Answers
Hello there. To solve this question, we'll have to remember some properties about trigonometric functions and the right triangle.
We want to find x such that:
[tex]\tan (x)=\sqrt[]{3}[/tex]We'll use the second right triangle to show what we want.
First, given a triangle:
We know that the hypotenuse will be:
[tex]\sqrt[]{x^2+y^2}[/tex]But most importantly, the tangent of the angles α and β can be calculated by only using the legs of the triangle: it is the ratio between the opposite side and the adjacent side to an angle.
[tex]\tan (\alpha)=\frac{y}{x}[/tex]and
[tex]\tan (\beta)=\frac{x}{y}[/tex]Now look at the triangle we have:
We can easily check that:
[tex]\sqrt[]{3}=\frac{\sqrt[]{3}}{1}[/tex]So it would be good to find something that relates the ratio between those two numbers: the tangent of 60º!!
Therefore, we have:
[tex]\tan (60^{\circ})=\frac{\sqrt[]{3}}{1}=\sqrt[]{3}[/tex]And the solution to x is:
[tex]x=60^{\circ}[/tex]
Related Questions
What’s the answer plss
Answers
Opposite Q is length PR
Adjacent is 7
Hypotenuse is 19
We got AH - which is CAH or cos
Cos-1( 7/19) = 68.38....
It's 68.4 degrees
The closest answer to this is B. So, choose that because it maybe due to a typing error.
Hope this helps!
Which of the following solution sets show all the values of x that can make the inequality -2x + 3 < 9 true?
A. x > 3
B. x < -3
C. x > -3
D. x ≥ -3
Answers
Answer:
B
Step-by-step explanation:
9 - 3 = 6
6 ÷ -2
= -3
I think it's b
write a phrase for each expression
X - 6
Answers
The phrase of the expression x - 6 is 6 less than a number.
Expression:
The expression refer the sentence with a minimum of two numbers/variables and at least one math operation in it.
Given,
Here we have the expression x -6.
And we need to convert this expression in order to get the phrase form.
In order to get the phrase form, we have to translate the given expression into word.
While we looking into the given expression we have identified the following three terms.
They are, x , (-) and 6.
Here x represents the unknown number.
(-) represents that we have to less the unknown number by the given number.
And 6 is the given number.
So, the phrase for this situation is 6 less than a number.
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Which is the equation of a line that is perpendicular to the line represented by ?
Answers
Answer:
It will be
.. y = -4/3x +c . . . . . for some value of c
_____
The slope of the perpendicular line will be the negative reciprocal of the slope of the given line, which is 3/4.
Find the distance between A(5,-4) and B(5,-5)
Answers
Answer:
1
Step-by-step explanation:
(5−5)^2+(−5−(−4))^2
0^2+-1^2
1
4. What is the solution of the following system? (1 point)
[x - y = 11
|-x + y = −11
a. (-3,-4)
b. no solutions
c. infinitely many solutions
d. (3, 4)
Answers
If the two equations are x - y = 11 and -x + y = -11 then the system has infinitely many solutions.
How to find the system of solutions?Let the two equations be
x - y = 11 ..................(1)
-x + y = -11 ..................(2)
Express the first equation in the term of x and substitute it into the second equation:
From (1) and (2), we get
-(y + 11) + y = -11
simplifying the above equation, we get
-y - 11 + y = -11
-y + y = 11 - 11
0 = 0
So, the system has infinitely many solutions.
Therefore, the correct answer is option c. infinitely many solutions.
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11. The graph models the linear relationship between the cost for cleaning and the number of rooms to clean in a house of two different cleaning companies. 200 180 160 140 Home Helper 120 Cost (In dollars) 100 80 scueaky cleaners 60 40 20 0 1 2 10 3 4 5 6 7 8 9 Number of Rooms to Clean in House What is the cost (in dollars) when Squeaky Cleaners and Home Helpers clean the same number of rooms? A. $60 B. $120 C. $150 D. $210
Answers
In the graph you can see two variables: Cost and Number of rooms to clean in house.
You can find the cost when both cleaning companies clean the same number of rooms as the point when the value in the varibles (y-axis and x- axis) are the same in the lines of both companies (the point where the lines cross each other)
Then, the cost when both companies clean the same number of rooms is $150 (the number of rooms to clean is 5 in both companies)A right triangle has a hypotenuse of length 3.80 m, and one of its angles is 31.0°. What are the lengths of the following sides?
Answers
Answer:
• (a)The length of the side opposite 31.0° is 1.96 meters.
