Answers
By means of trigonometric functions, the length of side BC is approximately equal to 11.6 centimeters.
How to determine a missing length in a system of triangles by trigonometric functions
In this problem we find a geometric system formed by two right triangles, from which we need to determine the exact measure of side BC. This can be done by means of trigonometric functions, that represents relationships between two sides of a right triangle:
sin θ = y / r
cos θ = x / r
tan θ = y / x
cot θ = x / y
sec θ = r / x
csc θ = r / y
Where:
r - Hypotenusex - Leg adjacent to the angle.y - Leg opposite to the angle.First, obtain the length of side BD:
cos θ = BD / AB
BD = AB · cos θ
BD = 5 · cos 30°
BD = 5√3 / 2 cm
Second, calculate the length of side BC:
sin θ = BD / BC
BC = BD / sin θ
BC = 5√3 / 2 / sin 22°
BC ≈ 11.6 cm
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Related Questions
Jody is buying a scrapbook and sheets of designer paper. She has $40 and needs at least $19.00 to
buy the scrapbook. Each sheet of paper costs $3.00. How many sheets of paper can she buy?
Answers
Answer:
7 sheets of paper
Step-by-step explanation:
$40-$19=$21
$21/$3=7 sheets of paper.
In words:
I did 40 minus 19 to get 21, and the divided 21 by 3 to get 7 sheets of paper.
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is, 3 / 5
We have to given that;
the terminal side of theta in standard position contains the point (6,-8)
Hence, For given condition we get;
The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is,
Here, x = 6, y = - 8
Hence, We get;
r = √x² + y²
r = √6² + 8²
r = √36 + 64
r = √100
r = 10
So, The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is,
cos θ = x / r
cos θ = 6 / 10
cos θ = 3 / 5
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Turner is deep-sea diving with two friends. Janelle is floating on the surface 15 meters above
Turner, and Ethan is exploring a coral reef 8 meters in front of Turner. How far apart are
Janelle and Ethan?
Answers
h=6q-2u q=3 and u=-5 what is the value of h
Answers
The value of h in the equation h = 6q - 2u , when q = 3 and u = -5 is h = 28 .
In the question ,
it is given that ,
the equation is h = 6q - 2u ,
we have to find the value of h , when q = 3 and u = -5 .
Substituting the value of q = 3 and u = -5 in the equation ,
we get,
h = 6q - 2u
h = 6(3) - 2(-5) ....because 6(3) = 18 and -2(-5) = 10
h = 18 + 10
Simplifying the above equation further ,
we get ,
h = 28
Therefore , The value of h in the equation h = 6q - 2u , when q = 3 and u = -5 is h = 28 .
The given question is incomplete , the complete question is
Find the value of h in the equation h = 6q - 2u , when q = 3 and u = -5 ?
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The sum of a number and twice the number is 24 what is the number?
Answers
Answer:
x = 8
Step-by-step explanation:
Step 1: Write out the expression
x + 2x = 24
Step 2: Combine like terms
3x = 24
Step 3: Isolate x
x = 8
And we have our final answer!
Answer:
X=8
Step-by-step explanation:
Elena and Jada are 12 miles apart on a path when they start moving toward each other. Elena runs at a constant
speed of 6 miles per hour, and Jada jogs at a constant speed of 3 miles per hour. After an hour, what percentage of
of the 12 miles will Elena travel? What about Jada?
Answers
Answer:
the answer is 1.5 hrs
Step-by-step explanation:
if your qouestion is Elena and Jada are 12 miles apart on a path when they start moving toward each other. Elena runs at a constant speed of 5 miles per hour, and Jada walks at a constant speed of 3 miles per hour. How long does it take until Elena and Jada meet?
Landon bought a tray of plants for $8.15. There were 16 plants in the tray. If Landon only bought 1 plant, about how much would it have cost?
