Find c.
Round to the nearest tenth.
20 ft
50°
15 ſt
c= [.? ]ft
Law of Cosines: c2 = 22 + b2 - 2ab cos C
![Find C.Round To The Nearest Tenth.20 Ft5015 Tc= [.? ]ftLaw Of Cosines: C2 = 22 + B2 - 2ab Cos C](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/KsjIDYNM1eD8MCsMzcQvbKKSDwu4Rfye.png)
Answers
Answer:
: c2 = a2 + b2 - 2ab cos C
c²=20²+15²-2×15×20×cos50
c²=400+225-600×0.64
c²=241
c=√241=15.5ft
The value of c for the given triangle can be obtained as 239.3 ft.
What is cosine law?The cosine law for a triangle is derived from the parallelogram law of addition for two vectors.
It is given as for a triangle having sides a, b and c, the cos of the angle between sides a and b is given by,
cos(x) = (a^(2) + b^(2) - c^(2)) / (2 × a × b).
For the given diagram of a triangle, law of cosines can be applied as,
c² = a² + b² - 2abCos C
Substitute a = 15, b = 20 and ∠C = 50° to obtain,
c² = 15² + 20² - 2 × 15 × 20Cos C
c² = 625 - 600Cos(50°)
⇒ c = 239.3
Hence, the length of the other side of the triangle can be obtained as 239.3 ft.
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Related Questions
Five friends earn a total of $50 doing yard work in their neighborhood. Each friend earns the same amount. Use the equation 5f = 50 to find f, the amount that each friend earns. _______________________
Answers
Answer:
Each friend earned 10 dollars. 50÷5=10
Study the pattern in the equations. Use your observations to solve the equation for a. Express your answer in terms of
log4x 2^a = 3
Answers
Answer:
(log64x³) / 2 log = a
Step-by-step explanation:
Given the equation :
log4x 2^a = 3
Recall: If :
loga b = c becomes ; a^c = b
log4x 2^a = 3 ; becomes ; (4x)^3 = 2^a
4^3 * x^3 = 2^a
64x^3 = 2a
log64x³ = log 2a
log64x³ = 2 log a
Divide both sides by 2 log
(log64x³) / 2 log = 2 log a / 2 log
(log64x³) / 2 log = a
A right triangle has legs with lengths of 10 and 24 inches. If the midpoints of all three sides of this triangle were connected, the resulting right triangle would have a hypotenuse with a length of?
(1) 5 inches
(2) 8 inches
(3) 12 inches
(4) 13 inches
Answers
Hope this helps
The resulting right triangle would have a hypothenuse with a length of; 13 inches.
According to the question;
We are required to length of the resulting right triangle when the midpoint of all three sides of this triangle were connected.The two legs given have lengths; 10 and 24 inches.
When the midpoints are connected, the new right triangle would then have legs; 5 and 12 inches.
Therefore, from Pythagoras theorem;
Hypothenuse length,
l = √(12² + 5²)l = √169l = 13 inches.
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Find the unit rates. 4 ounces for $5.89
Answers
Answer:
Around $1.47
Step-by-step explanation:
To find the unit rate you need to have a denominator of one. (5.89/4 = x/1)
All you have to do is divide 5.89 by 4 and you get 1.4725 and if you round that to the nearest 100th place you get 1.47.
So 1 once cost $1.47
I hope this helps, and have a great day!
A package of 11 slices of cheese costs $2.97. How much would a package with 18 slices cost at the same price per slice?
Answers
Answer:
$4.86
Step-by-step explanation:
2.97/11= .27 .27x18= $4.86
Three vertices of parallelogram DEFG are D(-4, - 2), E(-3, 1) and F(3, 3). Find the coordinates of G.
Answers
Given:
The three vertices of parallelogram DEFG are D(-4, - 2), E(-3, 1) and F(3, 3).
To find:
The coordinates of vertex G.
Solution:
Let the coordinates of vertex G are (a,b).
We know that, diagonal of parallelogram bisect equal other. It means, the midpoints of both diagonals are same.
Midpoint formula:
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
Two diagonals of the parallelogram DEFG are DF and EG.
