Answer:
18
Step-by-step explanation:
X^2 - 7 =
Since we need to evaluate the expression when X = 5, we replace X with 5.
= 5^2 - 7
Now, according to the correct order of operations, we need to do the exponent first. 5^2 = 5 * 5 = 25
= 25 - 7
Finally, we subtract.
= 18
Answer: 18
find the missing side. Round it the nearest tenth.
Answer: x= 11√3= 19.0525 = 19.1
Step-by-step explanation:
Let the reference angle be 30
so
cos 30 = b/h
√3/2 = x/22
or, 22√3 = 2x
or. x = (22√3)/2
so, x = 11√3
Answer:
x = 19.1 cm
Step-by-step explanation:
→ Find the name of the side you are not given
Opposite
→ Find a formula without opposite in it
Cos = Adjacent ÷ Hypotenuse
→ Rearrange to make adjacent the subject
Adjacent = Cos × Hypotenuse
→ Substitute in the values
Adjacent = Cos ( 30 ) × 22
→ Simplify
Adjacent = 19.1
Help me! thank you so much
Answer:
Step-by-step explanation:
[tex]\frac{sinxcos^3x-cos xsin^3x}{cos^42x-sin^42x} \\=\frac{sin x cos x(cos^2x-sin ^2 x)}{(cis^2 2x+sin^2 2x)(cos^2 2x-sin ^22x)} \\=\frac{2sin x cos x cos 2x}{2(1)(cos 4x)} \\=\frac{sin 2x cos 2x}{2 cos 4x} \\=\frac{2 sin 2x cos 2x}{4 cos 4x} \\=\frac{sin 4x}{4 cos 4x} \\=\frac{1}{4} tan 4x[/tex]
100 POINTS AND BRAINLIEST FOR THIS WHOLE SEGMENT
a) Find zw, Write your answer in both polar form with ∈ [0, 2pi] and in complex form.
b) Find z^10. Write your answer in both polar form with ∈ [0, 2pi] and in complex form.
c) Find z/w. Write your answer in both polar form with ∈ [0, 2pi] and in complex form.
d) Find the three cube roots of z in complex form. Give answers correct to 4 decimal
places.
Answer:
See Below (Boxed Solutions).
Step-by-step explanation:
We are given the two complex numbers:
[tex]\displaystyle z = \sqrt{3} - i\text{ and } w = 6\left(\cos \frac{5\pi}{12} + i\sin \frac{5\pi}{12}\right)[/tex]
First, convert z to polar form. Recall that polar form of a complex number is:
[tex]z=r\left(\cos \theta + i\sin\theta\right)[/tex]
We will first find its modulus r, which is given by:
[tex]\displaystyle r = |z| = \sqrt{a^2+b^2}[/tex]
In this case, a = √3 and b = -1. Thus, the modulus is:
[tex]r = \sqrt{(\sqrt{3})^2 + (-1)^2} = 2[/tex]
Next, find the argument θ in [0, 2π). Recall that:
[tex]\displaystyle \tan \theta = \frac{b}{a}[/tex]
Therefore:
[tex]\displaystyle \theta = \arctan\frac{(-1)}{\sqrt{3}}[/tex]
Evaluate:
[tex]\displaystyle \theta = -\frac{\pi}{6}[/tex]
Since z must be in QIV, using reference angles, the argument will be:
[tex]\displaystyle \theta = \frac{11\pi}{6}[/tex]
Therefore, z in polar form is:
[tex]\displaystyle z=2\left(\cos \frac{11\pi}{6} + i \sin \frac{11\pi}{6}\right)[/tex]
Part A)
Recall that when multiplying two complex numbers z and w:
[tex]zw=r_1\cdot r_2 \left(\cos (\theta _1 + \theta _2) + i\sin(\theta_1 + \theta_2)\right)[/tex]
Therefore:
[tex]\displaystyle zw = (2)(6)\left(\cos\left(\frac{11\pi}{6} + \frac{5\pi}{12}\right) + i\sin\left(\frac{11\pi}{6} + \frac{5\pi}{12}\right)\right)[/tex]
Simplify. Hence, our polar form is:
[tex]\displaystyle\boxed{zw = 12\left(\cos\frac{9\pi}{4} + i\sin \frac{9\pi}{4}\right)}[/tex]
To find the complex form, evaluate:
[tex]\displaystyle zw = 12\cos \frac{9\pi}{4} + i\left(12\sin \frac{9\pi}{4}\right) =\boxed{ 6\sqrt{2} + 6i\sqrt{2}}[/tex]
Part B)
Recall that when raising a complex number to an exponent n:
