The rectangular form of Θ = 3π/4 will be; y + x = 0.
What are Complex value?Complex value z is written in a rectangular form as z = x+iy where (x, y) is the rectangular coordinates.
On converting the rectangluar to polar form of the complex number;
x = rcosθ and y = rsinθ
z = r(cosθ+isinθ)
r is the modulus of the complex number and θ is the argument
r =√x²+y² and θ = tan⁻¹y/x
Given the Θ = 3π/4
Therefore, θ = tan⁻¹y/x = 3π/4
y/x = tan (3π/4)
Now multiply both side by x
yx/x = tan (3π/4) x
y = tan (3π/4) x
Thus, y = -x
in rectangular form y + x = 0
Hence, the rectangular form of Θ = 3π/4 will be; y + x = 0.
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The area of the triangle formed by the x - and y -intercepts of the parabola y = 0.5(x − 3)(x + k ) is equal to 1.5 square units. Find all possible values of k
The possible values of k that forms a triangle with an area of 1.5 square units are 1 and 2/3
What is a triangle?A triangle is a three sided polygon.
The equation of the parabola is; y = 0.5•(x - 3)•(x + k)
The area of the triangle = 1.5 square units
A x-intercept of the equation, y = 0.5•(x - 3)•(x + k) is x = 3.
The area of a triangle, A, is found from the equation
A = 0.5 × Base length × Height
When x = 3, the height of the triangle is therefore;
A = 1.5 = 0.5 × 3 × Height
Height = 1.5 ÷ (0.5 × 3) = 1
Similarly, when the height is 3, the base length is 1
The y-intercept has a value of y = 0.5•(0 - 3)•(0 + k) = -1.5•k
Area of triangle = 0.5 × 1.5•k × k = 1.5
k = 1
When the x-intercept is 3, we have;
0.5 × 1.5•k × 3 = 1.5
k = 1/(1.5) = 2/3
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To prepare for Thanksgiving, Brittany bought four Tofurkys for $20.16 each. She also spent $29.78 on fruits and vegetables, and $12.53 on spices and sauces. Brittany served a total of seven people, plus herself. What was the
average cost per person for the meal?
Answer:
6.68
Step-by-step explanation:
[tex]20.16+20.78+12.53 = 53.47[/tex]
[tex]53.47 \div 8 = 6.68375[/tex]
suppose the population of iq scores in the town or city where you live is bell-shaped, with a mean of 107 and a standard deviation of 35. describe the frequency curve for possible sample means that would result from random samples of 100 iq scores.
The mean of samples of 100 IQ scores taken out from this population will have a distribution with mean M=104 and standard deviation s=3.5.
We know the population mean and standard deviation, that has a bell-shaped distribution:
μ= 107
σ=35
The sampling distribution, the distribution of the mean of samples of size n out of this population, will have the same mean as the population mean.
μ (m) = μ =107
The standard deviation will be related to the population standard deviation and the sample size as:
σ (m)= σ/[tex]\sqrt{N}[/tex]
= 35/10=3.5
Then, the mean of samples of 100 IQ scores taken out from this population will have a distribution with mean M=104 and standard deviation s=3.5.
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write the correct function represented in the table below
HELP ASAP
Answer:
Step-by-step explanation:
y=X-2
Pls help me!!!!!!!!!!!!!!!!
Answer:
240?
Step-by-step explanation:
Johnny has some nickels and dimes in his pocket, and the change is worth $0.75. He has twice as many dimes and nickels. How many of each type of coin does Johnny have? Whoever answers get brainiest.
The area of a rectangle is (x4 + 4x3 + 3x2 – 4x – 4), and the length of the rectangle is (x3 + 5x2 + 8x + 4). If area = length × width, what is the width of the rectangle? x + 1 x – 9 x + 4 x – 1.
If the Area= Length × Width
Then, The width of the rectangle is (x -1).
We know that area of rectangle is the number of unit square within the boundary of the rectangle.