[tex]\text{Midpoint of DF}=\text{Midpoint of EG}[/tex]
[tex]\left(\dfrac{-4+3}{2},\dfrac{-2+3}{2}\right)=\left(\dfrac{-3+a}{2},\dfrac{1+b}{2}\right)[/tex]
[tex]\left(\dfrac{-1}{2},\dfrac{1}{2}\right)=\left(\dfrac{-3+a}{2},\dfrac{1+b}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{-3+a}{2}=-\dfrac{1}{2}[/tex]
[tex]-3+a=-1[/tex]
[tex]a=-1+3[/tex]
[tex]a=2[/tex]
And,
[tex]\dfrac{1+b}{2}=\dfrac{1}{2}[/tex]
[tex]1+b=1[/tex]
[tex]b=1-1[/tex]
[tex]b=0[/tex]
Therefore, the coordinates of vertex G are (2,0).
The coordinates of vertex G of parallelogram DEFG is: (2, 0).
Recall:
Diagonals of a parallelogram bisects each other, meaning they divide each other into equal parts.Midpoint formula = [tex](\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]The given vertices of parallelogram DEFG are:
D(-4, - 2), E(-3, 1) and F(3, 3)
Let (x, y) = coordinates of vertex G.
DF and EG are diagonals of parallelogram DEFG, therefore:
midpoint of DF = midpoint of EGFind midpoint of D(-4, - 2) and F(3, 3) using [tex](\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]:
[tex](\frac{-4 + 3}{2}, \frac{-2 + 3}{2}) = (\frac{-1}{2}, \frac{1}{2})[/tex]
Find midpoint of E(-3, 1) and G(x, y) using [tex](\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]:
[tex](\frac{-3 + x}{2}, \frac{1 + y}{2})[/tex]
Make the midpoint of DF equal to the midpoint of EG, then solve for x and y.
[tex]\frac{-1}{2}, \frac{1}{2} = \frac{-3 + x}{2}, \frac{1 + y}{2}[/tex]
Solve for x:[tex]\frac{-1}{2} = \frac{-3 + x}{2}[/tex]
Cross multiply[tex]2(-1) = 2(-3 + x)\\\\-2 = -6 + 2x\\\\-2 + 6 = 2x\\\\4 = 2x\\\\\mathbf{x = 2}[/tex]
Solve for y:[tex]\frac{1}{2} = \frac{1 + y}{2}[/tex]
Cross multiply[tex]2(1) = 2(1 + y)\\\\2 = 2 + 2y\\\\2 - 2 = 2y\\\\0 = 2y\\\\\mathbf{y = 0}[/tex]
Therefore, the coordinates of vertex G of parallelogram DEFG is: (2, 0).
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Pietro is given a test question asking him to show that the sum of two odd integers is
always an even integer. Which choice is the best proof of his conjecture?
Answers
Answer: second option Let (2a +1) be an odd number. Let (2b +1) be a different odd number. Because the sum of these two numbers, 2(a + b + 1), is a multiple of 2, it is an even number.
B. Let (2A + 1) and (2B + 1) are different odd numbers. sum of these odd number is 2(A+ B +1) is a multiple of 2.
What is even and odd number?Whole numbers in mathematics can also be divided into even and odd numbers. There isn't a single number that can be both even and odd, making odd and even numbers distinct sets of numbers. A number can be either even or odd. Odd numbers are ones that are not entirely divisible by two, whereas even numbers are entirely divisible by two.
Let (2A + 1) and (2B + 1) are different odd numbers. the sum of these odd numbers is 2(A+ B +1) is a multiple of 2. furthermore, let 2a and 2b be two even numbers so the sum of those two will also be an even number. Therefore the sum of two odd numbers is always even.
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Which equation represents a line with a slope of -8 and
a y-intercept of 4?
y = -8x4
y = - 4x +8
y = -8x4
y = 8x+4
Answers
The equation y = -8x + 4 represents the given problem.
What is slope and y-intercept?'The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis.'
According to the given problem,
We know,
Equation of a line can be represented as,
y = mx + c, where, m = slope
c = y-intercept
Slope of the line = -8
Y-intercept of the line = 4
Therefore,
The equation of the line:
⇒ y = -8 + 4
Hence, we can conclude, the equation y = -8x + 4 represents the given line.
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A local stadium seats 27,250 fans. For a special event, 12% of the seats were reserved for students. What
was the total number of seats reserved for students?
Answers
Answer:
3270
Step-by-step explanation:
PLEASE HELP ASAP AND ONLY DO IT IF U KNOW HOW TO IM GIVING BRAINLIEST
Match each line to the correct equation.
Coorindate grid. Lines l, m, n, p.
