Answer:graphong, substitution, addition
Step-by-step explanation:
How do you solve and graph a piece wise function and state the domain and range?
The point $(r,\theta)$ in polar coordinates is $(7,5)$ in rectangular coordinates. what is the point $\left( 2r, \theta + \frac{\pi}{2} \right)$ in rectangular coordinates?
Final Answer:
The rectangular coordinates of the point[tex]$\left( 2r, \theta + \frac{\pi}{2} \right)$[/tex], where [tex]$(r, \theta)$[/tex] corresponds to the polar coordinates (7, 5), are approximately (-13.59, 11.54).
Step-by-step explanation:
In polar coordinates, a point is represented as [tex]$(r, \theta)$[/tex] , where [tex]$r$[/tex] is the distance from the origin, and $\theta$ is the angle with respect to the positive x-axis. In rectangular coordinates, the point is represented as (x, y).
Given that the point [tex]$(r, \theta)$[/tex] in polar coordinates is equivalent to the point (7, 5) in rectangular coordinates, we can express this relationship as:
[tex]\[ x = r \cos(\theta) \][/tex]
[tex]\[ y = r \sin(\theta) \][/tex]
For the given point $(7, 5)$, we have:
[tex]\[ x = 7 \cos(5) \][/tex]
[tex]\[ y = 7 \sin(5) \][/tex]
Now, you want to find the point [tex]$\left( 2r, \theta + \frac{\pi}{2} \right)$[/tex] in rectangular coordinates. This can be expressed as:
[tex]\[ x' = 2r \cos\left(\theta + \frac{\pi}{2}\right) \][/tex]
[tex]\[ y' = 2r \sin\left(\theta + \frac{\pi}{2}\right) \][/tex]
We know that [tex]$\cos\left(\theta + \frac{\pi}{2}\right) = -\sin(\theta)$[/tex] and [tex]$\sin\left(\theta + \frac{\pi}{2}\right) = \cos(\theta)$[/tex]. Substituting these into the equations:
[tex]\[ x' = -2r \sin(\theta) \][/tex]
[tex]\[ y' = 2r \cos(\theta) \][/tex]
Now, if we substitute the values of [tex]$r$[/tex] and [tex]$\theta$[/tex] from the given point (7, 5):
[tex]\[ x' = -2 \times 7 \times \sin(5) \][/tex]
[tex]\[ y' = 2 \times 7 \times \cos(5) \][/tex]
Calculating these values will give you the rectangular coordinates of the point $\left( 2r, \theta + \frac{\pi}{2} \right)$.
Using the given zero, 2 - 4i, find one other zero of f(x) = x4 - 4x3 + 21x2 - 4x + 20
The conjugate of the given zero 2 - 4i is 2 + 4i, which must also be a zero of the polynomial f(x) due to the Complex Conjugate Root Theorem.
Given the zero 2 - 4i of the polynomial function f(x) = [tex]x^4 - 4x^3 + 21x^2 - 4x + 20,[/tex] we know by the Complex Conjugate Root Theorem that if a polynomial has real coefficients, then any complex zeros must occur in conjugate pairs. Therefore, the conjugate of 2 - 4i, which is 2 + 4i, must also be a zero of the polynomial function.
As a result, the polynomial can be factored to include the factors (x - (2 - 4i)) and (x - (2 + 4i)). When these factors are multiplied out, they will give you a quadratic factor of the polynomial, which when multiplied with the remaining factors, will result in the original polynomial f(x). The two factors, when multiplied together, yield a quadratic with real coefficients, which means any remaining zeros must also satisfy this quadratic equation.
△DEF has vertices D (2,2), E (-2,-1), and F (-3,5). Complete the following charts indicating the location of △D′E′F′ and △D″E″F″.△DEF is reflected in the y-axis. Then it is translated along the vector ⟨3,−5⟩. Enter your answers as points using parenthesis and commas. Do not use any spaces.
helpppppppppppppppppppppp
Two lines, A and B, are represented by the following equations:
Line A: 3x + 3y = 12
Line B: x + y = 4
Which statement is true about the solution to the set of equations? (4 points)
It is (12, 4).
There are infinitely many solutions.
It is (4, 12).
There is no solution.
Exit Felix was given $125 for his birthday from his grandmother. He plans to put this money toward the purchase of a $250 skateboard. The remainder of the money he plans to earn mowing lawns for the rate of $35 each. What is the least number of lawns Felix will have to mow in order to have enough to buy the skateboard?