The formula of area of rectangle is:
Area = Length × width
⇒ Width = Length / Area
Given that,
(x⁴ +4x³ + 3x² -4x -4) / (x³ + 5x² + 8x + 4 ) = Width ----------------- (1)
Let's simply the expression :
Note that: x=1 is a zero of the numerator since the sum of the coefficient is zero.
So, (x-1) is a factor:
Putting the values in equation (1)
(x⁴ +4x³ + 3x² -4x -4) = (x-1) (x³ + 5x² + 8x + 4 )
(x⁴ +4x³ + 3x² -4x -4) / (x³ + 5x² + 8x + 4 ) = (x-1)
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Answer:
D on Edge 23
Step-by-step explanation:
because i said so
PLEASE HELP ASAP!!
find the value of x and y
What is the length of angle DF?
Using Midsegment theorem, the value of x and y are 17 and 2 respectively and the length of DF is 20 units.
How to use mid segment to find length of a triangle?The Midsegment theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side.
Therefore, DH is midsegment of triangle DEF.
Hence, let's find x
1 / 2 (28) = x - 3
14 = x - 3
add 3 to both sides of the equation
14 = x - 3
14 + 3 = x - 3 + 3
x = 17
Let's find the length DF as follows:
DF = y + 8 + x - 7
Recall x = 17
Therefore,
DF = y + 8 + 17 - 7
DF = y + 8 + 10
DF = y + 18
y+ 8 = 10
y = 2
Hence,
DF = 2 + 18
DF = 20 units
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Daily Word Problem
Elena has 5 boxes of donuts. Each box has 10 donuts in it.
She gives one box to her bus driver. She gives two boxes to
the school principal. She takes the rest to her classroom to
share with her classmates.
How many donuts does she have to share with her
classmates?
Show your work.
Answer: 20
Step-by-step explanation:
5 boxes with 10, 10, 10, 10, and 10 donuts in each box.
She gives one box away, so that is 50-10=40
Then she gives 2 boxes away, which is 40-20=20, so she has 20 donuts left to share with her classmates.
Answer: 20
Step-by-step explanation:
5 x 10 = 50 Donuts
50 Donuts - 10 for the Bus driver
40 Donuts - 20 for the school principal
=20
She can share 20 Donuts with her classmates.
without using technology, describe the behavior of f(x)=
The behavior of f(x) from given options is option (4) up on the left, up on the right.
What is the behavior of function:A function f(x) 's end behavior is how the graph of the function f(x) behaves as x gets closer to positive or negative infinity. The functions degree or the polynomial degree and leading coefficient of a given function will determine the end behavior of the function.
Here we have
f(x) = 3x³² + 8x² - 22x + 43
Here
polynomial degree of f(x) is 32
And leading coefficient is 3
Therefore,
The leading term of the given function is 3x³²
As the given polynomial has an even degree (32) and positive leading coefficient (3) then the graph will open upwards on both left and right.
Therefore,
The behavior of f(x) from given options is option (4) up on the left, up on the right.
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a random number generator produces a sequence of 12 digits (0, 1, ..., 9). what is the probability that the sequence contains at least one 3? (hint: consider the probability that it contains no 3's. round your answer to four decimal places.)
The probability that the number generated contains the digit 3 at least once is 0.7458.
Probability that there is digit 3 at least once = 1- P(no 3s in the number)
Total probability is, 10^13.
Here the digits are 0 to 9. we have 10 choices and the digits can be repeated hence the total probability is 10^13.
Now, if there is no 3, the choices will 9, hence the probability is 9^13.
Further, the probability of an event happening, is equal to the
favourable outcomes/total outcomes.
Hence, we get the probability of no 3's is 9^13/10^13
=0.2542
Probability that there is digit 3 at least once = 1- 0.2542
=0.7458
Therefore, the probability of at least one 3 is 0.7458.
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HELP PLS Two step equations that equal 11
Answer:
See below
Step-by-step explanation:
I hope this is what you're looking for!
Some examples include:
4x + 5 = 492x - 3 = 197x + 24 = 101Can you help with the last question, please? Ignore the writing on the paper.
