Write z in polar form:
z = 1 + √3 i = 2 exp(i π/3)
Taking the square root gives two possible complex numbers,
√z = √2 exp(i (π/3 + 2kπ)/2)
with k = 0 and k = 1, so that
√z = √2 exp(i π/6) = √(3/2) + √(1/2) i
and
√z = √2 exp(i 7π/6) = -√(3/2) - √(1/2) i
Find the correct algebraic representation of the dilation shown below.
a- (1/2x,1/2y)
b-(2/7x,2/7y)
c-(7/2x,7/2y)
d-(7x,7y)
Given:
The diagram of triangle DEF and triangle D'E'F' on a coordinate plan.
To find:
The algebraic representation of the dilation.
Solution:
The vertices of triangle DEF are D(0,7), E(7,-7) and F(-7,-7).
The vertices of triangle D'E'F' are D'(0,2), E(2,-2) and F(-2,-2).
We know that, the dilation factor is:
[tex]k=\dfrac{x\text{ or }y\text{ coordinate of the dilated point}}{x\text{ or }y\text{ coordinate of the corresponding original point}}[/tex]
For point D' the y-coordinate is 7 and for point D the y-coordinate is 2. So,
[tex]k=\dfrac{2}{7}[/tex]
The rule of dilation is:
[tex](x,y)\to \left(kx,ky\right)[/tex]
[tex](x,y)\to \left(\dfrac{2}{7}x,\dfrac{2}{7}y\right)[/tex]
The algebraic representation of the dilation is [tex]\left(\dfrac{2}{7}x,\dfrac{2}{7}y\right)[/tex].
Therefore, the correct option is b.
what values of x makes -6x =12 true
Answer:
=> —6x = 12=> —x = 12/6=> —x = 2=> x = —2Step-by-step explanation:
hope it's helpful :-)
In Problem, p is in dollars and q is the number of units.
(a) Find the elasticity of the demand function
p2 + 2p + q = 49 at p = 6.
(b) How will a price increase affect total revenue?
Answer:
-14
Explanation:
Elasticity of demand is the degree of change in demand after a change I'm price, basically demand's sensitivity to price change.
Formula for calculating price elasticity is: change in price/change in quantity =dq/dp
Since we are given p²+2p+q=49 and not initial and current amount of price and quantity, we differentiate to find demand elasticity, thus:
2p+2+dq/dp=0
dq/dp=-2p-2
Given p =6, we substitute:
dq/dp=-2×6-2
dq/dp=-12-2
dq/dp=-14
With a demand elasticity of -14 there is an inverse relationship between price and demand. While price increases, demand falls.
6. Donna adds 400 ml (milliliters) of water to 100 ml of coffee. What percentage of Donna's drink is coffee?
9514 1404 393
Answer:
20%
Step-by-step explanation:
100 mL of the drink is coffee
The total amount of drink is 100 mL +400 mL = 500 mL. Then the fraction that is coffee is ...
coffee/total = (100 mL)/(500 mL) = 1/5 = 1/5 × 100% = 20%
20% of Donna's drink is coffee.
Expand and simplify (b+6)(b-4)
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: {b}^{2} + 2b - 24}}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}[/tex]
[tex] \: (b + 6)(b - 4)[/tex]
➼[tex] \: b \: (b - 4) + 6 \: (b - 4)[/tex]
➼[tex] \: {b}^{2} - 4b + 6b - 24[/tex]
Combining like terms, we have
➼[tex] \: {b}^{2} + 2b - 24[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
1.
What is the slope of the line through the points (-2, -1) and (8, -3)?
Answer:
The slope of the line is [tex]-\frac{1}{5}[/tex] in fraction form or -0.2 in decimal form.
Step-by-step explanation:
To solve for the slope of the line, use the rise over run formula. The rise over run formula is a measure of how much something changes vertically compared to how much it changes in the horizontal direction. The rise over run formula calculates the difference between the two points in the vertical direction (rise) and then divide it by the difference in the horizontal direction (run). The formula looks like [tex]\frac{rise}{run}[/tex], but in terms of finding a slope, it looks like [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].
For finding the slope of this line with the points (-2,-1) and (8,-3), start by writing down the information given from the question.
[tex]y_{2}= -3[/tex]
[tex]y_{1}=-1[/tex]
[tex]x_{2}=8[/tex]
[tex]x_{1}= -2[/tex]
Next, plug in the information given from the question into the formula, and the formula will look like [tex]\frac{-3-(-1)}{8-(-2)}[/tex]. Then, simplify the equation, which will look like [tex]\frac{-2}{10}= -\frac{1}{5}[/tex]. The final answer will be [tex]-\frac{1}{5}[/tex] in fraction form or -0.2 in decimal form.
For how many minutes did Lynn run at a greater speed
than Kael?
