4. tan Θ if sin = 1/2 90° ≤ Θ ≤ 180°
a. -√(3)/2
b. -√(3)/3
c. √(3)/2
d. √(3)/3
5. Find the value of
tan Θ if cot Θ = 2 0 ≤ Θ < 90° (write your answer as a fraction)
tan =
Answers
9514 1404 393
Answer:
4. b =-√(3)/3
5. 1/2
Step-by-step explanation:
4. The tangent is negative in the second quadrant. The sine value tells you the reference angle is 30°, so the actual angle is 150°. The corresponding tangent is ...
tan(150°) = -(√3)/3
__
5. The cotangent is the inverse of the tangent, and vice versa.
tan = 1/cot
tan(θ) = 1/2
Related Questions
A person invested $540 in an account growing at a rate allowing the money to double
every 9 years. How much money would be in the account after 21 years, to the nearest
dollar?
Answers
Answer:2721
Step-by-step explanation:
The following dataset represents the math test scores for a class of 20 students. 90, 85, 95, 100, 100, 90, 100, 65, 100, 85, 80, 95, 80, 100, 85, 75, 100, 90, 90, 75 Would the mode be a good measure of central tendency for this dataset?
Answers
Answer:
yes
Step-by-step explanation:
The mode is the measure of the central tendency for the given data set. The mode represents the highest frequency of the number
Since in the given data set as we can see that the 100 would be appeared 6 times
So this represent that the mode is 100
So here the mode would be the good measure
In ΔUVW, the measure of ∠W=90°, VW = 29 feet, and UV = 69 feet. Find the measure of ∠U to the nearest degree.
Answers
Answer:
25
Step-by-step explanation:
Answer:
the answer is 25
Step-by-step explanation:
Part 3: Write the equation of and graph an ellipse.
Given the foci and vertices of an ellipse, complete the following steps.
Vertices at (4, -6 +-9)
Foci at (4, -6 +-5sqrt2)
a) What is the center of the ellipse? Explain how to determine this from the given points.
b) Write the standard equation of the ellipse. (3 points
c) What are the lengths of the major and minor axes? (2 points)
Major Axis:
Minor Axis:
d) Sketch a graph of the ellipse and label the center, foci, and the major and minor axes. (4 points)
Answers
Answer:
Step-by-step explanation:
The center is halfway between vertices, at (4, -6).
It is also halfway between foci.
:::::
The vertices are vertically aligned, so the parabola is vertical.
General equation for a vertical ellipse:
(y-k)²/a² + (x-h)²/b² = 1
with
center (h,k)
vertices (h,k±a)
co-vertices (h±b,k)
foci (h,k±c), c² = a²-b²
Apply your data and solve for h, k, a, and b.
center (h,k) = (4, -6)
h = 4
k = -6
vertices (4,-6±a) = (4,-6±9)
a = 9
foci (4,-6±c) = (4,-6±5√2)
b² = a² - c² = 9² - (5√2)² = 31
b = √31
The equation becomes
(y+6)²/81 + (x-4)²/31 = 1
:::::
length of major axis = 2a = 18
length of minor axis = 2b = 2√31
The various parts of the question needs to be answered.
Center: (4,-6)
Standard equation: [tex]\dfrac{(x-4)^2}{\sqrt{31}^2}+\dfrac{(y+6)^2}{9^2}=1[/tex]
Length of major axis: 18 units
Length of minor axis: [tex]2\sqrt{31}\ \text{units}[/tex]
Graph is attached.
EllipseThe Vertices are of the form
[tex](h,k\pm a)=(4,-6\pm 9)[/tex]
This means that the ellipse is symmetrical to the y axis.
The center of an ellipse is given by [tex](h,k)[/tex]
So, here the center is [tex](4,-6)[/tex]
[tex]a=\pm 9[/tex]
The foci are of the form
[tex](h,k\pm c)=(4,-6\pm 5\sqrt{2})[/tex]
So, [tex]c=\pm 5\sqrt{2}[/tex]
[tex]b=\sqrt{a^2-c^2}\\\Rightarrow b=\sqrt{9^2-(5\sqrt{2})^2}\\\Rightarrow b=\pm\sqrt{31}[/tex]
The standard equation for major axis being parallel to y axis is given by
[tex]\dfrac{(x-h)^2}{b^2}+\dfrac{(y-k)^2}{a^2}=1\\\Rightarrow \dfrac{(x-4)^2}{\sqrt{31}^2}+\dfrac{(y+6)^2}{9^2}=1[/tex]
Length of major axis is
[tex]2a=2\times 9\\ =18\ \text{units}[/tex]
Length of minor axis is
[tex]2b=2\sqrt{31}\ \text{units}[/tex]
Learn more about ellipse:
https://brainly.com/question/12205108
Y=-1|x-2|+1 how to solve
Answers
Answer:
if x ≥ 2, then y = x - 1
if x < 2, then y = -x + 3
Step-by-step explanation:
y = 1* |x - 2| + 1
y = |x-2| + 1
*** The rule on absolute value: |a| =a, if a ≥ 0; |a| = -a, if a < 0
If x-2 ≥ 0, then |x-2| = x-2, so y = (x - 2) + 1 = x - 1; y = x - 1
So if x ≥ 2, then y = x - 1
If x-2 < 0, then |x-2| = -(x-2) = -x + 2, so y = {-x + 2} + 1 = -x + 3; y = -x + 3
So if x < 2, then y = -x + 3
PLEASE HELP!!!!!! ILL GIVE BRAINLIEST *EXTRA 40 POINTS** !! DONT SKIP :((
Answers
Answer:
Yes
Step-by-step explanation:
(3, 2) is a solution to the given system of linear equations.
