Answer:
θ = 0° , 60°
Step-by-step explanation:
[tex]\cos^2\theta + \sqrt{3}\sin \theta \cos \theta = 1[/tex]
Substract both the sides from 1.[tex]=> \cos^2\theta + \sqrt{3}\sin \theta \cos \theta - 1 = 1 - 1[/tex]
[tex]=> \cos^2\theta + \sqrt{3}\sin \theta \cos \theta - 1 = 0[/tex]
Rearrange the terms in L.H.S.[tex]=> (\cos^2 \theta - 1 )+ \sqrt{3} \sin \theta \cos \theta = 0[/tex]
Replace the terms in brackets with '-sin²θ' by using the identity (sin²θ + cos²θ = 1).[tex]=> -\sin^2 \theta + \sqrt{3} \sin \theta \cos \theta = 0[/tex]
Take 'sinθ' common from the whole expression in L.H.S.[tex]=> \sin \theta(- \sin \theta + \sqrt{3}\cos \theta) = 0[/tex]
Now solve each part separately :-
1) [tex]\sin \theta = 0[/tex]
[tex]=> \theta = \sin^{-1}0 = 0[/tex]
2) [tex]-\sin \theta + \sqrt{3} \cos \theta = 0[/tex]
Divide both the sides by 'cosθ'.[tex]=> \frac{-\sin \theta + \sqrt{3}\cos \theta }{\cos \theta} = \frac{0}{\cos \theta}[/tex]
[tex]=> \frac{-sin \theta}{\cos \theta} + \frac{\sqrt{3} \cos \theta}{\cos \theta} = 0[/tex]
[tex]=> -\tan \theta + \sqrt{3} = 0[/tex]
Add both the sides with 'tanθ'.[tex]=> -\tan \theta + \sqrt{3} + \tan \theta = 0 + \tan \theta[/tex]
[tex]=> \tan \theta = \sqrt{3}[/tex]
[tex]=> \theta = \tan^{-1}\sqrt{3} = 60[/tex]
∴ θ = 0° , 60°
Answer:
Solution given:
[tex] \large{ {cos}^{2} \theta + \sqrt{3} sin \theta cos \theta = 1}[/tex]
[tex] 1-sin^{2} \theta+\sqrt{3} sin \theta cos \theta = 1[/tex]
[tex] 1-1 +sin^{2}\theta=\sqrt{3} sin \theta cos \theta = 1[/tex]
[tex] Sin\theta(sin\theta -\sqrt{3}cos\theta)[/tex]
Either
[tex] sin\theta=\sqrt{3} cos \theta [/tex]
[tex] \sqrt{sin\theta}{cos \theta}=\sqrt{3} [/tex]
[tex] Tan \theta =\sqrt{3}[/tex]
[tex] Tan \theta =Tan 60,Tan(180+60),Tan (360+60)[/tex]
[tex] \theta =60°,240°,420°[/tex]
in terms of π is
[tex] \theta =⅓π,\frac{4}{3}π,[/tex]
Or
[tex] Sin\theta=1[/tex]
[tex]Sin\theta=Sin0° ,Sin180°[/tex]
In terms of π is
[tex]\theta=0π,π[/tex]
so
[tex]\theta=0π,⅓π,π,\frac{4}{3}π,[/tex]
Someone please help me thank you
5x5
Answer:
25
Step-by-step explanation:
please help!! 40 points. if you guess or just comment to take my points i will make sure your account gets banned. thanks! i want a small simple explanation.
5) m<EBF= 474
6)m<ABC= 70
5) 20x-10= x+390
5) 20x-10 3x+15+60=474
20x-10=390
3x+15= 24
plug in the x into the equation: (x+20)---> (20x20)=400
400-10= 390
6) 3x+1+2x+14= 28
3x= 9
2x=4
plug in the x into the equation: (3x+1)----> 2x+14= 28
7 is a bit confusing...
8 G and F is confusing me sorry...
this was so fu-cking hard sorry it took long...
14. Jerry charges a fee of $45 plus $15 per hour to rent a motorbike. Write an equation to
calculate rental cost and tell what x and y mean. If you have $120 to spend, how long can you rent
for?
Answer:
5 hours, y= how much money it will cost, and x represents how many hours
Step-by-step explanation:
y= 15x+45
120= 15x+45
-45 -45
75= 15x
75/15×= 5 hours
A line passes through the points (3, –1) and (5, 4). What is the slope of the line?
Answer:
D) 5/2
Step-by-step explanation:
(3, –1) and (5, 4)
Slope:
m=(y2-y1)/(x2-x1)
m=(4 + 1)/(5 - 3)
m= 5/2
Answer:
5/2
Step-by-step explanation:
To find the slope, we can use the slope formula
m= (y2-y1)/(x2-x1)
= (4 - -1)/(5 - 3)
= (4+1)/(5-3)
= 5/2
Solve for k.
