By algebra properties, the standard form with rational coefficients is the polynomial x³ - 11 · x² + 7 · x + 51, whose lead coefficient is 1 and comprise the roots 3 and 4 + i.
How to determine a polynomial of least degree
A polynomials of least degrees includes all the roots and the given lead coefficient, which can used in the following formula:
p = a · Π (x - rₐ)
Where:
a - Lead coefficientrₐ - a-th root of the polynomial.If we know polynomial has rational coefficients, then the complex root 4 + i has a "twin" equal to 4 - i in accordance with the quadratic formula, otherwise the polynomial will have at least an irrational coefficient. Then, the least degree polynomial is introduced below:
p = 1 · (x - 3) · (x - 4 - i) · (x - 4 + i)
Then, we expand the expression by algebra properties:
p = (x - 3) · [x² - 8 · x - (16 - i²)]
p = (x - 3) · (x² - 8 · x - 17)
p = x³ - 8 · x² - 17 · x - 3 · x² + 24 · x + 51
p = x³ - 11 · x² + 7 · x + 51
The standard form is the polynomial p = x³ - 11 · x² + 7 · x + 51.
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A movie theater sells tickets for $12 for adults and $7 for children.
On one weekend, 267 people visited and the total ticket sales was $2379
How many adults attended?
Answer:
102 adults, 165 children
Step-by-step explanation:
Let a be the number of adults, and let c be the number of children. We set up and solve this system of equations:
a + c = 267---------> 7a + 7c = 1869
12a + 7c = 2379------->12a + 7c = 2379
-----------------------
5a = 510
a = 102, c = 165
find x=, if 1+x+2=5 ??
2
1) Let's evaluate 1+x+2=5
1+x +2=5 Adding the numbers on the left side
+3 = 5 S subtract 3 from both sides
x = 5-3
x = 2
2) Hence, the answer is x=2
1+ x +2 = 5
1+ 2+ 2 =5
5 = 5 True
im trying to solve this 8-6·4·10÷2
-112
1) To solve this expression, let's focus on the order of operations:
[tex]8-6\cdot4\cdot10\colon2[/tex]2) According to the PEMDAS order, we have:
P ower
E exponent
M multiplication
D division
A addition
S subtraction
So we can solve this way:
[tex]\begin{gathered} 8-(6\cdot4\cdot\frac{10}{2}) \\ 8-(24\cdot5) \\ 8-120 \\ -112 \end{gathered}[/tex]Note that we've placed a parenthesis inside just to better visualize it. Since there is a product and a division, we'll start with that.
3) Hence, the answer is -112
the squares for each quadratic, list the center and rais, labeling its translated center: (a) x2 + 2x + y2 - 4y = 4 (c) 2x2 + 2y2 + 3x - 5y = 2 (e) x2 + y2 + 3x = 4 (g) x2 + y2 + 4x = 0 (i) x2 + y2 + 2mx - 2ny = 0 (b) 32-95.0 (d) * - 25.- (1) Akh + 47 - 165 (h) 2 + y - 7y=0 (j) 32 + y2 - 203. 2. Determine which of the following equations represents a circle with (a) x2 + y2 + 10x = -30 (b) 3x2 + 3y2 (c) 4x2 + 4y2 + 18x - 8y = -85 (d) 36x2 + 36
Determine which of the following equations represents a circle with a real non-zero radius:
a) First equation:
[tex]x^2+y^2+10x=-30[/tex]We need to complete squares, i.e., make the equation look like a sum of squared binomials. Separating x's and y's:
What in cardinality?
If the value of a lies in between - 1 and 1 in the absolute value function y = a|x|, then the graph is farther from the ______________.y = -xy = xy-axisx-axis
SOLUTION:
If the value of a lies in between - 1 and 1 in the absolute value function y = a|x|, then the graph is farther from the y- axis. This is because the bounding lines of the function are the lines y = x and y = -x. Thus, when a varies from -1 to 1, the graph gets farther from the y-axis.
