Answer:
K = 17
Step-by-step explanation:
x = 8
describe the zeros & multiplicity of the function f(x)=2x^3+4x^2-8x-16
The zeroes of the expression f(x) = 2x³ + 4x² - 8x - 16 are (x-2), (x+2) and (x+2). And multiplicity of x = -2 is 2.
What is Cubic equation?
Cubic equations are polynomials of degree3. That means the maximum degree of polynomial is three.
And the standard form of cubic equation is;
f(x) = ax³ + bx² +cx +d, where a, b, c and d are constant coefficients a ≠ 0.
Given that the expression
f(x) = 2x³ + 4x² - 8x - 16
Now we find the roots or zeroes of equation;
for that we will try hit and trial method,
let x = 2
f(x) = 2 (8) - 4 (4) - 8(2) -16
f(x) = 0
That means (x-2) is one of roots of cubic equation.
Now to find other roots of the cubic equation, we will simplify the cubic expression
f(x) = 2x² (x-2) + 8x (x-2) + 8 (x-2)
f(x) = (x-2) (2x²+ 8x + 8)
Now we will find the roots of quadratic equation (2x²+ 8x + 8).
let g(x) = (2x²+ 8x + 8).
factors of quadratic equation is (x+2) and (x+2).
Therefore the zeroes of the expression f(x) = 2x³ + 4x² - 8x - 16 are (x-2), (x+2) and (x+2). And multiplicity of x = -2 is 2.
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A population of 50 deer are introduced into a wildlife sanctuary. It is estimated that the sanctuary can sustain up to 600 deer. Absent constraints, the population would grow by 90% per year. Estimate the population after one year p 1 = Estimate the population after two years p 2 =
Answer:
p1 = 95 p2 = 180
Step-by-step explanation:
50 + 90% = 95
95 + 90% = 180
The Greek letter ___ represents the correlation between two numerical variables for a population.
The Greek letter rho represents the correlation between two numerical variables for a population.
What is Rho?
The amount of money an option will lose or gain with a 1% change in interest rates is how Rho, which gauges an option's sensitivity to changes in the risk-free rate of interest (the interest rate paid on US Treasury bills), is calculated.
How is rho determined?
Rho's exact formula is challenging. The first derivative of the option's value with regard to the risk-free rate is however used to compute it.
Rho calculates the anticipated change in price of an option for a 1% change in the risk-free rate of a US Treasury bill.
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18. a. If ΔA B C is rotated 180° about the origin, what are the coordinates of B'
If Δ A B C is to be translated to ΔA'B'C' by the following motion rule:
(x,y)⇒(x-2,y+4)
What will be the coordinates of vertex A'?
a. The coordinates of vertex B is (-3, -4)
b. The coordinates of vertex A' is (3,8)
What do you mean by rotation 180° about the origin?
The rotation of 180° of any coordinate or vertex about the origin means that the coordinates are rotated to the negative axis that is (x, y) >>>>(-x,-y) or (-x,-y) >>>>(x, y).
Solution:
a. Current coordinate of vertex B is (3, 4).
After rotating it 180° it becomes B (-3 , -4)
b. After translation the coordinates of vertex A is (5-2,4+4)
Coordinates of vertex A is (3,8)
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If ΔA B C is rotated 180° about the origin, the coordinates of B' (-3, -4)
b. The coordinates of vertex A' is (3,8)
What do you mean by rotation 180° about the origin?
The rotation of 180° of any coordinate or vertex about the origin means that the coordinates are rotated to the negative axis that is (x, y) >>>>(-x,-y) or (-x,-y) >>>>(x, y).
Solution:
a. Current coordinate of vertex B is (3, 4).
After rotating it 180° it becomes B (-3 , -4)
b. After translation the coordinates of vertex A is (5-2,4+4)
Coordinates of vertex A is (3,8)
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how do i find the inverse of f(x)=[tex]\sqrt[3]{5x+5}[/tex]
The inverse of f(x) = ∛5x + 5 is f⁻¹ = ( x³ - 5 ) / 5
What is inverse of function?
To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.An inverse function is a function that undoes the action of the another function. A function g is the inverse of a function f if whenever y=f(x) then x=g(y).Change y in for the f(x) :
y = ∛5x + 5
Switch the x and y
x³ = 5y + 5
x³ - 5 = 5y
y = ( x³ - 5 ) / 5
f⁻¹ = ( x³ - 5 ) / 5
Hence, The inverse of f(x) = ∛5x + 5 is f⁻¹ = ( x³ - 5 ) / 5
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An executive committee consists of 9 members: 5 men and 4 women. 3 members are selected at random to attend a
meeting in Hawaii. The names are drawn from a hat. What is the probability that all 3 selected are men?
