Based on the given current and the given resistance, the voltage of the current is 14 + j8
How to determine the voltage of the current?From the question, we have the following parameters
current of 4+j2 amps and a resistance of 2-j3 ohms.
This can be rewritten as:
Current (I) = 4+j2 amps
Resistance (R) = 2-j3 ohms.
The formula to calculate voltage is given as
Voltage=(current) × (resistance)
Rewrite as:
V = I * R
Substitute the known values in the above equation
V = (4 + j2) * (2 - j3)
Expand the brackets
V = 8 - j4 + j12 + 6
Collect the like ters
V = 8 + 6 - j4 + j12
Evaluate the like term
V = 14 + j8
Based on the given current and the given resistance, the voltage of the current is 14 + j8
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Again I need help, If you tell me the answer that would be very nice! ,
Find the surface area of the composite figure :
The surface area of the given two rectangular prism is given as follows:
498 cm².
What is the surface area of a rectangular prism?The surface area of a rectangular prism of length l, width w and height h is given as follows:
S = 2(lw + wh + hl).
For this problem, there are two prisms, with dimensions given as follows:
l = 12 cm, w = 7 cm, h = 7 cm.l = 2 cm, w = 7 cm, h = 2 cm.Hence the surface area of the figure is the combined surface area of each figure, hence:
S = 2(7 x 7 + 12 x 7 + 12 x 7) + 2(2 x 7 + 2 x 2 + 7 x 2) = 498 cm².
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Mary walks from corner D to corner E to corner F on a city block that measures 264 feet wide and 900 feet long. Kate walks diagonally across the city block from corner D to corner F. How much less distance did Kate walk than Mary to get to corner F? Round your answer to the nearest whole foot. Enter only the number.
Step-by-step explanation:
we have a rectangle, that is then cut in half diagonally into 2 right-angled triangles.
in our problem it does not matter which side is the larger and which is the shorter one, because the distance calculation for both cases involve one short and one long side. the sequence does not matter.
Mary walks one short and one large side to get to the opposite corner (from D to F) :
264 + 900 = 1,164 ft
Kate walks diagonally. and that diagonal is the Hypotenuse of the right-angled triangle with a short and a long side of the rectangle.
so, Pythagoras applies :
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle), and a and b are the legs.
in our case that means
diagonal² = 264² + 900² = 69,696 + 810,000 =
= 879,696
diagonal = sqrt(879,696) = 937.9211054... ft ≈ 938 ft
so, Kate walked
1,164 - 938 = 226 ft
less than Mary.
Given the property:
a = am-n, for a 0
am
an
Explain the three cases for:
a. 0
b. 0
c.m=n
Could you try reposting the question clearly
10005²³ x + cos x = 11 sin²x = 9
If F(x) = 3x² - 8x + C and F(1) = -6, what is the value of C?
Answer:
The value of C will be -1.
Step-by-step explanation:
Greetings !
[tex]f(1) = - 6 \\ thus \: substitute \: in \: the \: equation \: \\ f(x) = 3x {}^{2} - 8x + c \\ - 6 = 3(1) {}^{2} - 8(1) + c \\ - 6 = 3 - 8 + c \\ - 6 = - 5 + c \\ - 1 = c \\ c = - 1 \\ therefore \: f(x) = 3x {}^{2} - 8x - 1 \\ f(1) = 3(1) {}^{2} - 8(1) - 1 \\ f(1) = 3 - 8 - 1 \\ f(1) =3 - 9 \\ f(1) = - 6[/tex]
f(x)=ax+b/2 then f^-1 (x-1) =2x-5/2 find a and b
From the given inverse function, we have
[tex]f^{-1}(x-1) = 2x - \dfrac52 \\\\ \implies f^{-1}(x) = f^{-1}((x+1)-1) = 2(x+1) - \dfrac52 = 2x-\dfrac12[/tex]
By definition of inverse function,
[tex]f\left(f^{-1}(x)\right) = x[/tex]
so that
[tex]f\left(2x-\dfrac12\right) = x[/tex]
[tex]a\left(2x-\dfrac12\right) + \dfrac b2 = x[/tex]
[tex]2ax - \dfrac a2 + \dfrac b2 = x[/tex]
[tex]\implies\begin{cases}2a=1 \\\\ -\dfrac a2+\dfrac b2 = 0\end{cases}[/tex]
[tex]\implies \boxed{a=\dfrac12}[/tex]
[tex]\implies \dfrac b2 = \dfrac a2 \implies \boxed{b=\dfrac12}[/tex]
the set of integers less than -20
In mathematical notation, the set of integers less than -20 as follows:
{-21, -22, -23, -24, -25, ...}
The set of integers less than -20 is the set of all whole numbers that are smaller than -20. Integers include both positive and negative whole numbers, as well as zero.