Final answer ;
ANSWER FAST PLS
Write and solve an equation that represents the following math sentence. Twenty-four equals the sum of 10.5 and the quotient of a number and 4.5. 24 = 10.5 + 4.5m; m = 60.75 24 = 10.5 + 4.5m; m = 3 24 equals 10.5 plus m over 4.5; m = 3 24 equals 10.5 plus m over 4.5; m = 60.75
Answer: I believe the answer is C
Step-by-step explanation: forgive me if im wrong im not completely sure
? 60 Thanks for helping me Will give good feedback
Answer: F. $1.25
Explanation:
First, we need to find the probability of the coin landing faceup and facedown. We know that landing faceup is 3 times the probability of landing facedown. Since the highest probability is 1 (100%):
[tex]\begin{gathered} 3x+x=1 \\ 4x=1 \\ x=\frac{1}{4}=0.25 \end{gathered}[/tex]With this, we know that:
probability of the coin landing faceup = 3×0.25 = 0.75
probability of the coin landing facedown = 0.25
To find the expected value of each toss, we need to solve for the total of each value multiplied by its probability:
[tex]\begin{gathered} EV=\$1(0.75)+\$2(0.25) \\ EV=\$1.25 \end{gathered}[/tex]Therefore, the expected value of each toss of Coin C is $1.25
The functions r and s are defined as follows.r(x)=– 2x-2s(x)=x²+2Find the value of s (r(4)).s(r(4)) = 006ХŚ
The given functions are
r(x) = - 2x - 2
s(x) = x^2 + 2
To find s(r(4)), the first step is to substitute x = - 2x - 2 into s(x) = x^2 + 2. Thus, we have
s(r(x)) = (- 2x - 2)^2 + 2
s(r(x) = (- 2x - 2)(- 2x - 2) + 2
s(r(x) = 4x^2 + 4x + 4x + 4 + 2
s(r(x)) = 4x^2 + 8x + 6
Finally, we would substitute x = 4 into s(r(x) = 4x^2 + 8x + 2. Thus, we have
s(r(4)) = 4(4)^2 + 8(4) + 6
s(r(4)) = 64 + 32 + 6
s(r(4)) = 102
How many solutions does this equation have?
-8-10z = -4 - 10z
5. What is the slope that runs through the points (-4, 10) and (-4, 3)?
To find the slope, we will use the formula;
slope = y₂ - y₁ / x₂- x₁
From the points give,
x₁ = -4 y₁= 10
x₂ = -4 y₂=3
slope = 3 - 10 / -4+ 4
slope = -7/0
slope = ∞
The slope is undefined.
The first half of this problem is complete, but I dont understand how to do the second part.
Okay, here we have this:
According with the provided info we obtain the following equation:
[tex]v=30\cdot(\frac{1}{2})^{\frac{t}{36}}[/tex]Let's calculate first the 20% of the initial leval:
[tex]30\cdot\frac{20}{100}=\frac{600}{100}=6mg[/tex]Now, let's replace in the equation "v" with 6 to find the estimated time:
[tex]\begin{gathered} v=30\cdot(\frac{1}{2})^{\frac{t}{36}} \\ 6=30\cdot(\frac{1}{2})^{\frac{t}{36}} \end{gathered}[/tex]And, finally let's clear t:
[tex]\begin{gathered} 6=30\cdot(\frac{1}{2})^{\frac{t}{36}} \\ \frac{6}{30}=(\frac{1}{2})^{\frac{t}{36}} \\ \frac{1}{5}=(\frac{1}{2})^{\frac{t}{36}} \\ \frac{t}{36}\ln (\frac{1}{2})=\ln (\frac{1}{5}) \\ t=\frac{36\ln\left(5\right)}{\ln\left(2\right)} \\ t=83.589 \\ t\approx84 \end{gathered}[/tex]Finally we obtain that after approximately 84 hours the valium concentration will reach 20% of it's initial level.
what is the y-intercept of the graph of y= 4.4 (0.34) x?
The y-intercept of the given graph would be (0, 0).
________________________________________
Hope this helps!