x - 8y = 3 - 8*2 = 3 - 16 = - 13
16x - 16y = 16(x - y) = 16( 3 - 2) = 16*1 = 16
9(7/4)-2= what in fraction form ? Can someone please help ?
Answers
Answer:
55/4
Step-by-step explanation:
You have a restaurant bill of $46.32. If you are taxed 7 1/2 and decide to tip your server 20%, how much is your total?
a.
$59.75
b.
$59.05
c.
$58.92
d.
$58.87
Answers
Answer:
The correct answer is B. $59.05.
Step-by-step explanation:
Given that I have a restaurant bill of $ 46.32, if I am taxed 7 1/2 and decide to tip my server 20%, to determine how much is my total, the following calculation must be performed:
1/2 = 0.5
46.32 + (46.32 x 0.075) + (46.32 x 0.2) = X
46.32 + 3.474 + 9.264 = X
49.79 + 9.26 = X
59.05 = X
Thus, the total amount that I must pay is $ 59.05.
Answer:
b
Step-by-step explanation:
trust
A sum amounted naira 2,590
at 10% Per annum for the
Period of 4 Years. Find the sum
Answers
Answer:
1,769
Step-by-step explanation:
The computation of the sum is shown below:
Future value = Present value × (1 + rate of interest)^number of years
2,590 = Present value × (1 + 0.10)^4
2,590 = Present value × 1.10^4
So, the present value is
= 2,590 ÷ 1.10^4
= 2,590 ÷ 1.4641
= 1,769
Prove (triangle)ABC is congruent to (triangle) DEF using ASA
Answers
Answer/Step-by-step explanation:
Two triangles can be proven to be congruent to each other if two angles and an included side of one triangle is congruent to the corresponding two angles and included side of the other triangle.
Two angles (<C and <A) in ∆ABC, are congruent to two angles (<D and <F) in ∆DEF. Also, the included side (AC) in ∆ABC is congruent to the included side (DF) in ∆DEF.
Therefore, based on the Angle-Side-Angle Congruence Theorem, ∆ABC is congruent to ∆DEF.
Answer:
Answer/Step-by-step explanation:
Two triangles can be proven to be congruent to each other if two angles and an included side of one triangle is congruent to the corresponding two angles and included side of the other triangle.
Two angles (<C and <A) in ∆ABC, are congruent to two angles (<D and <F) in ∆DEF. Also, the included side (AC) in ∆ABC is congruent to the included side (DF) in ∆DEF.
Therefore, based on the Angle-Side-Angle Congruence Theorem, ∆ABC is congruent to ∆DEF.
Step-by-step explanation:
y=4x+5 cuando x=9
Porfavor es para hoy
Answers
Answer:
y = 41
Step-by-step explanation:
y=4x+5 cuando x=9
y=4*9+5
y=36+5
y=41
Help!!!!!! Please!!!!
Answers
Answer: 30u
Step-by-step explanation:
If GY is 6u long, x=6. (4x-2) is 4x6 which is 32, 32 - 2 = 30u long
(U = units)
What is the area of the triangle?
Answers
9514 1404 393
Answer:
7 square units
Step-by-step explanation:
There are several ways the area of triangle EBD can be found.
find the lengths EB, BD, DE and use Heron's formula (messy due to roots of roots being involved).define point G at the lower left corner and subtract the areas of ∆DEG and BCD from trapezoid BCGE.figure the area from the coordinates of the vertices.use Pick's theorem and count the dots.We choose the latter.
__
Pick's theorem says the area of a polygon can be found as ...
A = i + b/2 -1
where i is the number of grid intersection points interior to the polygon, b is the number of grid points intersected by the border.
The attached figure shows the lines EB, BD, and DE intersect one point in addition to the vertices. So, b=4. A count of the red dots reveals 6 interior points (i=6). So, the area is ...
A = 6 + (4/2) -1 = 7
The area of ∆EBD is 7 square units.
Which trigonometric ratios are correct for triangle
ABC? Select three options.
