[tex]\( \cos(2x) = \frac{1}{2} \).[/tex]
Given that [tex]\( \sin(x) = -\frac{1}{2} \) and \( \tan(x) \)[/tex] is negative, we can find \[tex]( \cos(2x) \)[/tex]using the trigonometric identities.
First, let's find the value of [tex]\( \cos(x) \)[/tex] using the Pythagorean identity:
[tex]\[ \cos^2(x) = 1 - \sin^2(x) \][/tex]
Given [tex]\( \sin(x) = -\frac{1}{2} \),[/tex] we have:
[tex]\[ \cos^2(x) = 1 - \left(-\frac{1}{2}\right)^2 \][/tex]
[tex]\[ \cos^2(x) = 1 - \frac{1}{4} \][/tex]
[tex]\[ \cos^2(x) = \frac{3}{4} \][/tex]
Taking the square root of both sides, since [tex]\( \cos(x) \)[/tex] is positive in the first and fourth quadrants:
[tex]\[ \cos(x) = \pm \frac{\sqrt{3}}{2} \][/tex]
Given that [tex]\( \tan(x) \)[/tex] is negative, we know that ( x ) lies in either the second or fourth quadrant. In the second quadrant, both [tex]\( \sin(x) \) and \( \cos(x) \)[/tex] are negative. In the fourth quadrant, [tex]\( \sin(x) \)[/tex] is negative but [tex]\( \cos(x) \) i[/tex]s positive.
Since [tex]\( \cos(x) = \pm \frac{\sqrt{3}}{2} \),[/tex] we conclude that [tex]\( \cos(x) = -\frac{\sqrt{3}}{2} \)[/tex] (since [tex]\( \cos(x) \)[/tex] is negative in the second quadrant).
Now, using the double angle identity for cosine:
[tex]\[ \cos(2x) = 2\cos^2(x) - 1 \][/tex]
Substituting [tex]\( \cos(x) = -\frac{\sqrt{3}}{2} \):[/tex]
[tex]\[ \cos(2x) = 2\left(-\frac{\sqrt{3}}{2}\right)^2 - 1 \][/tex]
[tex]\[ \cos(2x) = 2\left(\frac{3}{4}\right) - 1 \][/tex]
[tex]\[ \cos(2x) = \frac{3}{2} - 1 \][/tex]
[tex]\[ \cos(2x) = \frac{3}{2} - \frac{2}{2} \][/tex]
[tex]\[ \cos(2x) = \frac{1}{2} \][/tex]
So, [tex]\( \cos(2x) = \frac{1}{2} \).[/tex]
solve the given inequality -2x - 5 < 3
Answer:
your answer would be X>-4
9.85×s;s=4 how do i solve this step by step
Answer:
39.40
Step-by-step explanation:
5 × 4 = 20 so you put down the 0 and carry the 2, 8 × 4 = 32 + 2 = 34 so you put down the 4 and carry 3, 9 × 4 = 36 + 3 = 39 so you put down 39. Don't forget to put the decimal place 2 spaces away from the answer. So you get 39.40.
The drawing can also help.
I need help please help me
Answer:
3 stamps for $5
Step-by-step explanation:
$5 times 3 is $15
Kendall just became a personal trainer and is finalizing her pricing plans. One plan is to charge $37 for the initial consultation and then $33 per session. Another plan is to charge $101 for the consultation and $32 per session. Kendall realizes that the two plans have the same cost for a certain number of sessions. How many sessions is that? What is that cost?
Final answer:
After 64 sessions, the cost of both of Kendall's plans would be the same, which would be $2149.
Explanation:
Kendall's two pricing plans can be represented by linear equations. Plan 1 is $37 + $33 per session, while Plan 2 is $101 + $32 per session. To find out after how many sessions the cost would be the same, we set the two equations equal to each other:
37 + 33x = 101 + 32x
This simplifies to:
33x - 32x = 101 - 37
x = 64
So, after 64 sessions, the cost of both plans would be equal. To find that cost, we substitute x back into either equation:
Total cost for Plan 1 = 37 + 33(64) = $2149
Therefore, the cost for 64 sessions is $2149 using either plan.