,• (b)The length of the side adjacent 31.0° is 3.26 meters.
Explanation:
In the right triangle:
• The length of the hypotenuse = 3.80 m
,• Let the side ,opposite ,angle 31.0° = x
• Let the side ,adjacent ,angle 31.0° = y
(a)
From trigonometric ratios:
[tex]\begin{gathered} \sin\theta=\frac{Opposite}{Hypotenuse} \\ \implies\sin31.0\degree=\frac{x}{3.80} \end{gathered}[/tex]Cross multiply:
[tex]\begin{gathered} x=3.80\times\sin31.0\degree \\ x=1.9571 \\ x\approx1.96\;m \end{gathered}[/tex]The length of the side opposite 31.0° is 1.96 meters.
(b)From trigonometric ratios:
[tex]\begin{gathered} \cos\theta=\frac{Adjacent}{Hypotenuse} \\ \implies\cos31.0\degree=\frac{y}{3.80} \end{gathered}[/tex]Cross multiply:
[tex]\begin{gathered} y=3.80\times\cos31.0\degree \\ y=3.2572 \\ y\approx3.26\;m \end{gathered}[/tex]The length of the side adjacent 31.0° is 3.26 meters.
Two cities A and B are shown on diagram. every 1 cm = 4 km.
1) Find scale
2) Find distance between A and B
3) "C" city is in west 12km from A, 20km from B. Locate "C" on diagram.
Answers
1. The scale is of 1:400,000.
2. The distance between A and B is of 36 km.
3. The diagram with city C is given at the end of the answer.
What is a scale?The scale of a drawing is how much each unit in the drawing represents in actual distance.
In the context of this problem, the scale is given as follows:
1 cm = 4 km
Meaning that each cm drawn represents 4 km of actual distance.
Using the same unit, we have that:
4 km = 4 x 100,000 cm = 400,000 cm.
Hence the scale is given by:
1:400,000.
Measuring on the drawing, the distance between A and B is of 9 cm, hence, applying the scale, the real distance is of:
9 x 4 km = 36 km.
In the diagram, considering the given scale, we want to position city C 3 cm from City A, to the west = to the left.
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suppose that the miles per gallon (mpg) rating of passenger cars is a normally distributed random variable with mean of 33.8 mpg and standard deviation of 3.5mpg. what is the probability that a randomly selected car gets less than 40 mpg?
Answers
The probability that a randomly selected car gets more than 40 mpg is equal to 0.771.
Let us assume that the miles-per-gallon rating of passenger cars be represented by random variable X. According to the question we know that X ≈ N (μ = 33.8 mpg and σ² = 3.5² mpg). Now, to compute the probability that a randomly selected passenger will gets less than 40 mpg will be given as
P(X < 40) = P(X - μ/σ > 40 - 33.8/3.5)
= P(Z < 1)
= P(Z > 1) - 1
= 1.771 - 1
= 0.771 which is the required probability.
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What is the smallest integer greater than 800 that is relatively prime to 10!
Answers
The smallest integer greater than 800 that is relatively prime to 10! is 801
How to determine the number greater than 800 that is relatively prime to 10!The term relatively prime refers to numbers who has a greatest common factor of 1. If two numbers have a greatest common factor of 1 the two numbers are said to be relatively prime
solving for 10!
10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
= 362880
prime factorization of 10!
= 2^7 * 3^4 * 5 * 7
prime factorization of 801
= 3^2 * 89
The greatest common factor of both numbers is 1, this is not included to the factors in the prime factorization but 1 is a known common factor already.
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What’s the answer plsss asp
Answers
The right angle, or 90°, is always one angle. The hypotenuse is the side with the 90° angle opposite.
If the side of DF = 7.7 cm then DE = 3.7 cm.
What is meant by right angle triangle?The right angle, or 90°, is always one angle. The hypotenuse is the side with the 90° angle opposite. The longest side is always the hypotenuse. The other two inner angles add up to 90 degrees.
A right triangle is a triangle in which one of the angles is at a right angle or two of the sides are perpendicular, or more formally, an orthogonal triangle, formerly known as a rectangled triangle. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
Given: DF = 7.7 cm and ∠ E = 29°
Let the equation be
sin θ = P/h = DF / DE
substitute the values in the above equation, we get
⇒ sin 29° = 7.7 / DE
⇒ DE = 7.7 / 0.48 = 3.696 = 3.7 cm
Therefore, the correct answer is option a) 3.7 cm.
