We need to identify the true statement for every polynomial P with degree n.
The degree n of a polynomial is the exponent of the highest power of x in that polynomial. For example, the polynomial
[tex]x³+3x²+3[/tex]has degree 3, since the highest power of x has exponent 3.
Thus, if the degree is n, then the highest power is n (not n-1). Therefore, (a) is False.
About the number of solutions to P(x) = 0, it can equal the number of the polynomial degree. For some polynomials, the solutions can repeat, so the number of solutions will be less than n. For some of them, the solutions may not belong to the real numbers.
As an example, for P(x) = x²+4, we have:
[tex]\begin{gathered} x²+4=0 \\ \\ x²=-4 \\ \\ x=\pm\sqrt{-4} \\ \\ x=\pm2\sqrt{-1} \\ \\ x=\pm2i \\ \\ x_1=-2i \\ \\ x_2=2i \end{gathered}[/tex]The above polynomial has degree 2 and 2 solutions. Therefore, (b) is False.
Each turning point is where the graph of the polynomial P(x) changes from decreasing to increasing or vice versa. The graph of any polynomial of degree n has at most n-1 turning points.
Therefore, (c) is True.
We can see that (d) is False from the following example:
the line P(x) = x+1 has degree n = 1 and n = 1 x-intercept, which is its zero x = -1.
Answer:
c) The graph of P has at most n-1 turning points
I need help asap and the coordinates are (1,3) (6,5)
I need the equation in point slope using either point I NEED HELP ASAPP
Answer: the Equation is y-3=0.4(x-1) or y-5=0.4(x-6).
Step-by-step explanation: I hope this helps.
A train ticket in a certain city is 3.00. People eho use the train also have the option of purchasing a frequent rider pass for 18.75 each month. With the pass, each ticket costs only 2.25. Determine the number of times in a month the train must be used so that the total monthly cost without the pass is the same as the total monthly cost with the pass.
The number of times for which the train must be used so that the monthly cost without the pass is same as with the pass is; 6.25 times.
How to solve Word Problems using algebraic expressions.It follows from the task content that the regular train ticket costs, 3.00.
Therefore, the cost for travelling x times with the month is; 3x.
On this note, for the total monthly cost without the pass to be same as that with the pass; the equation which must hold is;
3x = 18.75
x = 18.75/3
x = 6.25 times.
Therefore, after taking the train 6.25 times, the cost without the pass is same as that with the pass.
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Write your answer as a fraction in simplest form.
910+(−45)=
Answer:
-44.09
Step-by-step explanation:
Trust bro i am passing collage math at 15
Writing the Equation of a Line in Different Forms
Write the equation of the line MN, which is formed by the
points M(-3, 5) and N(2, 0).
Step 1: Identify the slope. m = -1v
Step 2: Write the equation in point-slope form:
y-0= -1(x - 2)
y0 = -1(x + 2)
y-5=-1(x - 3)
y-5=-1(x + 3)
y - 5 = -1 ( x + 3 ) is Equation of a Lin in slope intercept form,.
What is in slope-intercept form?
Given the slope of the line and the intercept it forms with the y-axis, the slope intercept form in mathematics is one of the forms used to determine the equation of a straight line. Y = mx + b is the slope intercept form, where m is the slope of the straight line and b is the y-intercept.Slope between the points M(-3, 5) and N(2, 0).
m = 0 - 5/2 + 3
m = -5/5 = -1
the equation of point-slope form
y - y₁ = m ( x - x₁ )
y - 5 = -1 ( x - ( -3 ))
y - 5 = -1 ( x + 3 )
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A plant s 6.2cm tall.
