If the equation is
- sin²(x) = cos(2x)
rewrite the left side using the Pythagorean identity,
sin²(x) = 1 - cos²(x)
and the right side using the double angle identity for cosine,
cos(2x) = 2 cos²(x) - 1
Then the equation transforms to
- (1 - cos²(x)) = 2 cos²(x) - 1
Solve for cos²(x) :
-1 + cos²(x) = 2 cos²(x) - 1
cos²(x) = 0
Take the square root of both sides to get
cos(x) = 0
Solve for x :
x = cos⁻¹(0) + 2nπ or x = cos⁻¹(0) - π + 2nπ
x = π/2 + 2nπ or x = -π/2 + 2nπ
where n is any integer. We get solutions in the interval [-π, π] when n = 0, giving the solutions
x = π/2 or x = -π/2
evaluate each expression |-16| - |4|
Which graph shows the following system of equations and its solutions? -0.1x-0.3y=1.2 and 0.2x-0.5y=2
Answer:
Option b is the correct answer as both the equations are true for given solution.
Step-by-step explanation:
Given equations are:
-0.1x-0.3y=1.2
0.2x-0.5y=2
We can observe each graph and find the point that is the solution and put the point in the equations to know if that point is the solution
For option A:
(0,4)
Putting x=0 and y = 4 in both equations
[tex]-0.1(0)-0.3(4)=1.2\\0-1.2 =1.2\\-1.2 \neq 1.2\\0.2(0)-0.5(4)=2\\0-2 = 2\\-2 \neq 2[/tex]
This is not the correct answer as both equations are not true with this solution
For Option B:
(0,-4)
Putting x = 0 and y = -4 in both equations
[tex]-0.1(0)-0.3(-4)=1.2\\0+1.2 = 1.2\\1.2 = 1.2\\0.2x-0.5y=2\\0.2(0)-0.5(-4) = 2\\2 = 2[/tex]
Both equations are true for (0,-4) hence it is the solution of the system.
For Option C:
(4,0)
[tex]-0.1(4)-0.3(0)=1.2\\-0.4-0 = 1.2\\-0.4 \neq 1.2\\0.2x-0.5y=2\\0.2(4)-0.5(0) = 2\\0.8 \neq 2[/tex]
Not true for both equations
Hence,
Option b is the correct answer.
Based on a large national sample of working adults, the U.S. Census Bureau reports the following information on travel time to work for those who do not work at home. Also given was the mean travel time, which was reported as 23.4 min.
Lower quartile 7 min
Median 18 min
Upper quartile 29 min
What is true of the travel time distribution?
A. It is positively skewed
B. It is approximately symmetric
C. It is negatively skewed
Answer:
Step-by-step explanation:
H3Y TH3R3 D1L1GH74 WH4T5 1T 71K3 1N NYC 1M 4 TH0US4-
Hay it is meh plz save me
Answer:
The distance is 1/3 :)
Your welcome
Answer:
1/3
Step-by-step explanation:
Hope it helps :)
Two angles are complementary. The measure of the larger angle is LaTeX: 30^\circ30 ∘more than 4 times the measure of the smaller. Find the measure of both angles.
Express -17/8 in decimal form
Answer:
Its -2.125
Step-by-step explanation:
I hope helps!
Find does angles
Help pls I have 15 min only .
Answer:
22 for x 45 for 4x+3 36 for 3x+2
Step-by-step explanation:
Trust me this is easy
Answer:
4x+2 =90°
3x+2=68°
x=22
Step-by-step explanation:
The interior angles of a triangle always add up to 180° so you will add the angles together and set them equal to 180° to solve for x. You will find that x should be equal to 22. Plug 22 into each equation to find the angle measure.
What is the greatest common factor for 12 and 54? enter your answer in the box.
Answer:
6
Step-by-step explanation:
Factors for 12: 1, 2, 3, 4, 6, 12
Factors for 54: 1, 2, 3, 6, 9, 18, 27, 54
It's 6.
The greatest common factor of the numbers 12 and 54 will be 6.
Given that:
Numbers, 12 and 54
The biggest chunk of the common factors is called the "Greatest Common Factor" (of two or more numbers).
The factors of the numbers 12 and 54 are calculated as,
12 = 2² x 3
54 = 2 x 3³
The value of the greatest common factor is calculated as,
GCF = 2 x 3
GCF = 6
More about the greatest common factor link is given below.
https://brainly.com/question/11221202
#SPJ6
Jon invests $4,100 into an account that pays 5 percent simple interest each year. What is the total balance in the account after 3 years?
Answer:
615
Step-by-step explanation:
4100*3 then you have to multiply by the rate in decimal form which is 0.05!
Answer:
a.
Step-by-step explanation: if i’m wrong lmk
Answer assp ill give points or brainly
Answer:
yo
Step-by-step explanation:
why need answer "assp"
1) What is the constant of proportionality that relates y to x
х
Y
8
6
20
15
28
21
a. 1.33
6,48
0.0.75
b. 14
f
Answer: The Answer Is A Because if u just add the numbers then divide them
Somebody knows how to this?
Which of the following slopes of a line passes through points (2, 3) and (4,7) ?
5
2
3
O
Answer:
2
Step-by-step explanation:
slope = (difference in y)/(difference in x)
slope = (7 - 3)/(4 - 2)
slope = 4/2 = 2
Answer: 2
As a computer technician, Andre makes $20 per hour to diagnose a problem and $25 per hour to fix a problem. He works fewer than 10 hours per week, but wants to make at least $200 per week. The inequalities 20x + 25y ≥ 200 and
x + y < 10 represent the situation. Which is true of the graph of the solution set? Check all that apply.