A rectangular prism has a length of 8 feet, a width of 3 feet, and a height of 5 feet. What is the surface area of the rectangular prism?
surface area = 2(wl +hl+hw)
w=3
l=8
h=5
wl=3*8 =24
hl=5*8 =40
hw=5*3 =15
24+40+15 = 79
2*79 = 158 feet^2
The surface area of the rectangular prism is 158 square feet.
What is surface area?The surface area of any given object is the area or region occupied by the surface of the object.
Formula for finding the surface area of rectangular prism:Surface Area = 2{(h × l) + (h × w) +(l × w)]
Where,
l is the length of the rectangular prism
h is the height of the rectangular prism
w is the width of the rectangular prism
According to the given question
Length of the rectangular prism = 8 feet
width of the rectangular prism = 3feet
height of the rectangular prism = 5 feet.
Therefore,
the surface area of the rectangular prism = 2[(8 × 5)+ ( 5 × 3) + ( 8 × 3)]
surface area of rectangular prism = 2[ 40 +15 +24} = 158 square feet.
Hence, the surface area of the rectangular prism is 158 square feet.
Learn more about the surface area of rectangular prism here:
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Determine whether the forces are pulling at right angles to each other. Explain. 3.5 lb, 6.2 lb, resultant force 9.1 lb
A. yes; 3.52 + 6.22 = 9.12
B. no; a + b > c
C. no; 3.52 + 6.22 ≠ 9.12
D. yes; a + b > c
There are 9 different positions on a baseball team. if a team has 18 players how many different line-ups can the team make?
Final answer:
To find the number of different line-ups a team can make, we use permutations. Using the formula for permutations, we arrive at the answer of 437,760 different line-ups.
Explanation:
To find the number of different line-ups a team can make, we need to use the concept of permutations. Since there are 9 positions on a baseball team and 18 players, we can arrange the players in a line-up using the formula for permutations:
P(n, r) = n! / (n-r)!
Where n is the total number of players (18) and r is the number of positions (9). Substituting the values, we get:
P(18, 9) = 18! / (18-9)! = 18!/9! = 437,760.
Therefore, there are 437,760 different line-ups that the team can make.
If f(x) = -2[x] + 8, what is f(-1.8) (PLS HELP ASAP)
Answer:
option c)10
Step-by-step explanation:
Given is a least integer function as
[tex]f(x) =-2[x]+8[/tex]
We are to find out the function value when x = -1.8
Substitute for x the value -1.8
we have
[tex]f(x) =-2[-1.8]+8\\[/tex]
-1.8 has the integer -1 to the left of it.
Hence we get
[tex]f(x) =-2[-1]+8=10[/tex]
Hence answer is option c)10
Solve the inequality. 4(p – 4) > 12
Suppose? 30% of the people in your town talk on their cell phones and drive at the same time. if you stood on a busy street corner and watched 50 people drive? by, about what proportion would you expect to see talking on their cell? phones?
An investment of $200 increases at a rate of 9.5% per year. What is the growth factor, b?
The standard form for rate equation is:
F = P (1 + r)^n
or
F = P b^n
So b = 1 + r
In this case, r is given as 9.5% or 0.095. Therefore:
b = 1 + 0.095
b = 1.095
The growth factor is 1.095.
What is the sum of?
A. S=1.5
B.S=2
C.S=4.5
D.=8
Use the remainder theorem to determine the remainder when d4 + 2d2 + 5d − 10 is divided by d + 4.
The remainder theorem states that the answer when d + 4 is substituted into the whole equation, the remainder would be the answer divided by d + 4. Therefore:
d + 4 = 0
d = -4
Evaluating when d = -4:
d^4 + 2 * d^2 + 5 * d − 10
= (- 4)^4 + 2 * (- 4)^2 + 5 * (- 4) – 10
= 256 + 2 * 16 – 20 – 10
= 256 + 32 – 30
= 258
Therefore basing on the remainder theorem, the remainder would then be:
Remainder = 258 / (d + 4) ---> Answer
Solve x2 – 4 = 5 by graphing the related function.
Answer:
Refer graph attached below
Step-by-step explanation:
Given equation [tex]x^2-4=5[/tex]
We have to Solve the given equation [tex]x^2-4=5[/tex] graphically.