In mathematical notation, we can represent the set of integers less than -20 as follows:
{-21, -22, -23, -24, -25, ...}
The set includes all numbers that are smaller than -20, going indefinitely in the negative direction. Each number in the set is obtained by subtracting 1 from the previous number in the set.
For example:
-21 is the integer immediately smaller than -20, so it is included in the set.
-22 is the next integer, smaller than -20, so it is also included in the set.
And this pattern continues indefinitely, encompassing all the integers less than -20.
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Which equation represents the data shown in the table below?
Answer:
B. y = x +3
Step-by-step explanation:
The fastest way to find this answer is to substitute offered values of x and y into the given equations to see if they are true.
SubstitutionUsing the first line in the table, (x, y) = (2, 5), we have ...
A 5 = 2(2) . . . . false
B 5 = 2 +3 . . . . true
C 5 = 3(2) . . . . false
D 5 = 2 +1 . . . . false
__
Additional comment
Checking answer choices against the problem statement is one of many possible strategies for answering multiple-choice questions.
This box plot represents the number of pages that several students in sixth grade have read in a month. Use the shape of the box plot to describe the data set. Select all that apply.
The total range of pages read is 20 .
The lowest quarter of data is more dispersed than the highest quarter of data.
One-half of the students have read between 72 and 86 pages.
The median number of pages of the sixth graders is 76.
One-fourth of the students have read weigh 72 and 76 pages.
One-fourth of the students read more than 76 pages.
One-fourth of the students have read less than 72 pages.
The true statements are:
The median number of pages of the sixth graders is 76.
One-fourth of the students have read less than 72 pages.
One-half of the students have read between 72 and 86 pages.
What are the true statements?A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers.
The end of the first line represents the minimum number and the end of the second line represents the maximum number. The difference between the minimum number and the maximum number is the range.
Range = 92 - 61 = 31
On the box, the first line to the left represents the lower (first) quartile. 1/4 of the score represents the lower quartile. The next line on the box represents the median. 1/2 of the score represents the median. The third line on the box represents the upper (third) quartile. 3/4 of the scores represents the upper quartile.
First quartile = 72
Third quartile = 86
Median = 76
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2. The sum to infinity of an exponential sequence with a positive common ratio is 25 and the first two terms is 16. find fifth term
Answer:
0
Step-by-step explanation:
hi
hi
haha
and
and
are doing
dog food
0 answer
(scroll to bottom for answer)The equation you want to be using is A(n)+1=(A(n))r because this is a exponential sequence
r represents the ratio, which you said was 25, so basically you said
A(n)
____ = 25
A(n)-1
rthe sum of the first 2 terms are 16, the first two terms being A1 and A2, they need to follow the equation:
A2
__ = 25
A1
lets give them variables to make this a bit easier-
A1 will be x and A2 will be y
x+y=16(1st equation)
y/x=25, 25x=y(2nd equation)
(if you multiply y/x=25 by x you will get that 25x=y, which is where that other equation came from)
going back to x+y=16
subtract y from both sides
x=16-y
use substitution and solve for the second equation
25(16-y)=y
distribute
400-25y=y
add 25y to both sides to get rid of the -25y on the left side while keeping the equation equal
400=26y
divide both sides by 26 and you get 400/26 which simplifies to 200/13
after all that you need to multiply 200/13 by 25, 3 separate times
200 1875000
___ x 25 x 25 x 25= _________
13 13
pull it into a calculator and you get something like
142846.153846
A bird flies 50km everyday to collect food for his offspring and 20km to drink water. To fly this distance takes him 1 hour and 40 minutes. What’s his average speed over the whole day?
