Answer:
[tex]\displaystyle x=\left\{\frac{\pi}{2}, \frac{7\pi}{6}, \frac{3\pi}{2}, \frac{11\pi}{6}\right\}[/tex]
Step-by-step explanation:
We are given the equation:
[tex](\sin(x)-\cos(x))^2=1+\cos(x)[/tex]
And we want to find all solutions for the equation within the interval [0, 2π).
First, we can expand. This yields:
[tex]\sin^2(x)-2\sin(x)\cos(x)+\cos^2(x)=1+\cos(x)[/tex]
From the Pythagorean Identity, we know that:
[tex]\sin^2(x)+\cos^2(x)=1[/tex]
Therefore:
[tex]-2\sin(x)\cos(x)+1=1+\cos(x)[/tex]
Simplify:
[tex]-2\sin(x)\cos(x)=\cos(x)[/tex]
Subtract cos(x) from both sides*:
[tex]-2\sin(x)\cos(x)-\cos(x)=0[/tex]
Factor:
[tex]\cos(x)\left(-2\sin(x)-1)=0[/tex]
Zero Product Property:
[tex]\cos(x)=0\text{ or } -2\sin(x)-1=0[/tex]
Solve for each case:
[tex]\displaystyle \cos(x)=0\text{ or } \sin(x)=-\frac{1}{2}[/tex]
Use the unit circle. So, our solutions are:
[tex]\displaystyle x=\left\{\frac{\pi}{2}, \frac{7\pi}{6}, \frac{3\pi}{2}, \frac{11\pi}{6}\right\}[/tex]
*Note that we should not simply divide both sides by cos(x) to acquire -2sin(x) = 1. This is because we do not know what the value of x is, and so one or may values of x may result in cos(x) = 0, and we cannot divide by 0. Hence, we need to subtract and factor and utilize the Zero Product Property.
in the diagram the measures of angle 1 and 4 is 100 the measure of 5 and 8 are 110 are c and d parallel
Answer:
no,because <1 and <5 are not congruent
Step-by-step explanation:
i did the test yw
Approximate the value of V61 to the nearest hundredth.
No links please!
What is the greatest common factor of
3x^3 – 9x + 3
Answer:
3(x^3-3x+1)
hope this helps!
You spin the spinner once. 8 9 7 2 6 3 5 4 What is P(even)? Write your answer as a fraction or whole number.
Answer:6
Step-by-step explanation:
please help me, I understand the properties but in this question we have to fill in the degrees
Answer:the qualirateral is in the wrong spot
Step-by-step explanation:
Which equation is y = (x + 3)2 + (x + 4)2 rewritten in vertex form?
y = 2 (x + seven-halves) squared minus one-fourth
y = 2 (x + seven-halves) squared minus one-half
y = 2(x + 7)2 – 73
y = (x + 7)2 – 24
Answer:
y = 2 (x + seven-halves) squared minus one-fourth [y = [tex](x + \frac{7}{2} )^{2} - \frac{1}{4}[/tex] ]
Step-by-step explanation:
We know that,
vertex form is y = a(x-h)² + k
vertex is (h, k)
Now,
Given that the equation is -
y = (x+3)² + (x+4)²
= x² + 3² + 2×3×x + x² + 4² + 2×4×x
= x² + 9 + 6x + x² + 16 + 8x
= 2x² + 14x + 25
= [tex]x^{2} + 7x + \frac{25}{2}[/tex]
= [tex]x^{2} + 7x + \frac{25}{2} + \frac{49}{4} - \frac{49}{4}[/tex]
= [tex](x + \frac{7}{2} )^{2} + \frac{25}{2} - \frac{49}{4}[/tex]
= [tex](x + \frac{7}{2} )^{2} - \frac{1}{4}[/tex]
∴ we get
The vertex form is -
y = [tex](x + \frac{7}{2} )^{2} - \frac{1}{4}[/tex]
So,
The correct option is - y = 2 (x + seven-halves) squared minus one-fourth (y = [tex](x + \frac{7}{2} )^{2} - \frac{1}{4}[/tex] )
Answer:
b
Step-by-step explanation:
edge 2021
if you subtract 12 from my number and multiply the difference by -6 the result is -90 what is my number
Answer:
n must be 27
Step-by-step explanation:
Let this number be x. Then -6(n - 12) = -90.
