Answers
Answer:
The answer is C. [tex]\frac{\sqrt{6} + \sqrt{2} }{4}[/tex]
Step-by-step explanation:
The value of cos(15°) is (√(6) + √(2))/4.
The correct option is C.
What is half-angle formula?The half-angle formula is a trigonometric identity that relates the trigonometric functions of half of an angle to the trigonometric functions of the original angle.
Using half-angle formula for cosine
cos(x/2) = √((1 + cos(x))/2)
In this case, x = 30°, so we have:
cos(15°/2) = √((1 + cos(30°))/2)
cos(15°/2) = √((1 + √(3)/2)/2)
Now, rationalize the denominator:
cos(15°/2) = √((2 + √(3))/4)
cos(15°/2) = √((1/2 + √(3)/4))
Finally, we factor the numerator by multiplying it by (√(2) + √(6))/(√(2) + √(6)):
cos(15°/2) = (√(2) + √(6))/(2√(2))
cos(15°) = (√(2) + sqrt(6))/(2√(2))
By rationalizing the denominator further, we get:
cos(15°) = (√(2) + √(6))/(2√(2)) (√(2)/sqrt(2))
cos(15°) = (√(2)√(2) + √(6)√(2))/(2√(2)√(2))
cos(15°) = (2 + √(12))/(2 x 2)
cos(15°) = (2 + 2√(3))/(4)
cos(15°) = (√(6) + √(2))/4
Therefore, the value of cos(15°) is (√(6) + √(2))/4.
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Related Questions
PLEASE HELP NEED IN 15 MINUTES! 20 POINTS!
42^2 + 69^2 = x^2
Pythagorean Theorem Formula is a^2 + b^2 = c^2.
Answers
Answer:
ok I did it two ways and got different answers
Step-by-step explanation:
addition
42^2 +69^2= x^2
1,764 +4,761=x^2
1,764 + 4,761= 6,525
Square root of 6,525 is 80.77 or 15/29
subtracting
4,761 -1,764= 2,997
Square root of 2,997 is 54.74 or 9/37
hope one of these are right, good luck
Someone help please. Its algebra 1.
Select the equation of a line in slope-intercept form that passes through (-2,2) and is perpendicular to the graph of y= 1/2x-3.
A. y= -2x +2
B. y= -2x -2
C. y= 1/2x -2
D. y= 1/2x +2
Answers
Answer:
B
Step-by-step explanation:
the line is perpendicular to y=1/2x-3
so its gradient, m, would be -2 (m¹m²= -1)
sub the coordinates and the gradient into this equation to find the equation of line in slope intercept form
y-y¹ = m(x-x¹)
The equation of the line in slope-intercept form that passes through (-2,2) and is perpendicular to the graph of y= 1/2x-3 is; y = -2x - 2
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Where x₁ - x coordinate, y₁ - y coordinate, m - slope
Point (-2,2)
Then the equation of a line perpendicular to the graph of y= 1/2x-3.
its gradient, m, would be; -2 (m¹m²= -1)
Now Write the equation as;
y-y₁ = m(x-x₁)
y - 2= -2(x + 2)
y = -2x - 2
Hence, the equation of the line in slope-intercept form that passes through (-2,2) and is perpendicular to the graph of y= 1/2x-3 is; y = -2x - 2
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A speedboat, at full throttle, can go 65.0 miles in 1.5 hours. What is the average speed of the boat?
Answers
how many solutions does a quadratic equation that can be written as the difference of squares have?
Answers
Answer:
there are teo solutions that can be written as tge difference of square have.
There are two possible solutions for the quadratic equation that can be written as the difference of squares.
What is a quadratic equation?A quadratic equation is of the form -
y = f(x) = ax² + bx + c
Given is a quadratic equation that can be written as the difference of squares.
A quadratic equation that can be written as the difference of squares is of the form -
(x² - a²)
For the roots, we can write the equation as -
(x² - a²) = 0
x² = a²
x = ± a
Therefore, there are two possible solutions for the quadratic equation that can be written as the difference of squares.
