Step-by-step explanation:
(cos(3A) − sin(3A)) / (1 − 2 sin(2A))
Use double angle formula:
(cos(3A) − sin(3A)) / (1 − 4 sin A cos A)
Use triple angle formulas:
(4 cos³A − 3 cos A − 3 sin A + 4 sin³A) / (1 − 4 sin A cos A)
Group and factor:
(4 (cos³A + sin³A) − 3 (cos A + sin A)) / (1 − 4 sin A cos A)
Factor the sum of cubes:
(4 (cos A + sin A) (cos²A − cos A sin A + sin²A) − 3 (cos A + sin A)) / (1 − 4 sin A cos A)
Use Pythagorean identity:
(4 (cos A + sin A) (1 − cos A sin A) − 3 (cos A + sin A)) / (1 − 4 sin A cos A)
Factor out cos A + sin A:
(cos A + sin A) (4 (1 − cos A sin A) − 3) / (1 − 4 sin A cos A)
Simplify:
(cos A + sin A) (4 − 4 cos A sin A − 3) / (1 − 4 sin A cos A)
(cos A + sin A) (1 − 4 cos A sin A) / (1 − 4 sin A cos A)
cos A + sin A
Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the die will be 6?
Answer:
6/36 (16.667%)
Step-by-step explanation:
Answer:
5/36
Step-by-step explanation:
Which graph represents the function p(x) = |x – 1|?
Answer:
it is this graph
Step-by-step explanation:
it is this graph
Answer:
B
Step-by-step explanation:
please help me i will mark brainliest
Answer:
see below
Step-by-step explanation:
The cube of something to the 1/3 power is the original something. The cube of a cube root of something is the original something. Since the cube of a cube root is the same as the cube of a 1/3 power, the 1/3 power is equivalent to the cube root.
The applicable rules of exponents are ...
(a^b)^c = a^(bc)
What are two lines that lie within the same plane and never intersect.
Answer:
Step-by-step explanation:
Parallel lines
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 6.3kg : 4.5kg
Answer:
63/10 : 9/2
Step-by-step explanation:
6.3 is 6 and 3/10
we can turn that into an improper fraction so its 63/10
4.5 is 4 and 1/2
we can turn this into an improper fraction with is 9/2
so now its 63/10 : 9/2 as a ratio
Hope this helps. Good luck.
[tex] \frac{ \frac{19}{3}kg }{ \frac{9}{2}kg } [/tex]
5/8 dived by 3/5
Help please
Answer:
5/6
Step-by-step explanation:
you must flip 3 over 5 and multiply
Which two complex numbers when added together and written in standard form equal 10-3i?
Answer:
A -3 − 4i C 13 + i
Step-by-step explanation:
We add the real part and the imaginary part separately.
Adding A and C will give us 10 - 3i:
-3 - 4i + 13 + i
= -3 + 13 - 4i + i
= 10 - 3i.
What is the value of m in the equation one-half m minus three-fourths n equals 16, when n equals 8? 20 32 44 48
Answer:
the answer is c: 44
hope it helps
:)
The value of m in the equation one-half m minus three-fourths n equals 16, when n equals 8 is 44.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
The equation form;
1/2m - 3/ 4n = 16
Substituting the value of n in the equation, we have;
½m - ¾n = 16
½m - (¾×8) = 16
½m - 6 = 16
½m = 16 + 6
½m = 22
m = 44
Hence, The value of m in the equation one-half m minus three-fourths n equals 16, when n equals 8 is 44.
Learn more about linear equations;
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Conjecture: How many solutions do x3 - 5x2 + 28 = 0 have? Find the real solution(s) of the equation. Then use polynomial long division to find the other solution(s).
Answer:
x = - 2 is confirmed to be the real solution of the equation.
Step-by-step explanation:
We are tasked with the following activities
Conjecture: How many solutions do [tex]x^3 - 5x^2 + 28 = 0[/tex] have?
Find the real solution(s) of the equation.
Then use polynomial long division to find the other solution(s).
