Need answers to this by 20 min please!
Dividing cubic polynomials by linear divisor
Answers
The solution to each of the given polynomials are:
1) x² + 3x - 4
2) x² - 4x + 4
3) x² - 7x + 8
4) x² - 13 - (15/(x + 3)
How to carry out polynomial division?1) We want to divide the polynomial. Thus:
x² + 3x - 4
x + 2| x³ + 5x² + 2x - 8
- x³ + 2x²
3x² + 2x
- 3x² + 6x
- 4x - 8
- -4x - 8
0
2) We want to divide the polynomial. Thus:
x² - 4x + 4
x - 2| x³ - 6x² + 12x - 8
- x³ - 2x²
- 4x² + 12x
- -4x² + 8x
4x - 8
- 4x - 8
0
3) We want to divide the polynomial. Thus:
x² - 7x + 8
x + 3| x³ - 4x² - 13x + 24
- x³ + 3x²
- 7x² - 13x
- -7x² - 21x
8x + 24
- 8x + 24
0
4) We want to divide the polynomial. Thus:
x² - 13
x + 3| x³ + 3x² - 13x - 15
- x³ + 3x²
- 0x² - 13x
- -7x² - 13x
0 - 15
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Related Questions
box of chocolates contains five milk chocolates, five dark chocolates and five white chocolates. You randomly select and eat three chocolates. What is the probability that the first piece is a milk chocolate, the second is a dark chocolate and the third is a white chocolate?
Answers
Answer: 25/546 chance
Step-by-step explanation:
total is 15 chocolates.
Five are milk, so chance of getting milk is 1/3. second is dark, so 5/14 chance. Then white, so 5/13 chance
1/3*5/14*5/13=25/546
ACTIVITY 1: Determine whether each of the following is a proposition or mere sentence. It is a
Proposition if the given is either true or false and Mere Sentence if the given can be both true and
false at the same time.
Answers
Answer:
number 1111q
Step-by-step explanation:
the answer is 1
What is the standard form of the equation for the circle
A. (X-3)^2+(y-2)^2=32
Answers
The standard form of the equation for the circle is (x - 3)² + (y - 2)² = 8.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.Note: A center that lies on the y-axis simply means the value of h on the x-axis is equal to 0.
Based on the information provided above, we have the following parameters:
Radius, r = √[(3 - 5)² + (2 - 4)²] = √8
Center, (h, k) = (3, 2).
By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - 3)² + (y - 2)² = (√8)²
(x - 3)² + (y - 2)² = 8.
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Complete Question:
A circle is shown on the coordinate plane. The graph shows a circle with the origin point A at (3, 2), and a point B on its circumference at (5, 4) and intersects the x-axis at 1 and 5 units. What is the standard form of the equation for the circle?
2. Graph x² + (y-2)² = 36
Answers
Answer:
The graph will be a circle with center (0, 2) and radius 6.
You are told that h is a one to one function with values h(-9)=5 and h(3)= -4 which of the following is true
Answers
If function "h" is one-to-one function which is having values h(-9) = 5, and h(3) = -4, then the inverse statement is (d) h⁻¹(-4) = 3.
We know that the function "h" is a one-to-one function, so, it has an inverse function (h⁻¹). To find the inverse function, we need to exchange roles of "x" and "y" and solve for y. This gives:
x = h(y)
y = h⁻¹(x)
The given values of function "h" are h(-9) = 5 and h(3) = -4, we find the values of h⁻¹(5) and h⁻¹(-4):
h(-9) = 5
So, h⁻¹(5) = -9 (by exchanging roles of x and y)
and h(3) = -4
So, h⁻¹(-4) = 3 (exchanging the roles of x and y)
The function "h⁻¹(-4) = 3" is represented in option (d).
Therefore, the correct option is (d).
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Piston movement compresses air in this type of air compressor. Medium size compressors Industrial compressors Small compressors Horizontal compressors
Answers
Piston movement compresses air in Small compressors type of air compressor
Piston movement compresses air in small compressors. Small compressors, also known as portable compressors, are commonly used for home improvement projects, powering tools, and inflating tires or other objects. The piston moves back and forth inside a cylinder, compressing air and increasing its pressure. The compressed air is then stored in a tank until it is needed to power a tool or inflate an object.
Small compressors are generally less powerful than medium or industrial compressors, but they are more affordable, portable, and easier to use for smaller tasks. They can be powered by electricity or gasoline, and they come in a range of sizes and capacities to meet different needs. Overall, piston-driven small compressors are an efficient and cost-effective way to compress air for various applications.
