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Equate the given to zero
[tex]\begin{gathered} \cos 2\theta=-\sin ^2\theta\Longrightarrow\cos 2\theta+\sin ^2\theta=0 \\ \\ \text{Use the identity }\cos 2\theta=1-2\sin ^2\theta,\text{ THEN the equation becomes} \\ \cos 2\theta+\sin ^2\theta=0 \\ (1-2\sin ^2\theta)+\sin ^2\theta=0 \\ \\ \text{simplify} \\ (1-2\sin ^2\theta)+\sin ^2\theta=0 \\ 1-2\sin ^2\theta+\sin ^2\theta=0 \\ 1-\sin ^2\theta=0 \\ \\ \text{Add }\sin ^2\theta\text{ to both sides} \\ 1-\sin ^2\theta+\sin ^2\theta=0+\sin ^2\theta \\ 1\cancel{-\sin ^2\theta+\sin ^2\theta}=\sin ^2\theta \\ 1=\sin ^2\theta \\ \text{OR} \\ \sin ^2\theta=1 \\ \\ \text{get the square root of both sides} \\ \sqrt[]{\sin ^2\theta}=\sqrt[]{1} \\ \sin \theta=\pm1 \\ \\ \text{The values for which }\sin \theta\text{ is equal to }+1\text{ or }-1\text{ is} \\ \theta=\frac{\pi}{2}+2\pi n,\theta=\frac{3\pi}{2}+2\pi n \end{gathered}[/tex]Related Questions
Evaluate the expression (-4-4i) +(-8-11) and write the result in the form a + bi.The real number a equalsThe real number b equals
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The answer is supposed to be in the form
[tex]a+bi[/tex]Therefore,
[tex](-4-4i)+(-8-1i)[/tex][tex]\begin{gathered} -4-4i-8-1i \\ \end{gathered}[/tex]combine like terms
[tex]-4-8-4i-1i[/tex]Finally,
[tex]-12-5i[/tex]a = -12
b = -5
Choose the graph that illustrates both g (x) andg (x+4)
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Explanation:
If we have a function f(x) = g(x + c), we can say that f(x) is g(x) shifted c units to the left.
So, the graph of g(x + 4) will be the same graph of g(x) shifted 4 units to the left
Answer:
The only graph that has two functions and one if equal to the other shifted 4 units to the left is the following:
A dinner party is being organized with the option of 7 dinner choices to serve at the venue. Since catering is expensive thehost asks everyone attending to rank each dish. The top ranked dish will be served at the venue. What is the probability thatyour favorite dish is the chosen dish served at the venue?• Write your answer as an exact fraction which is reduced as much as possible.
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Given:
Total number of dinner choices = 7
Let's find the probability that your favorite dish is the chosen dish at the venue.
Given that you are to choose just one dish.
Probability can be said to be a measure of the likeklihood of an event to occur.
The probability of an event is a number between 0 and 1.
To find the probability, apply the formula below:
[tex]\begin{gathered} P(\text{fav)}=\frac{\text{Number of favorite dish}}{\text{Total number of dishes}} \\ \\ P(\text{fav)}=\frac{1}{7} \end{gathered}[/tex]Therefore, the probability the that your favorite dish is the chosen dish at the venue is
[tex]\frac{1}{7}[/tex]ANSWER:
[tex]\frac{1}{7}[/tex]Grandma Meyer uses the recipe to make a soup.A.Draw a bar diagram to find how much vegetable stock and cream are needed.B. Find how many cups of soup will be made with all the ingredients. Explain your work.
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Prior to plotting our chart, we need to convert these mixed fractions to decimals. Since denominators are 4, we can easily multiply both sides of the fraction by 25 to give the fraction in terms of 100 and thus, easily convert to decimal.
[tex]ChickenBroth\colon2\frac{3}{4}=\text{ 2 + (}\frac{3\times25}{4\times25}\text{)= 2 + }\frac{75}{100}=\text{ 2 + 0.75 = 2.75}[/tex][tex]Water\colon1\frac{1}{4}=\text{ 1 + (}\frac{2\times25}{4\times25}\text{)= 2 + }\frac{50}{100}=\text{ 2 + 0.5 = 1.5}[/tex][tex]Cream\colon1\frac{1}{4}=\text{ 1 + (}\frac{1\times25}{4\times25}\text{)= 1 + }\frac{25}{100}=\text{ 1 + 0.25 = 1.25}[/tex][tex]Vegetablestock\colon2\frac{3}{4}=\text{ 2 + (}\frac{3\times25}{4\times25}\text{)= 2 + }\frac{75}{100}=\text{ 2 + 0.75 = 2.75}[/tex]B.