To start with the how many solutions that [tex]x^3 - 5x^2 + 28 = 0[/tex] have
suppose that -2 happens to be a root of the equation, we can easily replace x = - 2 in the given equation. Then , we will have :
[tex](-2)^3 - 5(-2)^2 + 28 = 0[/tex]
[tex]-8 - 5\times 4 + 28 = 0[/tex]
-8 - 20 + 28 = 0
-28 - 28 = 0
0 = 0
The equation resulted to 0 = 0 when x = -2 , as such -2 happens to be one root of the equation
So , as x = - 2
x + 2 = 0
x = - 2 is confirmed to be the real solution of the equation.
A picture showing the polynomial long division method used for solving the polynomial equation and other solution(s) can be found in the attached file below.
Is (5,2) a solution of the graphed system of inequalities
Answer:
yes
Step-by-step explanation:
Use the confidence interval to find the estimated margin of error. Then find the sample mean. A biologist reports a confidence interval of when estimating the mean height (in centimeters) of a sample of seedlings. The estimated margin of error is nothing. The sample mean is nothing.
Complete Question
A biologist reports a confidence interval of (3.5,4.9) when estimating the mean height (in centimeters) of a sample of seedlings. What is the estimated margin of error and the sample mean?
Answer:
The margin of error is [tex]E = 0.7[/tex]
The sample mean is [tex]\= x = 4.2[/tex]
Step-by-step explanation:
from the question we are told that
The upper limit is [tex]k = 4.9[/tex]
The lower limit is [tex]r = 3.5[/tex]
Generally the margin of error is mathematically represented as
[tex]E = \frac{k - r}{ 2}[/tex]
[tex]E = \frac{ 4.9 - 3.5 }{2}[/tex]
[tex]E = 0.7[/tex]
Generally the sample mean is mathematically evaluated as
[tex]\= x = k - E[/tex]
=> [tex]\= x = 4.9 - 0.7[/tex]
=> [tex]\= x = 4.2[/tex]
Use the given confidence interval limits to find the point estimate and the margin of error E.
0.475
Answer:
The point estimate = 0.507
Margin error of a given confidence interval = 0.032
Step-by-step explanation:
The point estimate is calculated by using the sample statistics of a population.
Thus; point estimate can be expressed with the formula:
[tex]\overline x = \dfrac{\sum \limits ^n _{i=1} \ x _i}{n}[/tex]
Given that : 0.475 < p < 0.539
[tex]\overline x = \dfrac{0.475+0.539}{2}[/tex]
[tex]\overline x = \dfrac{1.014}{2}[/tex]
[tex]\overline x = 0.507[/tex]
The point estimate = 0.507
The margin of error which shows the percentage of points that the derived results would differ from that of the given population value can be calculated with the formula:
Margin error of a given confidence interval = [tex]\mathtt{\dfrac{upper \ confidence \ limit - lower \ confidence \ limit }{2}}[/tex]
Margin error of a given confidence interval = [tex]\dfrac{0.539-0.475}{2}[/tex]
Margin error of a given confidence interval = [tex]\dfrac{0.064}{2}[/tex]
Margin error of a given confidence interval = [tex]0.032[/tex]
DESPERATE! Please answer any of the questions :(( And explain bc im super confused
Answer:
Step-by-step explanation:
4. when bases are equal ,powers are also equal.
x+4=3x-1
3x-x=4+1
2x=5
x=5/2=2.5
Which of the following could be a rational number? Group of answer choices the sum of a rational number and an irrational number the product of a rational number and an irrational number the product of two irrational numbers the sum of two irrational numbers
Answer:
Is the number rational or irrational?
30‾‾‾√
rational
irrational
Step-by-step explanation: help ;-;
Option (3) the product of two irrational numbers is a rational number is a correct option.
What is a rational number?"Rational numbers are numbers that can be expressed as a fraction or part of a whole number. It includes the integers, plus all fractions, or terminating decimals and repeating decimals".
What is an irrational number?"Irrational numbers are numbers that cannot be expressed as a fraction or ratio of two integers".
For the given situation,
We need to analyze the all options.
Option 1:
The sum of a rational number and an irrational number is an irrational number.
Option 2:
The product of a rational number and an irrational number is an irrational number.
Option 3:
The product of two irrational numbers is a rational or an irrational number based on the numbers taken.
Option 4:
The sum of two irrational numbers is an irrational number.
Hence we can conclude option(3), the product of two irrational numbers is a rational number is a correct option.
Learn more about rational numbers here
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Please help...............
Answer:
C' ( -10 , 4)
D' (-10 , 6)
E' (-8 , 6)
F' (-8 , 4)
Find the value of z.
