Use the properties of 30-60-90 and 45-45-90 triangles to solve for x in each of the problems below. Then decode the secret message by matching the answer with the corresponding letter/symbol from the exercises.
Answers
These problems are solved using the trigonometric function. Trigonometric functions provides the ratio of different sides of a right-angle triangle.
What are Trigonometric functions?The trigonometric function refer to function that are periodic in nature and which lend insight to the relationship between angles and the sides of a triangle that is right angled.
The solutions to x in the respective problems is given as follows:
1st.) x = 5 /Sin(30°)
x = 10
!) sin(45°) = 4/x
x = 4/sin(45°)
x = 4√2
I) Cos(45°) = √3 / x
x = √3 / Cos(45°)
x = √6
E) Tan(60°)
= (3√3) / x
x = (3√3) / 3
W) It is to be noted that for right-triangle that is isosceles in nature, the angle made by the legs and the hypotenuse is always 45°.
x = 45°
N) x² + x² = (7√2)²
x = 7
V) Tan(60°) = 7 / x
x = 7√3/3
K) x² + x² = (9)²
x = 9/√2
Y) Sin(60°) = 7√3/x
x = 14
M) Sin(30°) = x/11
x = 11/2
T) Sin(45°) = x/√10
x = √5
A) x + 2x + 90° = 180°
x = 30°
O) Sin(45°) = √2 / x
x = 2
R) Tan(30°) = x / 4
x = 4/√3
= 4√3 / 3
S) Sin(60°) = x / (10/3)
x = (5√3) / 3
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Related Questions
The students in Ms. Yuri's class reported the number of hours they watched television last week.
Which is the interquartile range of the number of hours last week that the students watched television?
Answers
The interquartile range is 12.
What is the interquartile range?The interquartile range is the difference between the third quartile and the first quartile. The first quartile is the first line on the box while the third quartile is the third line on the box.
First quartile = 11
Third quartile = 23
Interquartile range = 23 - 11 = 12
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In right triangle ABC, ZB is the right angle and mZC = 30°. If AC= 10, what Is AB?
OA 5
OB. 5√3
OC 20
OD. 5√3
Answers
Answer:
i think its c wouldve helped if i saw a pic of the triangle tho
Step-by-step explanation:
The length of side AB is 5√3.
Option B is the correct answer.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
We can use trigonometry to solve this problem.
Let's start by finding the length of BC.
sin(30°) = BC/AC
sin(30°) = BC/10
BC = 5
Now, we can use the Pythagorean theorem to find the length of AB.
AB² = AC² - BC²
AB² = 10² - 5²
AB² = 75
AB = 5√3
Therefore,
The length of side AB is 5√3.
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There are 8 apples and 14 oranges in the bowl. What is the ratio of apples to total fruit in the bowl?
O a 7/11
Ob 4/7
Oc 4/11
Od 7/4
Answers
Answer:
C
Step-by-step explanation:
Solution
There are 8 apples in the bowl
There are 8 + 14 = 22 total fruits in the bowl.
Ratio apples / total = 8 / 22. But that is not the answer. You can divide top and bottom of the ratio by 2.
When you do that, you get 4/11 which is C
Answer: 4/11 or C
You buy a lottery ticket to a lottery that costs $10 per ticket. There are only 100 tickets available to be sold in this lottery. In this lottery there are one $475 prize, two $95 prizes, and four $30 prizes. Find your expected gain or loss. (Round your answer to two decimal places.)
Answers
There is a profit of $39.7.
It is given that there 100 tickets costing $10 per ticket.
You must look first for the probability of the 4 prizes which are $475, $195, $30, and no prize.
P ($475 prize) = 1/100 or 0.01
P ($95 prize) = 2/100 or 0.02
P ($30 prize) = 4/100 or 0.04
P (No prize) = 100/100 – 1+2+4/100 =93/100 .93
Expected gain or loss is computed by: (P(x)* n)
E= (475-10)*.01 + (95-10)*0.02 + (30-10)* 0.04 + (-10)*.93
= 46.5 + 1.70 + 0.8 – 9.3
E = 39.7
There is a profit of $39.7.
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I'm renting to own a house for $80,000 I paid down $6000 leaving a balance of $74,000 For the past eight years I’ve paid 768.57 a month. How much have I paid from May 2014 to July 2022?