Find the volume of a cone with a base diameter of 6 yd and a height of 8 yd.Use the value 3.14 for 1, and do not do any rounding.Be sure to include the correct unit in your answer.
ANSWER
[tex]\begin{equation*} 75.36\text{ }yd^3 \end{equation*}[/tex]EXPLANATION
The volume of a cone is given by:
[tex]V=\frac{1}{3}\pi r^2h[/tex]where r = radius of the base of the cone
h = height of the cone
The diameter of the base of the cone is twice the radius. This implies that the radius of the cone is:
[tex]\begin{gathered} D=2r \\ r=\frac{D}{2} \\ r=\frac{6}{2} \\ r=3\text{ }yd \end{gathered}[/tex]Hence, the volume of the cone is:
[tex]\begin{gathered} V=\frac{1}{3}*3.14*3^2*8 \\ V=75.36\text{ }yd^3 \end{gathered}[/tex]That is the answer.
Solve this please !!!!
Given
[tex]1.5(x+4)-3=4.5(x-2)[/tex]To find: The value of x.
Explanation:
It is given that,
[tex]1.5(x+4)-3=4.5(x-2)[/tex]That implies,
[tex]\begin{gathered} 1.5(x+4)-3=4.5(x-2) \\ 1.5x+6-3=4.5x-9 \\ 1.5x+3=4.5x-9 \\ 4.5x-1.5x=9+3 \\ 3x=12 \\ x=\frac{12}{3} \\ x=4 \end{gathered}[/tex]Hence, the value of x is 4.
GH has a midpoint at M(-4.5, 5.5). Point G is at
(-10, 14). Find the coordinates of point H.
Answer:
(-1, 3)
Step-by-step explanation:
We could imagine the point G and H are points on a straight line.
We know that:
Point G is at (-10, 14)
Midpoint at M (-4.5, 5.5)
To calculate the x coordinate of the mid-point, we suppose to subtract x coordinate of H from coordinate x of G, divide by 2 to get the x coordinate of the midpoint m, which is -4.5
To calculate the y coordinate of the mid-point, we suppose to subtract y coordinate of H from y coordinate of G, divide by 2 to get the x coordinate of the midpoint m, which is 5.5
Therefore, x coordinate of H:
(- 10 - x) / 2 = -4.5
-10 - x = -9
- x = 1
x = - 1
And y coordinate of H:
(14 - y) / 2 = 5.5
14 - y = 11
- y = -3
y = 3
Determine g(x−1) for the following function. g(x)=−4x−1
The function operation g( x - 1 ) of the function g( x ) = −4x − 1 is -4x + 3.
What is the function operation g( x - 1 ) in the given function?A function is simply a relationship that maps one input to one output.
Given the data in the question;
g( x ) = −4x − 1g( x - 1 ) = ?To find g( x - 1 ), replace all the occurrence of x with ( x - 1 ) in the function and simplify.
g( x ) = −4x − 1
g( x - 1 ) = −4( x - 1 ) − 1
Simplify by distributive property
g( x - 1 ) = −4( x - 1 ) − 1
g( x - 1 ) = x( -4 ) - 1( -4 ) - 1
g( x - 1 ) = -4x + 4 - 1
g( x - 1 ) = -4x + 4 - 1
Add 4 and -1
g( x - 1 ) = -4x + 3
Therefore, the function operation g( x - 1 ) is -4x + 3.
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A rectangle is drawn so that the width is 2 feet shorter than the length. The area of the rectangle is 35 square feet. Find the length of the rectangle.
(Blank) feet.
Show your work!
Explain your answer!
No spam answers!
No incorrect answers!
No nonsense answers!
Thanks!
Based on the calculations, the length (L) of this rectangle is equal to 5 feet.
What is a rectangle?A rectangle can be defined as a type of quadrilateral in which its opposite sides are equal and all the angles formed are right angle.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.Given the following data:
Area of rectangle, A = 35 square feet.
Width of rectangle, W = (L + 2) feet.