The height of the plant increases by 11% each week
Find how tall the plant will be after 2 weeks
The height of plant will be 7.56cm tall after 2 weeks
How to calculate the height of the plant ?The original height of the plant is 6.2cm
The height increases by 11% each week
= 11/100
= 0.11
The increase of the plant in a week
= 0.11 × 6.2
= 0.682
The height of the plant after two weeks can be calculated as follows
= 0.682 + 0.682
= 1.364
= 6.2 + 1.364
= 7.56
Hence the height of the plant after 2 weeks is 7.56cm
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Angle classification/relationships
Angles are another way to categorize triangles. Each of the three angles in an acute triangle is acute (less than 90 degrees). One right angle and two acute angles make up a right triangle. Additionally, an obtuse triangle has two acute angles and one obtuse angle (greater than 90 degrees).
What does the triangle's angle relationship mean?
Angles and sides in relation to one another The biggest side and angle in any triangle are in opposition to one another. The smallest side and angle in every triangle are on opposing sides. The middle side and middle angle are always in opposition to one another in triangles.
A congruent triangle ,
if all of two triangles' sides match, then they are said to be congruent.
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Jimmy thought he had purchased 7folders, but he had only purchased 6.What was his percent error? round to the nearest percent
We can define the percent error as the difference between the estimated value and the actual value, divided by the actual value.
In this case, the estimated value (what Jimmy thought he had purchased) is 7 and the actual value is 6.
Then, the percent error is:
[tex]e=\frac{E-A}{A}=\frac{7-6}{6}=\frac{1}{6}\cdot100\%=16.666\ldots\%\approx16\%[/tex]The percent error is 16%.
Find the quotient and remainder using synthetic division.−x2 + x − 7x + 1quotient remainder
Given:
[tex]\begin{gathered} -x^2+x-7 \\ x+1 \end{gathered}[/tex]Required:
To find the quotient and remainder using synthetic division.
Explanation:
Consider
[tex]\begin{gathered} x+1=0 \\ x=-1 \end{gathered}[/tex][tex]\begin{gathered} -1|-1\text{ }+1\text{ }-7 \\ \text{ }|\text{ }+1\text{ }-2 \\ ------------------- \\ \text{ }-1\text{ }+2\text{ }-9 \\ \end{gathered}[/tex][tex]-x+2-\frac{9}{x+1}[/tex]Here the quotient is
[tex]-x+2[/tex]And the remainder is
[tex]-9[/tex]Final Answer:
Quotient :
[tex]-x+2[/tex]Remainder : -9.
Which equation can be rewritten as x + 4 = x²? Assume x > 0.
Answer:
We have been given an equation . We are also told that x is greater than 0. We are asked to choose the equation that can be written as our given equation.
Since x is greater than, so we will take positive root on both sides of our given equation as:
Upon looking at our given choices, we can see that option C is same as our answer.
Step-by-step explanation:Therefore, option C is the correct choice.
Answer:2=x
Step-by-step explanation:
x+4=x^2
0+4=x^2
Square root 4 = square root x^2
2=x
twenty-five percent of all automobiles undergoing an emissions inspection at a certain inspection station fail the inspection. (round your answers to three decimal places.) among 15 randomly selected cars, what is the probability that at most 5 fail the inspection?
The required probability is 0.852
Here, n=15
P(X ≤5) = P(X = 1)+...+ P(X = 5)
= [(¹⁵₀)(0.25)⁰ (1-025)¹⁵⁻⁰ +...(¹⁵₅)(0.25)⁵ (1-0.25)¹⁵⁻⁵]
= 0.01336+...+0.16515
= 0.85163
= 0.852 (Round to 3 decimal place)
Hence, the required probability is 0.852
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a large industrial firm purchases several new word processors at the end of each year, the exact num- ber depending on the frequency of repairs in the previ- ous year. suppose that the number of word processors, x, purchased each year has the following probability distribution: x 0 1 23 f(x) 1/10 3/10 2/5 1/5 if the cost of the desired model is $1200 per unit and at the end of the year a refund of 50x2 dollars will be issued, how much can this firm expect to spend on new word processors during this year?