8(10 - k) = 2k
answer: k=8
Answer:
k=8
explaining the answer
80 - 8K = 2K
A pyramid with a slant height 4.6 in whose triangular base measures 8 in on each side.Each altitude of the base measures of 6.9 in
Answer:
82.8 in²
Step-by-step explanation:
The surface area a triangular based pyramid :
Base area + 1/2(perimeter * slant height)
Base = 8 inches ; Slant height = 4.6 inches ; altitude of base measure = 6.9 inches
Base area of triangle :
1/2 * base * height
1/2 * 8 * 6.9
4 * 6.9
Base area = 27.6 in²
The perimeter, P = sum of sides ; (s1 + s2 + s3
P = 8 + 8 + 8 = 24 in
Hence,
Surface area = 27.6 in² + 1/2(24*4.6)
Surface area = 27.6 in² + (12 * 4.6) in²
Surface area = (27.6 + 55.2)
Surface area = 82.8 in²
.Answer only the second question and show steps
Answer:
Step-by-step explanation:
Perimeter is found by adding all the sides of a figure together. We have 2 lengths that are 10.5 long, and 2 widths that are 8.75 wide. Adding these together:
10.5 + 10.5 + 8.75 + 8.75 = 38.5 cm
this answer for # 2 question
Question 21 of 25
Which of the following is the coefficient in the algebraic expression 12x+ 24?
O A. 4
O B. x
C. 12
D. Z
SUBMIT
Answer:
12
Step-by-step explanation:
Coefficient is the number before the variable
Look at the graph below.
Which point can you add to the graph to make this graph NOT A
FUNCTION?
(2,6)
(5.3)
(7.5)
(8,8)
Answer:
B. (5, 3)Step-by-step explanation:
Given points:
(3, 5), (5, 8), (9, 7)The graph should have a same x-value with a different y-value.
From the list we have only point (5, 3) which makes this a non-functional relationship.
Correct choice is B
Points here are
(3,5)(5,8)(9,7)As per definition of function
Every domain has a unique rangeCheck option B
If we put than
The. f(5) would have 2 values 8 and 3
Which won't be a function
HELP!! An apartment building is infested with 6.2 x 10^3 rats. on average each of these rats produces 5.5 x 10^1 offspring each year. assuming no rats leave or die, how many additional rats will live in this building one year from now? write your answer in standard form.
The additional rats will live in this building one year from now is 3.41 x 10^5.
What is the additional number of rats?Standard form is used in expressing large numbers in smaller numbers. In order to write a number in standard form, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.
(6.2 x 10^3) x ( 5.5 x 10^1) = 34.10 x 10^4
= 3.41 x 10^5
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The most Brendan can afford to pay per year in mortgage payments is $10,500, and his credit score is currently 544. According to the following table for a $150,000 mortgage, by how many points would he need to improve his credit score in order to take a mortgage for $150,000? FICO Interest Monthly Score Rate Payment 720-850 700-719 675-699 620-674 560-619 500-559 5.59% 5.71% 6.25% 7.40% 8.53% 9.29% $860 $872 $924 $1039 $1157 $1238 O A. 16 points B. 156 points C. 76 points D. 131 points
Answer:
B. 156
Step-by-step explanation:
Brendan would need to improve his credit score by 75 points to qualify for a $150,000 mortgage with a monthly payment of $875 or less.
We have,
To determine Brendan's interest rate and monthly payment for a $150,000 mortgage, we need to find which range his FICO score falls in.
From the table, we see that his score of 544 falls in the range of 500-559, which corresponds to an interest rate of 9.29% and a monthly payment of $1238.
Next, we can use the mortgage payment of $10,500 per year to determine the maximum monthly payment Brendan can afford.
i.e
$10,500 per year / 12 months
= $875 per month
Since this amount is less than the monthly payment for the 500-559 FICO score range, Brendan would need to improve his credit score to qualify for a $150,000 mortgage.
To determine how many points he needs to improve, we can look at the next lowest interest rate and payment in the table, which corresponds to a FICO score range of 560-619.
The monthly payment for this range is $1157, which is below Brendan's maximum payment of $875.
So, he needs to improve his credit score to fall into this range.
To determine how many points he needs to improve,
we can subtract the minimum FICO score in the 560-619 range (560) from his current FICO score (544), and then add that difference to the maximum FICO score in the 560-619 range (619).
i.e
(619 - 560) + (560 - 544)
= 59 + 16
= 75
Therefore,
Brendan would need to improve his credit score by 75 points to qualify for a $150,000 mortgage with a monthly payment of $875 or less.
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A rectangular prism has a length of 5 cm, a width of 2. 25 cm, and a height of 0.5 cm.
What is the surface area of the rectangular prism?
A. 5.625 cm2
B. 7.25 cm2
O C. 14.875 cm
D. 29.75 cm?
D. 29.75 is Right answer...
I hope you understand....
which expression is equivalent to 5+5t+3t+?
Answer:
10t+3
Step-by-step explanation:
Answer:
10t+3
Step-by-step explanation:
Simple math! Please help!!!!
[tex] c.\:{x}^{ - 4} [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] \frac{7 {x}^{4} }{7 {x}^{8} } \\ = \frac{ {x}^{4} }{ {x}^{8} } \\ = {x}^{4 - 8} \\ = {x}^{ - 4} [/tex]
Note:-
[tex] {x}^{m} \times {x}^{n} = {x}^{m + n} \\ {x}^{m} \div {x}^{n} = {x}^{m - n} [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]
Select the correct solution set.
