mile per minute.
2/3 x 60 minutes per hour = 40 miles per hour.
40-30 = 10
Bison runs 40 miles per hour
The bison runs 10 miles an hour faster than the deer
Answer:
American bison is faster than the white-tailed deer by 10 more miles per hour.
Step-by-step explanation:
In 1 hour there are 60 minutes.
=> 3520 feet = 1 minute
=> 60 minutes = 3520 x 60
=> 211200 feet = 60 minutes
So, 211200 feet can be converted in miles.
=> 1 mile = 5280 feet
=> 211200 feet = x miles
=> x = 211200 / 5280
=> x = 40 miles per hour.
So, a white-tailed deer can run up to 30 miles per hour.
an American bison can run up to 40 miles per hour.
American bison runs 10 more miles per hour than a white-tailed deer.
also being timed help!
Answers
Answer: 4
Step-by-step explanation:
I beed help nowww hjbiuhkju uhbjknjhiuy
Answers
Answer:
answer hoga 3/2 ok.....
Answer: 3/2
Step-by-step explanation:
Can Someone help ill rate brainliest!!
Answers
Answer:
2
Step-by-step explanation:
Let Ishan’s age equal an unknown quantity we’ll call “x”.
An age 4 times Ishan’s would be 4 times x, written “4x”.
An age 6 years older than Ishan’s would be written “x+6”.
Now, through the magic of algebra, we can write an equation: 4x = x+6 . This means that “four times Ishan’s age is equal to his age plus six.”
The magic continues: you can subtract an”x” from each side of the equation. You can subtract any quantity from either side, but subtracting”x” will leave 6 on the right and “3x” on the left: 3x = 6.
Divide both sides by the same quantity: 3.
This will give you x =2. This indicates Ishan’s age is 2.
Answer:
Ishaan is 2 years old.
Step-by-step explanation:
We can create a systems of equations for this, assuming b is Ben's age and i is Ishaan's age.
[tex]b = 4i[/tex]
[tex]b = i+6[/tex]
Let's solve via substitution.
[tex]4i = i+6[/tex]
Subtract i from both sides:
[tex]3i = 6[/tex]
Divide both sides by 3:
[tex]i = 2[/tex]
So Ishaan is 2 years old. Ben is:
[tex]4(2) = 8[/tex] years old.
Hope this helped!
Need help with mark brainlist.
Nam worked on a job for 10 days. On each of the last 2 days, he worked 2 hours more than the mean number of hours he worked per day during the first 8 days. If he worked 69 hours in all, how many hours did he work during the last 2 days together?
Answers
Answer: 17 hours
Step-by-step explanation:
Given that On each of the last 2 days, he worked 2 hours more than the mean number of hours he worked per day during the first 8 days. That is he worked additional 4 hours for the two days.
Let the total hours for the 8 days = E
The mean = E/8 = 0.125E
For the two last days, he worked
( 0.125E + 2 ) × 2 = 0.25E + 4
If he worked 69 hours in all, then
E + 0.25E + 4 = 69
Collect the like terms
1.25E = 69 - 4
1.25E = 65
E = 65/1.25
E = 52.
Now find the mean of the first 8 days
Mean = 52 / 8 = 6.5 hours
Nam works during the last 2 days together for:
(6.5 + 2)×2
8.5 × 2 = 17 hours
Solve 2(x - 5) = 48 - 4(x + 1)
Answers
2x - 10 = 48 - 4x - 4
6x = 54
x = 9
Answer:
x = 9
Step-by-step explanation:
first remove the brackets
2x - 5 = 48 - 4x + 1
then take numbers to the opposite sides
2x + 4x = 48 + 5 + 1
I have used addition because since your taking-5 to the other side it becomes+5 and -4 becomes +4
now solve
2x + 4x= 6x
48+5+1= 54
6x = 54
now solve for x
divide both sides by 6x
x = 9
-4-(3+6²)÷13-1²•(-12)=
Answers
Answer:
5
Step-by-step explanation:
-4-(3+6²)÷13-1²•(-12)=
PEMDAS
parrenthesis:
-4-81÷13-1² x (-12)
exponent:
-4-81÷12 x (-12)
multiplication:
-4-81÷ (-144)
divison:
- 4 - (- 9)
subtraction (Actaully addition +):
= 5
-(- makes plus so -4 + 9 makes 5
Hope this helps, have a good day!! :)
A son is 8 years old. His father is 5 times as old. How old was the father when his son was born?