[tex]\displaystyle z^n = r^n\left(\cos (n\cdot \theta) + i\sin (n\cdot \theta)\right)[/tex]
Therefore:
[tex]\displaystyle z^{10} = r^{10} \left(\cos (10\theta) + i\sin (10\theta)\right)[/tex]
Substitute:
[tex]\displaystyle z^{10} = (2)^{10} \left(\cos \left(10\left(\frac{11\pi}{6}\right)\right) + i\sin \left(10\left(\frac{11\pi}{6}\right)\right)\right)[/tex]
Simplify:
[tex]\displaystyle z^{10} = 1024\left(\cos\frac{55\pi}{3}+i\sin \frac{55\pi}{3}\right)[/tex]Simplify using coterminal angles. Thus, the polar form is:
[tex]\displaystyle \boxed{z^{10} = 1024\left(\cos \frac{\pi}{3} + i\sin \frac{\pi}{3}\right)}[/tex]
And the complex form is:
[tex]\displaystyle z^{10} = 1024\cos \frac{\pi}{3} + i\left(1024\sin \frac{\pi}{3}\right) = \boxed{512+512i\sqrt{3}}[/tex]
Part C)
Recall that:
[tex]\displaystyle \frac{z}{w} = \frac{r_1}{r_2} \left(\cos (\theta_1-\theta_2)+i\sin(\theta_1-\theta_2)\right)[/tex]
Therefore:
[tex]\displaystyle \frac{z}{w} = \frac{(2)}{(6)}\left(\cos \left(\frac{11\pi}{6} - \frac{5\pi}{12}\right) + i \sin \left(\frac{11\pi}{6} - \frac{5\pi}{12}\right)\right)[/tex]
Simplify. Hence, our polar form is:
[tex]\displaystyle\boxed{ \frac{z}{w} = \frac{1}{3} \left(\cos \frac{17\pi}{12} + i \sin \frac{17\pi}{12}\right)}[/tex]
And the complex form is:
[tex]\displaystyle \begin{aligned} \frac{z}{w} &= \frac{1}{3} \cos\frac{5\pi}{12} + i \left(\frac{1}{3} \sin \frac{5\pi}{12}\right)\right)\\ \\ &=\frac{1}{3}\left(\frac{\sqrt{2}-\sqrt{6}}{4}\right) + i\left(\frac{1}{3}\left(- \frac{\sqrt{6} + \sqrt{2}}{4}\right)\right) \\ \\ &= \boxed{\frac{\sqrt{2} - \sqrt{6}}{12} -\frac{\sqrt{6}+\sqrt{2}}{12}i}\end{aligned}[/tex]
Part D)
Let a be a cube root of z. Then by definition:
[tex]\displaystyle a^3 = z = 2\left(\cos \frac{11\pi}{6} + i\sin \frac{11\pi}{6}\right)[/tex]
From the property in Part B, we know that:
[tex]\displaystyle a^3 = r^3\left(\cos (3\theta) + i\sin(3\theta)\right)[/tex]
Therefore:
[tex]\displaystyle r^3\left(\cos (3\theta) + i\sin (3\theta)\right) = 2\left(\cos \frac{11\pi}{6} + i\sin \frac{11\pi}{6}\right)[/tex]
If two complex numbers are equal, their modulus and arguments must be equivalent. Thus:
[tex]\displaystyle r^3 = 2\text{ and } 3\theta = \frac{11\pi}{6}[/tex]
The first equation can be easily solved:
[tex]r=\sqrt[3]{2}[/tex]
For the second equation, 3θ must equal 11π/6 and any other rotation. In other words:
[tex]\displaystyle 3\theta = \frac{11\pi}{6} + 2\pi n\text{ where } n\in \mathbb{Z}[/tex]
Solve for the argument:
[tex]\displaystyle \theta = \frac{11\pi}{18} + \frac{2n\pi}{3} \text{ where } n \in \mathbb{Z}[/tex]
There are three distinct solutions within [0, 2π):
[tex]\displaystyle \theta = \frac{11\pi}{18} , \frac{23\pi}{18}\text{ and } \frac{35\pi}{18}[/tex]
Hence, the three roots are:
[tex]\displaystyle a_1 = \sqrt[3]{2} \left(\cos\frac{11\pi}{18}+ \sin \frac{11\pi}{18}\right) \\ \\ \\ a_2 = \sqrt[3]{2} \left(\cos \frac{23\pi}{18} + i\sin\frac{23\pi}{18}\right) \\ \\ \\ a_3 = \sqrt[3]{2} \left(\cos \frac{35\pi}{18} + i\sin \frac{35\pi}{18}\right)[/tex]
Or, approximately:
[tex]\displaystyle\boxed{ a _ 1\approx -0.4309 + 1.1839i,} \\ \\ \boxed{a_2 \approx -0.8099-0.9652i,} \\ \\ \boxed{a_3\approx 1.2408-0.2188i}[/tex]
Write the name of the definition, postulate, property or theorem that justifies the statement about the diagram.