100,007,001 in word
Answer:
one hundred million seven thousand and one
Answer:
One hundred million seven thousand and one
Step-by-step explanation:
What is the greatest common factor of 21 and 27?
Answer: 3
Step-by-step explanation: We found the factors and prime factorization of 21 and 27. The biggest common factor number is the GCF number. So the greatest common factor 21 and 27 is 3.
The greatest common factor of 21 and 27 is 3.
What is Greatest common Factor?A set's greatest common factor (GCF) is the largest factor that all of the numbers share.
For example, 12, 20, and 24 have two common factors: 2 and 4. The largest is 4, so we say that the GCF of 12, 20, and 24 is 4.
We have the number 21 and 27.
Now, factories 21 and 27 as
21 = 3 x 7
27 = 3 x 3 x 3
So, the common factor of 21 and 27 is 3.
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help me pleaseeee due tmr
Answer:
A
Step-by-step explanation:
if you multiply the top by 2 the coefficients for x will be the same in both equations
4*2=8
The equations have equal x-coefficients is to A. Multiply both sides of the top equation by 2.
Multiplying both sides of the top equation by 2 results in:
8x + 4y = 8
This makes the x-coefficients equal in both equations, as they are both now 8x.
Option B would not work, as dividing both sides of the top equation by 4 would result in an x-coefficient of 1x in the first equation and 8x in the second equation.
Option C would also not work, as dividing both sides of the top equation by 2 would result in an x-coefficient of 2x in the first equation and 8x in the second equation.
Option D would work, as multiplying both sides of the top equation by 4 would result in an x-coefficient of 8x in both equations. However, option A is the simplest and most direct way to achieve the desired result.
Therefore, the correct answer is A. Multiply both sides of the top equation by 2.
simplify sqrt(p^2) Please solve this. I will give whoever solves this points.
It's a bit of a trick question. The principal square root of a real number, as indicated by the radical sign, is never negative. So if p is negative we'll get -p as the result. We write this with absolute value:
[tex]\sqrt{p^2} = |p|[/tex]
ASAP! A biologist is to set up an aquarium in his laboratory. He intends to buy 11 piranhas and 5 sharks. He has a budget of £200. If p represents one piranhas and s one shark, write down an equation for the price of one piranhas in terms of the price of sharks.
Answer:
[tex]p=\frac{200-5s}{11}[/tex]
Step-by-step explanation:
Let
p ---> the price of one piranhas
s ---> the price of one shark
we know that
The price of one piranhas multiplied by 11 plus the price of one shark multiplied by 5 must be equal to the budget of £200
so
The linear equation that represent this situation is
[tex]11p+5s=200[/tex]
Solve for p
That means ----> isolate the variable p
subtract 5s both sides
[tex]11p=200-5s[/tex]
Divide by 11 both sides
[tex]p=\frac{200-5s}{11}[/tex]
identify the range of the function
Answer:
(-4, 0)
Step-by-step explanation:
range applies to the y values.
The lowest y value it hits is -4, while the highest is 0.
Therefore, range is (-4, 0)
A knitter wants to make a rug for a dollhouse. The length of the rug will be 2 inches more than it’s width. The total area of the rug ( in square inches) based on the width W of the rug (in inches ) is given by A(w) = w (2+w) If the desired area of the rug is 15 square inches, what is the width of the rug, in inches?