Answers
Answer:
he was 32
Step-by-step explanation:
8x5 is 40 because he was born 8 years ago you subtract 8 from 40 to get 32
Rory records the percentage of battery life remaining on his phone throughout a day. The battery life decreases as Rory uses the phone, but will increase or stay at 100% while charging. The graph represents the percentage of battery life remaining after a certain number of hours.
A graph titled Phone Battery Life. The horizontal axis shows Elapsed Time (hours) numbered 2 to 20, and the horizontal axis shows Battery Life (%) numbered 10 to 120. A line begins at 100% in 0 hours, to 20% in 8 hours, to 100% from 10 to 12 hours, to 60% in 16 hours, to 100% from 17 to 20 hours.
At which times could Rory's phone have been plugged into the charger? Select three options.
Answers
Answer:
9 hours
11 hours
19 hours
Step-by-step explanation:
The graph represents the percentage of battery life remaining after a certain number of hours is attached below.
At which times could Rory's phone have been plugged into the charger? Select three options.
6 hours
9 hours
11 hours
14 hours
19 hours
Answer: From the graph, the line segment with negative slope (that is decreasing value) shows that the phone is not plugged but being used while the line segment with positive slope (increasing value) or stays at 100% shows that the phone is plugged to the charger.
As shown, from 0 to 8 hours their is a decreasing value, the phone is not plugged. From 8 to 10 hours their is an increasing value therefore the phone is plugged also from 10 to 12 hours the phone is plugged since it is constant. From 12 to 16 hours it is not plugged. From 16 to 18 hours it is plugged and from 18 to 20 hours it is plugged.
From the options it is plugged at 9 hours, 11 hours and 19 hours
Answer:
B - 9 HOURS
C - 11 HOURS
E - 19 BHOURS
Step-by-step explanation:
i took the test
solve for x 3(x+2) + 4(x-5)=10
Answers
Answer:
x= 3.43
Step-by-step explanation:
First, use the distributive property and multiply 3 by x and 3 by 2:
3x + 6
next use the distributive property again and multiply 4 by x and -5:
4x - 20
Combine Like terms: 3x + 6 + 4x - 20
3x + 4x = 7x
6 - 20 = -14
Now Add 14 to both sides: 7x - 14 = 10
10 + 14 = 24
Now divide 7 by both sides: 7x = 24
24 / 7 = 3.428571429 = 3.43
Answer:
x=24/7 or 3 3/7
Step-by-step explanation:
3(x+2) + 4(x-5)=10 parenthesis first
3x+6+4x-20=10
7x-14=10 addition on both sides
7x-14+14=10+14
7x=24
x=24/7
check the answer:
3(x+2) + 4(x-5)=10
3(24/7+2)+4(24/7-5)=10
72/7+6+96/7-20=10
168/7-14=10
24-14=10
10=10 correct
10.The sum of first 16 terms of the AP: 10, 6 ,2, ....is
− 320− 320
320320
640640
− 352 − 352
Answers
Answer:
- 320Step-by-step explanation:
a₁ = 10
a₂ = 6
d = a₂ - a₁ = 6 - 10 = -4
n = 16
a₁₆ = a₁ + (n-1)•d = 10 + (16-1)•(-4) = 10 - 60 = -50
[tex]S_{n}=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{16}=\dfrac{10-50}{2}\cdot 16=-40\cdot8=-320[/tex]
What characteristics do similar triangles share? a They have the same sides and angles. b They have the same sides but different angles. c They have the same ratios for the sides. d They are the exact same.
Answers
Answer:
b. they have the same sides but different angles
Step-by-step explanation:
this answer makes the most sense
Answer:
C they have the same ratios for the sides
Step-by-step explanation:
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion. In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length.
You pull one card at random from a standard deck and you shuffle the remaining cards. Then you pull another card. Is the event independent or dependent?
Answers
Answer:
If an event is affected by previous events then it is a dependent event, while if an event is not affected by the previous event then it is an independent event.
Since we have replaced the card that we first drew from the deck, it wont affect the event of pulling a card second time.
So, we can say that it is an example of independent event.