-7x ≥ 56
{x | x ≥ -8}
{x | x ≤ -8}
{x | x ≥ 8}
Answer:
{x | x ≤ -8}
Step-by-step explanation:
-7x ≥ 56
Divide each side by -7, remembering to flip the inequality since we are dividing by a negative
-7x/-7 ≤ 56/-7
x ≤ -8
I need help like big time! PLEASE I NEED THIS ANSWERED!!
Answer:
x = 94
Step-by-step explanation:
[tex]x + (\frac{1}{2}x + 39) = 180[/tex]
1.5x + 39 = 180
Subtract 39 from each side.
1.5x + 39 - 39 = 180 - 39
Simplify.
1.5x = 141
Divide each side by 1.5.
1.5x ÷ 1.5 = 141 ÷ 1.5
x = 94
Use the picture to find each of the following: HELPPP
BE
What is the rate of change of the function represented by the table?
Х
1
у
5
2
5
3
5
4
5
1
оооо
5
description of turning effects
Answer:
The turning effect of a force is known as the moment. It is the product of the force multiplied by the perpendicular distance from the line of action of the force to the pivot or point where the object will turn.
Please help!!!! Giving brainliest and extra points!!!! (Click on the photo)
Answer:
i dont understand the question much cuz its only told berries so i think is both rasberry and strawberry
Step-by-step explanation:
if so here my solve: Both berries are 38% of the graph, we have equation 38%×290 = 110,2
hmmmm maybe the ans is D. 110
There are 8 different actors auditioning for the roles of Larry, Curly and Moe. How many ways could the roles be cast? Best answer get Brainliest.
Which statement best describe the diagonals of a rhombus?
A) Is a parallelogram with congruent diagonals
B) Is a parallelogram with diagonals that bisects a pair of opposite angles and the diagonals are perpendicular
C) Is a parallelogram with the diagonals that intersect but does not form 90 degree
D) Is a parallelogram with diagonals that are congruent and perpendicular
Answer:
Is a parallelogram with congruent diag............ option is best describing better
The statement which best describes the diagonals of a rhombus is B. Is a parallelogram with diagonals that bisects a pair of opposite angles and the diagonals are perpendicular.
What is Rhombus?A rhombus is a two dimensional shape which consists of four equal sides with opposite side being parallel and opposite angles being equal.
So, rhombus is a parallelogram with all sides being equal.
The diagonals of a rhombus are not of equal length, so they are not congruent.
Also, the two diagonals of a rhombus cuts each other in to two equal halves and the intersecting angle is 90 degrees.
This means that the diagonals of a rhombus are perpendicular bisectors of each other.
Also, the diagonals bisect the pair of opposite angles through which the line passes.
Hence the correct option is B. Is a parallelogram with diagonals that bisects a pair of opposite angles and the diagonals are perpendicular.
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Graph the function.
f(x)=4⋅(3/2)^x
Answer:
Graph the function.
Step-by-step explanation:
Ravi solved this question. His teacher told him he made a mistake. Can you helphim to get the correct step ? 56–(–73) = 56 + __________
Answer:
56+73
Step-by-step explanation:
Help ASAP. With lots of points will give brainiest!
I only need help explaining and showing the steps
STRUCTURE Tell whether the triangles are similar.
Answer:
yes it's similar triangle because it has same shape but size is not equal
Someone please help me out!!
Answer:
D 3/4
Step-by-step explanation:
imagine a circle with its center in point A and going through point C.
the radius of that circle is 50 (AC).
remember, tan of an angle is sin/cos of that angle.
now rotate in our imagination that triangle to the right around point A, so that the side AB becomes the bottom base line.
now you see that 30 = sin(A)×radius = sin(A)×50
and 40 = cos(A)×radius = cos(A)×50
so, tan(A) = (sin(A)×50)/(cos(A)×50) = sin(A)/cos(A) = 30/40
= 3/4
Which equation best describes the situation below?
5 less than a number is 15.
Let the number is X
So the equation will be X-5 = 15
Ninas car exponentially depreciate at a rate of 8% per year. If Nina bought the car when it was 6 years old for 12,045 , what was the original price
Answer: $19,864.60
Step-by-step explanation:
The future value formula could have been used to find the price in the 6th year. As we now know the price, the formula can now be used to find the original price.
Price at 6th year = Original price * ( 1 + rate) ^ number of years
12,045 = Og * ( 1 - 8%) ⁶
12,045 = Og * 0.606355001344
Og = 12,045 / 0.606355001344
Og = $19,864.60
Rate is subtracted because price was reducing.
49 divided by what gives you 7
Answer:
49 ÷ 7 = 7
Step-by-step explanation:
49 ÷ y = 7
7 = 49 ÷ y
7 · y = 49 ÷ y · y
7y = 49
7y ÷ 7 = 49 ÷ 7
y = 7
Jessica's family took a 7-hour-and-27-minute trip on a train. They left at 7:00 a.m.
What time did Jessica's family arrive?