An acute angle θ is in a right triangle with sin θ = two thirds . What is the value of cot θ?
Answers
Answer:
six divided by the square root of thirteen
Step-by-step explanation:
hey there,
< sin θ = [tex]\frac{O}{H}[/tex]
So that means O = 2 and H = 3. In order to find cot θ, first let's find tan θ.
tan θ = [tex]\frac{O}{B}[/tex]
We only know what O is equal to, not B. So let's draw out a triangle.
7
◢ 6
B
As you can see (sorry for the poor triangle), this is a right triangle. In order to find an unknown part, use [tex]a^2 + b^2 = c^2[/tex]!
[tex]6^2 + B^2 = 7^2[/tex]
B = ±√13
Obviously, a side of a triangle can't be negative, so it stays positive. Now we can find tangent!
tanθ = [tex]\frac{6}{\sqrt{13} }[/tex]
But, we're not done here. We're trying to find cotθ.
cotθ = [tex]\frac{1}{tan}[/tex]θ
[tex]\frac{1}{\frac{6}{\sqrt{13} } }[/tex] = [tex]\frac{\sqrt{13} }{6}[/tex]
That's your final answer! >
Hope this helped! Feel free to ask anything else.
Related Questions
Find the equation of the perpendicular line passing through the midpoint of the line segment connecting (−1, 7) and (2, 3). incorrect: your answer is incorrect.
Answers
(04.02 LC)
The graph represents function 1 and the equation represents function 2:
Function 2
y = 3x + 1
How much more is the rate of change of function 2 than the rate of change of function 1?
1
2
3
4
Answers
y=3 it has a slope of zero.
Function 2 is
y=3x+1, it is in slope-intercept form, y=mx+b where m is the slope and b is the y=intercept so in this case it has a slope of 3.
So the difference in slopes is 3-0=3
The rate of change of function 2 is 3 times greater than the rate of change of function 1.
Explanation:The rate of change of a function measures how much the output of the function changes when the input changes by 1 unit. In function 1, since the graph is a straight line, the rate of change is constant. We can find the rate of change of function 1 by finding the slope of the line, which represents the rate of change. In function 2, the equation is y = 3x + 1, so the rate of change is 3. Therefore, the rate of change of function 2 is 3 times greater than the rate of change of function 1.
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How can x2 = x2 + 2x + 9 be set up as a system of equations?
Answers
Final answer:
To set up x^2 = x^2 + 2x + 9 as a system of equations, we would have x^2 = x^2 + 2x + 9 and x = -4.5.
Explanation:
To set up x2 = x2 + 2x + 9 as a system of equations, we can separate it into two separate equations:
Equation 1: x2 = x2 + 2x + 9
Equation 2: 0 = 2x + 9
By rearranging Equation 2, we can rewrite it as:
x = -4.5
Therefore, the system of equations for x2 = x2 + 2x + 9 is: x2 = x2 + 2x + 9 and x = -4.5.
A researcher wishes to find out whether giving a student $1 million in cash will improve or ruin the student's grades in school. A high school class consists of the 8 students numbered in the following list. 0 Juanita 1 Tuan 2 Harry 3 Greta 4 William 5 Hiroshi 6 Betty 7 Jane Help the researcher by using the line from a table of random numbers (shown below) to assign 4 of these students to the treatment group. 39661 55832 02589 52612 25414 19879 60880 30641 55259 35324 Which students go in the treatment group?
Answers
Answer:
Greta, Betty, Tuan and Hiroshi
Step-by-step explanation:
Start from the beginning:
3 - Greta
Then, continue with the next numbers:
9 - skip (there is no student numbered with a 9)
6 - Betty
6 - skip (Betty is already chosen)
1 - Tuan
5 - Hiroshi
a gas-filled balloon rises 40 feet in the 1st minute, 60 feet in the 2nd minute, and 80 feet in the 3rd minute, how many feet will the balloon rise during the 15th minute?
Answers
so
[tex]g_1=40[/tex] ft , means that in the 1st minute, the balloon rose 40 feet
[tex]g_2=60[/tex] ft, means : in the 2nd minute the balloon rose 60 feet
[tex]g_3=80[/tex]
we notice that each minute, the balloon rises a multiple of 20, feet:
[tex]g_1=40=2*20[/tex]
[tex]g_2=60=3*20[/tex]
[tex]g_3=80=4*20[/tex]
so it is clear that [tex]g_n=(n+1)*20[/tex]
during the 15th minute the balloon rises [tex]g_1_5=16*20=320[/tex](feet)
Answer: 320
Let f(x) = 16x5 − 48x4 − 8x3 and g(x) = 8x2. Find f of x over g of x.