Substituting the given parameters into the formula, we have;
35 = L(L + 2)
35 = L² + 2L
L² + 2L - 35 = 0
Solving the quadratic equation by using the factorization method, we have:
L² + 7L - 5L - 35 = 0
L(L + 7) - 5(L + 7) = 0
(L + 7)(L - 5) = 0
Therefore, the length (L) of this rectangle is equal to 5 feet since the dimension can not be negative.
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isabella bought tickets for 84 people. each ticket cost $16.22. how much did isabella spend on tickets
The total money Isabella spent on tickets will be $1362.48
In the given question, it is stated that Isabella bought a total of 84 Tickets. Each of the tickets she bought cost $16.22. We have to find out the total amount that she spent on buying tickets for everyone. From this given situation we know:
The cost of one ticket: $16.22
Total number of tickets: 84
From this formula, we can calculate the total amount spent
Total Amount = Total ticket * cost of one ticket
Putting values in this formula, we get:
=> Amount = cost*number
=> Amount = 16.22*84
=> Amount = 1362.48
Hence, the Total amount that she spent on Tickets will be $1362.48
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Miami Beach and similar coastal regions are experiencing rising sea levels at a rate of 12 inches every 5 years. How many inches will the sea level rise in the next 18 years if this rate remains constant?
Answer:
43.2 inches
Step-by-step explanation:
Hello!
According to the question Miami Beach and similar coastal regions are experiencing sea levels at a rate of 12 inches every five years how many inches will the sea level rise in the next 18 years if this rate remains constant
Firstly find rate per year
In order to find rate per year, divide 12inches by 5
➟ 12/5
➟ 2.4
Lastly Multiply 2.4 by 18
➟ 2.4 • 18
➟ 43.2
So, The sea level rise in the next 18 years is 43.2 inches
How do I solve this problem? Write an equation in slope intercept form, if that is not possible write it in standard form. 30. Passes through the point (-3,11) and is parallel to the line y=8
NSWER
y = 11
EXPLANATION
wo lines are parallel if they have the same slope and diffenrent y-intercepts.
In this case, we have to write the equation of a line parallel to the line y = 8, which is a line with a slope of 0 - i.e. it is a horizontal line. Therefore, the equation of the line we have to find must have the same form - y equal to a constant. This constant is the y-coordinate of the point where the line must pass through, (-3, 11).
Hence, the equation of the described line is y = 11.
this week Linda got a promotion at work that came with a 4% pay increase. If now her monthly salary is $2,496, how much was he making before the raise?
We will say that x is the salary before the raise, to calculate how much the salary grows, we just have to take the given percent from x, in this case, the payment increased by 4% (0.04 expressed in decimal form) then the increased amount would be x times 0.04.
Salary increase = x*0.04 = 0.04x
Adding 0.04 x to the original salary x (before applying the increase) we get the actual monthly salary, $2,496, then we can formulate the following expression:
Current salary = original salary + salary increase
2,496 = x + 0.04x
From this equation, we can solve for x like this:
1. Factoring x on the right side of the equation:
2,496 = x(1+0.04)
2. making the sum inside the parentheses:
2,496 = x*1.04
3. Dividing both sides by 1.04:
2,496 / 1.04 = x * 1.04 / 1.04
2400 = x
x = 2400
Then, Linda was making $2400 before the pay increase
Help me answer this question.
nswer:
Explanation:
ere, we want to find the values of x for the function g where there is a local maximum
From what we have in the question, we can see some hills and some valleys
The hills represent the maximum positions while the valleys represent the
mark is trying to remeber is account number his account has 6 digits he knows that the 6 digit are 2,3,5,7,8 and 9 but he cant rember the sequen in the correct order how many possible ways are there for mark to find the correct order
Answer:
720
Step-by-step explanation:
Formula: P (n,r) = n! ÷ (n - r)!
n = Total number of objects in a set
r = The number of items you choose
Mark knows the account number includes the numbers 2,3,5,7,8, and 9. There are obviously 6 numbers in total in this set and 6 he must choose in order to have a 6 digit account number, which the problem also directly states he has.