The number of cups of soup will be a total of the ingredient,
[tex]\begin{gathered} \text{Total = 2.75 + 1.5 + 1.25 + 2.75 = 8.25} \\ To\text{ get back as mixed fractions,} \\ (8\text{ + }\frac{25}{100})\text{ + (8 +}\frac{1}{4}\text{) = 8}\frac{1}{4} \end{gathered}[/tex]14) What is the slope of the line below *
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homework practice what is the 5th term of this sequence?
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What is the domain of the cubic function f(x)= 9x³ + 2x-12 ?
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GIVEN:
We are given the function below;
[tex]f(x)=9x^3+2x-12[/tex]Required;
To find the domain of the cubic function.
Step-by-step solution/explanation;
The domain of a function is the set of all input values (that is, x values) for which the function is defined.
For the function given, there is no constraint, which means the function is always true for any value of x.
Therefore,
ANSWER:
[tex]Domain=(-\infty,+\infty)[/tex]The domain is the set of all real numbers.
Option B
Solve the system using the addition method 5x-2y=32x-y=0What is the y-valueA. 3B. 6C. -3D. none of the above
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First, we multiply the first equation by "2":
[tex]\begin{gathered} 2\times\lbrack5x-2y=3\rbrack \\ 10x-4y=6 \end{gathered}[/tex]Then, we multiply the second equation by "-5":
[tex]\begin{gathered} -5\times\lbrack2x-y=0\rbrack \\ -10x+5y=0 \end{gathered}[/tex]The two new equations are:
[tex]\begin{gathered} 10x-4y=6 \\ -10x+5y=0 \end{gathered}[/tex]We add both equations and solve for y. The steps are shown below:
[tex]\begin{gathered} 10x-4y=6 \\ -10x+5y=0 \\ ----------- \\ y=6 \end{gathered}[/tex]The correct answer is y = 6.
AnswerBWhat is the approximate area of the shaded region? 6 5 3 a 2 1 X 0 1 2 3 4 5 6 O A. 3 units? B. 6 units c. 10 units D. 13 units
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Area aof shaded region is
Difference of areas between square, and circle
Area of square is = (5-1)^2 = 16
Area of circle is = π•[(5-1)/2]^2 = π•2^2 = π•4
Shaded Area = 16 - (π•4) = 16 - 12.564 = 3.436
THEN option A , is the value most aproximate to 3.436
Solve the system of linear equations using the graphing method. Use “no solution” and “infinitely many” when appropriate.
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Given the system of equations:
[tex]\begin{gathered} y=\frac{1}{2}x+2 \\ \\ y=\frac{1}{2}x+1 \end{gathered}[/tex]Let's solve the system using graphing method.
Let's plot both equations on a graph. The point where both lines meet.
• Equation 1:
Let's plot using 3 points.
Substitute random values of x and solve for y.
We have:
[tex]\begin{gathered} x=-4;\text{ y = }\frac{1}{2}(-4)+2=-2+2=0 \\ \\ x=0;y=\frac{1}{2}(0)+2=0+2=2 \\ \\ x=4;y=\frac{1}{2}(4)+2=2+2=4 \end{gathered}[/tex]For equation 1, we have the points:
(x, y) ==> (-4, 0), (0, 2), (4, 4)
Plot the points and connect the points with a straight line.
• Equation 2:
Let's create 3 points:
[tex]\begin{gathered} x=-2;y=\frac{1}{2}(-2)+1=-1+1=0 \\ \\ x=0;y=\frac{1}{2}(0)+1=0+1=1 \\ \\ x=2;y=\frac{1}{2}(2)+1=1+1=2 \end{gathered}[/tex]FOr equation 2, we have the points:
(x, y) ==> (-2, 0), (0, 1), (2, 2)
Now, plot the points and connect using a straight line.
We have the graph of both equations below:
From the graph, we can see that both lines do not meet at any point.
They are parallel lines,
Since they will not meet at any point, there is NO SOLUTION.