Dividing both sides by -6 yields n - 12 = 15.
Add 12 to both sides.
Then n must be 27.
Check: subtract 12 from 27; this yields 15. Now multiply this result by -6. The result is -90, which was expected.
EVERYTHING IS IN THE PICTURE!
Answer:
The answer is B From my calculations
Jessica and Jonathan do some research to gather all their ingredients and figure out their costs. As shown in the table below, they will use 6 containers of lemon juice, which each contain 0.75 cup of juice.
What is the total volume of lemon juice they will use in their recipe, in cups?
Answer:
4.5 cups
Step-by-step explanation:
Answer:
4.5
Step-by-step explanation:
On freckle
PLSSSSSSSSS HELPPPPP!!!!!!!
Wednesday
3. A student answers 90% of the
questions on a math exam correctly, how
many questions are on the exam?
Answer:
its kind of a vague question, it could be 9/10 or it could be 90/100 ??
Step-by-step explanation:
In a right triangle one angle measure 28° more than the other acute angle. Use equations to solve for the measures of the two unknown angles.
Answer:
One acute angle is 31 degrees and the other acute angle is ( 31+28=) 59 degrees.
Step-by-step explanation:
In the right angled triangle one angle is always equal to 90 degrees.
Suppose <a= 90 degrees
< b= x degrees
< c= x+28 degrees
The sum of all the angles of the triangle are always equal to 180 degrees
therefore
<a+ <b+<c= 90 + x+ x+28 = 180
or
2x= 180- 28- 90
2x=62
x= 31 degrees
One acute angle is 31 degrees and the other acute angle is ( 31+28=) 59 degrees.
An acute angle is an angle which has less than 90 degrees in measurement .
Hence both angles of the right angle triangle are acute angles , 31 and 59 degrees.
What is the answer please show the work
it is 30 because it says 1 and 20 soooooo
classify the polynomial. 5b^2+1
is it a quadratic trinomial, quartic binomial, quadratic binomial, or quartic polynomial?
y varies directly as x, and y = 55 when x = -5.
Answer:
Step-by-step explanation:
I'm not sure what you are asking here????
I think it can be a triangle but want another opinion
Answer:
I think It's a triangle too
Step-by-step explanation:
Use the information provided to solve the word problem below. The cost of a school banquet is $65 + $11n, where n is the number of people attending. Which is the cost for 70 people? a. $147 b. $834 c. $835 d. $146 Please select the best answer from the choices provided A B C D
Answer:
$835 (Answer c)
Step-by-step explanation:
Write out the Cost function: C(n) = $65 + ($11/person)n
Then the total cost for 70 people would be C(70) = $65 + ($11/person)(70 people)
C(70) = $65 + $770 = $835 (Answer c)
Hi guys please help me with this! exlapin how you got the answer instead of just putting down a random letter for points, thanks! :)
Solve the system by substitution.
x=-6y 4x + 10y = 14
Answer:
x = 6
y = -1
Step-by-step explanation:
x = - 6y ----------------------(I)
4x + 10y = 14 ------------------(II)
Substitute x = -6y in equation (II)
4*(-6y) + 10y = 14
-24y + 10y = 14 {Combine like terms}
-14y = 14 {Divide both sides by 1-4}
y = 14/-14
y = -1
Now, substitute y = -1 in equation (I)
x = - 6*(-1)
x = 6
PLEASE HELP I NEED TO FINISH SOON!!! I WOULD REALLY APPRECIATE IT
CAN SOMEONE HELP ME WITH THIS PLEASE?