Group of answer choices
Line l (red line)
Line m (black line)
Line n (green line)
Line p (blue line)
Answers
Answer:
Line l (red line): y=4
Line m (black line): y=-2x+4 or y=4-2x
Line n (green line): y=x-1
Line p (blue line): x=-4
Step-by-step explanation:
Line l (red line):
Line l is horizontal. Horizontal lines have y equal to a constant, in this case 4.
y=4
Line m (black line):
Find slope using two points (0,4) and (2,0)
(y2-y1)/(x2-x1)
(4-0)/(0-2)
4/-2
-2
y=mx+c, where m is the slope and c is a number
y=-2x+c
sub in a point (eg (-1,6))
6=-2(-1)+c
6=2+c
c=4
y=-2x+4 or y=4-2x
Line n (green line):
Find slope using two points (3,2) and (2,1)
(y2-y1)/(x2-x1)
(2-1)/(3-2)
1/1
1
y=mx+c, where m is the slope and c is a number
y=1x+c
y=x+c
sub in a point (eg (1,0))
0=1+c
c=-1
y=x-1
Line p (blue line):
X value is constant at -4. x=-4
The amount of cases in Gotham city is 540
people for the first 12 of 2020. In July, a spike at the rate
of 5.2 people for each day in the month hits. Additionally, the
joker has infected all of Arkham Asylum's 225 patients with the
virus. What month will you hit 1,000 cases of cases in Gotham?
Answers
Answer: October, the 10th month
Step-by-step explanation:
540/12 = 45[with this in mind , we can assume that this is how many people get infected per month, except for July, and some factors.]
July is special for it not only has the specific unqiue rate of 5.2 infections per day. with this in mind, lets multiply....
5.2 x 31 = 161.2And to top it off, we have another 225 infections to consider.
So with consideration of 161.2, 225, 540, and the fact that 45 people get infected on an average month, lets add....
161.2 + 225 + 540 = 926.2
926.2 + 45 = 971.2
971.2 + 45 = 1016.2
It only took until the 10th month of october to hit 1000.
Can I please have help real answers only
Answers
Answer:
Sure.
Step-by-step explanation:
ok, so you basically just count from 0 going left three spaces. and the same going 5 spaces. For positive numbers you go (starting at 0) from left to right. for negative numbers (starting from 0 on the line) you go right to left.
I will make a G for where the green dot goes and a P for the pink dot.
<--I--I--I--I--I--I--I--I--I--I--I--I--I--I--I--I-->
P G 0 3 5
Hope this helps.
- Mach Speed.
pleaseeeeeee helppppppp
Answers
Answer:
what is the substitution method???
Step-by-step explanation:
You are building a doghouse for Fido, your loyal poodle. The blueprint of the doghouse uses a scale of 1 : 14. The floor of the doghouse measures 2" x 2.5" on the blueprint. b) The wood you are using for the floor costs $3.50 per square foot. How much will it cost to buy the material for the floor, assuming you can buy a piece exactly the right size? Show your work.
Answers
John and Lucy take turns rolling two dice. If John rolls a pair larger than or equal to 10 he wins and the game stops. If Lucy rolls a pair strictly smaller than 10, she wins and the game stops. They keep rolling in turn until one of them wins. Suppose John rolls first. What is the probability that Lucy wins
Answers
Answer:
56.25%
Step-by-step explanation:
If John rolls first and Lucy rolls second, in order to find the probability that Lucy wins we need to multiply the probability that John's roll is less than 10 by the probability that Lucy's roll is less than 10. There are a total of 12 possible outcomes that can occur in a pair of dice, therefore John's probability of rolling less than a 10 would be [tex]\frac{9}{12}[/tex] which would also be the same probability of Lucy rolling smaller than a 10. Now we simply multiply this probability by itself...
[tex]\frac{9}{12} * \frac{9}{12} = \frac{81}{144}[/tex] or 0.5625
We can multiply this decimal by 100 to get the percentage probability
0.5625 * 100 = 56.25%
The probability of Lucy winning the game is 56.25%
A bag of candy containing 320 pieces is to be divided up into 18 smaller bags for distribution with fourteen left over. How many pieces will go in each bag?
Answers
Answer:
17
Step-by-step explanation:
A bag of candy contains 320 pieces
It is to be divided into 18 smaller bags with fourteen left over
Therefore the pieces that will go in each bag after the distributorn can be calculated as follows
= 320/18
= 17 remainder 14
Hence 17 pieces of candy will be in each bags
D 7. What are two different ways to name the line below? Explain how you know
Answers
Answer:
[tex] \overleftrightarrow{GI} [/tex]
[tex] line m [/tex]
Step-by-step explanation:
We can decide to make the line by using the two points of the line only. Thus, the two points are G and I. We can name the line as [tex] \overleftrightarrow{GI} [/tex]
We can also simply call the line with a letter in small caps. Thus, the line can be called [tex] line m [/tex]
Factorise fully 3m+12
Answers
Answer:
The answer is 3(m+4)
hope it helps..