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The equation y = 10x + 15 models the amount of money y, in dollars, that Jack earns shoveling snow for x hours. How many hours does Jack need to work to earn $55?
Answers
y = 10x + 15
We need to find the number of hours Jack needs to work to earn $55, which means we need to solve for x when y = 55.
So, we substitute y = 55 into the equation and solve for x:
55 = 10x + 15
Subtracting 15 from both sides, we get:
40 = 10x
Dividing both sides by 10, we get:
x = 4
Therefore, Jack needs to work for 4 hours to earn $55.
1+1 hardest problem in the world
Answers
The statement "1+1 is the hardest problem in the world" is generally meant to be taken as a joke or a humorous exaggeration.
What does the phrase of 1 + 1 being hard mean ?The phrase may be used ironically to emphasize the difficulty of a seemingly simple task or to highlight the importance of attention to detail. For example, a complex mathematical proof may require multiple steps and involve intricate calculations, but the simplest mistake, such as an error in basic arithmetic, could render the entire proof invalid.
In this context, the phrase "1+1 is the hardest problem in the world" could be used to underscore the importance of checking and double-checking even the most basic assumptions and calculations in complex problem-solving.
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Exercice 10;
58 La Figure 2 est une réduction de la Figure 1.
Figure 1
Figure 2
C.
4 cm
7cm
B
D
A 2,1 cm I
1. Calculer le coefficient de réduc
tion existant entre les deux figures.
2. Déterminer les longueurs man-
quantes et les angles manquants.
B
D
Coup de pouce
Calcule le rapport de deux
sur les deux figures.
longueurs correspondantes
Answers
Answer:
Step-by-step explanation:
If angle a is 125 degrees, what is angle h
Answers
I need help with this AP Stats question.
Answers
The probability that the team wins the debate is 0.6475
How to solve the probabilityP(win) = P(win | S)P(S) + P(win | J)P(J) + P(win | R)P(R)
= (0.25)(0.2) + (0.6)(0.35) + (0.85)(0.45)
= 0.6475
Therefore, the probability that the team wins the debate is 0.6475.
In order to simulate the probability that a Sophomore is never selected to give the closing argument in the next 5 debates, we can use the following steps:
Create a table of random digits with enough rows and columns to simulate the 5 debates. Each row represents a debate and each column represents a team member.
Assign the digits 0, 1, and 2 to represent the events that a sophomore, junior, and senior gives the closing argument, respectively.
Starting from the first row and first column, read the digits from the table and determine which team member gives the closing argument for the first debate.
If a sophomore is selected, record a 0 for that debate. Otherwise, record a 1.
Repeat steps 3 and 4 for the remaining debates, filling in the table as you go.
Calculate the proportion of simulations where a Sophomore is never selected to give the closing argument in the next 5 debates.
Repeat steps 1-6 many times (e.g., 10,000 times) to get a more accurate estimate of the probability.
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50 Points! Algebra question, photo attached. Please show as much work as possible. Thank you!
Answers
Michio's answer not correct. He made a mistake when he was trying to convert the equation to logarithmic form. The right answer is 2.57
What is the right way Michio could have converted to logarithmic form?Looking at the equation 2(3)ˣ = 34, the best way to convert to logarithm is by isolating x.
we divide 2(3)ˣ = 34 by 2 on both side.
= (3)ˣ = 17
In logarithm form 3 becomes the base of the log
x = log₃(17)
x= 2.578
The answer above is based on the information seen in the picture.
Michio wanted to find the value of x in the equation 2(3)ˣ = 34. He first converted the equation to log₃2x = 17. Next, he wrote 2x = 3¹⁷ and used a calculator to find x = 64,570,081.5. Was his answer correct? If not, what was his mistake and what is the right answer? Justify your answer.
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Select the correct answer from each drop-down menu.
Rectangle ABCD is dilated by a scale factor of 1/4 to form A'B'C'D. Point T is the center of dilation and lies on line segment AB as shown. In A'B'C'D. line segment A'B has a slope of ____ and a length of _____.
