A polynomial of degree 4 in factored form with zeros 1, -4, 0, and 6 is
f(x) = x(x - 1)(x + 4)(x - 6).
What are polynomials?An algebraic expression known as a polynomial requires that all of its exponents be whole numbers.Any polynomial must have variable exponents that are non-negative integers. The degree of a polynomial is the highest or biggest exponent of the variable in the polynomial.Given:
x₁ = 1
x₂ = -4
x₃ = 0
x₄ = 6
Utilize the fact that x - b is a factor of the polynomial if b is a root.
Simply take each zero, modify its sign, and add an x in front of it to obtain the four factors.
The polynomial is,
f(x) = (x - x₁)(x - x₂)(x - x₃)(x - x₄)
f(x) = (x - 1)(x - (-4))(x - 0)(x - 6)
= (x - 1)(x + 4(x)(x - 6)
Therefore,a 4 degree polynomial in factored form with zeros 1, -4, 0,and 6 is x(x - 1)(x + 4)(x - 6).
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I need help solving this
Solution:
Given:
[tex]108,105,102,...,15[/tex]This is an arithmetic sequence because it has a common difference.
From the nth term of an arithmetic sequence,
[tex]\begin{gathered} a_n=a+(n-1)d \\ a=108 \\ d=105-108=102-105=-3 \\ a_n=15 \\ \\ Hence,\text{ the number of terms in the sequence is;} \\ 15=108+(n-1)-3 \\ 15-108=-3(n-1) \\ -93=-3(n-1) \\ \frac{-93}{-3}=n-1 \\ 31=n-1 \\ 31+1=n \\ 32=n \\ n=32 \end{gathered}[/tex]The sum of an arithmetic sequence is given by;
[tex]\begin{gathered} S_n=\frac{n}{2}(a+l) \\ \\ where: \\ first\text{ term, }a=108 \\ last\text{ term, }l=15 \\ n=32 \\ \\ Hence, \\ S_n=\frac{32}{2}(108+15) \\ S_n=16(123) \\ S_n=16\times123 \\ S_n=1968 \end{gathered}[/tex]herefore, the sum oft the sequence is 1968
What is the equation of the line that is perpendicular to y = 3x + 3 and passes through the point (−6, 9)?
The equation of the line will be equal to 3y = -x + 21.
A line may be defined as the straight figure drawn which has no end points. The equation of a line can be written in slope intercept form as y = mx + c where m is the slope of line, c is y intercept an x and y are independent and dependent variables. If a point (x₁, y₁) is given then equation of line is (y - y₁) = m (x - x₁). The slope of line which is perpendicular to a given line having slope m is equal to -1/m.
Now, equation of line is y = 3x + 3. If we compare with slope intercept form then, m = 3. Now, slope of line perpendicular to this line is equal to -1/3. Now, equation of line passing through point (-6, 9) is given as
(y - 9) = -1/3 (x + 6)
3y - 27 = -x - 6
=> 3y = -x + 21 which is the required equation of line.
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Which of the following could be an equation of g?
A) g(x)= (x-5)(x-9)
This is the answer because basically you need to find the roots of the function, since the function g intersects the x-axis at x=5 and x=9 you can conclude easily that those are the roots.
If:
x=5
g(5)=(5-5)(5-9)=0(-4)=0
and
If:
x=9
g(9)=(9-5)(9-9)=(4)(0)=0
Find an equation for the line perpendicular to the line −7x+2y=3 having the same y-intercept as 9x+3y=−2.
The equation of the line perpendicular to the line −7x+2y=3 having the same y-intercept as 9x+3y=−2 is y = - 2 / 7x - 2 / 3
How to find equation of a line?The equation of a line can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line is perpendicular to −7x+2y=3.
−7x+2y=3
2y = 7x + 3
y = 7 / 2 x + 3 / 2
Perpendicular lines follows the rule below:
m₁ m₂ = -1
7 / 2 m₂ = -1
7m₂ = -2
m₂ = - 2 / 7
Therefore, the equation of the line also haver the same y-intercept as
9x + 3y = −2.
3y = - 9x - 2
y = -3x - 2 /3
The y-intercept of the equation is - 2 / 3.
Hence
the equation of the line is y = - 2 / 7x - 2 / 3
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which of the given values are in the interval (-3,1]?