Answer:
42km/h
Step-by-step explanation:
70km=100 minutes
7km= 10min
42km=60min
42km/h
Write an equation for a rational function with: Vertical asymptotes at x = 4 and x = 1 x-intercepts at x = -3 and x = 6 y-intercept at 5
The rational equation with the desired asymptotes and intercepts is given by:
[tex]f(x) = \frac{-10(x^2 - 3x - 18)}{9(x^2 - 5x + 4)}[/tex]
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.The vertical asymptotes are related to the roots of the denominator, hence:
[tex]f(x) = \frac{a}{(x - 4)(x - 1)} = \frac{a}{x^2 - 5x + 4}[/tex]
The x-intercepts are related to the numerator of the function, hence:
[tex]f(x) = \frac{a(x + 3)(x - 6)}{x^2 - 5x + 4} = a\frac{x^2 - 3x - 18}{x^2 - 5x + 4}[/tex]
The y-intercept is to find a, hence, when x = 0, y = 5, thus:
-18a/4 = 5
18a = -20
a = -10/9
Hence the function is:
[tex]f(x) = \frac{-10(x^2 - 3x - 18)}{9(x^2 - 5x + 4)}[/tex]
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Z+1 3. Given that Z & W are complex numbers. Prove that |Z + W|² - |z − w|² = 4Re(Z)Re(W)
Let z=a+bi, w=c+di
[tex]|z+w|^2 -|z-w|^2 \\ \\ = |(a+c)+i(b+d)|^2 -|(a-c)^2 +i(b-d)|^2\\\\=(a+c)^2 +(b+d)^2-(a-c)^2 -(b-d)^2\\\\=a^2 +2ac+c^2 +b^2 +2bd+d^2 -a^2 +2ac-c^2 -b^2+2bd-d^2\\\\=4ac+4bd\\\\=4Re(z)Re(w)+4Im(z)Im(w)[/tex]
The answer to this problem please and thank you
Answer:
C
Step-by-step explanation:
The red dotted line we see is the asymptote, which is a line that the functions will never cross.
The asymptotes we see currently is:
x = -3
and
x = 2
We can find the vertical asymptotes using the denominator of the function since the x value that makes the denominator 0 is the asymptote. Since -3 and 2 is the asymptote, the denominator of the function will be:
(x-2) (x+3)
If we look at the answer choices, we can see that C is the only option with a denominator of (x-2)(x+3), so that is our answer.
Answer:
C
Step-by-step explanation:
there are 2 vertical asymptotes at x = - 3 and x = 2
then the factors on the denominator will be (x + 3) and (x - 2)
then
f(x) = [tex]\frac{1}{(x-2)(x+3)}[/tex]
Solve the inequality and enter your solution as an inequality in the box below.
Do not use spaces in your answer.
2+ x>-8
Answer:
x > -10
Step-by-step explanation:
2 + x > -8
x > -8 - 2
x > -10
Answer:
x>-10
Step-by-step explanation:
2+x-2>-8-2
x>-10
Let A, B, C be three points on a circle
with AB = BC. Let the tangents at A and
B meet at D. Let DC meet again
at E. Prove that the line AE bisects the segment
BD. (Hint: Why do we care about a chord bisecting a tangent line?)
The proof that the line AE bisects the segment can be seen below.
How to get the proof
Let us have
Γ1 and 2 are the two intersecting circles. to be the circumcircle of the shape ADE. Then we can see that Γ1 is tangent to the line DB.
A common tangent would have to touch T1 at A and also touch T2 at B
Such that what we would have would be
<ADB = 180◦ − 2<ABD = <ABC = <AEC
This would then tell us that the line is tangent to the segment.
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Multiply each of the following(2a-3b)and(a^2+2b^2)
Answer: [tex]\Large\boxed{2a^3+4ab^2-3a^2b-6b^3}[/tex]
Step-by-step explanation:
Given expression
(2a - 3b) (a² + 2b²)
Apply the FOIL method (First Outer Inner Last)
Please refer to the attachment below for a graphical understanding
= 2a · a² + 2a · 2b² - 3b · a² - 3b · 2b²
Simplify by multiplication
=2 (a · a²) + 4 (a · b²) - 3 (b · a²) - 6 (b · b²)
[tex]\Large\boxed{=2a^3+4ab^2-3a^2b-6b^3}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
Your answer is 2a³ + 4ab² - 3a²b - 6b³.