Answer:P(3 men) =
Step-by-step explanation:
I'm needing some help please with the graph
Answer:
If you are having trouble understanding the graph, it may be helpful to break it down into smaller pieces. Start by looking at each axis and what it represents. Then, look at each data point and see how it relates to the axes. Finally, look at the overall shape of the graph and what it is trying to tell you. If you are still having trouble understanding the graph, you may want to reach out to someone who is knowledgeable about graphs or data analysis for assistance.
Step-by-step explanation:
Use the formula A=P(1+r/n)ⁿt to solve the compound interest problem
Find how long it takes a $ 1700 investment to earn $ 500 interest if it is invested at 2 % interest compounded quarterly
$ 500 interest will be earned in approximately years. (Round to the nearest tenth.)
The required time will be 12.9 years.
What is compound interest?
The interest charged on a loan or deposit is referred to as compound interest. It is the idea that we employ the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest.
Given, P = $1700
I = $500
A = P + I = 1700 + 500 = $2200
r = 2% = 0.02
compounded quarterly, n = 4
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
or, 2200 = 1700(1+ (0.02/4))^(4t)
or, 1.294 = 1.005^4t
or, t = 12.9 years
Hence, the required time will be 12.9 years.
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Find the missing measures listed below given that the picture below is an incenter.
m∠MJL=__
m∠JLP=__
The required measures of angles are:
∠MJL = 78°
∠JLP = 28°
What is incenter ?
One of the triangle's centers where the bisectors of the inner angles converge is known as the incline. The incenter is often referred to as the incircle's center in a triangle. An incenter might have several distinct types of characteristics.
The junction point of the central axis, which is the center of the triangle's inscribed circle, places this point at an equal distance from each of the triangle's sides. Since the biggest circle that might fit within a triangle is the incenter, it is also referred to as the center of the triangle's circle.
In the figure,
∠PJL = ∠MJP = 39°
∠MJL = ∠PJL + ∠MJP = 39° + 39° = 78°
∠PLK = 28°
∠JLP =∠PLK = 28°
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The required measures of angles are:
∠MJL = 78°
∠JLP = 28°
What is the incenter of a triangle?
The inclination is one of the triangle's centers where the inner angles' bisectors converge. The incenter is frequently referred to as the triangle's incircle's center. Multiple different types of features could apply to an incenter.
This point lies at an equal distance from each of the triangle's sides because it is the intersection point of the central axis, which is also the center of the inscribed circle. The incenter is also referred to as the triangle's circle's center since it is the largest circle that could possibly fit inside a triangle.
In the figure,
∠PJL = ∠MJP = 39°
∠MJL = ∠PJL + ∠MJP = 39° + 39° = 78°
∠PLK = 28°
∠JLP =∠PLK = 28°
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Let f(x)=\sqrt(3x-9) and g(x)=3x^(2)-9
A) what is the inverse of function f?
b) is f an inverse of g? Please show all work
A) The inverse of f(x) is f⁻¹(x) = (x² + 9)/3 and B) f is not an inverse of g.
What is an inverse function?First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.
We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.
Given, f(x) = [tex]\sqrt{3x - 9}[/tex].
y = [tex]\sqrt{3x - 9}[/tex].
y² = 3x - 9.
3x = y² + 9.
x = (y² + 9)/3.
y = (x² + 9)/3.
f⁻¹(x) = (x² + 9)/3 and g(x) = 3x² - 9, so f is not an inverse of g.
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Find the volume of a cone with a radius of 11.5 inches and a height of 15 inches. Enter the answer in terms of pie
The volume of a cone with diameter 11.5 inches and a height of 15 inches is 519 in³.
What is a cone?A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreases to a certain point.
The volume of a cone is (1/3)πr²h.
The total surface area of a cone is πr(r + l).
The curved surface area is πrl.
Given, A cone with a radius of 11.5 inches and a height of 15 inches.
Now, The diameter is 11.5 inches, hence radius is 11.5/2 = 5.75 inches.
We know the volume of a cone is (1/3)πr²h.
∴ The volume of a cone is = (1/3)×π×(5.75)²×15 inch³.
= 519 in³.
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Click to review the online content. Then answer the question(s) below, using complete sentences. Scroll down to view additional
questions.
Online Content: Site 1
One of the advantages to an employer of paying employees piece rate or commission is that the employee is paid based solely on
their performance. What is one disadvantage of this type of pay?
BIUS X, X²
ΕΞΩ
I
B
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The disadvantage of piece rate pay is that the cost of producing higher quantities of a product can be a reduction in the quality of the items produced.