The width of the rug is 3 inches
Step-by-step explanation:
A knitter wants to make a rug for a dollhouse
The length of the rug will be 2 inches more than it’s widthThe total area of the rug ( in square inches) based on the width w of the rug (in inches ) is given by A(w) = w (2 + w)The desired area of the rug is 15 square inchesWe need to find the width of the rug
∵ The area of the rug is A(w) = w(2 + w)
- Simplify the right hand side
∴ A(w) = 2w + w²
∵ The desired area of the rug is 15 square inches
- Equate A(w) by 15
∴ 2w + w² = 15
- Subtract 15 from both sides
∴ 2w + w² - 15 = 0
- Its a quadratic equation arrange its terms from the greatest power of x
∴ w² + 2w - 15 = 0
Factorize it into two binomial factors
∵ w² = w × w
∵ 15 = 3 × 5
∵ 5w - 3w = 2w
∴ w² + 2w - 15 = (w -3)(w + 5)
∴ (w - 3)(w + 5) = 0
- Equate each factor by 0
∴ w - 3 = 0 OR w + 5 = 0
∵ w - 3 = 0
- Add 3 to both sides
∴ w = 3
∵ w + 5 = 0
- Subtract 5 from both sides
∴ w = -5 ⇒ rejected because no dimension with -ve value
∴ w = 3 only
The width of the rug is 3 inches
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is the square root of 3 irrational
Answer: Yes it is irrational
Step-by-step explanation:
Answer:
Yes.
Step-by-step explanation:
sqrt(3)=1.73205080...
Therefore, it's irrational.
The cloth top of the gazebo in Mr. Chang’s backyard has ripped from weathering. He needs to know the area of the cloth so he can replace it.
How much cloth, in square feet, will Mr. Chang need, assuming he does not need to replace the cloth at the bottom of the figure?
60
96
120
156
Answer:
The correct answer is A. 60 square feet.
Step-by-step explanation:
1. Let's review the data provided to us for solving the question:
The gazebo in Mr. Chang's backyard, according to the figure, is a square pyramid because its base is a square of 6 feet as length of its sides.
Length of the sides of the base = 6 feet
Slant length = 5 feet
Height = 4 feet
2. How much cloth, in square feet, will Mr. Chang need, assuming he does not need to replace the cloth at the bottom of the figure?
Area of a square pyramid = Base area + 1/2 Perimeter * Slant length
Replacing with the real values, we have:
Area of a square pyramid = 6 * 6 + 1/2 (6 + 6 + 6 + 6) * 5
Area of a square pyramid = 36 + 1/2 (24) * 5
Area of a square pyramid = 36 + 12 * 5
Area of a square pyramid = 36 + 60
Area of a square pyramid = 96 feet ²
3. But remember than Mr. Chang doesn't need to replace the cloth at the bottom of the gazebo.
So we need to subtract the area of the base to the area of the square pyramid:
Area of the square pyramid - area of the base
Area of the base = 6 * 6 = 36 feet ²
96 feet ² - 36 feet ² = 60 feet ²
The correct answer is A. 60 square feet.
Answer:
60
Step-by-step explanation:
e d g e n u I t y
Help me find the missing variables
Answer: n=45 degrees, m=20 degrees
Step-by-step explanation:
the smaller triangle is isosceles
since one of the angles is 90 degrees that the other have to be 45 degrees each
so n=45 degrees
the big triangle is also isosceles meaning that m+n=(180-50)/2
m+n=65
we know n=45
so m=20
You invested money in two funds. Last year, the first fund paid a dividend of 8% and the second a dividend of 5%, and you received a total of $1330. This year, the first fund paid a 12% dividend and the second only 2%, and you received a total of $1500. How much money did you invest in each fund?
You invested 11000 in in 2st fund and 9000 in 2nd fund
Solution:Given that, You invested money in two funds.
Last year, the first fund paid a dividend of 8% and the second a dividend of 5%, and you received a total of $1330.
This year, the first fund paid a 12% dividend and the second only 2%, and you received a total of $1500.