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Triangles FAD and DCE are translations of triangle ABC.
Select all the statements that must be true. (Lesson 1-21)
A. Points B, A, and F are collinear.
PERIOD
E
(B.) The measure of angle BCA is the same as the measure of angle CED.
C. Line AD is parallel to line BC.
D. The measure of angle CED is the same as the measure of angle FAD.
(E.) The measure of angle DAC is the same as the measure of angle BCA.
F. Triangle ADC is a reflection of triangle FAD.
Answers
The statements about triangles FAD and DCE which are translations of triangle ABC include the following:
A. Points B, A, and F are collinear.
(B.) The measure of angle BCA is the same as the measure of angle CED.
C. Line AD is parallel to line BC.
(E.) The measure of angle DAC is the same as the measure of angle BCA.
The types of transformation.Generally, there are four (4) main types of transformation and these include the following:
ReflectionDilationRotationTranslationWhat is a translation?In Geometry, a translation can be defined as a type of transformation which moves every point of a geometric figure (object) in the same direction, as well as for the same distance.
Since triangles FAD and DCE both represent the translations of triangle ABC (see attachment), we can logically deduce the following information:
Points B, A, and F all lie on the same line BF, which makes point B, A, and F collinear.All of the sides and angles of triangle ABC (ΔABC) are equal to triangle DCE (ΔDCE), which makes angle BCA (m∠BCA) equal to angle CED (m∠CED).Line AD and line BC are parallel lines because they can never meet.The measure of angle DAC (m∠DAC) is the same as the measure of angle BCA (m∠BCA).Read more on translation here: https://brainly.com/question/19880883
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Please help this is due soon
Answers
Hello!
Let's solve:
The sum of all the angles of a triangle is ==> 180 degrees[tex]\hookrightarrow \text{In other words: } x + 59+ 84 + x + 51=180[/tex]
Solve the equation to find the value of 'x'[tex]x + 59 + 84 + x + 51= 180\\2x + 194=180\\2x = -14\\x = -7[/tex]
Since m∠A = x + 51, we just need to plug in x's valuem∠A = x + 51 = -7 + 51 = 44
Answer: 44
Hope that helps!
Recall that the formula for the area of a rectangle is, A = l×w where l represents the length of the rectangle and w represents its width.
Find the area of a rectangle that has a length of 3.5 centimeters and a width of 2.2 centimeters. The answer is 7.7
Answers
Using the formula for the area of a rectangle is, A = l×w where l represents the length of the rectangle and w represents its width, the area of a rectangle with the length of 3.5 centimeters and a width of 2.2 centimeters will be 7.7 cm^2.
What is the area of a rectangle?The area of the rectangle can be calculated using the formula,
(A = l×w )
and the l = the length of the rectangle
w = represents the width of the rectangle
Then to calculate the area of the rectangle, we can substitute the values that is been given as :
(A = l×w )
A = (2.2 * 3.5) = 7.7 cm^2
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Answer:
7.7
Step-by-step explanation:
The answer was already in the question... He must've edited it or somethin'
Given the costs for several of the same grocery items in two countries, find the rate of the total cost for these items in the United Kingdom to that of the total cost of
items in Australia.
Answers
Using ratios and assuming the given values, the rate of the total cost for items in the United Kingdom to that of the total cost of items in Australia is 2/3.
How do you calculate the ratio?A ratio shows how often one number is contained in another. The ratio of oranges to lemons, for instance, is eight to six if there are eight oranges and six lemons in a bowl of fruit.The ratio of oranges to all fruits is 8:14, whereas the ratio of lemons to oranges is 6:8.A ratio is a comparison of two items when it is expressed in numbers or amounts. For instance, the boy-to-girl ratio in a room with 10 males and thirty girls is 1:3, or one to three.Assume that the costs are:
United Kingdom = 10.78Australia = 21.23The ratio would be:
Ratio = United Kingdom: AustraliaSo, we have:
Ratio = 10.78:21.23Simplify:
Ratio = 2 : 3Express as rate
Rate = 2/3Therefore, using ratios and assuming the given values, the rate of the total cost for items in the United Kingdom to that of the total cost of items in Australia is 2/3.