Answers
The total amount you have paid from May 2014 to July 2022 is $75,319.86
Balance of rentTotal cost of the house = $80,000Amount paid down = $6000Amount to balance = $74,000Amount paid per month = $768.57May 2014 to July 2022 = (12 × 8) + 2= 96 + 2
= 98 months
Total amount paid from May 2014 to July 2022 = $768.57 × 98 months
= $75,319.86
The total amount paid so far from May 2014 to July 2022 is $75,319.86
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Complete the point-slope equation of the line through (6,4)(6,4)left parenthesis, 6, comma, 4, right parenthesis and (7,2)(7,2)left parenthesis, 7, comma, 2, right parenthesis. use exact numbers.
Answers
The point-slope equation of the line is y-2=-2(x-7)
How will we find the equation of line?
First, we will find the slope of line using the given points then put slope and point in the formula to get equation of line.
We can find the equation as shown below:
Given points (6,4) and (7,2)
slope(m)= (2-4)/ (7-6)
m=-2/1
m=-2
The point slope form:
(y-y1) = m(x-x1)
y1=2, x1=7
putting in formula
(y-2) = -2(x-7)
y-2=-2(x-7)
Hence, the point-slope equation of the line is y-2=-2(x-7)
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Answer:
Step-by-step explanation:
25x^-4-99x^-2-4=0
How do I solve for this?
Answers
Given
[tex]25x^{-4} - 99x^{-2} - 4 = 0[/tex]
consider substituting [tex]y=x^{-2}[/tex] to get a proper quadratic equation,
[tex]25y^2 - 99y - 4 = 0[/tex]
Solve for [tex]y[/tex] ; we can factorize to get
[tex](25y + 1) (y - 4) = 0[/tex]
[tex]25y+1 = 0 \text{ or } y - 4 = 0[/tex]
[tex]y = -\dfrac1{25} \text{ or }y = 4[/tex]
Solve for [tex]x[/tex] :
[tex]x^{-2} = -\dfrac1{25} \text{ or }x^{-2} = 4[/tex]
The first equation has no real solution, since [tex]x^{-2} = \frac1{x^2} > 0[/tex] for all non-zero [tex]x[/tex]. Proceeding with the second equation, we get
[tex]x^{-2} = 4 \implies x^2 = \dfrac14 \implies x = \pm\sqrt{\dfrac14} = \boxed{\pm \dfrac12}[/tex]
If we want to find all complex solutions, we take [tex]i=\sqrt{-1}[/tex] so that the first equation above would have led us to
[tex]x^{-2} = -\dfrac1{25} \implies x^2 = -25 \implies x = \pm\sqrt{-25} = \pm5i[/tex]
HEELLLPPMEEEEEEEE PLS 30 pointss
Suppose that x≠0 and y≠0. We know from our work in this section that 1/x∙1/y is equivalent to 1/xy. Is it also true that 1/x+1/y is equivalent to 1/(x+y)? Provide evidence to support your answer.
Answers
Answer:
No
Step-by-step explanation:
Let's assume that x=2 and y=3.
1/2+1/3≠1/5
Also, when adding fractions, you cannot simply add the denominator. You have to make the denominators of all fractions the same and then add.
So, if you are given 1/x +1/y, you should get (y+x)/xy, not 1/(x+y)
Rashaad leans a 22-foot ladder against a wall so that it forms an angle of 65° with the ground. How high up the wall does the ladder reach? Round vour answer to the nearest hundredth of a foot if necessary.
Answers
The ladder reaches 19.938 foot high from the ground on the wall.
What is a Right Angled Triangle ?A right angled triangle is a triangle that has one of its angle measure as 90 degree.
It is given that
Ladder Length = 22 foot
The angle between the ladder and the ground is 65 degree.
When the ladder leans on a wall , the wall makes 90 degree with the ground and the ladder is the hypotenuse of the right angled triangle formed.
The figure is attached with the answer.
sin 65 = Height of the wall / Hypotenuse
0.9063 = Height of the wall / 22
Height of the wall = 19.938 foot
Therefore the ladder reaches 19.938 foot high from the ground on the wall.
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Answer:
19.94
Step-by-step explanation:
The population of a small industrial town was 12 910 in 2000. Each year, the population
decreases by an average of 5%. Estimate the population in the year 2020. Round to the nearestwhole number.