Answer:
C. [tex] z = 82 [/tex]
Step-by-step explanation:
To find z, find x first:
[tex] 105 = \frac{1}{2}(x + 120) [/tex] (angle of intersecting chord theorem)
Solve for x
[tex] 105*2 = \frac{1}{2}(x + 120)*2 [/tex]
[tex] 210 = x + 120 [/tex]
[tex] 210 - 120 = x + 120 - 120 [/tex]
[tex] 90 = x [/tex]
[tex] x = 90 [/tex]
Find z:
Full circle = 360°
Therefore,
[tex] x + z + 68 + 120 = 360 [/tex]
[tex] 90 + z + 68 + 120 = 360 [/tex]
[tex] z + 278 = 360 [/tex]
[tex] z + 278 - 278 = 360 - 278 [/tex]
[tex] z = 82 [/tex]
how many ways are there to select 12 countries in the United Nations to serve on a council if 3 are selected from a block of 45 , 4 are selected from a block of 57 and the others are selected form the remaining 69 countries
Answer:
The value is [tex]Z = 6.299*10^{16} \ ways[/tex]
Step-by-step explanation:
From the question we are told that
The number of countries is n = 12
Generally the number of way of selecting 3 from a block of 45
[tex]\left 45} \atop {}} \right.C _3 = \frac{ 45! }{ (45-3) ! 3!}[/tex]
[tex]\left 45} \atop {}} \right.C _3 = 14190[/tex]
Generally the number of way of selecting 4 from a block of 57
[tex]\left 57} \atop {}} \right.C _3 = \frac{ 57! }{ (57-4) ! 4!}[/tex]
[tex]\left 57} \atop {}} \right.C _3 = 395010[/tex]
Generally the number of way of selecting (12 - (4 + 3) = 5) from a block of 69
[tex]\left 69} \atop {}} \right.C _5 = \frac{ 69! }{ (69-5) ! 5!}[/tex]
[tex]\left 69} \atop {}} \right.C _3 = 11238513[/tex]
The ways of selecting 12 countries in the United Nations serve on a council is mathematically represented as
[tex]Z = 14190 * 395010* 11238513[/tex]
[tex]Z = 6.299*10^{16} \ ways[/tex]
In a two digit number, the tens digit is twice the ones digit.The difference of the ones digit and half the tens digit is 0
Answer:
C: infinitely many solutions
Step-by-step explanation:
write an equation in point-slope form for the line through the given point with the given slope (10,-9);m=-2
Answer:
The answer is
[tex]y + 9 = - 2(x - 10)[/tex]Step-by-step explanation:
To find the equation of a line given a point and slope we use the formula
y - y1 = m(x - x1)where
m is the slope
( x1 , y1) is the point
From the question
Slope / m = - 2
The point is ( 10, - 9)
Substitute the values into the above formula
That's the final answer is
[tex]y + 9 = - 2(x - 10) [/tex]Hope this helps you
Which symbols could be used to make the folllowing statement true -15 -19
Answer:
-15 > -19
Step-by-step explanation:
-15 > -19
-15 is closer to 0 than -19 so it is greater than
find the measure of angle C in the parallelogram. Round your answer to the nearest degree
Answer:
75°
Step-by-step explanation:
In a parallelogram, any two adjacent angles are supplementary. In other words, they total 180.
Angle D and Angle E are adjacent. Thus, they are supplementary. In other words:
[tex]\angle D +\angle E =180[/tex]
Substitute them for the equations:
[tex]7x+21+15+5x=180[/tex]
Combine like terms and add on the left:
[tex]12x+36=180[/tex]
Subtract 36 from both sides:
[tex]12x=144[/tex]
Divide both sides by 12:
[tex]x=12[/tex]
Thus, the value of x is 12.
Note that Angle D and Angle C are also adjacent. Thus, their angles also equal 180.
So:
[tex]\angle D+\angle C =180[/tex]
Substitute the equation for D:
[tex]7x+21+\angle C=180[/tex]
Plug in 12 for x:
[tex]7(12)+21+\angle C =180[/tex]
Simplify:
[tex]84+21+\angle C =180\\105+\angle C =180[/tex]
Subtract 105 from both sides:
[tex]\angle C =75\textdegree[/tex]
Thus, Angle C is 75 degrees.