Answers
In A'B'C'D, line segment A'B has a slope of 0 and a length of 5/4
Calculating the slopes and the lengths of the segment A'B'From the question, we have the following parameters that can be used in our computation:
A = (1, 4) and B = (6, 4)
The line AB is a horizontal line that passes through the point y = 4
This means that the slope of the segment A'B' is 0
The length is then calculated as
A'B' = difference in the x-coordinate * scale factor
Substitute the known values in the above equation, so, we have the following representation
A'B' = (6 - 1) * 1/4
Evaluate
A'B' = 5/4
Hence, the length A'B' is 5/4
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The amount of laps remaining, y, in a swimmer's race after x minutes can be represented by the graph shown.
coordinate grid with the x axis labeled time in minutes and the y axis labeled number of laps remaining with a line from 0 comma 30 to 10 comma 0
Determine the slope of the line and explain its meaning in terms of the real-world scenario.
The slope of the line is negative one third, which means that the swimmer completes a lap in one third of a minute.
The slope of the line is −3, which means that the swimmer will complete 3 laps every minute.
The slope of the line is 10, which means that the swimmer will finish the race after 10 minutes.
The slope of the line is 30, which means that the swimmer must complete 30 laps in the race.
Answers
The given slope of the graph is explaining about the swimmer's lap completion throughout the time of 10 minutes.
In the given graph on the x-axis, we can find the time (in minutes) of 10 minutes.
On the y-axis, the graph represents the number of laps the swimmer is completing.
When we observe closely, the slope is giving very important information. At initial time=0, the no. of laps remaining for swimmer is 30. We can show this data clearly as below:
Number of laps remaining----------Time (in minutes)
30 --- 0
27 --- 1
24 --- 2
21 --- 3
18 --- 4
15 --- 5
12 --- 6
9 --- 7
6 --- 8
3 --- 9
0 --- 10
From the above slope data, we can conclude that for every 1 minute of time elapsing, the swimmer is completing 3 laps.
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Which of the following is a biconditional statement?
A) If x2 = 25, then x = 5 or x = –5
B) x = 5 if x2 = 25
C) x = 5 if and only if x + 5 = 10
D) If x ≠ 5 then x2 ≠ 25
Answers
Answer:
C) x = 5 if and only if x + 5 = 10
Step-by-step explanation:
You want to identify the biconditional statement among those that are given.
ConditionalA conditional statement is of the form ...
If P, then Q.
ConverseThe converse of the above conditional statement is ...
If Q, then P.
BiconditionalWhen both the statement and its converse are intended, the statement can be written as the biconditional ...
If and only if P then Q.
The given example of a biconditional statement is ...
x = 5 if and only if x +5 = 10.
__
Additional comment
This can be abbreviated ...
Iff P then Q
meaning "if P then Q, and if Q then P", or "if and only if P, then Q."
Drag the cards to create a number that matches these rules.
. The number ends in the thousandths place.
2 is the nearest one when rounding
.
A 2 is in the thousandths place
.
1 1 2.2
Answers
Answer is 16.4. Hope this helpsAnswer:
Step-by-step explanation:
I need help please
here is the picture is about Row Ops
Answers
Solving the given matrix operation gives us the solution as: y = -1.4
How to solve simultaneous equations with matrix?From the matrix expression given, we can say that the simultaneous equations it represents are:
x - 4y = 8
3x - 2y = 10
We are told to Multiply eq 1 by -3 and add to row 2 and this means we have:
eq 3: -3x + 12y = -24
Adding to row 2 gives us:
10y = -14
y = -1.4
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The volume of a cube that is 2.9 x 5 x 4
Answers
The volume of the cuboid is 58 cubic units.
What is a cuboid?A cuboid is a 3 dimensional figure that has six rectangular faces. So that the volume of a cuboid can be determined by;
volume of cuboid = length x width x height
From the given question, we have;
the volume of a cuboid that is 2.9 x 5 x 4 can be determined as follows;
volume of cuboid = length x width x height
= 2.9 x 5 x 4
= 58
The volume of the cuboid with the given dimension is 58 cubic units.
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what are the answers to these questions?