Answers
Answer:
Options (1), (3) and (4)
Step-by-step explanation:
From ΔABC given in the picture,
By Pythagoras theorem
Hypotenuse² = (Leg 1)² + (Leg 2)²
BC² = AB² + AC²
(18)² = 9² + AC²
AC = [tex]\sqrt{324-81}[/tex]
AC = [tex]9\sqrt{3}[/tex] cm
sin(C) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{AB}{BC}[/tex]
= [tex]\frac{9\sqrt{3}}{18}[/tex]
sin(C) = [tex]\frac{\sqrt{3} }{2}[/tex]
sin(B) = [tex]\frac{AC}{BC}[/tex]
= [tex]\frac{9}{18}[/tex]
= [tex]\frac{1}{2}[/tex]
cos(B) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{9\sqrt{3}}{18}[/tex]
= [tex]\frac{\sqrt{3} }{2}[/tex]
tan(B) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{AC}{AB}[/tex]
= [tex]\frac{9}{9\sqrt{3} }[/tex]
= [tex]\frac{1}{\sqrt{3} }[/tex]
tan(C) = [tex]\frac{AB}{AC}[/tex]
= [tex]\frac{9\sqrt{3}}{9}[/tex]
= [tex]\sqrt{3}[/tex]
Therefore, Options (1), (3) and (4) are the correct options.
Answer:
Options (1), (3) and (4)
Step-by-step explanation:
From ΔABC given in the picture,
By Pythagoras theorem
Hypotenuse² = (Leg 1)² + (Leg 2)²
BC² = AB² + AC²
(18)² = 9² + AC²
AC =
AC = cm
sin(C) =
=
=
sin(C) =
sin(B) =
=
=
cos(B) =
=
=
tan(B) =
=
=
=
tan(C) =
=
=
Therefore, Options (1), (3) and (4) are the correct options.Step-by-step explanation:
Evaluate 150 - ( 2 +x)^ 3 when x - 2
Answers
Answer:
86
Step-by-step explanation:
(2+2=4) 4 to the 3rd power is 64. 150 minus 64 is 86
Geometry
please help if you can!
picture included
Answers
Answer:
x = 12.5
Step-by-step explanation:
Based on the interesting chords theorem, we would have the following:
2*x = 5*5
2x = 25
Divide both sides by 2
x = 25/2
x = 12.5
Plzz help me
A.36
B.48
C.144
D.288
Answers
Answer:
D.288
Step-by-step explanation:
6×4×12
Multiply 6 and 4 to get 24.
24×12
Multiply 24 and 12 to get 288.
288
Here is an expression: 3+ t2 1 Evaluate the expression when t is 2
Answers
Step-by-step explanation:
it would be 45 if you add it as 21 but you didn't put another symbol hope I can help :)
PLEASE HELP ITS DUE IN 3 HOURSSS!!!
Answers
Answer:
the 3rd option because Imma fresh man bro
QUICK ITS TIMED PLS HELP QUICK!!!!!
How is the product of 3 and -2 shown using integer tiles?
Answers
Answer:
The first one . +++ --
Step-by-step explanation:
The measure of an angle is 72 degrees what is the measure of its conplementary angle
Answers
Answer:
18
Step-by-step explanation:
Can someone help meee
Answers
Answer:
A= 90 (right angel )
E= 90 - 67 = 23
I hope im right!!
Factorise
15 a^3 b - 35ab^3
Answers
Answer:
15 a^3 b - 35ab^3
taking common
5ab(3a²-7b²)
Answer:
[tex] \huge \boxed{ \boxed{ \red{3ab(5 {a}^{2} - 7 {b}^{2} )}}}[/tex]
Step-by-step explanation:
to understand thisyou need to know about:factoringtips and formulas:therefore are many ways to factor. In this question to factor we just need to figure out GCF of the following expressionfactor out the GCFgiven:15a³b-35ab³let's solve:rewrite 15a³b as 3×5×a×a×a×brewrite -35ab³ as -1×7×5×a×b×b×btherefore the GCF of the expression is 5ablet's factor out 5ab:5ab(3a²-7b²)and
we are done
If it takes the pendulum 1.5 seconds to move back and forth once,the length of the pendulum is approximately what feet?
Answers
Answer:
Suppose that it takes a simple pendulum 1.2 seconds to swing from its leftmost point to its ... pendulum to complete one full back-and-forth motion – from its rightmost point back to its ... A pendulum with a string of length 2 m has a period of about 2.8 s. ... A pendulum with a period of 1.8 s on Earth is moved to another planet.
Step-by-step explanation:
what is the value? when r equals 0
Answers
Answer:
I do not know the answer to this question
Step-by-step explanation:
using the commutative property, what would be the equivalent expression for 5+6= ?
Answers
find the perimeter of the shape below
Answers
Answer:
It doesn't show the whole picture
Step-by-step explanation:
What is 54288 divided by 6.24
Answers
A new parking lot is being built for a medical office. The expression representing the number of parking spots in the new lot is StartFraction 15 x over 4 EndFraction minus 9, where x represents the number of parking spots in the first row. How many spots are in the parking lot if there are 32 parking spots in the first row?
79
88
111
129
Answers
Answer:
111
Step-by-step explanation:
A variable is a letter, for example x, y or z, that represents an unspecified number. To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12.
Answer:
C
Step-by-step explanation:
Can someone please help meeeee
Answers
Answer:
53
Step-by-step explanation:
Complementary angles are summed up to be 90 degrees. If we already know that one if the angles is 37, all we need to do is subtract 37 from 90.
90-37 = 53
Hope this helps.