PLEASE HELP ASAP
A. Describe the difference between the remainder theorem and the factor theorem
B. Using long division or synthetic division divide a polynomial function above the binomial (x-3)
C. Interpret what the solution means and how you know
D. Identify all X intercepts of the Polynomial function
Answers
The solutions for the given Cubic equation y = x³ - x² - 41 x + 105 are x = -7 and x = 5.
What is a cubic equation?A three-degree equation is referred to as a cubic equation. All cubic equations have roots that are either three real roots or one real root and two imaginary roots. Polynomials are referred to as cubic polynomials if they have a degree of three.
Given, a polynomial y = x³ - x² - 41x + 105
The difference between the remainder theorem and the factor theorem:
The remaining factor theorem really consists of two theorems that link a polynomial's roots to its linear factors. The theorem is frequently applied to avoid using long division while factoring polynomials. This gives us a strong tool to factor polynomials, especially when coupled with the rational root theorem.
Use the factor theorem to find the roots of a cubic equation.
possible roots are factors of the constant theorem.
Once you get one root then you can use synthetic division to get the other roots.
For instance,
x³ - x² - 41x + 105 = 0,
use synthetic division
3 1 -1 -41 105
1 2 -35
1 2 -35 0 (1, 2, -35 are co-efficient of the quadratic equation)
So now we have
x³ - x² - 41x + 105 = (x-3 )( x² + 2x - 35)
(x-3 )( x² + 2x - 35)
(x-3)(x(x+7)-5(x+7))
(x- 3)(x +7) (x - 5)
Solution means that at values 3, -7, and 5 of x, y will be zero.
Therefore, all X intercepts of the given Polynomial function are 3, -7, and 5.
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Related Questions
Jayden has $7.69. His coach will give him $3.21 every mile he runs If he run 18 miles how much will he have
ASAP!!! HURRY!!
Answers
Answer:
Jayden will earn $3.21 x 18 = $<<3.21*18=57.78>>57.78 from running 18 miles.
So he will have $7.69 + $57.78 = $<<7.69+57.78=65.47>>65.47 in total.
Step-by-step explanation:
What is the solution to the system of equations x-y=-1 and x-3y=-13?
why did you choose this answer?
Answers
Answer:
(5,6)
Step-by-step explanation:
x -y = -1
x - 3y = -13 ⇒ multiply through by -1 ⇒ -x + 3y = 13 Add this to the first equation
-x + 3y = 13
x - y = -1
2y = 12 Divide both sides by 2
y = 6
To find y substitute 6 for y in the equation x - y = -1
x - 6 = -1 Add 6 to both sides
x = 5
(5,6)
Need help asap! Im confused, i dont get the question.
Answers
Answer:
6
Step-by-step explanation:
See the screenshot below.
help please I need it
Answers
Answer:
x =5 units
Mark me as a brainiest
Pls, answer the question below.
Answers
Answer:
-6 , 19 , 29
Step-by-step explanation:
range = output which is required
domain = input which are given -2,3,5
simply plot the value domain one by one in given equation
You have 99 cats and 77 dogs and 10998 horses what is the ratio of dogs to cats?
Answers
The ratio of dogs to cats is 7 to 9
How to determine the ratio of dogs to cats?From the question, we have the following parameters that can be used in our computation:
You have 99 cats and 77 dogs and 10998 horses
The ratio is represented as
Ratio = Dogs : Cats
Substitute the known values in the above equation, so, we have the following representation
Dogs : Cats = 77 : 99
Divide by 11
Dogs : Cats = 7 : 9
Hence, the ratio is 7 to 9
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Cmonnn I will give Brainly just be quick plssss
Answers
Answer:
D) 7----------------------------------
Solve the equation:
-3 - (- 8) - (- 2) = x-3 + 8 + 2 = x-3 + 10 = x10 - 3 = x7 = xx = 7Answer:
[tex] \sf \: d) \: x = 7[/tex]
Step-by-step explanation:
Given equation,
→ -3 - (-8) - (-2) = x
Now the value of x will be,
→ -3 - (-8) - (-2) = x
→ x = -3 - (-8) - (-2)
→ x = -3 + 8 + 2
→ x = 5 + 2
→ [ x = 7 ]
Hence, the value of x is 7.