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HELP MEEEEEEEEEEEEEE
Answers
Answer:
(2,-3)
Step-by-step explanation:
[tex]\frac{\left(y+3\right)^2}{9}-\frac{\left(x-2\right)^2}{2}=1\\\frac{\left(y-k\right)^2}{a^2}-\frac{\left(x-h\right)^2}{b^2}=1\:\mathrm{\:is\:the\:standard\:equation\:for\:an\:up-down\:facing\:hyperbola}\\\frac{\left(y-\left(-3\right)\right)^2}{3^2}-\frac{\left(x-2\right)^2}{\left(\sqrt{2}\right)^2} =1\\(2,-3)[/tex]
A cylindrical oil tank 8 ft deep holds 580 gallons when filled to capacity. How many gallons remain in the tank when the depth of oil is 3 1/2 ft.
Answers
Solution
[tex]\begin{gathered} 8ft=580\text{ gallons} \\ 3\frac{1}{2}ft=x \end{gathered}[/tex]Solution
[tex]\begin{gathered} \frac{8}{3.5}=\frac{580}{x} \\ cross\text{ multiply} \\ 8x=3.5\times580 \\ 8x=2030 \\ divide\text{ both sides by 8} \\ \frac{8x}{8}=\frac{2030}{8} \\ x=253.75 \end{gathered}[/tex]The final answer
253.75 gallons remain in the tank when the depth of oil is 3.5 ft
Find the area.
a.1604 ft
b.2600 ft
c.2160 ft
d.2180 ft
Answers
Answer:
d.2180
Step-by-step explanation:
add the two sides and subtract that one number on top I believe
eamonn has just taken a statistics exam, and he wants to calculate a confidence interval to represent the exam scores in his class. the test mean was 75, with a standard deviation of 5. there are 30 students in the class. the 90% confidence interval for the class is:
Answers
The 90% confidence interval for the class is [73.49, 76.51].
Confidence interval is defined as the range of values where a parameter might fall at a given confidence level. It can be calculated using the formula below.
CI = μ ± z x SD/√n
where CI = confidence interval
μ = sample mean = 75
z = found by using a z-score table
SD = sample standard deviation = 5
n = sample size = 30
At 90% confidence level, the area in each tail of the standard normal curve is 5, and the cumulative area up to the second tail is 95.
(100 - 90) / 2 = 5
100 - 5 = 95
Find 0.95 in the z-table to get the value of z.
At p = 0.95, z = 1.65
Plug in the values to the formula for confidence interval, CI.
CI = μ ± z x SD/√n
CI = 75 ± 1.65 x 5/√30
CI = 75 ± 1.51
CI = [73.49, 76.51]
Hence, for every 100 samples, at 90% confidence level, the mean will be between 73.49 and 76.51.
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What's the number of possible outcome when a coin is tossed four times
Answers
Answer:equal
Step-by-step explanation: no number but equal as it is tossed 4 times
Answer:
16
Step-by-step explanation:
The number of possible outcomes at each coin toss = 2.
The total number of possible outcomes after 4 times = 2⁴ = 16.
Find sides AM and side AR
AR-9x-2 RM-2x+6 AM-5x-3
Answers
Using the segment addition postulate, the lengths of the sides are given as follows:
AM: 4.5625.AR: -0.8125.Segment Addition PostulateThe segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the smaller segments.
In this problem, the line AM is divided into two segments by point R, as follows:
AR = 9x + 2.RM = 2x + 6.The total length of the line is given by:
AM = -5x + 3.
Hence the solution for x is given as follows:
AR + RM = AM
9x + 2 + 2x + 6 = -5x + 3
11x + 8 = -5x + 3
16x = -5.
x = -5/16
x = -0.3125.
Hence the lengths are:
AM = 5x - 3 = -5(-0.3125) + 3 = 4.5625.AR = 9x - 2 = 9(-0.3125) + 2 = -0.8125.There is a typo in the signals as we have a negative length, which is not possible, but the procedure is as shown in this problem.
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P(3,-3) Q(8,7) R(5,-2)
Given S(11,1) is a point which lies on the extended line PR where QS is a perpendicular line to PRS. Find the area of triangle PQR.