The money which is expected to spend on new word processors during this year is
The probability distribution is
x: 0 1 2 3
f(x) [tex]\frac{1}{10}[/tex] [tex]\frac{3}{10}[/tex] [tex]\frac{2}{5}[/tex] [tex]\frac{1}{5}[/tex]
If the cost of the desired model is $1200 per unit and at the end of the year a refund of 50x2 dollars
So total money spent in this year is [tex]1200x-50x^2[/tex]
Then the equation of expenses will be
[tex]\text{Expenses}=E(1200x-50x^2)[/tex]
We can rewrite it as
[tex]\text{Expenses}=E(1200x)-E(50x^2)[/tex]
[tex]\text{Expenses}=1200E(x)-50E(x^2)[/tex] -----------------(1)
Now the mean of the probability distribution is ,
[tex]E(x)=\sum_{ }^{ }((x_i)(f(x_i))\\=(0\times\frac{1}{10})+(1\times\frac{3}{10})+(2\times\frac{2}{5})+(3\times\frac{1}{5})\\=\frac{3}{10}+\frac{4}{5}+\frac{3}{5}\\\\=\frac{3+8+6}{10}\\\\=\frac{17}{10}\\\\=1.7[/tex]
The variance of the function is
[tex]E(x)=\sum_{ }^{ }(x_i^2)(f(x_i)[/tex]
[tex]=(0^2\times\frac{1}{10})+(1^2\times\frac{3}{10})+(2^2\times\frac{2}{5})+(3^2\times\frac{1}{5})[/tex]
[tex]=\frac{3}{10}+\frac{8}{5}+\frac{9}{5}[/tex]
[tex]=\frac{37}{10}[/tex]
[tex]=3.7[/tex]
On substituting the values in equation (1)
[tex]\text{Expenses}=1200E(x)-50E(x^2)[/tex]
[tex]=1200(1.7)-50(3.7)^2[/tex]
[tex]=2040-684[/tex]
[tex]=1855[/tex]
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SHIPPING The OOCL Shenzhen, one of the world's largest
container ships, carries 8063 TEUS (1280-cubic-feet containers).
Workers can unload a ship at a rate of 1 TEU every minute. The
equation y = 8063 - 60x represents the number of TEUs on the
ship y after x hours of the workers unloading the containers from
the Shenzhen.
a. Find the x- and y-intercepts and interpret their meaning in the
context of the situation.
Graph the equation by using the intercepts
Answer:
23
Step-by-step explanation:
Hello, I’m struggling with my geometry homework. It’s number 2
An inscribed circle is the largest circle contained in the polygon (triangle):
• Bisects two angles of the triangle.
,• The angle bisector will intersect at the intercenter.
Procedure
To draw the inscribed circle, we have to use the intercenter (O, in our case) as the center, pointing one of the compass points in O, and draw the circle touching the edges.
Point A(3, 5) was dilated, and the point after dilation was A'(6, 10). What was the scale factor used?
Answer:2 is the scale factor
Step-by-step explanation:
write the slope intercept form:through: (4, -5), perp. to x= -4
The line should be perpendicular to x = -4
x= -4 is a vertical line crossing the x axis at x= -4
The slope is undefined in x =-4
For an equation in slope intercept form, the general form is ;
y= mx + b where m is the slope and b is the y-intercept
So for any y value, x is always -4
Thus the slope for line x = -4 is not defined
A line perpendicular to x = -4 will thus be a horizontal line with slope 0
For the equation of this line
0= y--5/x-4
0 = y+5 /x-4
0{x-4} = y +5
0 = y+5
y= - 5
a package boodins weighs 6.2 ounces. A package of rews weighs 9.97 ounces. how much more does a package of rews weigh than a package of boondins
Based on the package of boondins and the package of rews, the package of rews will have a weight in relation to the package of boondins that is 3.77 ounces
How to find the different in weights?To find how much more that the package of rews weighs over the boondins, deduct the weight of the package of boondins from the weight of a package of rews.