Answer:
Step-by-step explanation:
3(m+4)
100 points for answer. please help
Answers
Answer:
19.09
Step-by-step explanation:
4x÷3+8x÷3
4x+8x÷3×3
12x²÷6
x²=6/12
x²=3/6
3/6x²
√3/6
Answer:
19.09
Step-by-step explanation:
Pretend your friend is struggling to solve equations and has asked you for help.
Describe how you would solve the equation below for y: 5(3y - 2) + 6y = 11
Answers
Multiply 5 with what is in the brackets =15y - 10 + 6y= 11
Add the numbers 15y and 6y
21y2 - 10= 11
Minus 10 from 21
11y2to the power 2
Divide by y
Therefore answer will be 11
Y =11
Simplify the expression
14(n − 3) + 5(n - 6)
Answers
[tex]\bold{14(n-3)+5(n-6) }[/tex]
[tex]\sf{[(14\times n)-(14\times 3)]+[(5\times n)-(5\times 6)] }[/tex]
[tex]\longrightarrow \bold{14n-42+5n-30 }[/tex]
[tex]\longrightarrow \bold{ 14n+5n-42-30 }[/tex]
[tex]\longrightarrow \bold{19n-42-30 }[/tex]
[tex]\dashrightarrow\bold{19n-72 }[/tex]
The profileration of the internet has given rise to a new method of advertising, called spamming, that essentially is a more cost-effective method of the telephone solicitations method known as cold calling. If a company buys three mailing list with 2,500, 3,500, and 4,000 email addresses respectively and spam them with promotional material, how many potential customers has it reached?
A. 5,000
B. 10,000
C. 15,000
D. 20,000
Answers
Answer:
10,000
Step-by-step explanation:
2500 + 3500 + 4500 = 10,000
Simplify
(45x6y%) = (5x4y2
Answers
Answer:
0 would be your anwswer
Step-by-step explanation:
Write a function rule for "The output is half of the input x."
Answers
Answer:
[tex]y = \frac{x}{2}[/tex]
Step-by-step explanation:
Functions:
Functions have the following format:
y = f(x)
In which y is the output, x is the input, and f is the relation between them.
In this question:
The output is half of the input x. This means that:
[tex]y = \frac{x}{2}[/tex]
Functions can be represented using equations and mathematical statements
The function rule is y = 0.5x
The statement is given as:
The output is half of the input x."
Let the output be y.
So, we have:
y = 0.5 * x
Evaluate the product
y = 0.5x
Hence, the function rule is y = 0.5x
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please help! im failing and i really need help!
Answers
The varsity of girls' basketball team has a ratio of seniors to juniors that 3 to 2. If there are 6 juniors how many seniors are on the team
Answers
Answer:
I think its 9
because seniors=3 and juniors=2 so, if there are now 6 juniors there would also be 9 seniors considering all they did was multiply by 3
4^4= pls i need some help
Answers
Hey there!
4^4
= 4 • 4 • 4 • 4
= 4 • 4 ➡️ 16
= 16 • 16
= 256
Answer: 256 ☑️
Good luck on your assignment and enjoy your day!
~ Amphitrite1040:)
Which of the following descriptions best defines the term logistic growth?
A. A type of growth that is exponential at first but slows as the
amount reaches a certain maximum value
B. A type of growth that is linear at first but slows as the amount
reaches a certain maximum value
C. A type of growth that is linear at first but slows as the amount
reaches a certain minimum value
D. A type of growth that is exponential at first but slows as the
amount reaches a certain minimum value
Fr
Answers
Anthony has 46 pieces of gum and eats 2 pieces per day. Javier has 54 pieces of gum and eats 3 pieces of gum each day. In how many days will Anthony and Javier have the same amount of gum?
Answers
Because
D1 :46 / 54
D2 : 44 /51
D3: 42/48
D4:40/45
D5:38/42
D6:36/39
D7:34/36
D8:32/33
D9:30/20
Answer:
in 9 days
Step-by-step explanation:
..
Two angles are supplementary if the sum of their measures is 180∘. If the measure of one angle is 4 x degrees, represent the measure of its supplement as an expression of x
Answers
Supplementary angles= 180°
4x+x=180
5x=180
X=180/5
X= 36
The second number is 36
The first number is 4x
Since we know that x=36°
That means 4(36)=144°
36+144=180°
Im not sure if this is the solution