We first solve the given equation [tex]x^2-4=5[/tex]
Consider the given equation [tex]x^2-4=5[/tex]
Adding 4 both sides, we have
[tex]\Rightarrow x^2-4+4=5+4[/tex]
Simplify, we get,
[tex]\Rightarrow x^2=9[/tex]
[tex]\Rightarrow x^2-9=0[/tex]
To plot the graph let [tex]x^2-9=y[/tex] be the equation
It will be a parabola with vertex (0,9).
Refer graph attached below
A quadratic equation is shown below:
4x^2 − 12x + 10 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 2x^2 − 13x + 21 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
A new truck that sells for 29,000 depreciates 12% each year. What is the decay factor b?
Write the expression in standard form.
three divided by quantity three minus twelve i.
Answer:
What was the answer?!?!!?!? >-<
When 23 is subtracted from 4 times a certain number the result is 4
If f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x, which graph shows the graph of (f + g)(x)?
Answer:
Given the functions: [tex]f(x)= -x^2 +3x+5[/tex] and [tex]g(x) = x^2+2x[/tex]
Now, calculate first [tex](f+g)(x)[/tex] ;
[tex](f+g)(x) = f(x) + g(x)[/tex]
Substitute the given values we have;
[tex](f+g)(x) = -x^2+3x+5+x^2+2x[/tex]
Combine like terms;
[tex](f+g)(x) =5x+5[/tex]
Let y = [tex](f+g)(x)[/tex]
Then, we have y = 5x+5
Now, Graph the equation of the line y =5x +5
Using slope intercept form: An equation of line is given by :
y = mx +b ; where m is the slope of the line and b is the y-intercept.
On comparing we get;
m = 5 (Since, slope is positive which means a line moves upward on a graph from left to right)
Now, find the intercepts of the equation: y=5x+5;
x-intercepts: The graph or line crosses the x-axis i.,e
Substitute y = 0 and solve for x;
0 = 5x +5
Subtract 5 on both sides we get;
-5 = 5x
Divide both sides by 5 we get;
x = -1
x-intercepts= = (-1, 0)
Similarly for y-intercept:
Substitute the value of x= 0 and solve for y;
y = 5(0)+5
y = 5
y-intercepts = (0, 5)
Now, using these point we can draw a graph of function [tex](f+g)(x) =5x+5[/tex] as shown below in the attachment.
What is the common ratio in the sequence -27, 9, -3, 1....?
A. 3
B. -3
C. 1/3
D. -1/3
Marisol receives total employee benefits that are 14.5% of her gross annual pay. If Marisol has a gross annual pay of $50,000, how much in total employee benefits does she receive?
If Marisol has a gross annual pay of $50,000 and receives total employee benefits of 14.5% of her gross annual pay, then you can find how many benefits she receives, using proportion:
[tex] \$50,000 - 100\%,\\ \$x - 14,5\% [/tex].
Then
[tex] \dfrac{50000}{x} =\dfrac{100}{14.5} ,\\\\ x=\dfrac{50000\cdot 14.5}{100}=500\cdot 14.5=7250 [/tex].
In total she will receive $50,000+$7250=$57250.
Answer: $57250.
Which mathematical statement represents “17 more than a number is 26”?
17 + x = 26
17 +n = 26
n + 17 = 26
something like those, you didn't give options to choose from.
Answer:
x + 17 = 26
Step-by-step explanation:
mathematical statement represents “17 more than a number is 26”
Let x be the unknown number
17 more means we add 17 with the unknown number x
so it becomes x+17
'is' represents an = sign
So the equation for the mathematical statement “17 more than a number is 26” becomes x + 17 = 26
The second term in a geometric sequence is 20. The fourth term in the same sequence is 11.25. What is the common ratio
Write an algebraic equation for the following. The product of three and a squared number is twice the sum of the number and four.
A county has been experiencing a mean of 35.935.9 motor vehicle deaths each year. Use the Poisson distribution to answer the following. a. Find the mean number of deaths per day. b. Find the probability that on a given day, there are more than 2 motor vehicle deaths. c. Is it unusual to have more than 2 motor vehicle deaths on the same day
Given 5n² + 6n + 7 = n² - 4n : a. Find the value of the discriminant. b. State the number and type of roots/solutions/zeros.[2 real, 2 imaginary, 1 real]
Terry earns $22,500 annually. What is the total amount of each paycheck if she is paid biweekly?
52 weeks per year
biweekly means she gets paid every 2 weeks
so 52/2 = 27
22500/27 = 833.33 each paycheck