What is piece rate?Piece rate is any type of job in which a worker is paid a set amount for each unit produced or action performed, regardless of time. Some employees may be paid on a piece rate or on a commission basis.
Employees are paid on a piece rate, and commission payments are based on results rather than an hourly or weekly pay rate. This means that the employee's weekly pay will vary depending on how much work they do. One of the drawbacks of piece rate pay is that the cost of producing larger quantities of a product may result in a decrease in the quality of the items produced.
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Please help me
Solve the answer
Arc QR =
Arc RS =
Applying the inscribed angle theorem, the measures of the angles and arcs in the image given are:
Arc QR = 48°
Arc RS = 96°
Arc QPS = 216°
Arc PSR = 186°
Arc SRQ = 144°
What is the Inscribed Angle Theorem?The inscribed angle theorem state that the measure of an intercepted arc is equal to twice the measure of the inscribed angle.
Find arc PSR:
Arc PSR = 2(93) [based on the inscribed angle theorem]
Arc PSR = 186°
Find arc QR:
Arc QR = 360 - arc PQ - arc PSR
Substitute
Arc QR = 360 - 126 - 186
Arc QR = 48°
The value of ARC QR is 48
Arc RS = arc PSR - arc PS
Arc RS = 186 - 90
Arc RS = 96°
The value of ARC RS is 96
Arc QPS = 126 + 90
Arc QPS = 216°
Arc PSR = arc PS + arc RS
Arc PSR = 90 + 96
Arc PSR = 186°
Arc SRQ = arc RS + arc QR
Arc SRQ = 96 + 48
Arc SRQ = 144°
Therefore the value of ARC QR is 48° and ARC RS is 96°
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A unicorn is racing a chinchilla. The chinchilla is one hundred feet a head of the unicorn
and running at a rate of 5.75 feet per second. The unicorn is running at a rate of 30 feet
per second. Write an inequality that shows when the unicorn gets ahead of the
chinchilla.
The inequality that shows when the unicorn gets ahead of the chinchilla is 30s > 100 + 5.75s.
What is the inequality that shows when the unicorn gets ahead?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Let the number of seconds be represented by s.
The chinchilla is one hundred feet a head of the unicorn and running at a rate of 5.75 feet per second. This will be 100 + 5.75s.
The unicorn is running at a rate of 30 feet
per second. This will be 30s
The inequality will be 30s > 100 + 5.75s.
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Kaitlin the trainer has two solo workout plans that she offers her clients: plan A and plan B each client does either one or the other (not both) on Friday there were 3 clients who did plan A and 8 who did plan b on Saturday there were 5 clients who did plan A and 2 who did plan b Kaitlin trained her friday clients for a total of 7 hours and her Saturday clients for a total of 6 hours how long does each of the workout plans last
The length and width of two sides of a rectangle are consecutive odd integers. The area of the rectangle is 143 square units.
Find the dimensions of the rectangle.
The width of the rectangle is blank and length is blank
The dimensions of the rectangle are 70.5 by 72.5 units.
What is a dimension?
A length measurement that only goes one way. Dimensions include things like width, depth, and height. One dimension is that of a line, two dimensions are found in a square, three dimensions are found in a cube, and one dimension is that of something's height, length, or width. For instance, the room is 26 feet by 15 feet in size.
Solution Explained:
Given,
Area = 143 unit^2
A/Q,
Let length be x and width be x + 2.
So, Area = l X w
143 = x + x + 2
143 = 2x + 2
x = (143 - 2)/2
x = 70.5
So width = x + 2 = 70.5 + 2 = 72.5
So, the dimensions are 70.5 by 72.5
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If cos (0) = -3.29, what is cos (+0)?
A. -3.29
B. 3.29
C. 73.1°
D. -73.1°
Answer:
A
Step-by-step explanation:
There is no difference between -0 and +0.
So the ans is -3.29 itself.
What is this equal to: (3*2)+6
Answer:
12
Step-by-step explanation:
(3x2) + 6
6 + 6 = 12
Answer:
12
Step-by-step explanation:
3 × 2 is 6
6 + 6 is 12
thus answer is 12
If you make $31.65 in 8 hours, how much in total?
Answer:
$253.20
Step-by-step explanation:
help me please thank youuuu
Answer:
g(x)= -x^2 - 3
Step-by-step explanation:
We know the vertex is (0, -3) and the parabola is opening downward that means the a value has to be negative. And if you know the transformation that -3 moves the parabola down by 3 units as f(x) represents the parent function y= x^2
Knowledge Check
The graph below shows the numbers of orders received by a company for five months.
Number of orders
3400
3300-
3200-
3100-
3000-
2900+
2800-
March
April
May
Month
une
(a) What was the greatest number of orders in a month?
orders
(b) When did the number of orders have the greatest
decrease?