Answers
Amadi is three times as old as Chima. The sum of their ages is 24
Answers
Answer:
Amadi: 20 years old
Chima : 4 years old
Consider the polynomial
(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)
Combine all like terms and enter the coefficients for each term into the blanks below
Answers
(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)
First, let's remove the parentheses:
4mn^2 - 2mn + 6 + 6mn^2 - 1 - mn^2 + 2 - 9mn
Next, let's combine like terms by adding or subtracting coefficients of the same variables:
(4mn^2 + 6mn^2 - mn^2) + (-2mn - 9mn) + (6 + 2 - 1)
Simplifying further:
9mn^2 - 11mn + 7
So, the coefficients for each term are:
9, -11, 7
Jake is comparing the prices of two mattress cleaning companies. Company A charges $30 per mattress and an additional $13 as service charges. Company B charges $28 per mattress and an additional $15 as service charges.
Part A: Write equations to represent Company A's and Company B's total mattress cleaning charges for a certain number of mattresses. Define the variable used in the equations. (1 point)
Part B: Which company would charge less for cleaning 4 mattresses? Justify your answer. (1 point)
Part C: How much money is saved by using the services of Company B instead of Company A to clean 7 mattresses?
Answers
The equations are y = 30x + 13 and y = 28x + 15. And the charge less for cleaning 4 mattresses is $127 given by company B. Then the amount of money saved to clean 7 mattresses is $22.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Let 'x' be the number of mattresses and 'y' be the total cost. Then the equations are given as,
Company A: y = 30x + 13
Company B: y = 28x + 15
The amount for x = 4 is given as,
Company A: y = 30 (4) + 13 = $133
Company B: y = 28 (4) + 15 = $127
The amount for x = 4 is given as,
Company A: y = 30 (7) + 13 = $223
Company B: y = 28 (7) + 15 = $211
Then the amount of money saved is given as,
⇒ $233 - $211
⇒ $22
The amount of money saved to clean 7 mattresses is $22.
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In the diagram a || b. Use the diagram to answer the question. Name the alternate interior angle to <2
Answers
The angle 7 is the alternative interior angle to angle 2.
Given that,In the diagram a || bWe need to find the alternate interior angle to <2 .Alternate interior angles are the angles that are formed when a transversal crosses two parallel lines.
They are the angles that are on opposite sides of the transversal and inside the two parallel lines.
Thus, in the given diagram, the angle that is opposite to angle <2 and is inside the two parallel lines a and b is the alternate interior angle to angle <2.
We can see that the alternate interior angle to angle <2 is <7. Therefore, the alternate interior angle to angle <2 is <7.
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Two numbers are in the ratio 7:5. The smaller number is 16 less than the bigger number. What is the bigger number ?
Answers
Answer:
The bigger number is 56
Step-by-step explanation:
\(\frac{x}{y}\) = \(\frac{7}{5}\) cross multiply
5x = 7y
y = x -16 substage x-16 in the equation above for y
5x = 7( x - 16)
5x = 7x - 112 Subtract 7x from both sides
-2x = -112 Divide both sides by -2
x = 56
Check:
y = x - 16
y = 56 - 16
y = 40
5x = 7y
5(56) = 7(40)
280 = 28
y = x - 16
40 = 45-16
40 = 40
I need help with geometry! I need to find x and y, please help asp
Answers
Check the picture below.
Which of the following is the most serious effect of water pollution for humans? a. infectious diseases b. algal blooms c. toxic food chain effects d. low-oxygen water
Answers
Answer:
The answer is A: Infectious Diseases.
Step-by-step explanation:
I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!
The most serious effect of water pollution for humans should be option A. Infectious Diseases.
What are Infectious Diseases?
Infectious diseases is the disease that should be caused by the microorganism i.e. pathogenic. It involved the fungi, viruses, bacteria,etc. It should be spreaded from the environment even from person to person that leads to the illness.
So for the serious impact with respect to the water pollution it should be option A.
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Can someone help me please
Answers
Answer:
A) At least 1 Right angle
Step-by-step explanation:
As you can seel all the shapes here have atleast 1 right angle, but all the shapes don't have all the things that the other answer choices are saying.
So hence, your answer is A) At least 1 Right Angle
Thanks!
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A pre-election survey showed that two out of every three eligible voters would cast ballots in the county election. There are 390,000 eligible voters in the county. How many people are expected to vote in the election?
Answers
The number of people that nare expected to vote in the election is 260,000. people.
How to illustrate the fraction?Simply put, a fraction is a portion of a whole. Mathematically, the number is represented as a quotient with split numerator and denominator. The numerator and denominator of a simple fraction are both integers. On the other hand, a complex fraction has a fraction in either the numerator or the denominator.