Answers
The values of the expression are,
⇒ x₂ = - 9.4
⇒ x₃ = - 9.4 - (e³⁸ + 38 + 1) / (2e³⁸ + 2)
Given that;
Expression is,
e²ˣ = - 2x - 1
Hence, Function is,
⇒ f (x) = e²ˣ + 2x + 1 = 0
⇒ f' (x) = 2e²ˣ + 2
Now, By newton's method;
⇒ x (n + 1) = x (n) - f (x (n)) / f' (x(n))
⇒ x₂ = x₁ - f (x₁) / f' (x₁)
⇒ x₂ = - 5 - (e¹⁰ + 10 + 1)/(2e¹⁰ + 2)
⇒ x₂ = - 5 - (e¹⁰ + 11)/(2e¹⁰ + 2)
⇒ x₂ = - 5 (2.6 + 11) / ( 2 x 2.6 + 2)
⇒ x₂ = - 68 / 7.2
⇒ x₂ = - 9.4
⇒ x (n + 1) = x (n) - f (x (n)) / f' (x(n))
⇒ x₃ = x₂ - f (x₂) / f' (x₂)
⇒ x₃ = - 9.4 - (e³⁸ + 38 + 1) / (2e³⁸ + 2)
Thus, The values of the expression are,
⇒ x₂ = - 9.4
⇒ x₃ = - 9.4 - (e³⁸ + 38 + 1) / (2e³⁸ + 2)
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Which statements are true about a decagonal (10-sided) pyramid? Select 3 options.
It has one face that is a decagon.
It has two faces that are decagons.
It has 11 faces.
It has 20 edges.
It has 20 vertices.
Answers
The correct statements are,
B)It has two faces that are decagons.
C)It has 11 faces.
D)It has 20 edges.
What is decagonal pyramid?
A decagonal pyramid is a solid whose base is a decagon or a ten sided figure, regular or irregular. The surfaces are ten isosceles triangles, in case of a regular decagonal pyramid with all the ten vertices meeting at a point.
Here The decagonal prism is formed by two regular decagons as its bases and 10 squares as its other faces. the top of the decagonal prism is a regular decagon, so is the bottom face.
We know that decagonal pyramid has 11 faces and 20 edges and 11 vertices.
Hence the correct statements are,
B)It has two faces that are decagons.
C)It has 11 faces.
D)It has 20 edges.
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The table below shows the number of concert tickets bought by people of different age groups. Ages Number of tickets, 14 and under are (17tickets), 15 - 18 (25) ,19 - 22 (38), 23 - 30 (26 ) ,31 - 40 (18), 40 and older (6) When making a histogram of these data, what height would you make the bar for the 15 -18 age range?
Answers
We would make the bar for the 15-18 age range with a height of 25 on the y-axis of the histogram.
What is a histogram?A histogram is a type of chart used to represent the distribution of a set of continuous numerical data. It is a graphical representation that consists of a series of vertical bars, where the height of each bar represents the frequency or count of observations falling within a specific interval or "bin" of values.
To make a histogram, we need to plot the age groups on the x-axis and the corresponding number of tickets on the y-axis. The bars in the histogram should represent the frequency of each age group.
From the given data, the number of tickets bought by people of age 15-18 is 25. Therefore, we would make the bar for the 15-18 age range with a height of 25 on the y-axis of the histogram.
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Use the unit circle to find the exact value of the trig function
Cos(45°)
Answers
Answer: √2/2
Step-by-step explanation: Starting from the positive x-axis (angle 0), we rotate the ray counterclockwise by 45 degrees, or π/4 radians. Since the point on the unit circle corresponding to 45 degrees lies on the line y = x, its coordinates are (cos(45), sin(45)) = (√2/2, √2/2).
Find the amount that results from the given investment.
$700 invested at 4% compounded daily after a period of 4 years
After 4 years, the investment results in $.
(Round to the nearest cent as needed.)
C
Answers
After 4 years, the investment of $700 at 4% compounded daily results in a future value of $821.45.
How is the future value determined:The future value represents the present value or investment compounded at an interest rate periodically for a certain number of years.
The future value can be determined using the FV formula or an online finance calculator.
N (# of periods) = 1,460 days (4 years x 365)
I/Y (Interest per year) = 4%
PV (Present Value) = $700
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $821.45
Total Interest = $121.45
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Correct answer gets brainliest
Answers
Answer:
D. its a two dimensional object
Answer:
A. It is a polygon
C. It is a one-dimensional object
The shape is a polygon in two dimensions since a polygon must have at least three straight sides.
In a class of 52 students, 13 excel in Science and Mathematics, 16 excel in Science and Arts, 12 excel in Mathematics and Arts, 24 excel in Arts and 2 excel in none. Twice as many students excel in science only as do in mathematics only. The number of students who excel in mathematics only is six times the number of students who excel in Arts only. Determine the number of students who excelled in: (a) All the three subjects (b) Two subjects
Answers
14 students excel in all three subjects.
How to solveLet's use the Principle of Inclusion-Exclusion to solve this problem.