0 12
O 17
O 23
O 28
Answer:
D. ✔ 28
Step-by-step explanation:
E 2021
write cos2x as sinx
please help with this
Answer:
[tex]\cos(2\, x) = 1 - 2\, (\sin(x))^2[/tex].
Step-by-step explanation:
Angle sum identity for cosine: [tex]\cos(a + b) = \cos(a) \, \cos(b) - \sin(a) \, \sin(b)[/tex].
Pythagorean identity: [tex](\cos(a))^{2} + (\sin(a))^{2} = 1[/tex] for all real [tex]a[/tex].
Subtract [tex](\cos(x))^{2}[/tex] from both sides of the Pythagorean identity to obtain: [tex](\sin(a))^{2} = 1 - (\cos(a))^{2}[/tex].
Apply angle sum identity to rewrite [tex]\cos(2\, x)[/tex].
[tex]\begin{aligned}&\cos(2\, x)\\ &= \cos(x + x) \\ &= \cos(x) \, \cos(x) - \sin(x)\, \sin(x) \\ &= (\cos(x))^{2} + (\sin(x))^{2}\end{aligned}[/tex].
[tex](\sin(a))^{2} = 1 - (\cos(a))^{2}[/tex] follows from the Pythagorean identity. Hence, it would be possible to replace the [tex](\cos(x))^{2}[/tex] in the previous expression with [tex](1 - (\sin(x))^{2})[/tex].
[tex]\begin{aligned}&(\cos(x))^{2} - (\sin(x))^{2}\\ &= \left[1 - (\sin(x))^{2}\right] - (\sin(x))^{2} \\ &= 1 - 2\, (\sin(x))^{2} \end{aligned}[/tex].
Conclusion:
[tex]\begin{aligned}&\cos(2\, x) \\ &= (\cos(x))^{2} + (\sin(x))^{2} \\ &=1 - 2\, (\sin(x))^{2}\end{aligned}[/tex]
find the radius of this circle.
Answer:
r = 5 units
Step-by-step explanation:
Given:
Angle subtended at the centre (∅) in radians = 2π/3
Arc length (S) = 10π/3
radius (r) = ?
Required:
Radius (r)
Solution:
Formula for arc length given the central angle in radians is:
S = r∅
Make e the subject of the formula by dividing both sides by ∅
S/∅ = r∅/∅
r = S/∅
Plug in the values
r = (10π/3) / (2π/3)
Change the operation sign to multiplication and turn the fraction by your right upside down
r = 10π/3 × 3/2π
r = (10π × 3)/(3 × 2π)
Cross out terms that can divided each other
r = 5
Use the diagram shown to find 4 ÷ 1/3
Answer:
12
Step-by-step explanation:
Since there is no diagram. I will just tell you the answer. first convert into multiplcation keep everything but the 1/3. Change 1/3 into 3/1 (3). Multiply 4*3=12.
Sorry if I don't have a graph.
Hope this helps!
The table represents the equation y= 8x what y= value is missing from the table?
Answer:
24
Step-by-step explanation:
y=8(3)= twenty four
you just fill in the x
The net of a rectangular prism is shown.
8 in.
2 in.
2 in.
8 in.
2 in.,
1
1
1
6 in.
1
2 in. :
1
is the correct answer lol ez stuff
Help help help help help
Answer:
x2+y2−12x+4y−60=0
The center of the circle is point: C=(6,−2).
The radius of the circle is r=10.
A sequence is defined by the formula f(n+1)=f(n)-3. If f(4)=22, what is f(1)?
10h
3
31
34
==============================================
Explanation:
The recursive rule
f(n+1)=f(n)-3
can be rearranged to
f(n) = f(n+1)+3
after adding 3 to both sides
----------------
Now let's say we plug in n = 3
f(n) = f(n+1)+3
f(3) = f(3+1)+3
f(3) = f(4)+3
f(3) = 22+3
f(3) = 25
Repeat for n = 2
f(n) = f(n+1)+3
f(2) = f(2+1)+3
f(2) = f(3)+3
f(2) = 25+3
f(2) = 28
Each time we keep adding 3 to get the previous term (since the original recursive rule says to subtract 3 to get the next term; we just go backwards of what the instructions say).
Lastly, we can find that f(1) = f(2)+3 = 28+3 = 31 making the answer to be choice C.
Solve each equation.