ANSWER:
No solution.
the paper didnt explain how to do this clearly could you take me step by step how to do this
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Given data:
The given point is (2,-2).
The equation of the line is y= -2x+3.
The standard equation of the line is,
[tex]y=mx+c[/tex]Compare the given equation with the above equation.
[tex]m=-2[/tex]Two parallel lines have equal slope, the equation of the line parallel to the given line and passing through (2, -2) is,
[tex]\begin{gathered} y-(-2)=m(x-2) \\ y+2=-2(x-2) \\ y+2=-2x+4 \\ y=-2x+2 \end{gathered}[/tex]Thus, the equation of the line is y= -2x+2.
6)Find the solution set of the quadratic equation over the set of complex numbers.5x2 + 12x + 8 = 0A)x = −34 − i4 or −34 + i4B)x = −65 − 2i5 or −65 + 2i5C)x = −25i(11 − 2i) or −25i(11 + 2i)D)x = −16i(11 − 2i) or −16i(11 + 2i)
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The given quadratic equation is expressed as
5x^2 + 12x + 8 = 0
The standard form of a quadratic equation is expressed as
ax^2 + bx + c = 0
By comparing both equations, we have
a = 5, b = 12, c = 8
We would solve for x by applying the general formula for solving quadratic equations which is expressed as
[tex]\begin{gathered} x\text{ = }\frac{-\text{ b }\pm\sqrt[]{b^2-4ac}}{2a} \\ By\text{ substituting the values, we have} \\ x\text{ = }\frac{-\text{ 12}\pm\sqrt[]{12^2-4(5\times8)}}{2\times5}\text{ } \\ x\text{ = }\frac{-\text{ 12 }\pm\sqrt[]{144\text{ - 160}}}{10}\text{ = }\frac{-\text{ 12}\pm\sqrt[]{-\text{ 16}}}{10} \\ x\text{ = }\frac{-\text{ 12}\pm4i}{10} \\ x\text{ = }\frac{-\text{ 12 + 4i}}{10}\text{ or x = }\frac{-\text{ 12 - 4i}}{10} \\ x\text{ = }\frac{-\text{ 12}}{10}\text{ + }\frac{4i}{10}\text{ or x = }\frac{-\text{ 12}}{10}\text{ - }\frac{4i}{10} \\ x\text{ = }\frac{-\text{ 6}}{5}+\text{ }\frac{2i}{5}\text{ or x = }\frac{-6}{5}-\text{ }\frac{2i}{5} \end{gathered}[/tex]on a graph if it has (-5,5) and (5,5) is it proportional or non- proportional
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A proportional graph is when y increases/decreases, if x increases. The graph shows that as x increases, the value of y stays the same, therefore it is not proportional.
Suppose you have a standard deck of 52 carts. What is the probability that if you select a card at random that it does not have a face value of 9? Round your answer to two decimals
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A deck of cards has 13 face values: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King. These face values are present for four different suits (Clubs, Diamonds, Hearts, and Spades) for a total of 52 cards.
An event's probability in an experiment with equally likely outcomes is defined by the following formula, where P (event) means the probability of the event occurring and is founding by dividing the number of outcomes in the event by the number of outcomes in the sample space:
[tex]P(event)=\frac{Number\text{ }of\text{ outcomes in the event}}{Number\text{ of outcomes in the sample space}}[/tex]The probability of not getting the event is given to be:
[tex]P^{\prime}(event)=1-\frac{Number\text{ }of\text{ outcomes in the event}}{Number\text{ of outcomes in the sample space}}[/tex]Since there are 4 cards with a face value of 9, the probability of getting a 9 is:
[tex]P(9)=\frac{4}{52}=\frac{1}{13}[/tex]Therefore, the probability of not getting a 9 is given to be:
[tex]\begin{gathered} P^{\prime}(9)=1-\frac{1}{13} \\ P^{\prime}(9)=\frac{12}{13} \end{gathered}[/tex]In two decimal places, the probability that the card picked does not have a face value of 9 is 0.92.
I need help finding my equation for the question. I’m very confused
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1)
The ratio of cookies to hours spent cooking = C : H
= 300 : 4
= 75 : 1
2)
How many hours does it take to bake 225 cookies
[tex]\begin{gathered} =\text{ }\frac{225}{75}\text{ } \\ =\text{ 3 hours} \end{gathered}[/tex]The sequence below shows the number of trees that a nursery plants each year.2, 8, 32, 128 ...Let an represent the current term in the sequence and an-1 represent the previous term in thesequence. Which formula could be used to determine the number of trees the nursery will plantin year n?