Let A be the set of students excelling in Arts, B be the set of students excelling in Science, and C be the set of students excelling in Mathematics.
|A| = 24, |B| = 16, |C| = 13
|A ∩ B| = 16, |B ∩ C| = 13, |A ∩ C| = 12
Let x be the number of students who excel in all three subjects.
|A ∩ B ∩ C| = x
We are given that 2 students excel in none of the subjects.
So, |A ∪ B ∪ C| = 52 - 2 = 50
Using the Principle of Inclusion-Exclusion:
|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |B ∩ C| - |A ∩ C| + |A ∩ B ∩ C|
Substituting the given values, we get:
50 = 24 + 16 + 13 - 16 - 13 - 12 + x
Solving for x, we get:
50 = 24 - 12 + x
x = 38 - 24
x = 14
So, 14 students excel in all three subjects.
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PLEASE SOMEONE HELP ME THIS IS SO HARD. ILL GIVE 60 POINTS TO WHOEVER HELPS ME. PLEASE I GIVE BRAINLIEST
Answers
Answer:
B
Step-by-step explanation:
Vertex form is: y=a(x-h)²+k
Vertex would be (h,k)
Based on this, the only equation in vertex form is B
Answer:
Step-by-step explanation:
B is the easiest way to see vertex because that is the vertex form:
y=a(x-h)²+k where (h,k) is the vertex
Vertex (2, 27)
Use the given feasible region to find the maximum possible value of the objective function f=5x+6y
Answers
The calculated value of the maximum possible value of the objective function is 46
Finding the maximum possible value of the objective functionFrom the question, we have the following parameters that can be used in our computation:
Objective function, F = 5x + 6y
The coordinates of the feasible region are
(0, 6), (1, 6.5) and (2, 6)
Substitute (0, 6), (1, 6.5) and (2, 6) in the above equation, so, we have the following representation
F(0, 6) = 5(0) + 6(6) = 36
F(1, 6.5) = 5(1) + 6(6.5) = 44
F(2, 6) = 5(2) + 6(6) = 46
The maximum value above is 46 at (2, 6)
Hence, the maximum possible value of the objective function is 46
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The graph of line T passes throug the points listed beow.
(a,-b)and (-C,d) Line s is parallel to linet. What is the slope of line s?
Answers
Therefore, the slope of line s is equal to (d + b) / (a - c).
What is slope?In mathematics, the slope is a measure of the steepness of a line. It is defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between those same two points. In other words, the slope is the change in the y-coordinate divided by the change in the x-coordinate. If the slope is positive, the line is increasing from left to right and has an upward direction. If the slope is negative, the line is decreasing from left to right and has a downward direction. If the slope is zero, the line is horizontal. If the slope is undefined, the line is vertical. The concept of slope is important in various fields of mathematics, science, and engineering, as it helps to describe the relationship between two variables and make predictions based on that relationship. It is also used in calculus to find the rate of change of a function, and in geometry to find the equation of a line or the angle between two lines.
Here,
Since line s is parallel to line t, it has the same slope as line t. The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula:
slope = (y₂ - y₁) / (x₂ - x₁)
In this case, the points on line t are (a, -b) and (-c, d), so the slope of line t is:
slope of t = (d - (-b)) / (-c - a)
slope of t = (d + b) / (a - c)
Since line s is parallel to line t, it has the same slope as line t:
slope of s = (d + b) / (a - c)
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Assignments...
Library Search
Khan Academy
Estimate the solution to the system of equations.
You can use the interactive graph below to find the solution.
fy=
=−x+2
Get Al Guide
y = 3x -4
Donate
Answers
The solution of the given system of equations is (1, 2.5)
How to explain the equationFrom the graph attached, it van be seen that two intersecting lines represent the system of equations.
And the solution of the system of equations is a common point where these lines intersect.
The graph shows both the line are intersecting each other at (1, 2.5).
Therefore, the solution of the given system of equations will be (1, 2.5).
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suppose the function f(t) = e^t describes the growth of a colony of bacteria, where t is hours. find the number of bacteria present at 5 hours
a) 59.598
b) 148.413
c) 8.155
d) 79. 432
Answers
The number of bacteria present at 5 hours is 148.413. The Option B is correct.
What is the number of bacteria present at 5 hours?In exponential growth, a population's growth rate stays the same regardless of population size which makes the population grow faster and faster as it gets larger.
To get number of bacteria present at 5 hours, we need to evaluate the function [tex]f(5) = e^5.[/tex]
Using a calculator, we get:
[tex]f(5) = e^5\\f(5) = 148.413159103\\f(5) = 148.413.[/tex]
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