Sean and Hannah are 540 inches apart and begin walking towards each other. Sean walks 2.6 times as fast as Hannah. Let x represent the distance Hannah has walked (in inches) and y represent the distance (in inches) between Hannah and Sean.
Answer:
Distance covered by Sean
= 540-x-y inches
Distance covered by Hannah =x
Step-by-step explanation:
Sean and Hannah are 540 inches apart and begin walking towards each other. Sean walks 2.6 times as fast as Hannah
Distance covered by Hannah =x
Distance between sean and Hannah= y
Distance covered by Sean= 540-x-y
Sean speed= (540-x-y)/t
Hannah speed= x/t
(540-x-y)/t /(x/t )= 2.6
(540-x-y)/x = 2.6
(540-x-y)= 2.6x
540 = 3.6x +y ...
Write all the steps plzzzzzz
Answer:
Step-by-step explanation:
See attachment
Several books are placed on a table. These books have a combined weight of 25 N and cover an area of 0.05 m2. How much pressure do the books exert on the table? The pressure the books apply to the table top is __ Pa. please need help!!
Answer:
500 pa
Step-by-step explanation:
[tex]Force = 25N\\Area = 0.05m^2\\\\Pressure = \frac{Force}{Area}\\ \\Pressure = \frac{25}{0.05}\\\\ Pressure = 500 Pascals[/tex]
48+4^2+3/5
Help me it asks to evaluate
Answer:
325/3
Step-by-step explanation:
[tex]48+4^2+\frac{3}{5}\\\\\mathrm{Convert\:element\:to\:fraction}:\quad \:48=\frac{48\cdot \:5}{5}\\\\=\frac{48\cdot \:5}{5}+\frac{3}{5}\\\\\mathrm{Since\:the\:denominators\:are\:equal,\\\\\:combine\:the\:fractions}:\\\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\=\frac{48\cdot \:5+3}{5}\\\\48\cdot \:5+3=243\\\\=4^2+\frac{243}{5}\\\\=16+\frac{243}{5}\\\\=\frac{16\cdot \:5}{5}+\frac{243}{5}\\\\=\frac{16\cdot \:5+243}{5}\\\\16\cdot \:5+243=323\\\\=\frac{323}{5}[/tex]
Find the length of UW(with a line over it) if W is between U and V, UV = 16.8 centimeters, and VW = 7.9 centimeters.
Please explain as well.
Answer:
8.9 is the answer i just took the test
Simplify the expression. : 5 + 4 x (8 - 6) square
Answer:
8x+5
Step-by-step explanation:
8-6=2
2× 4x= 8x
8x+5
Answer:
[tex] \boxed{ \huge{ \bold{ \sf{ \boxed{21}}}}}[/tex]Step-by-step explanation:
Use PEMDAS rule :
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
Let's solve :
[tex] \sf{5 + 4 \times {(8 - 6)}^{2} }[/tex]
⇒[tex] \sf{5 + 4 \times {2}^{2} }[/tex]
⇒[tex] \sf{5 + 4 \times 4}[/tex]
⇒[tex] \sf{5 + 16}[/tex]
⇒[tex] \sf{21}[/tex]
Hope I helped!
Best regards!
M^2 = 0.04 how do you solve this
Answer:
[tex]m = 0.2[/tex]
Step-by-step explanation:
To solve this equation we're basically trying to isolate m on one side.
The equation is [tex]m^2=0.04[/tex].
If we want to make it [tex]m=x[/tex], we have to find the square root of both sides, as the square root of something squared is just that something.
[tex]\sqrt{m^2} = \sqrt{0.04}[/tex]
To find the square root of 0.04, we need to think "what number multiplied by itself get us 0.04?"
This number is 0.2.
So:
[tex]m = 0.2[/tex]
Hope this helped!
Will mark brainliest
Will mark the brainliest!!!!
Answer:
options a is correct
4/7 likely
Probability = Favourable outcomes/ Total outcomes
All outcomes that we have are = 1,2,3,4,5,6,7,8
→ Total outcomes are 8 .
Favourable outcomes are = 1,3,5,7
→ Favourable outcomes are 4.
P(odd) = 4 divided by 8
→ P( odd) is 1/2 , 50% , equally likely.
So option 2nd is correct .