5. Gabi will graph f(x) = x and m(x) = f(x). Mark each statement as true or false. If false,
rewrite as true in the space below.
a. The slope of m(x) will be steeper than f(x).
_b. The y-intercept of m(x) will be units up from f(x).
a. False, the slope of f(x) will be steeper than m(x).
b. False, the y-intercept of m(x) will be equal to f(x).
What is a slope?
Slope and slant both refer to an incline away from a reference surface or line that is generally straight. The definition of slope is "a vertical inclination in an oblique direction" Here, the land abruptly slopes either upward or downhill.
Here, we have
f(x) = x and m(x) = 3/5f(x)
a. m₁ = slope of f(x) = x is 1
m₂ = slope of m(x) = 3/5f(x) is 3/5
m₁ > m₂
f(x) = x is more steeper than m(x) = 3/5f(x).
b. a₁ = intercept of f(x) = x is 0.
b₁ = intercept of m(x) = 3/5f(x) is 0.
The y-intercept of m(x) will be equal to f(x).
Hence, a. False, the slope of f(x) will be steeper than m(x).
b. False, the y-intercept of m(x) will be equal to f(x).
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The state sales tax rate in North Carolina is 4.5% estimate the state sales tax on a model of the wright brothers’ airplane that costs $139.99.
Please show work
Answer:
$6.30
Step-by-step explanation:
The state sales tax rate in North Carolina is 4.5% estimate the state sales tax on a model of the wright brothers’ airplane that costs $139.99.
You are asked to estimate meaning $139.99 should be rounded to $140. Because 4.5% = 0.045
sales tax (estimated):
0.045 * $140 = $6.30
CHECK:
Exact amount is:
0.045 * 139.99 = $6.29955
Terrence signed up for the safe venture driving school. He will spend 10 hours driving with an instructor and will also attend weekly 2-hour classes. When terrence completes the 26 total hours of instruction, he will take his driver's test. Which equation can you use to find w, the number of weeks the driving classes last?.
2w + 10 = 26 can you use to find w, the number of weeks the driving classes last the driving test will last for 8 weeks.
What is Linear Equation ?A linear equation is an algebraic equation of the form y = mx + b. involving only a constant and a first-order ( linear ) term, where m is the slope and b is the y - intercept.
If w is the number of weeks,
The equation to represent this equation is to be 2w + 10 = 26
2w = 26 - 10
If any variable or constant changes it's side then changes its sign . From +ve to -ve and product to division and vice versa .2w = 16
w = [tex]\frac{16}{2}[/tex]
w = 8
Hence the driving test will last for 8 weeks.
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Which expression has a greater value: log3 1/3 or logb 1/b? Explain how you know.
Answer:
They are equalStep-by-step explanation:
Given[tex]log_3 1/3 \ and\ log_b 1/b[/tex]Compare the expressions[tex]log_31/3=log_33^{-1}=-1[/tex][tex]log_b1/b=log_bb^{-1}=-1[/tex]As we see the two expressions are equal in value
Answer:
log3 1/3 = logb 1/b
(Both expressions are equal)
Step-by-step explanation:
Now we have to,
→ find the expression with greater value.
Then the greatest value is,
→ log3 1/3 = logb 1/b
→ log3 3^(-1) = logb b^(-1)
→ -1 = -1
→ [ LHS = RHS ]
Hence, both have same value.
QUESTION 5/10 HELP ASAPP
Answer:
d) {(-2,0), (-1,0), (1,0), (2,0)}
Step-by-step explanation:
We know that,
→ A set function has different x values.
Then the set function will be,
a) {(1,0), (1,1), (2,2), (2,2)}
→ The x values underlined are repeated.
Hence, it is not a set function.
b) {(0,0), (1,1), (1,1), (3,3)}
→ The x values underlined are repeated.
Hence, it is not a set function.
c) {(0,-2), (0,-1), (0,1), (0,2)}
→ The x values underlined are repeated.
Hence, it is not a set function.
d) {(-2,0), (-1,0), (1,0), (2,0)}
→ There are no repeated values for x.