Solve for mzA:
D
M/A=
C
101
B
Answers
The value of ∠A is 101°.
What is parallelogram?A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees.
Given a quadrilateral,
whose opposite sides are parallel, the figure is parallelogram,
property of a parallelogram says
ABCD is a parallelogram, where AB || CD and AD || BC.
Also, AB = CD and AD = BC
so ∠A = ∠C & ∠B = ∠D
given ∠C = 101°
so ∠A = ∠C = 101°
Hence the value of ∠A is 101°.
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The bearing of P from Q is 040°.
The bearing of R from Q is 124°.
QR = QP.
Work out the bearing of R from P.
Answers
The bearing of R from P is 172°.
What are bearing(angles)?The horizontal angle between an object's direction and either north or another object is known as a bearing or azimuth in navigation. You can specify the angle value in a number of different angular units, including degrees, mils, and grad.
The angle between the magnetic north and the absolute bearing
The angle between the craft's forward motion and the relative bearing.
Given The bearing of P from Q is 040°.
The bearing of R from Q is 124°.
QR = QP.
Bearing angles are 180 degrees different than forward-bearing angles. This difficulty can be resolved by combining these relations with the standard angle sum relation for triangles.
Angle PQR will be the difference in the bearings from Q to P and Q to R:
∠PQR = 124° -40° = 84°
Triangle PQR is isosceles, so the base angle at P will be ...
∠QPR = (180° - 84°)/2 = 48°
The bearing from P to R will be 48° less than the bearing from P to Q. The bearing from P to Q is 180° more than the bearing from Q to P.
PR bearing = PQ bearing - ∠QPR
= PQ bearing - 48°
= (40° +180°) - 48° = 172°
Hence, The bearing of R from P is 172°.
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Previous 5
2023 F
5
Graphing Polynomial Functions: Mastery Test
Select the correct answer.
Identify the end behavior and the zeros of function h.
h(z) = -³ 92² + 4x + 96
Based on these key features, which statement is true about the graph representing function h?
The graph is positive on the intervals (-8, -4) and (3, 0o).
The graph is negative on the intervals (-oo, -8) and (-4, 3).
O C. The graph is positive on the intervals (-00, -8) and (-4, 3).
OD. The graph is negative on the intervals (-3, 4) and (8,00).
OA.
OB.
Reset
Next
Answers
According to the end behavior of the function h(z) = 5x³-9x²+4x+96, the graph is positive on the intervals (-∞, -8) and (-4, 3).
What is a polynomial function?
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.
The given polynomial function is -
h(z) = 5x³-9x²+4x+96
The end behavior of a function f(x) describes the behavior of the function as x approaches +∞, and as x approaches -∞.
Domain of function h(z) = -∞<x<∞
The end behavior of the function h(z) is -
lim x→∞, (5x³-9x²+4x+96) = ∞
as x→∞, h(z)→∞
lim x→-∞, (5x³-9x²+4x+96) = -∞
as x→-∞, h(z)→-∞
Therefore, the graph is positive on the intervals (-∞, -8) and (-4, 3).
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Mrs. Olson and Mrs. Alcorn went shopping together for spring break. Mrs. Olson bought six shirts and four pairs of shorts that cost her 106.80. Mrs. Alcorn bought 3 shirts and 3 pairs of shorts that cost her 68.85. How much does one shirt cost.
Answers
Answer:
One shirt costs $7.50.
One pair of shorts cost $15.45
Step-by-step explanation:
what is the slope of line that passes through points (-2,7) and (-3,3)
Answers
Considering the expression of a line, the slope of line that passes through points (-2,7) and (-3,3) is 4.
What is a linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are the variables.m is the slope.b is the ordinate to the origin and represents the y-intercept of the line.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m can be calculated as:
m= (y₂ - y₁)÷ (x₂ - x₁)
Slope in this caseIn this case, being (x₁, y₁)= (-2, 7) and (x₂, y₂)= (-3, 3), the slope can be calculated as:
m= (3 -7)÷ (-3 -(-2))
m= (3 -7)÷ (-3 +2)
m= (-4)÷ (-1)
m= 4
Finally, the slope is 4.