The following are the statement justifications and explanatory reasons ;
(a) AD + DB = AB; Is justified by segment addition postulate
Reason
Segment addition postulate states that let A and B represent two points,
Then a third D can be on the line joining A and B, if and only if the
relationship between the points is according to the equation, AD + DB = AB
only
(b) m∠1 + m∠2 = m∠CDB; Is justified by angle addition postulate
Reason
Angle addition postulate states that given that a point B lies between an angle m∠AOC, then we have;
m∠AOC = m∠AOB + m∠BOC
(c) ∠2 ≅ ∠6; Is justified by vertically opposite angles theorem
Reason
Vertical angles formed by the crossing of two lines are always equal
(d) If D is the midpoint of [tex]\overline{AB}[/tex], then AD = [tex]\dfrac{1}{2}[/tex]×AB; Definition of midpoint
Reason
The midpoint of a line is the point that is of equal distance from both ends of the of the line. It is the point halfway between the endpoints
(e) If [tex]\underset{DF}{\rightarrow}[/tex] bisects ∠CDB then ∠1 ≅ ∠2; Definition of angle bisector
Reason
An angle bisector is a ray or line that divides an angle into two angles that are congruent
(f) m∠ADF + m∠FDB = 180°; Linear pair postulate
Reason
The linear pair postulate states that where we have two angles that form a linear pear (their addition forms a straight line), then the two angles are supplementary (their sum is 180°)
(g) ∠ADF and ∠4 are supplements, then m∠ADF + m∠4 = 180°; Definition of supplementary angle
Reason
Supplementary angle are defined as angles that when added together, have a sum of 180°
(h) If ∠4 is complementary to ∠5, and ∠6 is complementary to ∠5, then ∠4 ≅ ∠6; Transitive property
Reason
Transitive property states that given three real numbers, a, b, and c, if a = b and c = b, then a = c
Learn more about angle properties postulates, and theorems here;
https://brainly.com/question/14437065
What is the quotient?
(-3)
(-3)²
O-9
1
o
1
9
100
O 9
Answer:
(-3)
Step-by-step explanation:
follow me if you want
help lol i forgot everything of the summer time
fill in the table using this function rule
Answer:
hope it help you
Step-by-step explanation:
mark me brailiest answer
Determine the sum of the first 33 terms of the following series:
−52+(−46)+(−40)+...
Answer:
1320
Step-by-step explanation:
Use the formula for sum of series, s(a) = n/2(2a + (n-1)d)
The terms increase by 6, so d is 6
a is the first term, -56
n is the terms you want to find, 33
Plug in the numbers, 33/2 (2(-56)+(32)6)
Simplify into 33(80)/2 and you get 1320
Between which two numbers does 46 lie?
A.
between 8 and 9
B.
between 6 and 7
C.
between 5 and 6
D.
between 7 and 8
Answer:
So the sqrt(46) is between 6 and 7
Step-by-step explanation:
sqrt(46)
5*5 = 25
6*6=36
7*7=49
So the sqrt(46) is between 6 and 7
SAT/ACT What is the solution of 1,200 – 5(3x + 30) = 600? A 30 B 50 C 150 D 200 E 250
The answer you are looking for is letter A, x=30.
