Answer:
2.5 mm
Step-by-step explanation:
Help, Help, Please
[tex] \sf find \: the \: value \: of \: \theta \: when \: \theta \: is \: acute\: angle[/tex]
[tex] \sf \cos^{2}(\theta) - \sin^{2}(\theta) =2-5 \cos(\theta) [/tex]
[tex]\text{note:explanation is a must}[/tex]
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]Given the equation of the line -6x + 2y = 10
Answer:
x= 1 /3 y+ −5 /3
y=3x+5
Step-by-step explanation:
brainliest?
Answer:
Give my man brainliest
Step-by-step explanation:
Don't report this
Question 16
What is the slope of a line passing through (2, 2) and (3,5)?
5 because of slope equation
17. Write an equation in slope-intercept form for the line perpendicular to y = 3x - 9 that passes through the point (9,-9). Explain how you got your answer.
Answer:
y=-1/3x-6
Step-by-step explanation:
Perpendicular lines have slopes that are negative and reciprocal; if you multiply them together, the result is -1
so, to find the slope of the new line:
3m=-1
divide by 3
m=-1/3
the slope of the new line is -1/3
Slope-intercept form is written as y=mx+b, where m is the slope and b is the y intercept.
Here's our equation so far:
y=-1/3x+b
since the line passes through the point (9,-9), we can use it to solve for b
substitute into the equation:
-9=-1/3(9)+b
-9=-3+b
-6=b
b is -6
here's our equation
y=-1/3x-6
hope this helps! :D
What is the measure of angle 1?
VX
920
2
0869
0889
o 90°
92
Mark this and retum
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HELP PLEASE!! need this asap.
y = 4x + 3
y = -x - 2
Answer:pls check out the image. The answer is in the image ans hope this helps and can u give me brainliest
Step-by-step explanation:
please help asap.1-5.
help me really plz!!!
Answer:
I have made it in above picture
Triangle JKL is shown below.
K
24
L
28
Which equation should be used to find the
length of JK?
Amanda slept for 1/3 of the day. She played with her friends for 1/5 of the day. She spent the rest of the day working on a school project. What fraction of the day did she spend working on her project
Answer:
Amanda spent 7/15 of the day working on her project.
Step-by-step explanation:
1/3 x 5/5 = 5/15 1/5 x 3/3 = 3/15 5/15 + 3/15 = 8/15 15/15 - 8/15 = 7/15Between which two points can you draw a line with a negative slope? Pls answer quick
Answer:
Between A and C.
Step-by-step explanation:
A negative slope rises to the left (\).
Answer:
a line between a and c
Step-by-step explanation:
if you were to draw a line between point a and point c the slope would be [tex]-\frac{3}{4}[/tex]
PLISS ANSWER :C DONT ANSWER IF YDK THAnKSSS
*also pls look at both images :)*
Answer:
First image: (6, -1)
2nd image: y = 63
Explanation:
1)
2x + y = 11
1/2x - 5y = 8
y = -2x + 11
1/2x - 5(-2x + 11) = 8
1/2x + 10x - 55 = 8
10.5x - 55 = 8
10.5x = 63
x = 6
2x + y = 11
2(6) + y = 11
12 + y = 11
y = -1
(x , y) = (6, -1)
2)
1/4(8y - 4.8) = 2 (0.9y + 5.4) + 3/5
2y - 1.2 = 1.8y + 10.8 + 0.6
0.2y - 1.2 = 11.4
0.2y = 12.6
y = 63
What does S in Math means?