Emma changed £500 into rand before going on holiday to South Africa.
The rate of exchange at the time was £1 = 10.4 rand.
Emma spent 4000 rand on holiday. When she got home, she changed her leftover rand into pounds.
The exchange rate was now £1 = 9.8 rand. How much money did she get back in pounds?
Answers
Answer:
I'm sorry but I can give exact numbers but I would like to help work it out so...
Step-by-step explanation:
So overall she had £500 to start with
And £1 is equal to 10.4 rand
So you would divide 100 by 10.4 and get the potential difference between the average of money which she has then because she spent 400 rand in holiday you would divide 400 by the amount of the potential difference which was given then change that back to pounds
Hope this helps
If this seems incorrect please comment and I will change my answer thanks:)
In this activity, you will help Darin compare the unit prices, in price per pound, of clementines and navel oranges. Clementines are sold in three-pound bags, and navel oranges are sold by the pound. The table represents the cost of three-pound bags of clementines. Number of Bags Cost 1 $5.00 2 $10.00 3 $15.00 The equation c = $1.49p represents the cost of the navel oranges, where c is the cost and p is the number of pounds. Darin needs to know the price per pound of clementines. What needs to change in the table so that the data on clementines is in units of pounds and cost?
Answers
Answer:
The table gives the cost for the number of three-pound bags of clementines. you need to change the number of bags to pounds to be able to get the data for the clementines in units of pounds and cost.
Step-by-step explanation:
each of the bags are three pounds each so 1 bag times 3, 2bags times 3, and then 3bags times 3, hope this answers your question.
The table gives the cost for the number of three pounds bag of clemintines we need to change the number of bags to pounds to get the data or clemintines in units of pounds and cost.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that Clementines are sold in three-pound bags, and navel oranges are sold by the pound
The table represents the cost of three-pound bags of clementines.
Number of Bags Cost
1 $5.00
2 $10.00
3 $15.00
The equation c = $1.49p represents the cost of the navel oranges, where c is the cost and p is the number of pounds.
The table gives the cost for the number of three pounds bag of clemintines we need to change the number of bags to pounds to get the data or clemintines in units of pounds and cost.
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Given that ΔABC is a right triangle with a right angle at C, if tan A = [tex]\frac{5}{4}[/tex], find the value for tan B.
A. tanB = [tex]\frac{3}{4}[/tex]
B. tanB = [tex]-\frac{4}{5}[/tex]
C. tanB = [tex]\frac{4}{5}[/tex]
D. tanB = [tex]-\frac{5}{4}[/tex]
Answers
Answer:
C
Step-by-step explanation:
tan A = [tex]\frac{5}{4}[/tex] = [tex]\frac{opposite}{adjacent}[/tex] , thus
The opposite side is the adjacent side for B and the adjacent side is the opposite side for B, thus
tan B = [tex]\frac{4}{5}[/tex]
Please help
Maths....
Answers
6 cm from what im seeing
Answer: 7 cm
Step-by-step explanation:
Complete the recursive formula of the geometric sequence 7, -14, 28, -56, ....
Answers
Answer:
[tex]a_{n}[/tex] = - 2[tex]a_{n-1}[/tex]
Step-by-step explanation:
A geometric recursive formula has the form
[tex]a_{n}[/tex] = r[tex]a_{n-1}[/tex]
where r is the common ratio
Here r = - 14 ÷ 7 = - 2, thus
[tex]a_{n}[/tex] = - 2[tex]a_{n-1}[/tex] with a₁ = 7
Martha estimated there were 86 marbles in a jar for a contest. The actual number of marbles in the jar was 108. What was the percent error of Martha's estimation?
Answers
Answer:
Roughly 20.4%
Step-by-step explanation:
Use the formula of percent of error:
| Actual number - Guess / Actual number | (100)
The actual number is 108 and the guessed number is 86:
| 108 - 86 / 108 | (100)
= | 22/108 | (100)
= | 0.2037037037 | (100)
The vertical lines indicate absolute value. This means that anything inside of it must be turned into its positive form. Since it is already positive, just take the signs away:
0.2037037037(100)
≈ 0.204(100)
= 20.4
Turn this into a percent:
20.4%
Martha's percent of error is 20.4%
Please tell me if I was right or not. I really hope this helps!