Answers
2x^3-6x^2-x
It is given in the question that
[tex]f(x) = 16x^5 -48x^4-8x^3 \ and \ g(x) = 8x^2[/tex]
And we have to find the value of
[tex]\frac{f(x)}{g(x)}[/tex]
Substituting the values of two functions, we will get
[tex]=\frac{16x^5 -48x^4 -8x^3}{8x^2}[/tex]
8x^3 is common in the numerator, and on taking it out, we will get
[tex]= \frac{8x^3(2x^2 -6x-1)}{8x^2} = x(2x^2 -6x-1)[/tex]
And that's the required answer .
if two triangles share a common side what else must be true for the SAS triangle congruence theorem to apply
Answers
The conditions to be added are:
The two triangles have congruent angles between the sides that are not the common side.
The two triangles have congruent lengths for the sides adjacent to the congruent angles.
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,
The SAS (Side-Angle-Side) triangle congruence theorem states that if two triangles have two sides and the included angle of one triangle is congruent to two sides and the included angle of the other triangle, then the two triangles are congruent.
Therefore, in addition to sharing a common side, the two triangles must have congruent angles between the sides that are not the common side. Specifically, the angle opposite the common side must be congruent in both triangles.
To summarize, for the SAS triangle congruence theorem to apply, the following conditions must be met:
The two triangles share a common side.
The two triangles have congruent angles between the sides that are not the common side.
The two triangles have congruent lengths for the sides adjacent to the congruent angles (the "included" side).
Thus,
The conditions to be added are:
The two triangles have congruent angles between the sides that are not the common side.
The two triangles have congruent lengths for the sides adjacent to the congruent angles.
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The standard form of the equation of a parabola is x=y^2+6y+1. What is the vertex form of the equation?
A. X=(y+3)^2-8
B. X=(y+3)^2-5
C. X=(y+6)^2-35
Answers
What you want to do is get the quadratic (y^2+6y+1) into it's root factor form, in other words, the quantity of (y+what) squared will equal y^2+6y+1. Well it's not a perfect square so we'll have to play around with it a little.
In the format ay^2 + by + c, completing the square first requires finding out what value would do that: c = (b/2)^2 = (6/2)^2 = 3^2 = 9
So we need y^2+6y+1 to have the last number (c) to equal 9 to have (y+b/2)^2, or (y+3)^2
How do we get 9 down to the 1 that we have for c?? 9-1=8, so just subtract 8.
That means that y^2+6y+1 is the same as (y^2+6y+9)-8, and y^2+6y+9 = (y+3)^2, so now we have: y^2+6y+1 = (y+3)^2-8, which is answer [A]
The cost of painting a circular traffic sign is $3.50 per square foot. How much, to the nearest dollar, will it cost to paint the sign if its diameter measures 36 INCHES.
Answers
area of a circle = pi x r^2
using 3.14 for pi
radius = 36/2 =18
area = 3.14 x 18^2 = 1017.36 square inches
1 sq ft = 144"
1017.36/144 = 7.065 sq ft
7.065*3.50 = $24.73 to the nearest dollar = $25
An isosceles trapezoid has bases of 4 and 10. If the base angle is 45°, find the area.
A: 42 sq. units
B: 21√2 sq. units
C: 21 sq. units
Answers
DC, the larger one (=10)
From A & B draw the altitude AA' & BB'. You notice that ABA'B' is a rectangle and A'B' = 4,. You conclude that DA' = B'C = 3 .
Now let's calculate the altitude AA'.
The right triangle ADA' is also an isosceles right triangle:
( angle DA'A=90, angle ADA' = 45 and angle DAA' =45) , then
DA' = AA' (altitude) = 3 units. Now we can calculate the area of the trapezoid:
Area = (B+b).H/2
Area = (4+10)x3/2 = 14x3/2 = 42/2 = 21 sq.unit
Answer:
21 sq. units
Step-by-step explanation:
A number is chosen at random from the integers between 11 and 99, inclusive. what is the probability that the number contains the digit 2?