Answers
Answer: the area of triangle PQR is 7.5 square units
Step-by-step explanation:
[tex]\displaystyle\\A_{PQR}=\frac{PR*QS}{2} \\\\1.\ (3,-3)\ \ \ \ \ (5,-2)\\\\PR=\sqrt{(5-3)^2+(-2-(-3))^2}\\\\PR=\sqrt{2^2+(-2+3)^2} \\\\PR=\sqrt{4+1^2} \\\\PR=\sqrt{4+1}\\\\ PR=\sqrt{5} \ units[/tex]
[tex]\diplaystyle\\2.\ (8,7)\ \ \ \ \ (11,1)\\\\QS=\sqrt{(11-8)^2+(1-7)^2} \\\\QS=\sqrt{3^2+(-6)^2} \\\\QS=\sqrt{9+36} \\\\QS=\sqrt{45}\\\\QS=\sqrt{9*5} \\\\QS=\sqrt{3^2*5} \\\\QS=3\sqrt{5}[/tex]
[tex]\displaystyle\\Hence,\\A_{PQR}=\frac{\sqrt{5}*3\sqrt{5} }{2} \\\\A_{PQR}=\frac{(\sqrt{5}*\sqrt{5}) *3 }{2} \\\\A_{PQR}= \frac{5*3}{2}\\\\A_{PQR}=\frac{15}{2}\\\\A_{PQR}=7.5 \ units^2[/tex]
Omar went shopping for a new video game because of a sale. The price on the tag was $37, but Omar paid $25.90 before tax. Find the percent discount.
Answers
Answer:
30%
Step-by-step explanation:
Omar went shopping for a new video game because of a sale. The price on the tag was $37, but Omar paid $25.90 before tax. Find the percent discount.
(37 - 25.9)/37 = 0.3 or 30% discount
check:
70% of $37 = $25.90
Part A Write the multiplication expression shown by the model. Do not solve the problem. Part B
Explain the expression written in Part A. Include the final product and how it is shown with the model.
Answers
Part A: The multiplication expression is L×w
Part B: The expression is written as N= r+ g + w + b
The final product = 200 boxes
How to determine the expressionIt is crucial to note that the formula for determining the area of a rectangle is expressed as;
Area = lw
Given that;
l represents the length of the rectanglew represents the width of the rectangleThe area can be calculated by multiplying the length and the width and also by then adding the number of boxes.
We have the expression as;
10( 4 + 5 + 4 + 7)
Also,
L × w = r + g + w + b
Hence, we have that L×w is a multiplication expression.
Total number of boxes for the length = 20
Total number of boxes for the width = 10
Total area = L×w = 20×10=200
Number of available red boxes = 46Number of available green boxes = 46Number of available blue boxes = 46Number of available white boxes = 62We have;
N= r+ g + w + b
but r = g = b
Also,
L×B = 3r + w
Hence, a multiplication expression is an expression that has its variables or numbers being multiplied.
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Which answer is equivalent to
OA.
B. √
(4
OB.
C.
16
49
D.
16
49
3/16
349
√16
(49
? Please helpppp
Answers
Answer:
C [tex]\sqrt \frac{16}{49}[/tex]Step-by-step explanation:
looking at all the stress you're in I knew I had to help so all your lists are bunched up, so I went of the picture C is correct because B 4 and 7 aren't even a part of the question itself and A has 16 and 49 but it doesn't have sqrt so it's not = to the question and D is not correct either because it doesn't have one sqrt it has two on top of each other. HOPE THIS HELPED!
I need help with the question below please:A painter must thin some paint for use in a sprayer. If the recommended rate is 1/9 pint of water per gallon of paint, how many total gallons will there be after thinning 36 gallons of paint?
Answers
Juanita has a part-time job that pays $12/hour and works about 50 hours every month. Her
withholdings are Social Security. (6.2%), Medicare (1.45%) and federal income tax (10%). What
is her approximate net pay?
a. $120
b. $500
c. $600
d. $700
Answers
B. 500 is the answer
The approximate net pay of Juanita is $500. Therefore, option B is the correct answer.
Given that, Juanita has a part-time job that pays $12/hour and works about 50 hours every month.
What is the net pay?Net pay means take-home pay or the amount employees earn after all payroll deductions are subtracted from their gross pay.
Now, total money earned in a month
= 12 × 50 = 600
Now
6.2% of 600 = $37.2
= 600 - 37.2 = $562.8
1.45% of 562.8 = $8.1606
= 562.8 - 8.1606 = $554.6394
10% of 554.6394 = $55.46394
= 554.6394 - 55.46394 = $499.17546
Total deductions = $499.17546
So, net pay = grass pay - deductions
= 600 - 105.9
= $499.17546
The approximate net pay of Juanita is $500. Therefore, option B is the correct answer.
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geometry topic 2 test
Answers
Answer:
what is the question?
Step-by-step explanation:
Need help with writing a rule to describe each transformation
Answers
Explanation
By observation, we can see that the transformation from the original to the image, is a rotation of 90 degrees counterclockwise about the origin.
Answer: Option D