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According to the given sequence, the formula that could be used to determine the number of trees the nursery will plant in year n is [tex]a_{n}= 4a_{n-1}[/tex]. Thus, option (A) is correct.
The given sequence of the number of trees that a nursery plants each year is -
2, 8, 32, 128, .....
[tex]a_{n}[/tex] = The current term in the sequence
[tex]a_{n-1}[/tex] = The previous term in the sequence
We have to find out the formula that could be used to determine the number of trees that the nursery will plant in the year n.
From the sequence we can see that -
8 = 2*4
32 = 8*4
128 = 32*4
So, this can be said that the current term in the sequence ([tex]a_{n}[/tex]) is 4 times the previous term in the sequence ([tex]a_{n-1}[/tex]).
=> [tex]a_{n}= 4a_{n-1}[/tex]
Thus, according to the given sequence, the formula that could be used to determine the number of trees the nursery will plant in year n is
[tex]a_{n}= 4a_{n-1}[/tex]
Thus, option (A) is correct.
To learn more about sequence visit https://brainly.com/question/21961097
#SPJ9
Please help!! I keep getting crazy fractions for the one for equation of a line and for the other one I have no idea how to solve. I'll be eternally grateful!
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We will find the equation of the line passes through the points:
[tex](\frac{5}{8},\frac{31}{16})and(-\frac{-5}{7},\frac{13}{14})[/tex]The general neral
Are the triangle below congruent? If so, write a congruence statement and say why
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Yes, they ARE congruent. Even if the shape has been reflected/flipped or rotated and is the same size, the shapes will always stay congruent.
If it wasn’t congruent:
If the size has changed between shapes, it would NOT be congruent.
Square Root Function and inverse
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Answer:
[tex]f^-^1(x)=\frac{x+1}{8}[/tex]
Step-by-step explanation:
f(x) = 8x - 1
==> replace "f(x)" with y
y = 8x - 1
==> inter exchange x and y
x = 8y - 1
==> solve for y now, first step would be to add 1 to both sides
x + 1 = 8y
==> divide both sides by 8
(x+1)/8 = y
==> replace y with f^-1(x)
f^-1(x)=(x+1)/8y
Distributive Property equation8x4=(_x_)+(_x_)
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Answer:
8 x 4 = (8 x 2) + (8 x 2)
Explanation:
The distributive property says that:
a x (b + c) = (a x b) + (a x c)
Then, we can write 4 as (2 + 2), so:
8 x 4 = 8 x ( 2 + 2)
Now, we can apply the distributive property:
8 x 4 = (8 x 2) + (8 x 2)
Therefore, the answer is:
8 x 4 = (8 x 2) + (8 x 2)
What is the measure of the 5x+25
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As you can see:
RM+MT = RT
Where:
RM = 5x + 9
MT = 8x - 6
RT = 198
Replacing the data:
5x + 9 + 8x - 6 = 198
Add like terms:
(5x + 8x) + (9 - 6) = 198
13x + 3 = 198
Solve for x:
Subtract 3 from both sides:
13x + 3 - 3 = 198 - 3
13x = 195
Divide both sides by 13:
13x/13 = 195/13
x = 15
Three support beams for a bridge form a pair of complementary angles. Find the measure of each angle.(2x - 20)INNISmaller angle:Larger angle:O0UNSFANA(4x - 10)
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SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Define complementary angles
When the sum of two angles is 90°, then the angles are known as complementary angles.
STEP 2: Write the pairs of the angles formed
[tex]\begin{gathered} (2x-20)\degree \\ (4x-10)\degree \end{gathered}[/tex]STEP 3: find the value of x
Following the definition in step 1, this goes that;
[tex]\begin{gathered} (2x-20)+(4x-10)=90\degree \\ 2x-20+4x-10=90\degree \\ 6x-30=90 \\ 6x=90+30 \\ 6x=120 \\ x=\frac{120}{6}=20 \end{gathered}[/tex]STEP 4: Find the two pair of angles
[tex]\begin{gathered} (2x-20)=2(20)-20=40-20=20\degree \\ 4x-10=4(20)-10=80-10=70\degree \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} smaller\text{ }angle=20\degree \\ Larger\text{ }angle=70\degree \end{gathered}[/tex]Given triangle ABC below, if angle B=(x-60)^ and angle C=(x- 45)^ find the measure of angle x
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Given:
m∠B = (x - 60)°
m∠C = (x - 45)°
Opposite angle = x°
Let's find the measure of angle x.