Answers
HELPPPPPP make sure your right !:)
Answers
Write an equation for each translation of y=lxl
7 units up
Answers
[tex]\bf % template detailing \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]
[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{{{ B}}}[/tex]
with that template in mind.. .let's see
[tex]\bf y=|x|\implies \begin{array}{lllcll} y=&1|&1x&+0|+&0\\ &\uparrow&\uparrow &\uparrow &\uparrow \\ &A&B&C&D \end{array}[/tex]
7 units up, meaning D = 7
Which is the best approximation for the value of √102?
A.10
B.11
C.50
D.51
Answers
which would be round to 10 because after the decimal the number is 0 below 5 so 10 stays as 10
so √102 is approximately 10
Suppose you toss a coin 100 times and get 76 heads and 24 tails. based on these results, what is the probability that the next flip results in a head?
Answers
The probability that the next flip results in a head is 50% or 0.5.
We have,
Total number of coins tossed = 100
Number of heads outcome = 76
Number of tails outcome = 24
Now,
The probability of getting heads in the tossing of coins 100 times.
= 76/100
= 0.76
= 76%
Now,
Generally for an unbiased coin.
The probability of getting a head in tossing a coin is 50%.
So,
Based on the results of the first 100 coin tosses, even if the probability of getting a head is 76% the probability that the next flip results in a head is still 50%.
Thus,
The probability that the next flip results in a head is 50% or 0.5.
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Can someone help me with this one real quick ? Thanks a lot! Please explain and show your work :)
Answers
You were given the proof.
b. Corresponding angles are congruent.
Since angles 1 and 2 are corresponding, then if one is 130, then the other one is also 130.
c. Vertical angles are congruent.
Angles 2 and 3 are vertical, meaning they'll also be congruent.
d. Transitive Property of Equality.
If angles 2 and 3 are vertical, then if 2 is 130, then 3 is also 130.
Evaluate the limit lim h → 0 (−5 + h)2 − 25 h
Answers
(-5 + 0)^2 -25(0) = 25 -0 = 25
you invest 2,600 in an account that pays an interest rate of 8.5% compounded continuously. Calculate the balance of your account after 5 years
Answers
A=p e^rt
A future value?
P present value 2600
R interest rate 0.085
T time 5years
E constant
A=2,600×e^(0.085×5)
A=3,976.94
what is the vaule of 3.85+0.004+0.117 ?
Answers
Find the equation of the line specified.
The slope is 3, and it passes through ( -4, -7).
a.
y = 6x + 5
c.
y = 3x - 7
b.
y = 3x + 5
d.
y = 3x - 19
Please select the best answer from the choices provided
A
B
C
D
Answers
B. y = 3x + 5
Answer:
B
Step-by-step explanation:
Edge 2021
Which of the relations given by the following sets of ordered pairs is a function?
Select one:
a. {
(2,4),(2,6),(2,8),(2,10),(2,12)
(2,4),(2,6),(2,8),(2,10),(2,12)
}
b. {
(−5,−4),(−4,−3),(−3,−2),(−4,−5),(−2,−1)
(−5,−4),(−4,−3),(−3,−2),(−4,−5),(−2,−1)
}
c. {
(0,3),(−6,8),(−3,5),(0,−3),(7,11)
(0,3),(−6,8),(−3,5),(0,−3),(7,11)
}
d. {
(8,1),(−4,1),(3,5),(0,4),(−1,2)
(8,1),(−4,1),(3,5),(0,4),(−1,2)
}
Answers
ur answer would be D....because ur x values (8,-4,3,0,-1) are all different
Since no two different ordered pairs have the same x -coordinate, relations D given by the following sets of ordered pairs is a function.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The relation might be put up as a table of ordered pairs. The next step is to determine if each element in the domain matches precisely one element in the range.
A function is a collection of ordered pairs where no two ordered pairs are the same in terms of x-coordinate. A function is defined by an equation that yields such a collection of paired objects.
The relations given by the following sets of ordered pairs is a function is,
d. {(8,1),(−4,1),(3,5),(0,4),(−1,2)(8,1),(−4,1),(3,5),(0,4),(−1,2)}
Thus, no two different ordered pairs have the same x -coordinate, relations D given by the following sets of ordered pairs is a function.
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What is the value of
x/3y, when x = 18 and y = 3?