Solution/Explanation:
First, write out the equation,
1200-5(3x+30)=600
Next, using the Distributive Property,
1200-15x-150=600
Simplify the left side of the equation just a little bit more,
1050-15x=600
Reverse order of terms on the left side, to make it a little bit easier to solve,
-15x+1050=600
Now, subtract 1050 from both sides,
-15x+1050-1050=600-1050
Now, simplify this part of the equation,
-15x=-450
Finally, divide both sides by -15,
So, therefore, the final answer is x=30.
I hope this helped you. Enjoy your day, and take care!
help help help help
Answer:
abc is a triangle so ,
a is ( 9,6 )
b is ( 9,3 )
and c is ( 3,3 )
If a line has a midpoint at (2,5), and the endpoints are (0,0) and (4,y), what is the value of y? Please explain each step for a better understanding:)
Answer:
y = 10
Step-by-step explanation:
To find the y coordinate of the midpoint, take the y coordinates of the endpoints and average
(0+y)/2 = 5
Multiply each die by 2
0+y = 10
y = 10
Amy, a nature photographer, randomly sampled photographs she took within the last year. She wanted to find out how many of her photographs contained flowers. The proportion of photographs that had flowers was 0.61, with a margin of error of 0.04. Construct a confidence interval for the proportion of her photographs taken within the last year contained flowers.
The Constructed confidence interval for the proportion of her photographs taken within the last year contained flowers is
[tex]CI\ E(0.57,0.65)[/tex]
From the question we are told that:
The proportion of photographs that had flowers P= 0.61
Margin of error of M.E= 0.04
Generally, the equation for Confidence interval for proportion is mathematically given by
[tex]CI=0.61 \pm 0.04[/tex]P \pm M.E
Therefore Confidence interval is
[tex]CI=0.61 \pm 0.04[/tex]
And can also be written as
[tex]CI\ E((0.61+0.04),0.61-0.04))[/tex]
[tex]CI\ E(0.57,0.65)[/tex]
In conclusion the Confidence interval is
[tex]CI\ E(0.57,0.65)[/tex]
For more information on this visit
https://brainly.com/question/24131141?referrer=searchResults
Helpppp pleaseeee !!!!!!
Answer:
149 inches squared
Step-by-step explanation:
top rectangle: 25 * 7 = 175
second rectangle: 8 * (25 - 17) = 8^2 = 64
triangle in bottom right: 1/2 * (13 - 8) * (15 - 11) = 10
175 + 64 + 10 = 149 sq in
hopefully got this right!
Simplify (Asap️ )
please answer this if you know
(full steps required )
(please no spam answers)
see the attachment hope this helps you
Find the measure of the indicated angle to the nearest degree.
Answer:
? ≈ 37°
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos? = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{5}[/tex] , then
? = [tex]cos^{-1}[/tex] ([tex]\frac{4}{5}[/tex] ) ≈ 37° ( to the nearest degree )
A factory inspector found flaws in 3 out of 18 wooden boxes. What is the experimental probability that the next wooden box will be flawed?
Write your answer as a fraction or whole number.
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]\frac{1}{6}[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Box Probability}}\\\\\rightarrow \frac{\text{# of boxed flawed}}{\text{# of boxes checked}} \\\\\rightarrow \frac{3}{18}\\\\\rightarrow \frac{3/3}{18/3}\\\\\rightarrow\boxed{\frac{1}{6}}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Evaluate 4(3 - 1)^2..
Answer:
16
Step-by-step explanation:
4(3 - 1)^2
~Simplify using PEMDAS
4(2)^2
4(4)
16
Best of Luck!
F is on the bisector of angle BCD. Find the length of FD (with lines over FD)
Answer:
8n-2 = 6n+9
2n-2 = 9
2n = 11
n = 5.5
So C is correct
Let me know if this helps!
PLS HELP ME ON THIS QUESTION I WILL MRK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Which of the following measures is a measure of spread?
A. median
B. range
C. mode
D. mean
Answer:
range
Step-by-step explanation:
Answer:
B. range.
Step-by-step explanation:
others are:
» Standard variation.
» Interquatile range.
» Quatiles, deciles and percentiles.
» variance.
[tex]{ \underline{ \blue{ \sf{christ \: † \: alone}}}}[/tex]
Two observers are 300 ft apart on opposite sides of a flagpole. The angles of
elevation from the observers to the top of the pole are 20°
and 15°. Find the
height of the flagpole.
