Answer:
θ = [tex]\frac{\pi }{3}[/tex] (60° )
Step-by-step explanation:
Using the identity
sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x
Given
cos²θ - sin²θ = 2 - 5cosθ
cos²θ - (1 - cos²θ) = 2 - 5cosθ
cos²θ - 1 + cos²θ = 2 - 5cosθ
2cos²θ - 1 = 2 - 5cosθ ( subtract 2 - 5cosθ from both sides )
2cos²θ + 5cosθ - 3 = 0 ← in standard form
(cosθ + 3)(2cosθ - 1) = 0 ← in factored form
Equate each factor to zero and solve for θ
cosθ + 3 = 0
cosθ = - 3 ← not possible as - 1 ≤ cosθ ≤ 1
2cosθ - 1 = 0
cosθ = [tex]\frac{1}{2}[/tex] , so
θ = [tex]cos^{-1}[/tex] ([tex]\frac{1}{2}[/tex] ) = [tex]\frac{\pi }{3}[/tex] ( or 60° )
Answer:
[tex] \huge \boxed{ \boxed{\blue{ { \theta = 60}^{ \circ} }}}[/tex]
Step-by-step explanation:
to understand thisyou need to know about:trigonometryPEMDASlet's solve:[tex] \sf \: rewrite \: \sin ^{2} ( \theta) \: as \: 1 - \cos ^{2} ( \theta) : \\ \sf \implies \: \cos ^{2} ( \theta) - (1 - \cos ^{2} ( \theta)) = 2 - 5 \cos( \theta) [/tex][tex] \sf \: remove \: parentheses \: and \: change \: its \: sign : \\ \sf \implies \: \cos ^{2} ( \theta) - 1 + \cos ^{2} ( \theta)) = 2 - 5 \cos( \theta) [/tex][tex] \sf \: add : \\ \sf \implies \: 2\cos ^{2} ( \theta) - 1 = 2 - 5 \cos( \theta) [/tex][tex] \sf \: move \: left \: hand \: sides \: expression \: to \: right \: hand \: sides \: : \\ \sf \implies \: 2\cos ^{2} ( \theta) + 5 \cos( \theta) - 1 -2 = 0[/tex][tex] \sf \: rewrite \: 5\cos( \theta) \: as \: 6 \cos( \theta) - \cos( \theta) : \\ \sf \implies \: 2\cos ^{2} ( \theta) + 6 \cos( \theta) - \cos( \theta) - 3 = 0[/tex][tex] \sf \:factor \: out \: 2 \cos( \theta) \: and \: - 1 : \\ \sf \implies \: 2\cos ( \theta)( \cos( \theta) + 3 ) -1( \cos( \theta) + 3) = 0[/tex][tex] \sf \: group: \\ \sf \implies \: (2\cos( \theta) - 1) ( \cos( \theta) + 3 ) = 0[/tex][tex] \sf \: rewrite \: as \: two \: seperate \: equation: \\ \sf \implies \: \begin{cases}2\cos( \theta) - 1 = 0\\ \cos( \theta) + 3 = 0 \end{cases} [/tex][tex]\sf add \: 1 \: to \: the\: first \: equation \: and \: substract \: 3 \: from \: the \: second \: equation: \\ \sf \implies \: \begin{cases}2\cos( \theta) = 1\\ \cos( \theta) = - 3 \end{cases} [/tex][tex] \sf the \: second \: eqution \: is \: false \: \\ \sf because \: - 1 \leqslant \cos( \theta) \leqslant 1 \: \\ \sf but \: we \: can \: still \: work \: with \: the \: second \: equation[/tex]
[tex] \sf substract \: both \: sides \: by \: 2 : \\ \implies\frac{ 2\cos( \theta) }{2} = \frac{1}{2} \\ \implies\cos( \theta) = \frac{1}{2} \\ \therefore \: \theta \: = {60}^{ \circ} [/tex]WILL GIVE BRAINLEST
Keisha conducts a survey to determine how many siblings each of her classmates has. The data are shown below.
0, 1, 0, 2, 2, 1, 3, 0, 4, 0, 1, 2
What is the mean value of Keisha’s data?
A. 0.75
B. 1
C. 1.3¯
D. 2
Answer:
c
Step-by-step explanation:a
add up 0, 1, 0, 2, 2, 1, 3, 0, 4, 0, 1, 2
Answer:
C. 1.3
Step-by-step explanation:
0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 4
To find the mean, or average, we add up all the numbers to get the total number of siblings (16), and divide by the number of classmates she surveyed (12). 16/12 = 1.3
Please LMK if you have questions. Have a good day.
A plot of land for sale has a width of x ft, and a length that is 8 ft. less than its width. A farmer will only purchase the land if it measures 240 ft.
a. Create an equation in terms of w that models this situation
b. What is the width? What is the length?
Answer:
a
Step-by-step explanation:
Answer:
dunno
Step-by-step explanation:
25- 3x = 40 what is x
Which equation represents a linear function
Answer: B
Step-by-step explanation:
jane and kate share $240 in the ratio 5:7. show that kate receives $140
Answer:
$140
Step-by-step explanation:
5 + 7 = 12
240/12 = 20
20 x 7 = $140
Hope this helps!!
Alright fam, help me out here with these angles thanks!
Answer:
m∠3 = 127°
Step-by-step explanation:
From the given picture,
Two parallel lines have been given.
Angle 3 and another angle measuring 53° are located on a point of a straight line.
Therefore, both the angles will be supplementary.
m(∠3) + 53° = 180° [Property of supplementary angles]
m(∠3) = 180° - 53°
= 127°
bill bowled 3 games at a bowling alley and rented shoes, spending a total of $9.00. leann bowled 5 games at a the bowling alley and rented shoes, spending a total of $14.00. how much does it cost to bowl a game
The cost to bowl a game is $2.5.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let g represent the cost of bowling a game and s represent the cost of renting shoes.