Weight of package of rews = 9.97 ounces
Weight of package of boondins = 6.2 ounces
The difference in the weight of the packages is:
= 9.97 - 6.2
= 3.77 ounces
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The required difference in the package of the bodies and rews is 3.77 ounces.
As per the given in the question,
boudin is 6.2 ounces in weight and rews are 9.97 ounces in weight.
here,
As per observation, rews weighs more than bodies, and the difference between their weights is simply evaluated from the subtraction between the weight. So,
Weigh difference = weigh of rews - weigh of boodins
Substitute the value in the above equation,
Weigh difference = 9.97 - 6.2 = 3.77.
Thus, the required difference in the package of the bodies and rews is 3.77 ounces.
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What is the center of the hyperbola?
(y+3)^2/9 − (x−2)^2/2 = 1
Enter your answer by filling in the boxes.
The center of the hyperbola is (2, -3)
What is an hyperbola?A hyperbola is a curve that is open and that has two branches and it is symmetrical
How to solve the center of the hyperbola?The equation is given as
(y + 3)²/9 − (x − 2)²/2 = 1
A hyperbola is represented as
(y - k)²/a² − (x − h)²/b² = 1
Where the center of the hyperbola has the coordinates of (h, k)
The values of h and k in the given equation (y + 3)²/9 − (x − 2)²/2 = 1 are
h = 2 and k = -3
This means that:
(h, k) = (2, -3)
So, we have coordinates of the center to be (2, -3)
Hence, the center is (2, -3)
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what is the absolute value for this equation? : |-x| = 3
Answer:
The answer is |-3|
Step-by-step explanation:
The absolute value of a negative number will always be the same number but positive. Like the absolute value of |-4| will be 4.
A group of people were asked if they owned a dog. 191 responded "yes", and 485 responded "no".Find the probability that if a person is chosen at random, they own a dog. 191485 294191 191676
Given:
There are given that the number of people who said yes is 191 and who said no is 485.
Explanation:
According to the given question:
The total number of people is:
[tex]191+485=676[/tex]That means the total outcome is 676.
Now,
The probability that the person is chosen own dog is:
[tex]P=\frac{The\text{ number of people who have their own dog}}{\text{Total number of outcomes}}[/tex]So,
[tex]P=\frac{191}{\text{6}76}[/tex]Final answer:
Hence, the correct option is C.
Answer:
191/676.
Step-by-step explanation:
The total number of people asked is 191 + 485
= 676.
So. the required probability
= number of people owning a dog/ total number of people
= 191/676.
1.5 x 10 9
8.9 x 10 7
) assembly comprises 769 team members. given that tmm operates two shifts a day, and assembly has 353 stations, what is the proportion of team members not assigned to one of the stations?
Among the 769 team members, 706 of them are assigned to operates in 2 shifts schedule. The proportion of team members not assigned to one of the stations is 63 / 769
Proportion means a share from total set being discussed.
Data from the given case:
- The assembly has 769 team members.
- The assembly has 353 stations
- At each station, there are 2 shifts operations.
Assuming that 1 person is assigned to 1 shift operation, then there will:
353 x 2 = 706 person assigned.
The remaining team members that not assigned is:
769 - 706 = 63 person.
Therefore, the share or the proportion of unassigned team members is:
63/769
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A model car is a 1/40 if the length of the real car is 5.5 m what is the length of the model car
Answer:
0.14 meters, or 140 mm
Step-by-step explanation:
(1/40) means that the model car will have dimensions that are (1/40) the original car.
Real car = 5.5 meters.
Model car = (1/40)*(5.5 m) = 0.14 meters, or 140 mm
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answer:
The three options you would pick is
y2 – 5y = 750
750 – y(y – 5) = 0
(y + 25)(y – 30) = 0
Step-by-step explanation:
Hope this helps! :))
I figured x equals a specific number in every single question involving something like this. X is on all sides, there's no given number.
The angle x of the triangle is 60 degrees.
How to find the angles in a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is equals to 180 degrees.