Let the amount in Fund I be $x and amount in Fund II be $ y
Then, for last year ⇒ 0.08x+0.05y=1330 ----- eqn (1)
And for this year ⇒ 0.12x+0.02y=1500 ------- eqn (2)
Multiply (1) by 2 ⇒ 0.16 x + 0.1 y = 2660
Multiply (2) by 5 ⇒ 0.6 x + 0.1 y = 7500
Subtract the two equations
(2) ⇒ 0.6x + 0.1y = 7500
(1) ⇒ 0.16x + 0.1y = 2660
(-) --------------------------------
0.44x + 0 = 4840
x = 11000
Now, from eqn (2)
0.12(11000) + 0.02y = 1500
0.02y = 1500 – 1320
0.02y = 180
y = 9000
Hence, he invested 11000 in in 2st fund and 9000 in 2nd fund
how can I find the slope of a negative slope
Step-by-step explanation: To find the slope of a line with a negative slope, we would use the ratio rise/run between any two points that are on that line.
Let's look at an example which I have provided in the image attached. I have labeled two points which are points A and B.
Notice however that to get from point A to point B, we must first go down 3 units so we say that our rise is -3. From there we move 4 units to the right so our run is 4. So our slope or rise over run is -3/4.
A positive number is multiplied by itself and then 7 is added. The answer is 16. What is the number?
a. 4
b. 7
c. 3
d. 6
PLEASE ANSWER QUICKLY (:
Answer:
c
Step-by-step explanation:
let the number be n then multiplied by itself gives n², thus
n² + 7 = 16 ( subtract 7 from both sides )
n² = 9 ( take the square root of both sides )
n = [tex]\sqrt{9}[/tex] = 3
Final answer:
The positive number that when squared and increased by 7 equals 16 is 3, which corresponds to option (c).
Explanation:
The student is asking to find a positive number which, when multiplied by itself (squared), and then 7 is added, equals to 16. To find this number, we can set up a simple equation where x is the positive number we are looking for: x2 + 7 = 16. To solve for x, subtract 7 from both sides to get x2 = 9. Taking the square root of both sides gives us x = 3, since 32 = 9. Therefore, the correct answer is (c) 3.
realize the following operations and express the result in a+bi:
[tex](4 + 5i)( - 4 + \sqrt{ - 16} )[/tex]
Answer:
-4(i+9)
Step-by-step explanation:
(4+5i)(-4+sqrt(-16))
(4+5i)(-4+4i)
-16-20i+16i+20i^2
-16-4i+20(-1)
-16-4i-20
-4i-16-20
-4i-36
-4(i+9)
13 POINTS PLZ HELP!!
Find the slope, the y-intercept, and the x-intercept of the line y = 50 – 10x.
slope:
y-intercept:
x-intercept:
Answer:
Slope: -10
Y-intercept: 50
X-intercept: 5
Step-by-step explanation:
y-mx+b
y=-10x+50
m is slope so, slope is -10plug in 0 for x and solve to get y-intercept y=-10(0)+50 , y intercept is 50plug in 0 for y and solve to get x-intercept 0=-10x+50, x-intercept is 52 Points
Solve the system of equations and choose the correct ordered pair.
3x+4y= 38
5x - 5y=-30
O A. (2,6)
O B. (2,8)
O C. (3,9)
O D. (3,4)
Answer:
b
Step-by-step explanation:
the answer is b , x= 2 and y= 8, observe: 3.2+ 4.8= 6+32=38 , second ecuation 5.2-5.8= 10-40= -30
what's the equivalent of 3/7?
Answer:
6/14 or 0.43 it depends from a question
Help with 2y= 6x + 10 y=2x + 4
Answer:
2(2x+4)=6x+10
2x=2
x=2/2
x=1
y=2(-1)+4
y=-2+4
y=2
Solve this inequality and plz show how to work this out. Will give brainlest!!!!!!
-4(x-3)>5x-6
What is the solution of the proportion 22/11=r/13
PC-CSIL
Acuve
TIME REI
54-
Which best explains or justifies Step 1?
The first step for deriving the quadratic formula from the
quadratic equation, 0 = ax? + bx + c, is shown.
Step 1: -c = ax + bx
subtraction property of equality
completing the square
factoring out the constant
zero property of multiplication
The equality used is Subtraction property of equality
Option A is correct
Step-by-step explanation:
We need to identify which option best explains or justifies Step 1.