In this situation, the pre-election survey showed that two out of every three eligible voters would cast ballots in the county election and there are 390,000 eligible voters in the county.
The number of people expected to vote will be:
= Fraction of expected voters × Total number of people
= 2/3 × 390000
= 2 × 130000
= 260000
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3. Arrange these numbers from least to greatest.
-2.5
-1/3 1.7 27/4 -0.9
Answers
Answer: -2.5,, -0.9,, -1/3,, 1.7,, 27/4
Step-by-step explanation:
What conditions must be met to ensure that a function has an absolute maximum value and an absolute minimum value on an interval?Choose the correct answer below.A. A critical point must occur on a closed interval on (a,b).B. The function must be continuous on a closed interval (a,b).C. The function must be continuous for some subinterval on [a,b].D. The function must be continuous on an open interval (a,b).
Answers
For a function to have an absolute value, a critical point must occur on a closed interval on (a,b).
A critical point is a point where the derivative of a function is 0. Maximum and minimum values occur at these critical points.
The right answer is A.
Nora is going to invest in an account paying an interest rate of 6.4% compounded
daily. How much would Nora need to invest, to the nearest hundred dollars, for the
value of the account to reach $72,000 in 16 years?
Answers
The amount of money that Nora would need to invest is $25913.
How to determine the value of P?In Mathematics and Financial accounting, compound interest can be calculated by using the following mathematical equation (formula):
\(A(t) = P(1 + \frac{r}{n})^{nt}\)
Where:
A represents the future value.n represents the number of times compounded.P represents the principal.r represents the interest rate.T represents the time measured in years.By substituting the given parameters into the formula for compound interest, we have the following;
\(72,000 = P(1 + \frac{0.064}{365})^{365 \times 16}\\\\72,000 = P(1 + 1.75 \times 10^{-4})^{5,840}\\\\72,000 = P(1.000175)^{5,840}\)
P = 72,000/2.77849825425152
Principal, P = $25913.28 ≈ $25913
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y = -x + 4find Slope m = and Y-Intercept
Answers
This is the line's equation in slope intercept form.
Which is
\(y=mx+b\)Where
m is the slope
b is the y-intercept
Matching the given equation with slope intercept form:
\(\begin{gathered} y=mx+b \\ y=-x+4 \\ y=-1x+4 \\ m=-1 \\ b=+4 \end{gathered}\)So,
Slope (m) = -1Y-intercept (b) = 4Help please friendssssssssss
Answers
Answer: 6/(6+2x) ; (-infinity, -3) U (-3, infinity)
Step-by-step explanation:
(a) This can be read as f(x) composed of g(x). Plug in the expression given for g(x) for every x value in f(x):
(6/x)/(6/x+2)
I gave the terms in the denominator the same denominator to combine the bottom two terms into one term. 6/x + 2 is equal to 6/x + 2x/x -->
(6 +2x)/x
Do the classic keep, change, flip. \(\frac{6}{x} * \frac{x}{6+2x}\)
This simplifies to: \(\frac{6}{6+2x}\)
(b) Domain is all real numbers except for what makes the denominator equal to 0. 6 + 2x = 0 when x = -3. Therefore it is all real numbers except -3.
Techwiz electronics makes a profit of $35 for each mp3 and $18 for each DVD last week techwiz sold a combined total of 118 mp3 and DVD players. Let x be the number of mp3 sold last week write an expression for the combined total profit (in dollars) made last week
Answers
Answer:
The total profit is \(p = 17x + 2124\)
Step-by-step explanation:
From the question we are told that
The profit made on each mp3 is k = $35
The profit made on each mp3 is y = $18
The total amount sold is n = 118
Now given that the amount of mp3 sold is x then the amount of DVD sold is mathematically evaluated as
\(n - x\)
Now the profit made on the x number of mp3 sold is
\(x * 35 = 3x\)
And the the profit made from the n-x number of DVD sold is 18 (n-x ) = 18 - 18x
So the total profit made last week from the sales of both mp3 and DVD is
\(p = 35x + 18n - 18x\)
\(p = 17x + 18(118)\)
\(p = 17x + 2124\)
solve for x in the rhombus
sin(42)= x/50
Answers
Answer:
x = 33.45
Step-by-step explanation:
We need to find the value of x in the given expression i.e.