A triangle can be classified base on the sides and angles. For example equilateral triangle, scalene triangle and isosceles triangle.
Therefore, the angle x of the triangle can be found as follows:
x + x + x = 180
3x = 180°
divide both sides of the equation by 3
3x / 3 = 180 / 3
x = 180 / 3
x = 60 degrees.
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Answer:
the person below or above me is the answer. Yeah
Step-by-step explanation:
Select the correct answer. sean used cross multiplication to correctly solve a rational equation. he found one valid solution and one extraneous solution. if 1 is the extraneous solution, which equation could he have solved? a. the equation is = because 1 makes a denominator equal zero and is a solution of the equation derived from cross multiplying. b. the equation is = because 1 is a solution of both the original equation and the equation derived from cross multiplying. c. the equation is = is because 1 makes a numerator equal zero and is a solution of the equation derived from cross multiplying. d. the equation is = because 1 makes a denominator equal zero and is not a solution of the equation derived from cross multiplying.
The equation is = because 1 makes a denominator equal zero and is a solution of the equation derived from cross multiplying. A valid solution to a problem that vanished during the process of solving it is referred to as a missing solution.
What is extraneous equation?An extraneous solution in mathematics is a solution that develops during the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation. A valid solution to a problem that vanished during the process of solving it is referred to as a missing solution.
We have to open the equation by using cross multiplication
10(3x - 3) = 15(x² - 1)
= 30x - 30 = 15x² - 15
we would have to factorize
30(x-1) = 15(x-1)(x+1)
We have to divide by 15(x-1)
2 = x + 1
take the like terms
2 -1 = x
x = 1
Hence the equation that has the extraneous solution is option a because the solution is 1.
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Rewrite (156 + 243) using factoring
A. 3(52 + 81)
B. 6(24 + 40)
C. 12(13 + 21)
D. 18(9 + 13)
Use the Rational Zeros Theorem to list all possible zeros of the function below.
f(x) = 11x³ 2x² + x + 10.
-
[Enter all possible zeros predicted by the Rational Zero Theorem individually and separated by commas
(1,-1,-1/2,1/2,etc.) Note: You do not need to factor the polynomial.]
The all possible zeros predicted by the Rational Zero Theorem individually and separated by commas are ±1/1, ±1/11, ±2, ±2/11, ±5, ±5/11, ±10, ±10/11.
P(x) = 11x³ + 2x² + x + 10
The factors of the constant term 10 is ±1, ±2, ±5, ±10 (=p)
The factors of leading coefficient are ±1, ±11 (= q)
The possible rational zeros are p/q : ±1/1, ±1/11, ±2/1, ±2/11, ±5/1, ±5/11, ±10/1, ±10/11.
After simplification the possible roots are ±1/1, ±1/11, ±2, ±2/11, ±5, ±5/11, ±10, ±10/11.
Therefore, ±1/1, ±1/11, ±2, ±2/11, ±5, ±5/11, ±10, ±10/11. are the all possible zeros predicted by the Rational Zero Theorem individually and separated by commas.
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Please help me dont know the answer
Answer:
First answer is obtuse
The second answer is scalene
Step-by-step explanation:
Obtuse is when an angle is over 90
Scalene since all the angles are different, all the side lengths are different.
The line parallel to y=3x+5 that passes through the point (-8,-4)
Answer:
y = 3x + 20
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + 5 ← is in slope- intercept form
with slope m = 3
• Parallel lines have equal slopes , then
y = 3x + c ← is the partial equation
to find c substitute (- 8, - 4 ) into the partial equation
- 4 = - 24 + c ⇒ c = - 4 + 24 = 20
y = 3x + 20 ← equation of parallel line
Answer:
Step-by-step explanation: From the given point,
The line is: -8x-4y=0
viz, 2x+y=0
Help please! Solve this and show your steps: c = 6.00 + 29.99
Step-by-step explanation:
you don't a type your question. so if it correct i will be happy to help you