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which point represents 2 1/3 -5/6 and -3 1/2 on the number line
Answers
Answer:
Provided at image
Step-by-step explanation:
Green dot = -3.5
Red dot = -5/6
Orange dot = 2.3
Since there are 5 lines between every 1 number, you can divide 100/6 to see the distance between the lines (16.6666) and plug in the points.
how to solve the correlation coefficient are between the age of a car X and the car is mileage why is 0.639 what percent of the variation in mileage cannot be explained by differences in the cars ages
Answers
The percent of the variation in mileage that cannot be explained by differences in the cars ages is 36.1%.
What is correlation coefficient?A statistical indicator of the strength of a linear relationship between two variables is the correlation coefficient. A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively correlated, the value either rises or falls together.
The correlation r between the age of a car x , and the cars mileage, y is 0.639. This means that 63.9 % of the variation in mileage can be explained by the differences in the cars ages, 100 – 63.9 = 36.1% of the variation cannot be explained.
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C Dax packs cans into boxes.
He fits eight rows of five
cans into the bottom of
each box, and a second
layer of cans on top. How
many cans are in each
box?
Answers
The number of cans in each box is 80.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of rows in each layer = 8
Number of cans in each row = 5
Number of layers = 2
The total number of cans.
= Cans x Rows x Layer
= 5 x 8 x 2
= 40 x 2
= 80
Thus,
There are 80 cans in each box
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Factor f(x) = x² – 3x³ - 12x² + 54x - 40 with real coefficients given that 3-i is a zero of f(x).
f(x) = x² – 3x³ - 12x² +54x - 40 =
Answers
(x - 3 + i)(x² - 3x - 10) This means that 3 - i is a zero of f(x). This is because when f(3 - i) is evaluated, the result is 0. The factorization of f(x) shows that 3 - i is a zero of the function.
What is factorization?Factorization is the process of breaking a number or expression into its prime factors. This is done by expressing the number as a product of its prime factors. Factorization is a key concept in mathematics, particularly in algebra and number theory. Factorization can be used to simplify expressions and equations, and it is often used to solve problems involving divisibility and prime numbers. Factorization can also be used to find the greatest common divisor, least common multiple, and other properties of numbers.
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3. Which of the following expressions is best represented by the model below? 1000 1000 A. 3x1 10 B. 3x-2 0009 X -1 C. 3x6 D. 3x 8
Answers
Answer:
A I THINK
Step-by-step explanation:
if 1,100 completely satisfied 740 somewhat satisfied 160 not satisfied what percent of the people surveyed were completely satisfied with the car?
The answer would be 55% because if you add 1,100 740 and 160 you get 2000 which means that 2000 people were surveyed then you'll do 1,100 by 200 and get 55 and that's your percent.
Answers
The percentage of the people surveyed who were completely satisfied with the car was 55 %.
How to find the percentage ?To find the percentage of people surveyed who were completely satisfied with the car, you first need to find the number of people who were survyed. This can be found by adding up all the number of people who participated in the survey :
= 1, 100 + 740 + 160
= 2, 000 people
The percentage of the people surveyed who were completely satisfied with the car is therefore:
= People completely satisfied / Number of people who participated x 100 %
= 1, 100 / 2, 000 x 100 %
= 55 %
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It takes 4 oz. of cherry syrup, 4 oz. of grenadine, and 1
quart of white soda to make a batch of Shirley Temples.
To make them for a party, how much white soda would
you need to buy if you had a quart of cherry syrup and a
quart of grenadine?
Answers
Answer:
8 quarts of white soda
(Score for Question 2:
of 6 points)
2. One-half of the fudge at the fudge shop on Monday morning contain nuts. Helena works at the fudge shop
and prepares 10 pounds of fudge containing walnuts to fulfill a special order Monday afternoon. With this
additional amount of fudge, there are at least 24 pounds of fudge containing nuts at the fudge shop on
Monday.
(a) Write an inequality that represents the scenario. Begin by defining your variable.
(b) Solve the inequality. Show your work.
(c) Fudge is packaged into 1-pound boxes. What is the fewest number of boxes of fudge at the fudge
shop Monday moming? Show your work.
Answer:
Answers
a) The inequality that represents the scenario is 10 + x ≥ 24.
b) The solution of the inequality is x ≥ 14.
c) The fewest number of boxes of fudge at the fudge shop Monday morning is 14.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
a) Let x denote the amount of fudge at the shop.