Answers
The population in the year 2020 is 4628
How to determine the population?The given parameters are:
Initial, a = 12910
Rate, r = 5%
Since the population decreases, then we make use of an exponential decay function.
This is represented as:
f(n) = a * (1 - r)^n
So, we have:
f(n) = 12910 * (1 - 5%)^n
Evaluate the difference
f(n) = 12910 * 0.95^n
2020 is 20 years from 2000.
So, we have:
f(20) = 12910 * 0.95^20
Evaluate
f(20) = 4628
Hence, the population in the year 2020 is 4628
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Select the correct answer.
Convert sqrt3 + i to polar form.
Answers
The polar form of any complex number can be written as
[tex]z = |z| e^{i\arg(z)}[/tex]
where [tex]\arg(z)[/tex] is the argument of [tex]z[/tex], i.e. the angle it makes with the positive real axis in the complex plane.
If [tex]z=\sqrt3+i[/tex], then [tex]z[/tex] has modulus
[tex]|z| = \sqrt{\left(\sqrt3\right)^2 + 1^2} = \sqrt4 = 2[/tex]
and argument
[tex]\arg(z) = \tan^{-1}\left(\dfrac1{\sqrt3}\right) = \dfrac\pi6[/tex]
Then
[tex]\sqrt3 + i = 2e^{i\frac\pi6} = 2 \left(\cos\left(\dfrac\pi6\right) + i \sin\left(\dfrac\pi6\right)\right)[/tex]
Can someone help me please.
Answers
Answer: A
Step-by-step explanation:
The angle opposite the shortest side in a triangle has the smallest measure.
HEEEEEEEEEELP i dont get it
Answers
The ordered pair is (-9, -25) and the word statement is if x is equal to -9, then the value of h(x) is -25
Functions and tablesFrom the given table, f(x) = y means that the corresponding value of y given a value x.
For the function h(-9), we need to find the equivalent value of h(x) when x is -9. Hence h(-9) is -25
The ordered pair is (-9, -25) and the word statement is if x is equal to -9, then the value of h(x) is -25
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Calculate the force acting on a body of mass 0.8kg (g=9.8*-2; F=mg)
Answers
The force acting on a body of mass 0.8 kg is F = 7.84 kg-m-s⁻² or F = 7.84 N
What is mass?A tangible body's mass is the amount of matter it possesses. It's also a metric of inertial or the resistance to velocity when a net force is exerted.
We have:
The mass of the body m = 0.8 kg
As we know,
F = mg
F is the force acting on the body and g is the acceleration due to gravity.
g = 9.8 m-s⁻²
F = (0.8)(9.8)
F = 7.84 kg-m-s⁻²
or
F = 7.84 N
Thus, the force acting on a body of mass 0.8 kg is F = 7.84 kg-m-s⁻² or F = 7.84 N
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Each of the performers at a circus convention is either a unicyclist, a mime or an aerial artist. The ratio of unicyclists to mimes is 3: 14 The ratio of unicyclists to aerial artists is 9 : 11 There are 88 aerial artists. What percentage of the performers are unicyclists? Give your answer to 2 d.p.
Answers
Answer:
14.52% are unicyclists
Step-by-step explanation:
First, we can use proportions to find the number of unicyclists at the convention. Since we know that the ratio of unicyclists to aerial artists is 9:11, and there are 88 aerial artists, we can set up the following equation:
[tex]\frac{9}{11}=\frac{x}{88}[/tex]
If we cross multiply, we get that 11x = (88)(9). After we divide through by 11 to isolate x, we get that x = (8)(9) = 72
Second, we have to figure out the number of mimes at the convention to figure out the total number of people there. We know that the ratio of unicyclists to mimes is 3:14, and the number of unicyclists is 72. So, we can set up the following proportion:
[tex]\frac{3}{14}=\frac{72}{y}[/tex]
If we cross multiply, we get that 3y = 1008, or y = 336 mimes
The total number of people at the convention is 336 mimes + 72 unicyclists + 88 unicyclists = 496. Now we have to figure out what percent of 496 is 72 (the number of unicyclists). If we let z = the percentage, we can simply set up an equation that says that 72 is z% of 496:
[tex]72=0.01z*496\\0.01z=0.14516\\z=14.52[/tex]
This means that approximately 14.52% of the performers are unicyclists.