\(\sin(42)=\dfrac{x}{50}\)
Multiplying both sides by 50. So
\(\sin(42)\times 50=\dfrac{x}{50}\times 50\\\\x=\sin(42)\times 50\\\\x=33.45\)
So, the value of x is equal to 33.45.
If you extend a rectangle along its 3rd
dimension, you form a
A.cylinder
B.cube
C.rectangular prism
D.triangular prism
Answers
Answer:
C. rectangular prism
Step-by-step explanation:
You bought 5 chocolate bars and 8 blow pops for $23.25. Your sister bought 2 chocolate bars and 13 blow pops for $21.55. How much did each chocolate bar cost? Each chocolate bar cost $
Answers
Answer:
$2.65Step-by-step explanation:
Let chocolate bar cost be c and blow pop cost be b
Then we have equations:
5c + 8b = 23.252c + 13b = 21.55Multiply the first equation by 13 and the second one by 8 and subtract:
13(5c + 8b) - 8(2c + 13b) = 13(23.25) - 8(21.55)65c - 16c = 129.8549c = 129.85c = 129.85/49c = 2.65Chocolate bar costs $2.65
josslyn placed $4,400 in a savings account which earns 3.2% interest, compounded annually. How much will she have in the account after 12 years? Round your answer to the nearest dollar. Do NOT round until you have calculated the final answer.
Answers
Answer:80
Step-by-step explanation:
Answer:6421
Step-by-step explanation:
P=4400
r=3.2%
n=1
t=12
f=4400 * (1+3.2/100/1)^12
Iman and Mark went out for lunch. Part B: After adding a tip, the total lunch cost was $27.19. What percent tip did Iman and Mark leave?
Answers
Answer:
17
Step-by-step explanation:
As a bowling instructor, you calculate your students' averages during tournaments. In 5 games, one bowler had the following scores: 143, 156, 172, 133, and 167. What was that bowler's average?
Answers
Answer:
154.2
Step-by-step explanation:
143 plus
156 plus
172 plus
133 plus
167 = 771
divide by 5 equals 154.2
Solve: 2m³-5m² - 7m = 0
Answers
Answer:
m = - 1 , m = 0 , m = \(\frac{7}{2}\)
Step-by-step explanation:
2m³ - 5m² - 7m = 0 ← factor out common factor m from each term
m(2m² - 5m - 7) = 0
factorise the quadratic 2m² - 5m - 7
consider the factors of the product of the coefficient of the m² term and the constant term which sum to give the coefficient of the m- term
product = 2 × - 7 = - 14 and sum = - 5
the factors are + 2 and - 7
use these factors to split the m- term
2m² + 2m - 7m - 7 ( factor the first/second and third/fourth terms )
2m(m + 1) - 7(m + 1) ← factor out (m + 1) from each term
(m + 1)(2m - 7)
then
2m³ - 5m² - 7m = 0
m(m + 1)(2m - 7) = 0 ← in factored form
equate each factor to zero and solve for m
m = 0
m + 1 = 0 ( subtract 1 from both sides )
m = - 1
2m - 7 = 0 ( add 7 to both sides )
2m = 7 ( divide both sides by 2 )
m = \(\frac{7}{2}\)
solutions are m = - 1 , m = 0 , m = \(\frac{7}{2}\)
20 students each rolled dice 5 times each to measure the median. Here is the data in the picture attached. What can we infer from this graph by looking at the median data?
A. when rolling a dice multiple times, the median is less likely to fall between numbers 1 and 6.
B. it's not possible to tell the likelihood of where the median is going to be when measuring probability since rolling dice is completely randomized, etc.
C. some other response
Answers
We can deduce that option A is likely to be true based on the given graph of rolling dice median data.
What is the median?The median is the value in the middle of a data set, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median.
The graph illustrates that the median value of the rolls is closer to the center of the possible outcomes (numbers 3, 4, and 5) than the extremes (numbers 1 and 6).
This implies that when rolling a dice several times, the median is less likely to fall between the numbers 1 and 6.
However, because rolling the dice is a random process, there is always a degree of uncertainty in predicting the outcomes.
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