Lilian is building a swimming pool in the shape of a right rectangular prism. The area of the base of the swimming pool is 72 square meters. The depth of the swimming pool is 3 meters. What is the volume of the swimming pool?
Answer:
216
Step-by-step explanation:
Volume of a rectangular prism = area of base * depth
Area of base: 72
Depth: 3
Volume = 72 * 3 = 216
3a + 2 = 20
5(b+1) = 10
3 (2y - 3) - 2y = y-3
2+ (2+4p) =6p
Please answer these questions with steps please!
I NEEDDD HELPPP ITSSSSSS URGENTTTTT!!!
Basically count/add up the total amount of degrees that are include in the angle <FHD.
-- (central angles)
So, 35 + 65 = 100 degrees
Select the correct answer from each drop-down menu.
A company makes cylindrical vases. The capacity, in cubic centimeters, of a cylindrical vase the company produces is given by the
function C() = 6.2873 + 28.26x2, where x is the radius, in centimeters. The area of the circular base of a vase, in square
centimeters, is given by the function A () = 3.14.2
To find the height of the vase, divide
represents the height of the vase.
the expressions modeling functions C(x) and A(z). The expression
Answer:
divide, 2x+9
Step-by-step explanation:
got it right
What would it be tho 300 doesn’t show up in my options my options are
1/49 -1/49 -49 and 49
If LM = 9x + 27 and RS = 135, find x.
Answer:
x=12
Step-by-step explanation:
LM = RS
9x+27 = 135
Subtract 27 from each side
9x+27-27 =135-27
9x=108
Divide each side by 9
9x/9 = 108/9
x = 12
the boxes are equivalent so the one with a single dash is equal to the other with a single dash.
the one with 2 dashes is equal to the other with 2 dashes so on and so forth
SR=LM
LM=9x+27
RS=135
9x+27=135
so I solve it in my own weird way but you can solve it differently. 135-27=108
108/9=12
so your answer is 12
The chance of solving a problem by A and B is and 1/3 and 2/5 respectively. What is the probability the problem will be solved?
a)2/15
b)1
c)9/15
d)11/15
Books shows "c" as the answer.. I am confused..
We want to compute the probability P(A or B) because we could either solve it following path A, path B, or doing both paths.
P(A) = 1/3
P(B) = 2/5
P(A and B) = P(A)*P(B) assuming A,B are independent
P(A and B) = (1/3)*(2/5)
P(A and B) = 2/15
--------
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 1/3 + 2/5 - 2/15
P(A or B) = 5/15 + 6/15 - 2/15
P(A or B) = (5 + 6 - 2)/15
P(A or B) = 9/15
We could reduce this to 3/5, but it appears your teacher has chosen not to.
PLS HELP ME ON THIS ANSWER I WILL MARK YOU AS BRAINLIEST IF YOU KNOW TGE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
LOL
Answer:
D. The over 30s have a larger range and interquartile range than the under 30s
Step-by-step explanation:
In a data set, the range is the difference between the maximum and minimum. So, the range for under 30s is 20, while the range for over 30s is 24. Additionally, the interquartile range is the difference between Q3 and Q1. For a boxplot, Q3 is the line where the box ends and Q1 is the line where the box begins. Therefore, the IQR for the under 30s is 8, and the IQR for over 30s is 11. So, D must be correct.
What is the smallest 3-digit palindrome that is divisible by both 3 and 4?
Answer:
252
Step-by-step explanation:
To be divisible by 3, it's digits have to add to a number that is a multiple of 3.
To be divisible by 4 its last 2 digits have to be divisible by 3.
So let's start with 1x1 which won't work because 1x1 is odd. so let's go to 2x2 and see what happens.
212 that's divisible by 4 but not 3
222 divisible by 3 but not 4
232 divisible by 4 but not 3
242 not divisible by either one.
252 I think this might be your answer
The digits add up to 9 which is a multiple of 3 and the last 2 digits are divisible by 4
ax^2-y^2-x-y factorize
Answer:
x(ax-1)-y(y+1)
Step-by-step explanation:
you have to group the like terms
ax^2-x-y^2-y
x(ax-1)-y(y+1)
I hope this helps