Step 1 is: [tex]-c = ax^2 + bx[/tex]
The given equation is: [tex]0 = ax^2 + bx + c[/tex]
To get the equation for step 1 we need to subtract c on both sides of equation i.e using subtraction property of equality
[tex]0-c = ax^2 + bx + c-c[/tex]
[tex]-c = ax^2 + bx [/tex]
So, The equality used is Subtraction property of equality
Option A is correct.
Keywords: Solving Quadratic Equations
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Marcia ran m miles on Monday.On Tuesday,she ran 18% farther than she ran on Monday.Write an expression for how far Marcia ran on Tuesday
The expression for how far Marcia ran on Tuesday is 1.18m miles.
Explanation:To find the expression for how far Marcia ran on Tuesday, we can start by noting that she ran 18% farther than she did on Monday. Since she ran m miles on Monday, we can express the distance she ran on Tuesday as m + 18% of m.
To calculate the 18% of m, we need to multiply m by 18/100 or 0.18. Therefore, the expression for how far Marcia ran on Tuesday is m + 0.18m, which simplifies to 1.18m.
So, Marcia ran 1.18m miles on Tuesday.
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Select the correct answer. (-1,1) (0,-1) (5,-11) (10,-21) What is the domain of the set of ordered pairs above? A. {-1, 0, 5, 10} B. {1, -1, -11, -21} C. {-1, 10} D. {-1, 1}
Answer:
Domain of set of given ordered pair is { -1, 0, 5, 10}
Step-by-step explanation:
All of the values that can go into a relation or function (input) are called the domain.
The domain is the set of all first elements of ordered pairs (x-coordinates).
In the given question,
ordered pairs are (-1,1) , (0,-1) , (5,-11) , (10,-21)
Therefore,
Domain is the set of all first elements of ordered pairs.
i.e -1, 0, 5, 10
Hence the required set is { -1, 0, 5, 10}.
The domain of the set of ordered pairs is {-1, 0, 5, 10}.
Explanation:The domain of a set of ordered pairs represents all the x-values in the set. In this case, the set of ordered pairs is (-1,1), (0,-1), (5,-11), and (10,-21). The x-values in this set are -1, 0, 5, and 10. Therefore, the domain of the set of ordered pairs is A. {-1, 0, 5, 10}.
4.
(5x2)(-4x3)
the 2 and the 3 are exponents
Answer:
-20x⁵Step-by-step explanation:
[tex](5x^2)(-4x^3)=\bigg(5\cdot(-4)\bigg)(x^2x^3)\\\\\text{use}\ a^na^m=a^{n+m}\\\\=-20x^{2+3}=-20x^5[/tex]
is it possible for a figure to have 90° rotational symmetry but not 180° rotational symmetry.
Answer:
Well, It is but not because..rotation symmetry, and a square has -turn (or 90-degree) rotation symmetry. As you may have already observed, many figures have 180-degree rotation symmetry but no other rotation symmetry. A figure has 180-degree rotation symmetry if it looks the same when turned halfway around...Soo yeah..I think I am right, So sorry if I'm wrong.
Step-by-step explanation:
Yes, a figure can have 90° rotational symmetry but not 180° rotational symmetry.
Explanation:Yes, it is possible for a figure to have 90° rotational symmetry but not 180° rotational symmetry. To understand this, think about the number '6'. If you rotate it 90° clockwise, it looks exactly the same, but if you rotate it 180°, it becomes '9'. So, the figure has 90° rotational symmetry but not 180° rotational symmetry.
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Solve: 4^3x = 4^2
X=-3/2
X=-2/3
X=2/3
X=3/2
Answer:
[tex]\large\boxed{x=\dfrac{2}{3}}[/tex]
Step-by-step explanation:
[tex]4^{3x}=4^2\iff3x=2\qquad\text{divide both sides by 3}\\\\x=\dfrac{2}{3}[/tex]
Answer:
C is the answer
Step-by-step explanation:
just took the assignment, and got 100%