Answer:
14.52%
Step-by-step explanation:
U/A = 9/11 and A = 88 multiply by 8/8 ( to get A=88 as given)
9/11 * 8/8 = 72/88 = U / A so U = 72
Then U/M = 3/14 multiply by 24/24 ( to get U = 72 as found above)
then U/M= 72 / 336 M = 336
U / ( A + U + M ) x 100% = 14.52 %
Which of the following sets represents the range of the diagram below? 2 3. 00 4 4 5 5 f(x) O A. {2, 4, 5) OB. (1, 3, 4, 5} OC. (2, 3, 4, 5, 6, 7} D. {1, 2, 3, 4, 5)
Answers
Answer:
D
Step-by-step explanation:
the answer is D because the range is the lowest possible value up to the highest possible value and when listed it doesn't repeat
Find the measure of angle ABD.
Answers
Answer:
x=58
Step-by-step explanation:
Exterior angle of one interior angle in a triangle is equal to the sum of the other two remote interior angles. (Ext. Angle Th.) So, 3x-32=84+x
2x=116
x=58
Please explain this.
Answers
Angles EBA and DBC are congruent. The three angles EBA, EBD, and DBC are together supplementary, so their measures sum to 180°. This means
x + (4x + 11°) + x = 180°
6x + 11° = 180°
6x = 169°
x = (169/6)°
Then the measure of angle D is
2x + 8° = 2 (169/6)° + 8° = (193/3)°
The interior angles of any triangle sum to 180°, so if y is the measure of angle C, we have
(169/6)° + (193/3)° + y = 180°
y = (175/2)° = 87.5°
Sara has rs. 836 with her. she gives 9/11 of this to her sister. out of the remaining money, she gives rs. 38 to her brother. she now has a fraction of the original amount is left with her?
Answers
The original amount Sara has left is 172/209
The calculation can be done as follows
Let y represent the amount left
9/11 × 836
= 7524/11
= 110
Y can be calculated as follows
Y + 38 +110= 836
148 + Y= 836
Y= 836 - 148
Y= 688
Therefore the fraction is
688/836
= 172/209
Hence the fraction of the original amount left is 172/209
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Question: 7 After seven years, the age of father will be 4 times the age of his daughter. If x stands for the present age of the daughter and y stands for the present age of the father, which of th following linear equations represents the above statement?
x+y-17=0
2xy-187=0
x+y+17=0
2xy+187=0
Answers
Answer:
Here is your answer
Step-by-step explanation:
Step -1: Forming equations.
Let, present age of son = x
And, present age of father = 3x+3
3 years later, age of son = x+3
age of father = 3x+3+3=3x+6 ...(i)
According to the given condition, age of father = 10+2(x+3) ...(ii)
Step -2: Solving for x
From (i) and (ii)
∴3x+6=10+2(x+3)
⇒3x+6=10+2x+6
⇒3x−2x=10+6−6
⇒x=10
∴Present age of son = 10
and present age of father = 3x+3=3×10+3=33
Hence, son’s present age is 10 years and father’s
Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost each of one small box of oranges and one large box of oranges.
help :((
Answers
Joaquin deposits $1,000 into an account that accrues 4% annual interest continuously compounded. What is the value of his investment after 3 years to the nearest cent?
Answers
Deposit: $1,000
Annual interest: 4% = 0.04
Years: 3
For this type of question, when the question asks you to "continuously compound", you use this formula: [tex]Pe^{rt}[/tex]
Solving:
[tex]1000e^{(0.04)(3)} \\1000e^{0.12} \\=1127.50[/tex]
The value of Joaquin's investment after 3 years = 1,127.50$
PLS HELP! Which statement is true about the given function?
Answers
The statement which is true about the given graph is that f(x)<0 in the interval (-∞,3) which is option 3.
Given Graph of a function
We have to choose a statement which is correct about the function whose graph is given.
The graph of a function tells us about the domain and range of the function. The values on y axis are the codomain of the function and the values on x axis are the values of domain.
When we see the graph we can find that x=-∞ to x=3 the values are negative means when we put the values of x less than 0 we will get negative number. For example if we put the value of x=-1, we will get -20 which is a negative number.