That means P(n,r) = P(6,6)
!/Factorial = Product of all positive numbers less than or equal to the given positive number
Therefore, 6! = 1 x 2 x 3 x 4 x 5 x 6
P (n,r) = P(6,6) = 6! ÷ (6-6)! = 720
The linear parent function, f(x) = x, transformed to g(x) = x+ 7. Whichstatement correctly compares the graphs of the functions?A. The graph of g(x) is less steep than the graph of f(x) and theyintercept has been shifted down.B. The graph of g(x) is steeper than the graph of f(x) and theyintercept has been shifted up.C. The graph of g(x) is less steep than the graph of f(x) and theyintercept has been shifted up.D. The graph of g(x) is steeper than the graph of f(x) and theyintercept has been shifted down.
The parent function given is
[tex]\begin{gathered} f(x)=x \\ \text{its has a slope of 1} \end{gathered}[/tex]The transformed function given is
[tex]\begin{gathered} g(x)=\frac{1}{2}x+7 \\ \text{which has a slope of 1/2} \end{gathered}[/tex]There is a reduction in the slope of the functions which makes the transformed function become less steep
The slope reduced from
[tex]1\text{ to 1/2}[/tex]There is also a change in the intercept from
[tex]0\text{ to +7}[/tex]And this indicates that the transformed function has been shifted up by 7 units
With the explanation above, we can therefore conclude that the statement which compares the two graphs of the function is
The graph of g(x) is less steep than the graph of f(x) and the intercept has been shifted up
Hence, The correct answer is OPTION C
Five football players ate 15/17 of a lasagna. The 5 players ate equal amounts. How much of the lasagna did each player eat?
Answer:
Step-by-step explanation:
The answer is they ate 3/17ths each since 15/5 is 3.
answer if you will get full score on FINAL BIG TEST/SAT
see attachment below
Answer:
Find x first.
Since angle EOG = 90°,
x = 90 - 54 = 36°
Angle AOD = angle COB = 156° (vertically opposite angles)
y + 54 + 36 + 2y = 156
3y + 90 = 156
3y = 66
y = 22°
(-4,7)(2,3)(-2,-3)(-8,1)
Answer:
it is a square
Step-by-step explanation:
if you plot the 4 points and find the distance using the distance formula between each point, the distance is 2[tex]\sqrt{13}[/tex] on all 4 sides.
Answer:
the quadrilateral is a diamond of rhombusStep-by-step explanation:
sorry if it doesnt help
Danny and three friends went to the football game Friday night. It cost them $5 each to get into the game.
While at the game, the four of them together had two orders of nachos ($2.50 each), four large cokes ($1.50
each), four candy bars ($0.75 each), and two bags of popcorn ($1 each). At the end of the evening, they split
the $20 gasoline bill to help Danny.
Answer:
Danny spent 41 dollars, and his friends spent 5 dollars
If everyone split everything, each person would have paid $13
You didn't clarify which type of answer you wanted, but I gave the two most logical ones
Step-by-step explanation:
Tickets: 5 * 4 = 20.00
Nachos:2.5*2= 5.00
Cokes: 1.5*4 = 6.00
Candy: 75*4= 3.00
Popcorn: 1*2 = 2.00
Cost at the game: 36.00
Gas bill: 20/4 = 5 dollars per person
Food and gas: 36 + 5 = 41.00
Danny spent 41 dollars, and his friends spent 5 dollars
However, if everyone split everything, each person would have paid $13
What is the Area of 8 and 3 1/2
The area of the rectangle with 8 and 3 1/2 units is 28 sq. units.
How to estimate the area of the rectangle?The region occupied by a rectangle within its four sides or boundaries is known as its area. The area of a rectangle is determined by its sides. Essentially, the formula for area is equal to the product of the rectangle's length and breadth.
It is given that the length of the rectangle is 8 units and the breadth 3 1/2 units.
the area of the rectangle = length x breadth = 8 x 3 1/2 = 8 x 7/2 = 28 sq. units
So, the area of the rectangle is 28 sq. units.
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