July
X
Ś
The Greatest Number of orders were in the month = September
The Numbers of orders increased in month = August to September
What is a graph ?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.
The relationships between two or more items are frequently represented by the points on a graph.
According to the given information
From graph
We got to know
In may , orders = 3150
In June , orders = 3050
In July , orders = 2900
In August , orders = 3200
In September , orders = 3250
a) The Greatest Number of orders were in the month = September
b) The Numbers of orders increased in month = August to September
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Look at the number line below.
A number line labeled from 0 to 3 with tick marks every one-tenth unit. Tick marks 0, 1, 2, and 3 are labeled. There is a dot at the third tick mark to the right of 2.
Identify the point on the number line and write it as both a fraction and a decimal.
Fraction:
Decimal:
Answer:
fraction 23/10 that's 2 ³/10
decimal 2.3
4 2/3 - 3 3/8 + 4 3/5
Answer:
18.475?
Step-by-step explanation:
Which equation best represents a line perpendicular to a line passing through points (–1, 2) and (1, –8)?
Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0
The equation of the line passing through (-1, 2) and (1, -8). Then the equation of the line will be
y + 8 = [(-8 - 2) / (1 + 1)] (x - 1)
y + 8 = -5x + 5
y = - 5x - 3
The equation that best represents a line perpendicular will be y = - 5x - 3.
Find h in the parallelogram shown.
Answer: the answer is 4
Step-by-step explanation:
What is the total number of units (in millions) of electricity produced
each year based on the current extraction rates of coal from all
mines combined assuming all mines have an endless supply of
coal?
Answer:
Just by multiplying the extraction by the output per kilo for each mine and then summing it. The question asks to express it in millions and you have 8.2 million units
Step-by-step explanation:
Hope it helps
a plumber cuts 2 3/4 feet from pipe. The pipe is now 13 1/4 feet long. Write and solve an equation of to determine the original length if the pipe
2=3/4,13=1/4,2-3/4=0,13-1/4=0,2-3/4=0*13,13-1/4=0*2
HURRY HELP ME! A group of workers is harvesting berries at a constant rate. The following equation represents the total number of baskets of berries the workers picked over a period of time, in hours y = 10x + 5.
What are the slope and the y-intercept for the equation?
X represents the hours, what does y represent and measure in the context of this situation?
What are the rate of change and the initial amount? Explain the meaning of the rate of change and the initial amount in the context of the situation.
Use graph below to draw a graph for the equation y=10x+5. Label the axes appropriately for the situation.
Step-by-step explanation:
The equation y=10x+5 is in the y=mx+b format, where m is the slope and b is the y-intercept.
The slope is 10 and the y-intercept is 5.
Since x represent the number of hours picking berries, y would represent the total number of berries picked.
Y-intercept (or the initial amount) is 5, and slope (aka rate of change) is 10.
y=10x+5 replace x to 1 so it means that one hour has passed
y=10(1)+5 simplify
y=10+5
y=15 y represents the total number of berries picked
That means 15 berries would be picked in one hour.
I uploaded an image of how the graph would look like.
8. What is the equation of the function shown in the graph?
Yaxs
B.
C.
y=-3x
y=3x
y= x
y=-3x
Xanl
The equation of the given function is y = -1/3 x. By using the points through which the line passing through, we can find its equation. Option A is correct.
What is the formula for finding the equation of a line passing through two points?The equation of the line passing through two points such as (x1, y1) and (x2, y2) is
y - y1 = [(y2 - y1)/(x2 - x1)] × (x - x1)
Calculation:From the given graph, the line is passing through the points (0, 0), (-3, 1), and (3, -1).
The equation of the line passing through (-3, 1) and (3, -1) is
y - y1 = [(y2 - y1)/(x2 - x1)] × (x - x1)
⇒ y - 1 = (-1 - 1)/(3 + 3) × (x + 3)
⇒ y - 1 = -2/6 (x + 3)
⇒ y - 1 = -1/3 (x + 3)
⇒ 3y - 3 = -x - 3
⇒ 3y = -x
⇒ y = -1/3 x
So, option A is correct.
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Karen sold 15 hand-made bracelets, earning a total profit of $71.25. She plans to make 25 bracelets for her city’s arts and crafts market. If she sells all 25 bracelets, how much profit can Karen expect to earn?
Answer: $118.75
Step-by-step explanation: first to see how much one bracelet is, you have to do 71.25/15=4.75. one bracelet is $4.75. so now we multiply 4.75 by 25 to see how much 25 bracelets cost. 4.75x25=118.75. so, if Karen seems all of her bracelets, she can expect to make $118.75.