Answers
x=18 and y=3
[tex]\frac{18}{(3)(3)}=\frac{18}{9}=2[/tex]
this has been asked at least 3 times so far today
18/3*3 = 18/9 = 2
answer is 2
1 oz of walnuts were mixed with 4 oz of peanuts which cost $4/oz to make mixed nuts which cost $5/oz. what is the price per oz of walnuts
Answers
total cost of walnuts = 1oz * w
Total cost of peanuts = 4 oz * $4/oz = $16
Total cost of nuts = 5oz * $5 /oz = $25
=> 1oz*w + $16 = $25 => w = ($25 - $16) /1oz = $9/oz
Verfify:
1oz * $9/oz + 4oz * $4/oz = $9 + $16 = $25, which is equal to 5oz * $5/oz.
Answer: $9 per oz.
A stick 42 inches long is broken into two pieces, so that one piece is twice as long as the other one. How long are the two pieces ?
Answers
Let the shorter piece be x inches.
Thus, the longer piece is 2x.
2x + x = 42
3x = 42
x = 14
Therefore, the length of the two pieces are 14 inches and 28 inches.
The answer is 14 inches and 28 inches:
Total length of stick = 42 inches.
Let the shorter piece be x inches.
Thus, the longer piece is 2x.
2x + x = 42
3x = 42
x = 14
Therefore, the length of the two pieces are 14 inches and 28 inches.
Find the area of the triangle with the given measurements. round the solution to the nearest hundredth if necessary. b = 107°, a = 10 cm, c = 22 cm
Answers
Answer:
105.19 cm²
Step-by-step explanation:
The applicable area formula is ...
area = (1/2)ac·sin(B) = (1/2)(10)(22)sin(107°) ≈ 105.19 cm²
what is the greatest integer that satisfies the inequality 3x-4≤8 ?
A.4
B.5
C.6
D.7
Answers
3x ≤ 12
x ≤ 4
answer
A.4
For example, answer choice "A.)";
3(4) -4 <_ 8
We plugged in 4 for x.
Let's see if A.) is correct.
3(4) -4 <_ 8
12 - 4 <_ 8
8 <_ 8
This is the GREATEST possible integer, as the question asks for what the highest possible number would match the inequality.
Your correct answer choice is "A.)"
I hope this helps!
What is the slope of the line shown below?
Answers
Answer:
correct option is B) 2
Step-by-step explanation:
Slope of line is calculated by formula :-
Suppose two points on line are [tex](x_1, y_1) and (x_2 ,y_2)[/tex] then slope 'm' is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].
We can see two points on line of graph are :- (-1, -4) and (2,2)
then slope will be calculated as,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
since [tex]x_1 = -1, x_2 =2, y_1=-4\;and\; y_2=2[/tex]
now, put in formula
[tex]m=\frac{2-(-4)}{2-(-1)}[/tex]
[tex]m=\frac{2+4}{2+1}[/tex]
[tex]m=\frac{6}{3}[/tex]
[tex]m=2[/tex]
Hence, slope is 2 of the provided graph.
Therefore, correct option is B) 2
Generally, how would one work out the surface area of a frustum?
Answers
see the formula in the picture
R is larger diameter, r is smaller diameter
Express the sum of 8.79 m and 6.0 m using the correct number of significant digits.
Answers
8.8 in this cas, so
8.79 + 6.0 = 8.8 + 6.0 = 14.8
14.8 is the answer
Answer:
The sum of the numbers is [tex]8.79+6.0=14.79[/tex]
Step-by-step explanation:
To find : Express the sum of 8.79 m and 6.0 m using the correct number of significant digits.
Solution :
Writing the sum of the numbers according to significant digits by writing in their place value,
8 . 7 9
+6 . 0 0
----------
14 . 7 9
Therefore, The sum of the numbers is [tex]8.79+6.0=14.79[/tex]
There are 26.2 in a marathon .Write the number of miles using a fraction.
Answers
26.2 = 20+6+0.2
The decimal value 0.2 is read two tenth = 2/10
Writing 26.2 as mixed numbers
[tex]26.2=26 \frac{2}{10} [/tex]
If we want to write this as an improper fraction, multiply 26 by 10 then add the 2 to get the numerator
[tex]26.2 = 26 \frac{2}{10}= \frac{262}{10}= \frac{131}{5} [/tex]