Step-by-step explanation:
(2a - 3b) (a² + 2b²)
=2a (a² + 2b²) -3b (a² + 2b²)
=2a.a² + 2a.2b² - 3b.a² - 3b.2b²
=2a³ + 4ab² - 3a²b - 6b³ ans.
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Question: You can work 40 hours per pay period while attending school earning $12.50 an hour. There are two pay periods per month. NOW Assume you have deductions for health care of $25 per pay period and 401K deduction of $50 per pay period. These deductions are pretax.
Gross Pay per pay period: $
Taxable Income per pay period:
You pay 11% in federal taxes. Federal tax withholding per pay period: $
___
Use the state tax rates below and calculate State tax withholding per pay period: $
(round to two decimals)
_____
From the image:
Calculate FICA withholding per pay period: $
Calculate Medicare withholding per pay period: $
(round to two decimals)
What is your Net pay per pay period: $
(round to two decimals)
1) Based on the information, the following taxation calculations can be made:
a) Gross Pay per pay period: $500
b) Taxable Income per pay period: $425
c) Since you pay 11% in federal taxes, the Federal tax withholding per pay period is $46.75.
2) The State tax withholding per pay period is $20.
3) The calculation of FICA, Medicare, and the Net Pay per pay period is as follows:
FICA withholding per pay period: $25.50
Medicare withholding per pay period: $6.16
Net Pay per pay period = $326.59
Data and Calculations:Total hours worked per pay period = 40 hours
Rate per hour = $12.50
Pay periods per month = 2
Gross pay per pay period = $500 (40 x $12.50)
Deductions per pay period:Health care = $25
401K deduction = $50
Total deductions per pay period = $75
Taxable income per pay period = $425 ($500 - $75)
Federal taxes = 11%
Federal tax withholding per pay period: $46.75 ($425 x 11%)
Annual taxable income = $10,200 ($425 x 24)
State withholding tax (annual) = $480 {$120 + ($10,200 - $5,000) x 5%}
State withholding tax per pay period = $20 ($480/24)
FICA withholding per pay period: $25.50 ($425 x 6.2%)
Medicare withholding per pay period: $6.16 ($425 x 1.45%)
Net Pay per pay period:Gross Pay $500
Total deductions $75
Taxable income = $425
Federal Withholding = $46.75
State Withholding = $20
]FICA Withholding = $25.50
Medicare Withholding = $6.16
Net Pay per pay period = $326.59
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if X + Y = 212 and xy = 27 find the value of (x³+y³)
Type the correct answer in each box.
[3 x 6 1 -8 5] and -5A = [-15 35 -30 -5 40 y]
The value of x in A is ___ and the value of y in B is ___
The value of x in A is 7 and the value of y in B is -15
Functions and valuesFunctions are represented as a function of variable. Given the following sets of numbers.
A = [3 x 6 1 -8 5] and;
-5A = [-15 35 -30 -5 40 y]
Equate the individual values to have:
-5A= -15
Divide both sides by -5
-5A/-5 = -15/-5
A = 3
Determine the value of y
-5A = y
-5(3) = y
y = -15
Similarly;
5x = 35
x = 35/5
x = 7
Hence the value of x in A is 7 and the value of y in B is -15
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Answer:
The value of x in A is -7
The value of y in B is -25
Step-by-step explanation:
Everything in the first matrix can be multiplied by -5 to equal everything in the second matrix, since we are dealing with x and y, only the first and third rows matter.
In the first row, we know that 3 times -5 equals -15 and x times -5 equals 35
therefore, -5x=35, with basic algebra we find that X = -7
In the third row, we know that 8 times -5 is 40 and 5 times -5 equals y.
This takes just basic multiplication to find that Y = -25
SOMEONE PLS HELPP ASAP
Answer:
yes
Step-by-step explanation:
f the exterior angle of a polygon is given, then the formula to find the interior angle is Interior Angle of a polygon = 180° – Exterior angle of a polygon Method 3: If we know the sum of all the interior angles of a regular polygon, we can obtain the interior angle by dividing the sum by the number of sides
Find the value of x.
Round to the nearest tenth.