Step-by-step explanation:
subtract
i think this
write an equation of the line that passes through the given points (3,1) (0,10)
Answer:
y = -3x + 10
Step-by-step explanation:
10-1/0-3 = -3
y = -3x + b
1 = -3(3) + b
1 = -9 + b
10 = b
check your answer:
10 = -3(0) + 10
10 = 10
b should be 10
write a unit rate for 25 pounds in 10 weeks
Step-by-step explanation:
Answer:
= 2.5 Pounds per Week
Showing Work
This is a fraction equal to
25 Pounds ÷ 10 Weeks
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 10
25 Pounds ÷ 10
10 Weeks ÷ 10
=
2.5 Pounds÷1 Week
=
2.5 Pounds
__________
Week
= 2.5 Pounds per Week
Please hurry this is 7th grade hon
Answer:
1. place the circle on -1
2. open circle
3. Left
Step-by-step explanation:
A box of 500 envelopes costs $14.89. Before buying, Mr. Ruiz wants to know the price for one envelope. His son Alan quickly makes a calculation and says, "You can buy almost 34 envelopes for $1.00." Here is Alan's work. 500 500 +14.89 33.6 $14.89 $ 14.89 +14.89 $1.00 Mr. Ruiz thanked his son, but said that was not the answer he was looking for. What is the cost for one envelope to the nearest whole number in cents?
PLEASE HELP ME DON'T ANSWER IF YOUR NOT SURE!!
Answer: https://brainly.com/question/22661875?answering=true&answeringSource=feedPublic%2FhomePage%2F10
Step-by-step explanation: hope this helps
Find the smallest value of m such that the LCM of m and 34 is 374.
Answer:
11
first you use a number tree
34 374
/\ /\
2 17 2 187
/\
11 17
express the numbers in prime factors
374=2×11×17
34 =2×17
in finding LCM you use the highest prime factors in this case the highest prime factors are 2, 11 and 17
So m factors are 2 and 11
which means m is 2×11=22
22 in its smallest form is 11
What is the volume of the rectangular prism?
Question 8 options:
738 ft3
272 ft3
1296 ft3
34 ft3
Answer:
The volume is Lenght * width * Height
16 * 9 * 9 = 1296 ft cube
Justin went out to lunch. His bill was $3.18. If he gave the waitress $10.00, how much change should he receive? A. $7.82 B. $5.82 C. $6.82 D.
what is the exact value of cos5pie/12
Answer:
Exact Form: −e12
Decimal Form: −0.22652348…
Step-by-step explanation:
james bought an ipad for $450 his friends carl buys the same one for 12% off how much did carl pay
Answer:
$365.99
Step-by-step explanation:
$450 - 12% = $365.99
Order the following numbers from least to greatest : 2.67 5.28 1.73 4.92 2.56
Answer:
is this helpful i hope it is
There are 12 girls at a slumber party. 2/3 of the girls brought a sleeping bag. How many girls brought a sleeping bag?
Answer:
8 girlies
Step-by-step explanation:
12/3=4
4x2=8
Answer:
8
Step-by-step explanation:
since there are 12 girls we have an x amount of girls who brought sleeping bags and 12-x for those who didn't. so
x/12=2/3
multiply both sides by 12
(x/12)12=(2/3)12
x=8
Hope that helps :)
someone help please ⠀
⠀
⠀
⠀
⠀
⠀
Answer:
3/5 = 0.6 = 60%
16/25 = 0.64 = 64%
11/20 = 0.55 = 55%
4/25 = 0.16 = 16%
17/100 = 0.17 = 17%
7/20 = 0.35 = 35%
Plz, answer this question plz!
Answer:
the second option im pretty sure
Answer:
4/48. I don't know for sure, but I think B is the correct answer
PLZ HELP ME :( you can pick neither or both or one of the triangles in the screenshot
pls help! ill give brainless to the best answer !!
what is 25% of 75? show your work.
Answer:
18.75
Step-by-step explanation:
25% of 75 =
0.25 x 75 =
18.75
Hope that helps!
Answer:
18.75
Step-by-step explanation: I don't really know what work to show it was all mental
a=960 rounded to the nearest 10
b=89.0 rounded to 1 DP
Find the minimum (to 2 DP) of a÷b
Step-by-step explanation:
a÷b=960÷89=10.78651685=10.79 or 17.8
a car accelerates from 25 km/hr to 55 km/hr in 30 seconds. what is its accelerates ?
Here's link to the answer:
tinyurl.com/wpazsebu