2p = 2 p = _____
q - 3 = 7 q = _____
Answer:
[tex]\textbf{HELLO!!}[/tex]
[tex]2p=2[/tex]
[tex]\frac{2p}{2}=\frac{2}{2}[/tex] [tex]\hookleftarrow \mathrm{Divide\:both\:sides\:by\:}2[/tex]
[tex]=1[/tex]
[tex]\boxed{\boxed{\underline{\textsf{\textbf{P=1}}}}}[/tex]
---------------------
[tex]q - 3 = 7[/tex]
[tex]q-3+3=7+3[/tex] [tex]\hookleftarrow \mathrm{Add\:}3\mathrm{\:to\:both\:sides}[/tex]
[tex]=10[/tex]
[tex]\boxed{\boxed{\underline{\textsf{\textbf{q=10}}}}}[/tex]
-----------------------
[tex]\textbf{HOPE IT HELPS}[/tex]
[tex]\textbf{HAVE A GREAT DAY!!}[/tex]
Which compound inequality could be represented by the graph?
–4 ≤ x ≤ 4
–2 ≤ x ≤ –1
x ≤ –1 or x ≥ 0
x ≤ 3 or x ≥ –1
Answer:
It is D.
Step-by-step explanation:
x ≤ 3 or x ≥ –1
Answer:
D) X <_ 3 or X _> -1
Whole Unit Test Review Answers:
1) D
2)D
3)B
4)C
5)D
6)A
7)B
8)C
9)A
10)B
11)D
12)D
13)B
14)B
15)D
(I got a 100%, and these were my answers, hope they help!)
(The pic below is a screenshot of the 100%, for reassurance)
in a triangle the angle with the smallest measure is always the opposite the
Answer:
in a triangle, the angle with the smallest measure is always opposite the shortest side.
Step-by-step explanation:
The height of the saddle off horse above the base ofa carousel can be modeled 4t by the equation f-rr) : 12 sin ^ r 42, where I represents seconds after the ride started. I How much time does to take for the horse to complete one cycle of motion and return to its starting height. What is the maximum height and the minimum height of the horse's saddle above the base ofthe carousel
Answer:
(a) The time to complete 1 cycle and return is 16/3
(b) The minimum height is 30 inches and the maximum is 54 inches
Step-by-step explanation:
Given
[tex]f(t) = 12\sin(\frac{3\pi}{8}t) + 42[/tex]
Solving (a): Time to complete 1 cycle and return
This implies that we calculate the period. This is calculated using:
[tex]T = \frac{2\pi}{w}[/tex]
Where:
[tex]w =\frac{3\pi}{8}[/tex]
So, we have:
[tex]T = \frac{2\pi}{\frac{3\pi}{8}}[/tex]
[tex]T = \frac{2}{\frac{3}{8}}[/tex]
[tex]T = \frac{2*8}{3}[/tex]
[tex]T = \frac{16}{3}[/tex]
Solving (b): The maximum and the minimum height
To do this, we have:
[tex]-1 \le \sin(\theta) \le 1[/tex]
Which means:
[tex]-1 \le \sin(\frac{3\pi}{8}) \le 1[/tex]
So, the minimum is:
[tex]\sin(\frac{3\pi}{8}) =- 1[/tex]
And the maximum is:
[tex]\sin(\frac{3\pi}{8}) =1[/tex]
Recall that the height is:
[tex]f(t) = 12\sin(\frac{3\pi}{8}t) + 42[/tex]
So, the maximum and the minimum of are:
[tex]h_{min} =12 * -1 + 42[/tex]
[tex]h_{min} =30[/tex]
and
[tex]h_{max} =12*1+42[/tex]
[tex]h_{max} =54[/tex]
an electric guitar costs $790 with a 235 full replacement warranty if the manufacturer sells 500 and 98,274 warranties and has to honor 11% of them, how much profit did the manufacturer gain from the warrenties
Answer:
i got Profit = $125,129,007.1
Step-by-step explanation:
Multiple choice math problem
Answer:
ok so its a triangle with one side being
11
on side being
2
and one side is x
so we just use the formula
11^2+2^2=c^2
11^2+2^2=125
125 squared is 25
so
3 times the square root of 13 is 10.8166538264
so no
5 times the square root of 5 is 11.1803398875
so the answer i guess might be a?
Hope This Helps!!!
Pls Helppppp meeeeee!!