Helena prepares 10 pounds of fudge containing nuts.
The Inequality can be
10 + x ≥ 24
b) The inequality can be solved as
10 + x ≥ 24
x ≥ 24 -10
x ≥ 14
c) The fewest number of boxes would be almost 14 boxes.
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Which is the graph of y = 3^√x+1-2?
Answers
The graph of the function y = ∛(x +1 ) - 2 is represented by the graph represented by option 1.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.
The graph of the function y = ∛(x +1 ) - 2 is attached with the answer below,
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How to solve these problems?
Answers
The problems for production staff are solved as below.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
1. Knit
Number produced by 1 worker in a day = 50 pairs
Annual production goal = 780,000 pairs
Daily production goal = 780,000 / 260 = 3000 pairs
Production staff needed = 3000 / 50 = 60 workers
2. Tube
Number produced by 1 worker in a day = 40 pairs
Annual production goal = 946,400 pairs
Daily production goal = 946,400 / 260 = 3640 pairs
Production staff needed = 3640 / 40 = 91 workers
3. Athletic
Number produced by 1 worker in a day = 60 pairs
Annual production goal = 1,138,800 pairs
Daily production goal = 1,138,800 / 260 = 4380 pairs
Production staff needed = 4380 / 60 = 73 workers
4. Booties
Number produced by 1 worker in a day = 24 pairs
Annual production goal = 343,200 pairs
Daily production goal = 343,200 / 260 = 1320 pairs
Production staff needed = 1320 / 24 = 55 workers
5. Children's
Number produced by 1 worker in a day = 84 pairs
Annual production goal = 518,000 pairs
Daily production goal = 518000 / 260 = 1992.3 pairs
Production staff needed = 1992.3 / 84 = 23.7 workers
Hence the production staff needed has been solved.
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
Answers
The equation have the same solution as 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p
How to determine the equations that have the same solution?Given: 2.3p – 10.1 = 6.5p – 4 – 0.01p.
Using this given property, let's write the equation
We can subtract like terms (6.5p– 0.01p = 6.49p) to get:
2.3p – 10.1 = 6.5p – 0.01p – 4
2.3p – 10.1 = 6.49p – 4
Also, we can multiply both sides of the algebraic equation by 100:
(2.3p – 10.1) x 100 = (6.5p – 4 – 0.01p) x 100
230p – 1010 = 650p – 400 – p
Therefore, the equations have the same solution as 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p. The 2nd and 3rd options are the answers
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what is 3.2 times 3.2 to the second power to the fourth power to all
Answers
The value of 3.2 times 3.2 to the second power to the fourth power to all is [tex](3.2)^{12}[/tex].
What is exponent?The amount of times a number has been multiplied by itself is shown by its exponent.
3.2 to the second power is represented as [tex](3.2)^2[/tex].
3.2 times 3.2 to the second power, thus, is represented as:
[tex](3.2) (3.2)^2[/tex]
Since, the base is similar, the powers can be added:
[tex](3.2)^{1+2}\\\\(3.2)^3[/tex]
Now, the fourth power to all is represented as:
[tex]((3.2)^3))^4\\[/tex]
Using the rule of exponents [tex]((a^m))^n = a^{mn}[/tex] we have:
[tex](3.2)^{3*4}\\\\(3.2)^{12}[/tex]
Hence, the value of 3.2 times 3.2 to the second power to the fourth power to all is [tex](3.2)^{12}[/tex].
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25. What must be the value of y below so that the line passing through the points (4,4) and (-3, y) has a slope of -2 ?
A. 18
B. 10
C. 2
D. -6
Answers
Answer:
A. 18
Step-by-step explanation:
............... .....k
Loren and Julie have different part time jobs after school. They are both paid at a constant rate of dollars per he
The table below show Loren and Julie's total income (amount earned) for working a given amount of time.
Loren
Hours 2 4 6 8 10 12 14 16 18
Dollars 18 36 54 72 90 108 ? ? 162
Julie
Hours 3 6 9 12 15 18 21 24 27
Dollars 36 ? 108 144 180 216 ? 288 324
How much money would Julie eam for working 16 hours?