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when y= 4x, if y= 36, what is x?
Answers
Answer:
x=9, hope I helped :P
Please answer for brainliest!
Answers
Answer:
t>28
Step-by-step explanation:
Multiply both side of inequality by 4
t>28
What is the range of the function in this table x 1 2 3 4 Y 2 4 3 2
Answers
Answer:
(2, 4, 3)
Step-by-step explanation:
Range = Y
Anyone please answer only have 3 min
Answers
Answer:
A
Step-by-step explanation:
Answer:a
Step-by-step explanation:
i need help.please help me
Answers
Answer:
1) r >-5 2) x >9
Step-by-step explanation:
The temperature in Monarch, Wisconsin, was -3° F at 6:00 a.m. The temperature rose 12 degrees in 9 hours. What was the temperature in Monarch at 3:00p.m.?
Answers
Answer:
9 degrees
Step-by-step explanation:
The temperatire was -3 and then rose by 12, -3 + 12 = 9
Tehara has read 115 pages of a 305 page book she reads 10 pages each day how many days will it take to finish
Answers
Answer:
19 days
Step-by-step explanation:
305 - 115 = 190
190 ÷ 10 = 19
Patty measured a house and its lot and made a scale drawing. In real life, the front patio is 14 meters wide. It is 2 cm wide in the drawing. 1 cm is equal to how many meters?
Answers
. Express each exponent in expanded form: StartFraction 6 times 6 times 6 times 6 times 6 times 6 times 6 Over 6 times 6 times 6 times 6 EndFraction 2. Divide common factors: StartFraction 6 times 6 times 6 times 6 times 6 times 6 times 6 Over 6 times 6 times 6 times 6 EndFraction. 4 sixes in the numerator and denominator are crossed out. What is the exponent of the simplified power?
Answers
Answer:
The exponent of the simplified power is 3
Step-by-step explanation:
Given:
6 × 6 × 6 × 6 × 6 × 6 × 6 / 6 × 6 × 6 × 6
Dividing common factors ( cancel out 4 6's in the Numerator and Denominator
= 6 × 6 × 6 / 1
= 6^3 /1
= 6^3
The exponent of the simplified power is 3
Answer:
The exponent of the simplified power is 3
Step-by-step explanation:
NEED HELP FAST
the submarine is at a depth of -166 2/7 feet when the scientists detect a signal frequency from the ocean floor. they dive farther down to a depth of -180 4/7 feet to check the signal. the net change in their depth is [] feet
Answers
Answer:
-24 2/7
Step-by-step explanation:
-180 4/7 -166 2/7
-180 -166 = -24
4/7-2/7 = 2/7
-24 2/7
Answer:
I hope this helps
Step-by-step explanation:
someone please help! I’ll give brainliest!!
Answers
PLSS HELPP
Choose the equation for the line in slope-intercept form.
A y=2x+3
B y=1/2x+3
C y=1/2x−3
D y=−1/2x−3
Answers
Answer:
C or D, they look the same
Step-by-step explanation:
1. The graph passes through (2, -4) and (6, 0). You can use the rise over run formula to find the slope, so if you were to use the line to draw a triangle it would go to the right 2 spaces and up 1. Therefore the slope is 1/2.
2. Then you just need to see where the line crosses the y-axis (the vertical line). You can see here that it crosses at (0, -3).
3. Writing it in slope-intercept form is y = mx + (or -) b. Soooooo it would be y = 1/2x -3.
I hope this helped!
M is the midpoint of CF for the points C(3, 7) and F(5, 5). Find MF.
Answers
pair that describes <2 <3
Answers
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
The angles 2 and 3 are corresponding angles. So it's choice C.