To find the measure of angle x, apply the Exterior Angle Theorem which states that the exterior angle of a triangle is equal to the sum of the two opposite angles.
Thus, we have:
∠B + ∠C = x
(x - 60) + (x - 45) = x
Solve for x.
• Remove the parentheses and combine like terms:
x - 60 + x - 45 = x
x + x - 60 - 45 = x
2x - 105 = x
• Move all terms containing x to the left, then move 105 to the right
2x - x = 105
x = 105°
Therefore, the measure of angle x is 105°
ANSWER:
x = 105°
What is the perimeter of the figure below?34 mm40 mm88 mm96 mmI probably doing
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The perimeter is the sum of the length of the sides that form a boundary of the figure.
That is
[tex]\text{ The Perimeter =}8+2+4+6+12+8[/tex]Therefore
[tex]\text{ The Perimeter =}40\text{ mm}[/tex]The perimeter is 40 mm
Point C is located at (4, -2). It is translated 3 units to the left and 4 units up. Graph the location of the translated point.
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Answer:
Step-by-step explanation: Refer to the photo taken.
Piper works at a camera store. He is paid an hourly rate plus 16% commission on everything he sells. One week, he was paid $515 for working 20 hours and selling $1,500 worth of camera equipment. What is his hourly rate?
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His hourly rate is $13.75
Here, we want to get Piper's hourly pay at work
Let the hourly rate be h
Thus, for working 20 hours, the amount for this will be; 20 * h = 20h
Now, out of the $1500 sales, he is entitled to 16%
That means;
[tex]\frac{16}{100}\times\text{ 1500 = 240}[/tex]Thus, we have it that;
[tex]\begin{gathered} 20h\text{ + 240 = 515} \\ 20h\text{ = 515-240} \\ 20h\text{ = 275} \\ h\text{ = }\frac{275}{20} \\ h\text{ = \$13.75} \end{gathered}[/tex]Find the value of each variable in the parallelogram.5u – 10162u + 2V3U =0V=
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The diagonals of a parallelogram bisect each other. It means the segments, after bisection, are equal to each other.
From the figure, we can write:
[tex]\begin{gathered} 2u+2=5u-10 \\ \text{and} \\ 6=\frac{v}{3} \end{gathered}[/tex]We can solve the first equation and get the value of u:
[tex]\begin{gathered} 2u+2=5u-10 \\ 2+10=5u-2u \\ 12=3u \\ u=\frac{12}{3} \\ u=4 \end{gathered}[/tex]Solving the second equation, we find the value of v:
[tex]\begin{gathered} 6=\frac{v}{3} \\ 6\times3=v \\ v=18 \end{gathered}[/tex]Answer:
u = 4v = 18What type of angle is shown on the protractor below?
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Given data:
The given angle .
The given angle AOB is an obtuse angle.
Thus, third option is correct.
Nancy bought a pack of 10 cookies for her 3 children to share equally. How many cookies should each child get if the cookies are shared equally between the 3 children?
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Given:
Total pack is 10.
Share divied in 3 children.
So each children share is:
[tex]\begin{gathered} 3\text{ total share is 10} \\ for\text{ each share}=\frac{10}{3} \\ =3.33 \end{gathered}[/tex]each children share is 3.33 cookies.
Can you help me please? If there is a solution what’s the solution as well
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Solution:
Given;
[tex]-7y^2+7y+1=0[/tex]Where;
[tex]a=-7,b=7,c=1[/tex]Thus;
[tex]\begin{gathered} b^2-4ac=7^2-4(-7)(1) \\ \\ b^2-4ac>0 \end{gathered}[/tex]Hence, the quadratic equation has two different real solutions.
Then;
[tex]\begin{gathered} y=\frac{-7\pm\sqrt{7^2-4(-7)(1)}}{2(-7)} \\ \\ y=1.13,y=-0.13 \end{gathered}[/tex]