Answer:the line x+y<10 has a negative slope and a positive y intercept
The line representing 20x+25y>200 is solid and the graph is shaded above line
The overlapping region contains the point (4,5)
Step-by-step explanation:
;)
Answer:
The answers are B, C, and E.
Step-by-step explanation:
I got it right on edge
How do you write 7.3 x 10-1 in standard form?
Peter and Judy together earn $5060 per month. Their mortgage payment is $1265
pr month. What percentage of their household income goes toward paying the
mortgage?
Answer:
25 percent
Step-by-step explanation:
Use slope-intercept form, y= mx+b to find the equation of the line that passes through the points (-6,1) and (3,4).
plz help! will give brainliest!!!
Answer:
c
Step-by-step explanation:
If you have five red balls and five blue balls in a jar what’s the probability of the first ball being red?
Answer:
red balls = 5
blue balls = 5
total balls = 5 blue+5 red
= 10
[tex]p(first \: ball \: being \: red) = \frac{red \: balls}{total \: balls} [/tex]
[tex]p(first \: ball \: being \: red) = \frac{5}{10} = \frac{1}{2} [/tex]
Answer:
Step-by-step explanation:
Total number of red balls = 5
Total number of blue balls = 5
Total number of balls in jar = 5 + 5
= 10
Probability of the first ball being red = total number of the red ball/total number of balls in the jar
= [tex]\frac{5}{10}[/tex]
= [tex]\frac{1}{2}[/tex]
Therefore, the probability of the first ball being red = [tex]\frac{1}{2}[/tex], 50% or 0.5 (in any way you are instructed to write it in)
Perform the indicated operation and simplify the result, Leave your answer in factored form.
[tex]\frac{x^{2} }{5x-8} -\frac{64}{5x-8}[/tex]
Answer:
[tex]\frac{x^{2} }{5x-8}-\frac{64}{5x-8}=\frac{x^{2}-64 }{5x-8}=\frac{(x-8)(x+8)}{5x-8}[/tex]
Step-by-step explanation:
Last night, the Knicks made 12 free throws. If their free throw percentage is 75%, how many free throws were attempted? (READ CAREFULLY!)
Answer:
16
Step-by-step explanation:
12 / 16 = 0. 75
i found this by dividing 12 by 0.75
John picked 340 oranges. If he had 17 buckets to carry the oranges in, how many oranges would be in each bucket?
Answer: There would be 20 oranges in each bucket
Step-by-step explanation:
Answer:
20 oranges
Step-by-step explanation:
if john has to distribute the 340 oranges he picked amongst 17 buckets, the equation that represents his situation would be 340/17. just divide and you'll get 20, meaning there's 20 oranges in each bucket.
Please help me with this homework
Answer:
4, 2, 0, -2
Step-by-step explanation:
just plug the x value into y=-2x
Order these numbers from least to greatest.
Answer: -6 2/3, square root of 36, 6.4..., 71/11
Step-by-step explanation:
Turn the fractions into decimals for more understanding and solve for the square root of 36, 6.4... stays the same
Write a function formula for g using the function f.
g(x)=
Write a function formula for f using the function g.
f(x)=
Answer:
g(x) = -f(x+3)
f(x) = -g(x-3)
Step-by-step explanation:
Transformations
Function f can be obtained by knowing function g and vice-versa.
Suppose we know the expression of function f. If we reflect f across the x-axis, we get function g but displaced 3 units to the right.
Thus, we only have to translate the reflected f 3 units to the left:
g(x) = -f(x+3)
Similarly, if g(x) is reflected across the x-axis and translated by 3 units to the right, we get f(x), thus:
f(x) = -g(x-3)
PLS HELP I DONT UNDERSTAND :( WILL GIVE BRAINLIEST + 25 POINTS!!
Answer:
it is f
Step-by-step explanation:
Given the side lengths of 20,23 and 41, determine whether the triangle is acute, right, obtuse, or not a triangle.
=====================================================
Explanation:
In this case, a triangle is possible since adding any two sides leads to a sum larger than the third side
20+23 = 43 is larger than 4120+41 = 61 is larger than 2323+41 = 64 is larger than 20I'm using the triangle inequality theorem here.
----------------------------
To determine what kind of triangle we have, we'll use the converse of the Pythagorean theorem. Specifically, we'll use a corollary of it.
Consider a triangle with sides a,b,c. Let c be the longest side.
We have three possible cases:
If a^2+b^2 = c^2, then we have a right triangleIf a^2+b^2 > c^2, then the triangle is acute.If a^2+b^2 < c^2, then the triangle is obtuse.For this problem, we have a = 20, b = 23, c = 41.
We see that a^2+b^2 = 20^2+23^2 = 929 and c^2 = 41^2 = 1681.
In short, a^2+b^2 = 929 and c^2 = 1681.
Since 929 < 1681, this means a^2+b^2 < c^2.
Therefore, this triangle is obtuse.
Based on the P's and Q's of this polynomial (The Rational Zero Theorem), which of the following could NOT be a zero of the polynomial 4x3 + 4x2 - 11x-6?
Answer:
4
Step-by-step explanation:
P are the factors of the last coefficient (6) and Q are the factors of the first coefficient (4). Since p is divided by q, we could have 3/1, 6/1, 2/1, and 1/1, but not 4/1 since 4 is not a factor of 6
PLS HELP GUYS!!!
Select the correct step to solve 10x = 150.
Divide only one side of the equation by 150.
Divide both sides of the equation by 10.
Divide both sides of the equation by 150.
Divide only one side of the equation by 10.
Answer:
divide both sides of the equation by 10
There are 5 students in Mrs. Templeton's art class. Each student has 2 paintbrushes on his desk. Which of the following shows how to find the total number of paintbrushes in the classroom?