Hence, it is a set function.
Determine if the equation is linear, absolute value, quadratic, or polynomial. Then solve under complex numbers.
3x³ + 7x² - 10x = 0
Let A =
-4
6
Find 3A + 3B.
3A + 3B =
-3
1
and B =
2 - 4
0
0
The answer is [tex]3A+3B=\left[\begin{array}{ccc}-6&-21\\18&3\end{array}\right][/tex]
To solve the given expression, we have to first know about matrix addition and scalar multiplication.
Matrix addition is possible only when both matrices have equal dimensions. Scalar multiplication is the multiplication of a real number and a matrix. Each element of the matrix is multiplied by a scalar value in scalar multiplication.
To solve the given problem, first, substitute the value of A and B in the formula,
[tex]3A+3B=3\left[\begin{array}{cc}-4&-3\\6&1\end{array}\right] +3\left[\begin{array}{cc}2&-4\\0&0\end{array}\right][/tex]
Using scalar multiplication, multiply the real number and the matrix. So we get,
[tex]\begin{aligned}3A+3B&=\left[\begin{array}{ccc}3(-4)&3(-3)\\3(6)&3(1)\end{array}\right] +\left[\begin{array}{ccc}3(2)&3(-4)\\3(0)&3(0)\end{array}\right]\\&=\left[\begin{array}{ccc}-12&-9\\18&3\end{array}\right] +\left[\begin{array}{ccc}6&-12\\0&0\end{array}\right]\end{aligned}[/tex]
To add two matrices with the same dimension, add their corresponding element. So we get,
[tex]\begin{aligned}3A+3B&=\left[\begin{array}{ccc}-12+6&-9-12\\18+0&3+0\end{array}\right] \\&=\left[\begin{array}{ccc}-6&-21\\18&3\end{array}\right]\end{aligned}[/tex]
Therefore, the answer is [tex]3A+3B=\left[\begin{array}{ccc}-6&-21\\18&3\end{array}\right][/tex]
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Today, the mountain that contains Mount Rushmore is approximately 5,675 feet high. The height of the mountain is 622.5 feet less than 1.1 times its height before construction began.
The equation to find the height of the mountain prior to construction, represented by the variable h, is
1.1h – 622.5 = 5,675
Solve an equation to find the height of the mountain prior to construction, represented by the variable h.
h =
feet
5725 is the height of the mountain prior to construction, represented by the variable h.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
The mountain that contains Mount Rushmore is approximately 5,675 feet high.
The height of the mountain is 622.5 feet less than 1.1 times its height before construction began.
1.1h – 622.5 = 5,675 is the equation to find the height of the mountain prior to construction, represented by the variable h
1.1h – 622.5 = 5,675
We need to find the value of h
Add 622.5 on both the sides
1.1h=5675+622.5
1.1h=6297.5
Divide both sides by 1.1
h=6297.5/1.1
h=5725
Hence 5725 is the height of the mountain prior to construction, represented by the variable h.
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Divide.
(2x³ − 3x² + 5) ÷ (x − 4)
Answer: \frac{2x^3-3x^2+5}{x-4}
Step-by-step explanation:
g a farmer has 24002400 feet of fencing and wants to fence off a rectangular field that boarders a straight river. he needs no fence along the river. what are the dimensions of the field that has the largest area? (list the smallest dimension first)
Answer:
600 ft by 1200 ft
Step-by-step explanation:
You want the dimensions of the largest rectangular area that can be enclosed on three sides with 2400 feet of fencing.
PerimeterLet x represent the dimension of the field that is parallel to the river, and y the dimension out from the river. The sum of the three side lengths is ...
x + 2y = 2400
Solving for y gives ...
y = (2400 -x)/2
AreaThe area is the product of the two dimensions:
A = xy = x(2400 -x)/2
We observe that this is the factored form of a quadratic with zeros at x=0 and x=2400. Its leading coefficient is negative, so the graph opens downward, and the vertex is the point where area is a maximum.