Hence the third statement is true for the given graph which is that it has values less than zero in the interval (-∞,3).
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Please help me on this geometry question
Answers
At times, latitudes with values higher than ________ degrees can have ~ 24 hours of continuous sunshine.
Answers
At times, latitudes with values higher than 66.5 degrees can have ~ 24 hours of continuous sunshine.
Locations above the Arctic Circle (north of latitude 66.5 degrees, 90 degrees minus the tilt of the Earth's axis) are exposed to 24-hour sunlight. Below the Arctic Circle (latitude 66.5 degrees south), there is 24-hour darkness.
When at the equator, the sun is directly above – at the poles, the sun is on the horizon. However, regardless of the current location (from the pole to the equator), all parallels are bisected, so we have 12 hours a day and 12 hours a night in all locations.
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1. Vanessa and Renita are having a friendly competition at work. Their job is to unpack boxes. Vanessa has unpacked 3 fewer than twice the amount of boxes than Renita. Together they have unpacked 15 boxes. How many boxes did each uNpack
Answers
The number of boxes renita and Vanessa has unpacked each is 6 and 9 boxes respectively.
EquationNumber of boxes renita has unpacked = xNumber of boxes Vanessa has unpacked = 2x - 3Total boxes both unpacked = 15x + (2x - 3) = 15
x + 2x - 3 = 15
3x = 15 + 3
3x = 18
x = 18/3
x = 6
Therefore,
Number of boxes renita has unpacked = x
= 6 boxes
Number of boxes Vanessa has unpacked = 2x - 3
= 2(6) - 3
= 12 - 3
= 9 boxes
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Answer:
Step-by-step explanation:
The number of boxes renita and Vanessa has unpacked each is 6 and 9 boxes respectively.
Equation
Number of boxes renita has unpacked = x
Number of boxes Vanessa has unpacked = 2x - 3
Total boxes both unpacked = 15
x + (2x - 3) = 15
x + 2x - 3 = 15
3x = 15 + 3
3x = 18
x = 18/3
x = 6
Therefore,
Number of boxes renita has unpacked = x
= 6 boxes
Number of boxes Vanessa has unpacked = 2x - 3
= 2(6) - 3
= 12 - 3
= 9 boxes
pls help lol !!! i am unsure about this
Answers
The component form of the vectors shown is (-6, -5)
Difference of vectorsIn order to determine the component of the vectors shown, we will subtract the coordinate points from both each other.
Given the vector coordinates on the line. as (-5, -3) and (1, 2). Take the difference;
Difference = [(-5-1), (-3-2])
Difference = (-6, -5)
Hence the component form of the vectors shown is (-6, -5)
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what is
x. 10-x 3 D N C X = [?]
Answers
Equations are written by equating the expressions to each other. The value of x is 7
Equations and expressionsEquations are written by Equating the expressions to each other.
Given the equation below:
10 - x = 3
Subtract 10 from both sides
10 - x - 10 = 3 - 10
-x = -7
Multiply both sides by -1
-(-x) = -(-7)
x = 7
Hence the value of x is 7
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Suppose a large shipment of laser printers contained 12% defectives. If a sample of size 406 is selected, what is the probability that the sample proportion will be greater than 13%
Answers
The probability that the sample proportion will differ from the population proportion by less than 6% is 0.992.
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
цр = р
The standard deviation of this sampling distribution of sample proportion is:
бр = √ρ(1-ρ)÷n
The information provided is:
ρ = 0.22
ⁿ = 276
As the sample size is large, i.e. n = 276 > 30, the Central limit theorem can be used to approximate the sampling distribution of sample proportion.
Compute the value of P(р-p<0.06) as follows:
P(р-p<0.06) = P(р-p ÷ бp<0.06 ÷√0.22(1 - 0.22) ÷ 276
= P ( Z < 2.41 )
= 0.99202
≈ 0.992
Thus, the probability that the sample proportion will differ from the population proportion by less than 6% is 0.992.
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When simplifying the fraction 2x/4, madison wrote 2x/4 = 2x. EXPLAIN WHY her answer is wrong and write the correct answer.
Answers
Answer:
x/2
Step-by-step explanation:
Madison didn't cancel the common factor of 2 and that 4 that is why she is wrong.
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