Answer:
Y= 4 and X=2
Step-by-step explanation:
When you are trying to find the X or Y value for an equation, set the opposite value to zero. That means that if you are trying to find Y in 6x+3y=12, you would make the X zero. Since six is being multiplied by X and X now equals zero, your equation for finding the Y value is now 3y=12. Divide them both by three and you get Y=4. In order to find your X value you would do the same thing. Since you are trying to find X, set the Y value to zero. That makes your equation for finding the X value 6x=12. That is because, again, you set Y to zero, and three times zero is zero. 6x=12 equals X=2 because you divide both sides by 6.
Answer:4y 2x i need only one brainlist to upgrade my level pls
Ste-by-step explanation:
Graph this function: y =3/4x - 4 (you can just put the cordinants)
Helppppppppppppppp and imma make you BRAINLIESTTTTTTTTTTTTTT >:3 20 POINTSSSS
Answer:
hey sorry someone went on the question we were talking on and reported it they also reported where i said I was taking a quiz and the question so i had to put in the comments that it was after that quiz and during another quiz also they can't see the timeline so it was between quizzes that i posted it
Step-by-step explanation:
From the rectangle ABCD a square is cut off to leave rectangle BCEF. Rectangle BCEF is similar to ABCD. Find x and hence state the ratio of the sides of the rectangle ABCD
Where is the image?
Without an image this would be unanswerable
If Michelle can ride her bike 5 miles in 20 minutes, how far can she ride her bike in 50 minutes?
Answer:
12.5 miles
Step-by-step explanation:
1 mile= 4 min.
x miles= 50 min.
1/4 = x/50
*cross multiply
4x= 50
divide by 4
x= 12.5 miles
THIS IS NOT NEEDED FOR ANSWERING JUST TO GET THREE NEEDED QUESTIONS I NEED ANSWERED TODAY OUT INTO BRAINLY... AND ID EXPECT NO LINKS IN THIS OR IN THESE QUESTIONS... BUT I WILL PUT THE THREE QUESTIONS AS PHOTOS IN HERE IF YOU WANT TO ANSWER THEM HERE INSTEAD AS PHOTOS... IF YOU CANT SEE THEM HERE THEN GO INTO THE BRAINLY QUESTION LINKS
other Brainly questions i have today that also need answering:
brainly.com/question/22829066
brainly.com/question/22828757
brainly.com/question/22829297
Ω Entity001 And Project Omega Ω
EXAMPLE OF WHAT NOT TO TRUST BELOW:
Kyuubivi
Beginner
1 answer
6 people helped
Answer is in a photo. I couldn't attach it here, but I uploaded it to a file hosting. link below! Good Luck!
bit.ly/3mCQlPZ
Answer:
huh i am very confused
Step-by-step explanation:
identify the type of sequence
i just need the graph ones
WILL MARK BRAINLYEST!
Answer:
your answers are correct
the first graph isgeometric
the second graph is arithmeit
Which of the following fractions is in simplest form?
A) 6/20
B) 8/14
C) 9/16
D) 15/35
Answer:
C) 9/16
Step-by-step explanation:
Clara has 9 pounds of apples. She needs 1 1/4 pounds to make one apple pie. If she saves 2 pounds for applesauce, how many pies can she make?
Answer:
She can make 6 pies.
Answer:
She can make 6 pies.
Step-by-step explanation:
Subtract 9-1.5=7.5
then 7.5/1.25= 6.04
Help plz am desperate no links(will sue), no unhelpful answers (will report or sue), and plz have an explanation if you don't that's okay but brainliest for explanation. Thank y'all!
Answer: 19.625in
Step-by-step explanation:
Answer: 19.625in I think
Step-by-step explanation:
Solve using substitution x = 3y + 1 2x + 4y = 12
Answer:
x = 4
y = 1
Step-by-step explanation:
x = 3y + 1 (Multiply everything by -2)
2x + 4y = 12 (Transfer 4y to the right of the = sign)
2x = -4y + 12
-2x = -6y - 2
0 = -10y + 10
-10 = -10y
y = 1
x = 3y + 1
x = 3(1) + 1
x = 3 + 1
x = 4