The vertex is located on the line of symmetry at the x-value that is halfway between the zeros:
x = (0 +2400)/2 = 1200
y = (2400 -x)/2 = (2400 -1200)/2 = 600
The dimensions of the field that has the largest area are 600 ft by 1200 ft.
__
Additional comment
As we observed here, the side parallel to the "river" will use 1/2 of the fencing, and the remaining two sides will each use 1/4 of the fencing. This is the general solution to such a fencing problem.
From midnight to 6:00 am, the temperature rose 0.65°C each hour. If the temperature at 6:00 am was -0.1°C, what was the temperature at midnight? Please answer fast
The The temperature at midnight is -5.6°C.
What is the short definition of temperature?
Temperature is a unit of measurement that can be expressed on a variety of scales, including Fahrenheit and Celsius. Temperature shows the direction of the spontaneous flow of heat energy, i.e., from a hotter body (one with a higher temperature) to a colder body.It should be noted that there are 8 hours between midnight and 6 am.
Therefore, the equation will be:
x + (0.65 × 8) = -0.1
x + 5.5 = - 0.1
x = -0.1 - 5.5
x = - 5.6
The temperature at midnight is -5.6°C.
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Order these numbers from least to greatest.
1.2, 1.102, 1.1212, 1.12
Answer:
1.102, 1.12, 1.1212, 1.2
Step-by-step explanation:
Answer:
1 ) 1.102
2 ) 1.12
3 ) 1.1212
4 ) 1.2
Hope this helps! :)
Solve the following inequality and graph the solution set. |x+2|+1>6
The inequality can be simplified to:
-7 < x < 3
And the graph can be seen in the image at the end.
How to solve the inequality?Here we have the inequality:
|x + 2| + 1 > 6
To solve this, we need to isolate the variable x, so if we first subtract 1 we get:
|x + 2| +1 - 1 > 6 - 1
|x + 2| > 5
The absolute value part can be decomposed into two.
-5 < x + 2 < 5
Now we can subtract 2 in all the inequality, so we get:
-5 - 2 < x + 2 - 2 < 5 - 2
-7 < x < 3
The graph of this can be seen below
what is the slope of a line that is perpendicular to a line with a slope of 0.4? Do not include a decimal within a fraction in your final answer.
==========================================================
Explanation:
0.4 = 4/10 = 2/5
The original slope as a fraction is 2/5
Flip the fraction to get 5/2, then flip the sign to get -5/2 which is the perpendicular slope
The orginal slope 2/5 and perpendicular slope -5/2 multiply to -1. This is true of any pair of perpendicular lines where neither line is vertical nor horizontal.
Rephrased another way: -5/2 is the negative reciprocal of 2/5.
Please help!!! What are the range and the domain of C?
Answer:
the C(X) pattern is +4? i need more context but i can give u that much
Step-by-step explanation:
Graph an inequality to represent the possible number of people in the room if the room holds a maximum of 12 people.
Answer: x≤12
Step-by-step explanation: the room holds a max of 12 people, so the number of people will be less than or equal to 12
If -9x+8y=3and6x-6y=-3are true equations, what would be the value of -15x+14y?
The value of the expression -15x+14y as calculated from the given equations is 12.
The pair of simultaneous equations are given as
-9x+8y=3............................1
6x-6y=-3
Now we will solve these equation by elimination method.
6x-6y=-3
or, 2x-2y=-3.......................2
Now multiplying equation 2 by 4 and adding to equation 1 we get:
-9x+8y=3
8x - 8y = -12
or, -x = -9
or, x = 9
Now we use this value of x to find the value of y
-9x + 8y = 3
or , -81 -3 = -8y
or, y = 10.5
Hence the value of the expression -15x+14y is
=-15(9) + (14)(10.5)
=12
The theory of linear systems serves as the foundation for the field of linear algebra, which is used in most branches of modern mathematics. Computing techniques for obtaining the solutions, which are essential to the disciplines of engineering, physics, chemistry, computer science, and economics are included in numerical linear algebra.
It is useful to approximate a system of nonlinear equations by a linear system when developing a mathematical model or computer simulation of a relatively complex system.
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