Tip: Any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal.
if you place a 37 foot ladder against the top of a 12 foot building, how many felt will the bottom of the ladder be from the bottom of the building
Answers
Answer:
Would it be 25 that’s what I got
Step-by-step explanation:
WILL GIVE 100 POINTS AFTER YOU ANSWER
What is the median of this data set: 17, 13, 18, 20, 17, 15, 12
20
17
19
16
Answers
Answer:
b
Step-by-step explanation:
A sequence can be generated by using an=an−1+9, where a1=−5 and n is a whole number greater than 1. What are the first four terms in the sequence?
A.−5, 4, 13, 22
B.9, 4, −1, −6
C.−5, −45, −405, −3645
D. 9, −45, 225, −1125
Answers
Answer:
A
Step-by-step explanation:
For the sequence, the defining formula is given as;
an = Previous term + 9
So a2 will be -5 + 9 = 4
a3 will be 4 + 9 = 13
a4 will be 13 + 9 = 22
a5 will be 22 + 9 = 31
So the sequence of numbers will be;
-5, 4 , 13 , 22 , 31
how do I do slope? i know nothing about it and i need to learn it.
Answers
Answer:
slope is easy it is rise over run.
Step-by-step explanation:
rise/run
rise means up
run means move sideways.
Answer: what do you mean by slope?
Step-by-step explanation:
the game that you have to control a ball and you have power-ups and you have to stay on platforms and you have to avoid the red rectangles?
if y =32 when x =8 find y when x =30
Answers
Answer:
y = 120
Step-by-step explanation:
If y = 32 when x = 8, then y is 4 times the number of x. If x = 30, then (4)30 = 120.
If the area of a rectangle is 6m², then the dimensions must be 2 meters by 3 meters. True or False?
Answers
Answer:
true
Step-by-step explanation:
Which sequences of transformations confirm the congruence of shape II and shape I?
a reflection of shape I across the x-axis followed by a 90° clockwise rotation about the origin
a reflection of shape I across the x-axis followed by a 90° counterclockwise rotation about the origin
a reflection of shape I across the y-axis followed by a 90° counterclockwise rotation about the origin
a reflection of shape I across the y-axis followed by a 90° clockwise rotation about the origin
a reflection of shape I across the x-axis followed by a 180° rotation about the origin
Answers
A,B,C
Step-by-step explanation:
Answer:
A, B and C
Step-by-step explanation:
Round 3,004 to the nearest whole number HELPPPP
Answers
Answer:
3,000 is your answer.
Step-by-step explanation:
3
When rounding off to the nearest whole number all you do is look at the first decimal and see if it is bigger than 5 which in this case it isn't so, the 3 stays the same and that would be your answer. If it was bigger than 5 then your whole number changes to 4.
1) What is the VERTEX of the Quadratic Graph below?*
Answers
( 0, -4 ) is the vertex of the parabola
(GIVING BRAINLIEST TO FIRST CORRECT ANSWER)
What is the equation, in slope intercept form, for the given graph?
Answers
Answer:
y=1/2x-1
Step-by-step explanation:
0,-1
2,0
0--1 si 1
2-0 is 2
1/2
3-4 what is the answer I am dumb plz helq
Answers
Answer:
Its -1. Do not call yourself dumb, though, negatives are the easiest subject
Step-by-step explanation:
James gets $6 for his weekly allowance and spends $4 of it. His brother Mike gets $7 for his weekly allowance and spends $3 of it. Their mother's birthday is in 4 weeks. If they spend the same amount each week, how much money can they save together in that time to buy her present? 2 points
Answers
Answer:
$24
Step-by-step explanation:
James
Allowance per week = $6
He spends = $4
Balance = $6 - $4 = $2
Mike
Allowance per week = $7
He spends = $3
Balance = $7 - $3 = $4
Their mother's birthday is in 4 weeks
how much money can they save together in that time to buy her present?
James savings per week × 4 weeks
= $2 × 4
= $8
Mike's savings per week × 4 weeks
= $4 × 4
= $16
Total amount James and Mike can save together = $8 + $16
= $24