Answers
Since Julie earns a constant rate of $12 per hour, for working 16 hours based on mathematical operations, she will earn $192.
What are mathematical operations?The basic mathematical operations involve addition, subtraction, division, and multiplication.
These operations combine parts of the mathematical operations with their assigned operands and the equation symbol (=) to solve mathematical problems.
In this situation, we employ division and multiplication operations to solve the requirement.
Loren and Julie's Total Income Table
LorenHours 2 4 6 8 10 12 14 16 18
Dollars 18 36 54 72 90 108 ? ? 162
Loren's Constant Rate of Pay (Hourly Rate) = $9 ($162/18)
JulieHours 3 6 9 12 15 18 21 24 27
Dollars 36 ? 108 144 180 216 ? 288 324
Julie's Constant Rate of Pay (Hourly Rate) = $12 ($324/27)
Total hours worked = 16
Total earnings = $192 ($12 x 16)
Thus, when Julie works 16 hours, she earns $192.
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A sailor is on the top deck of a ship that is anchored near shore, 200 feet from a lighthouse. The sailor can see the top of the lighthouse by looking up at a 21° angle of elevation and can see the bottom of the lighthouse by looking down at a 14° angle of depression.
How tall is the lighthouse?
Enter your answer in the box. Round to the nearest tenth of a foot.
Answers
The height of the lighthouse is 76.4 feet.
What is the angle of elevation?
The angle is formed by the line of sight and the horizontal plane for an object above the horizontal.
We can use the concept of trigonometry to solve this problem. We know that the angles of elevation and depression are formed by the line of sight of the sailor and the height of the lighthouse.
We can use the tangent function to relate these angles to the height of the lighthouse.
Tangent of angle of elevation = opposite side / adjacent side
Tangent of angle of depression = opposite side / adjacent side
Let h be the height of the lighthouse.
tan(21) = h / 200
tan(14) = h / (200 + h)
now we can use these equations to find h,
h = (200 * tan(21)) = (200 * (opposite side/adjacent side)) = (200 * (h/200))
h = 200 * tan (21)
and
h = (200* h)/(200+h) * tan(14)
we can now use these equations to find the value of h.
h = 200 * tan(21) = 200 * 0.38197 = 76.394
Therefore, the height of the lighthouse is 76.4 feet (approx).
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Create pattern with the rule n x 2
Answers
Step-by-step explanation:
n×2=?
The n means 1 then. 1×2 series
1 × 2 = 2
Equal letters represent equal digits, and different letters represent different digits, Find the 5-digit number ABCDE
Answers
Observing the given question, This is the problem of cryptarithmetic , Using the rules based on cryptarithmetics, The answer is 10890.
What do you mean by cryptarithmetic problem?Mathematical conundrums called cryptarithmetic problems use letters from the alphabet in place of the digits. Use the trial-and-error procedure while keeping in mind the aforementioned considerations to solve cryptarithmetic problems by replacing values for the letters. Depending on whether we have a carry from A+A or not, A can now either be 2 or 3. However, since E=2, A must be 3, and there is a carry as a result.
Why is cryptarithm important?Cryptarithm, a type of mathematical game where the object is to solve an arithmetic puzzle in which the numerical digits have been replaced with letters. Cryptarithm, a type of mathematical game where the object is to solve an arithmetic puzzle in which the numerical digits have been replaced with letters.
Applying cryptarithmetic rules,
First alphabets can't be zero and same digit can't be used for different alphabets.
we get, CBDE + ABAE = AEDCE as 9480+1410 = 10890
AEDCE = 10890.
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It costs $2.25 to rent bowling shoes. Each game costs $2.50. You have $12.25 in your pocket.
Write and solve an equation to find how many x games you can bowl.
Answers
Answer:
You can bowl up to 4 games.
Step-by-step explanation:
2.25 + 2.50x ≤ 12.25
Let x = the number of games you bowl
2.25 + 2.50x ≤ 12.25 Subtract 2.25 from both sides
2.25 - 2.25 + 2.50x ≤ 12.25 - 2.25
2.50x ≤ 10 Divide both sides by 2.50
[tex]\frac{2.50x}{2.50}[/tex] ≤ [tex]\frac{10}{2.50}[/tex]
x ≤ 4