A
X
29
B
50
26
C
x = [?]°
Answer:
Below
Step-by-step explanation:
Using the given law of cosines c = 26 a = 50 b = 29
and cos c is cos x
26^2 = 50^2 + 29^2 - 2(50)(29) cos x
-2665 = -2900 cos x
cos x = 2665/2900
x = arc cos ( 2665/2900) = 23.2°
What is 6 wholes divided by 2/3 ?
Answer:
9
Step-by-step explanation:
6 ÷ 2/3 = 6 / (2/3 ) = (6/1) / (2/3) = 6/1 x 3/2 = 18/2 = 9
A large party balloon is being filled with helium at a constant rate. After 8 seconds, there is 2.5L of helium in the balloon.
b) The balloon will burst if there is more than 10 L of helium in it. How long will it take to fill the balloon with that much helium?
Answer:
32 seconds
Step-by-step explanation:
first 8 secknds gives us the value of set 2.5l
2.5L to make 10 =
10÷2.5=4
That said 2.5L fills 1pL by 4 giving us;
4×2.5= 10L
Determine the fifth term of the binomial expansion (x+y)^4
The expression, the fifth term of the binomial expansion is y^4
Binomial expansionBinomial expansion is a means of expanding expressions into terms
Given the expression (x+y)^4, according to the theorem, as the power of x is decreasing, the power of y will be increasing up till the power of the expression.
Expand (x+y)^4
(x+y)^4 = x^4y^0 + x^3y^1 + x^2y^2 + xy^3 + x^0y^4
Include the coefficients according to the Pascal triangle to have:
(x+y)^4 = x^4y^0 + 4x^3y^1 + 6x^2y^2 + 4xy^3 + x^0y^4
(x+y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4
From the expression, the fifth term of the binomial expansion is y^4
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The intersection point of an angle bisectors of a triangle
Answer: The point of intersection of angle bisectors of the 3 angles of triangle ABC is the incenter . The incircle touches each side of the triangle
If the vertex of a parabola is (-4,-7), what is the axis of symmetry?
Answer:
-4
Step-by-step explanation:
Given vertex, the axis of symmetry is x = h.
What is the mean of 13, 7, 8 and 4
Answer:
16
Step-by-step explanation:
Mean is same as average. To find the average, add all items and divide the sum by the number of items in the list.
Avg = (13 + 7 + 8 + 4) / 2 = 32 / 2 = 16
Hi there,
please see below for solution steps :
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
To find the mean you first need to add all numbers and divide by how many there are :
[tex]\sf{\dfrac{13+7+8+4}{4}}[/tex]
⨠ simplify
[tex]\sf{\dfrac{32}{4}}[/tex]
[tex]\boxed{\sf 8}[/tex] [tex]\tiny\pmb{\sf{Frozen \ melody}}[/tex]
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
All pies at the baked goods booth were cut into eighths. When Justina Hartley’s sift in the boot began, there were eight and one forth pies waiting to be sold. At the end of her shift there were only five pieces of apple pie left. How many pieces of apple pie were sold during Justina’s shift?
Answer: 3 1/4
Step-by-step explanation: you started with 8 1/4 subtract the 1/4 now ur left with 8-3 which equals 5
Maytag Company earns $2.60 per share. Today the stock is trading at $46. The company pays an annual dividend of $1.60 a. Calculate the price-earnings ratio (Round your answer to the nearest whole number.) Price-earings natio b. Calculate the stock yield. (Round your answer to the nearest tenth percent.) Stock yield
a. The price-earnings ratio of Maytag Company's stock is 17.
b. The stock yield of Maytag Company's stock is 3.48%.
What are the price-earnings ratio and stock yield?The price-earnings ratio is a financial measurement of the worth of Maytag Company.
The price-earnings (P/E) ratio is computed as the current stock price divided by the company's earnings per share.
The P/E ratio shows the potential investor how much to pay per share for each $1 of earnings.
The stock yield is a financial measurement that shows the dividends paid relative to the market value per share.
Data and Calculations:Earnings per share = $2.60
Current share price = $46
Annual dividend = $1.60
a. Price-earnings ratio = Price per share/earnings per share
= 17 ($46/$2.60).
b. Stock yield = Annual dividend per share/Current stock price x 100
= 3.48% ($1.60/$46 x 100)
Thus, while the price-earnings ratio is 17, the stock yield is 3.48%.
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