Answer:
G
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Simplifying the radicals in the expression
[tex]\sqrt{52}[/tex]
= [tex]\sqrt{4(13)}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{13}[/tex]
= 2[tex]\sqrt{13}[/tex]
------------------
[tex]\sqrt{117}[/tex]
= [tex]\sqrt{9(13)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{13}[/tex]
= 3[tex]\sqrt{13}[/tex]
Then
[tex]\sqrt{52}[/tex] + [tex]\sqrt{117}[/tex]
= 2[tex]\sqrt{13}[/tex] + 3[tex]\sqrt{13}[/tex]
= 5[tex]\sqrt{13}[/tex] → G
[tex]{\small\sf{The\:expression \sqrt{52} + \sqrt{117} \:is \: equivalent \: to}}[/tex]
[tex]\small\bf{F.} \: \sf{13} [/tex]
[tex]\small\bf{G.}\sf \:5 \sqrt{13} [/tex]
[tex]\small\bf{H.}\sf\:6 \sqrt{13} [/tex]
[tex]\small\bf{J.}\sf\:13 \sqrt{13} [/tex]
Solution:-[tex]\small\sqrt{52}+\sqrt{117}\sqrt{4•13} +\sqrt{9•13}\tiny\sf\purple{(Product\:Property)}[/tex]
[tex]\small{ \: \:\: \: \: \: \: \:=\sqrt{2²•13}+\sqrt{3²•13}\tiny\sf\purple{(Prime\:Factorization)}}[/tex]
[tex]\small{\: \:\: \: \: \: \: \:=\sqrt{2²}\sqrt{13}+\sqrt{3²}\sqrt{13}\tiny\sf\purple{(Product\:Property)}}[/tex]
[tex]\small{\: \:\: \: \: \: \: \:=2\sqrt{13}+3\sqrt{13}\tiny\sf\purple{(Simplify)}}[/tex]
[tex]\small{\: \:\: \: \: \: \: \:=5\sqrt{13}\tiny\sf\purple{(Simplify)}}[/tex]
Answer:-So, the correct option is D.
=======================#Hope it helps!
(ノ^_^)ノ
Find the value of n?
Answer:
[tex]n^{2} -3=39.2=78\\n^2=78+3=81\\n=\sqrt{81} \\n=9[/tex]
Step-by-step explanation:
what percentage of the appies are yellow?
Answer:
20%
Step-by-step explanation:
6 out of 30. = 1/5 = multiply 5*20= 100 and 1*20= 100 so it is 20% of 100.
15 points What’s the area‼️‼️‼️‼️‼️ please help me attach work too if you can
Answer:
66
Step-by-step explanation:
5x2= 10
7x8= 56
10+56= 66
Answer:
106
Step-by-step explanation:
split the shape, so you have 2 rectangles.
Multiply 8 and 7 = 56
add 2 and 8 =10, then multiply 10 by 5. =50
add 50 and 56
therefore your answer is 106.
A marketing research company needs to estimate which of two medical plans its employees prefer. A random sample of n employees produced the following 95% confidence interval for the proportion of employees who prefer plan A: (0253.0553). Identify the point estimate for estimating the true proportion of employees who prefer that plan.
a. 0.403
b. 0.253
c. 0.553
d. 0.15
Answer:
a. 0.403
Step-by-step explanation:
Confidence interval concepts:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
The margin of error is the difference between the two bounds, divided by 2.
Confidence interval of (0.253,0.553)
The bounds are 0.253 and 0.553, so the point estimate is:
[tex]p = \frac{0.253 + 0.553}{2} = 0.403[/tex]
This means that the correct answer is given by option A.
6. Roll a pair of dice. What is the probability that a total of 12 will be face up?
Answer:
The Probability would be 2.78%
Step-by-step explanation: Hope this helps :)
Mr. Smith wants to know if he can fit 4 trapezoid tables like the one shown below into a room. What is the total area of 4 trapezoid tables? Answer without units. NUMBER ONLY!
Answer:
(1/2)(2)(5+3)
8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
The area of a trapezoid is:
( a + b ) ÷ 2 x h
Where a & b are the bases, and h is the height.
Use formula with the given measurements:
(3 + 5) ÷ 2 x 2
= 8 ÷ 2 x 2
= 4 x 2
= 8
Hope this helps
DFGI is a trapezoid with midsegment EH. What is DI?
D
8 cm
F
7 cm
EH = 6.00 cm
FG = 4.00 cm
5 cm
G
6 cm
H
Answer:
a. 8 cm
Step-by-step explanation:
Given:
EH = 6 cm
FG = 4.00 cm
Based on the mid-segment theorem of a trapezoid, we have:
EH = ½(FG + DI)
Plug in the values
6 = ½(4 + DI)
Multiply both sides by 2
6*2 = 4 + DI
12 = 4 + DI
12 - 4 = 4 + DI - 4
8 = DI
DI = 8 cm
11x+7y=17
solve for y
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {\: y = \frac{17 - 11x}{7} }}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex]\\11x + 7y = 17[/tex]
[tex] \\➺ \: 7y = 17 - 11x[/tex]
[tex]\\➺ \: y = \frac{17 - 11x}{7} [/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
If Sarah turns 15 on august 27 and her graduation year is 2024 how old will she be when she graduates high school?
Answer:
She will be 17
Step-by-step explanation:
My sister is like that but she's graduating in 22'
It sort of depends where Sarah lives -.-
But if she starts high school when she's 15 (in 2021) and she graduates in 2024 it means high school is three years.
So 15 plus 3.
Sarah will be 18 when she graduates high school.