Bill bowled 3 games at a bowling alley and rented shoes, spending a total of $9.00
3g+s=9..(1)
Leann bowled 5 games at a the bowling alley and rented shoes, spending a total of $14.00.
5g+s=14..(2)
Subtract equation 2 from 1
3g+s-5g-s=9-14
-2g=-5
Divide both sides by 2
g=2.5
Hence, the cost to bowl a game is $2.5.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ2
Packs of dark chocolate contain 5 cookies, and packs of white chocolate cookies contain 6 cookies. If Daniel bought the same number of cookies of each the, what is the smallest number of each type he could have bought?
Answer:
30
Step-by-step explanation:
What are the distances from the point (x,y) to the focus of the parabola and the directrix, select two answers
Answer:
3,5
Step-by-step explanation:
axis
Which equation has infinitely many solutions?
5(2x + 4) = 10x – 12
5(2x + 4) = 10(x + 2)
5(2x + 4) = 12x
5(2x + 10) = 20(x + 1)
Answer:
5(2x + 4) = 10(x + 2)
Step-by-step explanation:
answer is 0 so it has infinite solutions
A number is selected, at random, from the set 1, 2, 3, 4, 5, 6, 7, 8. Find: p(odd)
25%
50%
100%
Answer:
50%
Step-by-step explanation:
Half of the numbers in the sequence are odd, so there's a 50% to have gotten an odd number randomly. Therefore, P = 50%
PLZ HELP WILL MARK BRANLIEST (No dum answers or I will delete your question - seriously don't be annoying)
Use the (x,y) coordinates in the figure to find the value of tan (2(pi)/3) or state that the expression is undefined.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answer:
A. tan(2π/3) = [tex]-\sqrt{3}[/tex]
How would I right subtract 1.9 from the product of 7.4 and 3
Answer:
24.1
Step-by-step explanation:
7.4x3=22.2
22.2+1.9=24.1
What is the radius of a cylinder with 490picm^3 of volume and 10 cm of height
hi can you help me to answer this?
Answer:
1) 85
2) 150
Step-by-step explanation:
The measure of a minor arc is EQUAL to the central angle
"The measure of a minor arc is equal to the measure of the central angle that intercepts the arc. We can also say that the measure of a minor arc is equal to the measure of the central angle that is subtended by the arc."
The graph of y = 8x + 16 is shown. Which statement is true about the function?
Answer:
A, The function has exactly one zero at x = -4
Step-by-step explanation:
As you can from the graph, the graph ONLY touches y = 0 at ONLY x = -4.
A cube has a volume of 64. What is the side length of one side
#15
Answer:
4
Step-by-step explanation:
volume is equal to a x a x a
This means that [tex]a^{3}[/tex] = V
Therefore, a = cube root of V, which is 4
HELPPPP PLEASEEE!!!!!!
Answer:
24.5
Step-by-step explanation:
please give me brainliest
1 + 1 = ? help now please asap!
Question:
1 + 1 = ? help now please asap!
Answer:
1 + 1 = 2
hope this helps :)
It cost $730 to put on a school play . How many tickets must be sold at $6 a piece in order to make a profit
Answer:
122
Step-by-step explanation:
if you do 730 divided by 6 the answer is 121.6666667 so you round it up to 122
Help with 8 pls thanks
Answer:
m<Y = 68°
Step-by-step explanation:
A tangent drawn to a circle makes a 90° angle with the radius that intersects it at the point of tangency. That means that m<X = 90°.
The sum of the measures of the angles of a triangle is 180°.
m<X + m<Y + m<Z = 180
90 + m<Y + 22 = 180
m<Y + 112 = 180
m<Y = 180 - 112
m<Y = 68
Explain how you can use proportional reasoning to determine the whole if you
know that 40 is 60% of the whole.
Which graph represents the table below?
х
-1
0
1
y
4
1
-2
I can't seem to get this one can someone please help me
Answer:
The answer should be C
Step-by-step explanation:
Answer
If 2x – 7y = 10 is a true equation, what would be the value of 2 + 2x – 7y?
Answer:
I believe that would be 12 because
Step-by-step explanation:
if 2x - 7y = 10
then if you were to add two to that it would be 12
Out of 1,200 students that attend Norman Rockwell Middle School, how many would most likely sign up for after school tutoring, if 48 out of 80 students randomly surveyed said they would like to have extra help after school?
Answer:
720
Step-by-step explanation:
Out of 80 students the no. of students who sign up=48
So, out of 1200 students 48×1200÷80=720 students sign up.
Graph the difference between (4.5, -1.5) and (4.5, 7.25)
Answer:
The difference is 8.75
Step-by-step explanation:
Plot the points or 7.25+1.5=8.75
Please help PLEASEEEEEEEEE
Answer:
15
Step-by-step explanation:
You know that it takes 3 mins for 45 sit-ups so then you wanna find how much for 1 minute. It shows 3 mins which is 3 times as much as 1 minute. There, 3/3 = 1. then you have to do it with the sit-ups too. so 45/3 = 15
How you use the Pythagorean theorem in 3D.
Answer:
If the base of the prism has dimensions x and y, and the diagonal along the base is represented by c, then x² + y² = c². The longest diagonal in the solid, s, is the hypotenuse of the triangle formed by the sides c and the height of the solid, z. So we know that, c² + z² = s².
Step-by-step explanation:
What is the area of the triangle below (in square units)?
2 mm
14 mm
Answer:
A = 14 mm²
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
Here b = 14 and h = 2 , then
A = [tex]\frac{1}{2}[/tex] × 14 × 2 = 7 × 2 = 14 mm²