The values coming in the interval (-3,1] are -2, -1, 0, and 1.
What is defined as the term interval notations?An interval is represented on a number line using interval notation. In all other sayings, it is a method of writing real number line subsets. An interval is made up of numbers that fall between two specific data set.Intervals can be categorized according to the numbers in the set.Interval Open: The endpoints of a inequality are not included in this type of interval.Interval Closure; The endpoints of a inequality are included in this type of interval.Interval with Half-Open Doors: This interval contains only one of inequality's endpoints.The given interval notation is;
(-3,1], it is the case of half open half close.
-3 comes with the open interval, it means its value will not be included in the interval.
1 is with the closed interval, it means its value will be included in the interval.
Thus, the values lying between the interval (-3, 1] are -2, -1, 0, and 1.
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A set of 25 two digit numbers are listed below 10,17,19.22,24,28,32,39,42,44,44,46,51,54,57,60,64,66,71,74,77,79,84,93,97,98
How can I get what is the probability of the sum of the number's digits is odd?
The probability that the sum of the number's digit is odd is 1/5.
What is the probability?
Probability is used to determine how likely it is that a random event would happen.
An odd number is a number that is not perfectly divisible by 2. Examples of odd numbers include 1, 3, 5.
Sum of the number's digits:
1 + 0 = 1 (odd number)
1 + 7 = 8
1 + 9 = 10
2 + 2 = 4
2 + 4 = 6
2 + 8 = 10
3 + 2 = 5 (odd number)
3+ 9 = 12
4 + 2 = 6
4+ 4 = 8
4 + 4 = 8
4 + 6 = 10
5 + 1 = 6
5 + 4 = 9 (odd number)
5 + 7 = 12
6 + 0 = 6
6 + 4 = 10
6 + 6 = 12
7 + 1 = 8
7 + 4 = 11 (odd number)
7 + 7 = 14
7 + 9 = 16
8 + 4 = 12
9 + 3 = 12
9 + 7 = 16
9 + 8 = 17 (odd number)
The probability that the sum of the digits is odd = number of odd digits / total number
5 / 25 = 1/5
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Homany zeros are in the product (6×5)×10^3
At the end of a snow storm, Julian saw there was a lot of snow on his front lawn. The
temperature increased and the snow began to melt at a steady rate. Let S represent
the depth of snow on Julian's lawn, in inches, t hours after the snow stopped falling.
A graph of S is shown below. Write an equation for S then state the z-intercept of
the graph and determine its interpretation in the context of the problem.
answer:
the y-intercept is 15 which is the initial total depth of the snow at t=0 hours.
The rate of melting is 1.5inches per hour. It will take 10 hours at the melting rate given of 1.5 to melt all the snow.
Step-by-step explanation:
the y-intercept is 15, and it might mean that the total depth of the snow is 15 inches.
The rate of melting is 1.5inches per hour.
At time = 0, S=15 - 1.5t = 15 - 1.5(0) = 15 inches to start
At time = 10, S=15 - 1.5t = 15 - 1.5(10) = 0 inches; meaning all snow has melted and it took 10 hours.
At a factory, there are 40 new cars produced every 8 hours. How many cars can be produced in a 40-hour week?
Answer:
200
Step-by-step explanation:
Multiplying by 5, we get 200 cars can be produced in 40 hours.
USING PROPERTIES Find the product. Write your answer as a fraction in simplest form. $\left[-\frac{2}{3}\ \ \cdot\left(-\frac{5}{7}\right)\right]\cdot\ \left(-\frac{9}{4}\right)=$
By algebra properties, the rational expression [(- 2 / 3) · (- 5 / 7)] · (- 9 / 4) is equivalent to the following rational expression in simplest form: - 15 / 14.
How to simplify the product of three fractions
In this problem we find a product of three rational numbers, which we must simplify by using algebra properties, especially those of related to rational numbers:
[(- 2 / 3) · (- 5 / 7)] · (- 9 / 4) Given
[(2 / 3) · (5 / 7)] · (- 9 / 4) (- a) · (- b) = a · b
(10 / 21) · (- 9 / 4) Multiplication of fractions
- [(10 / 21) · (9 / 4)] (- a) · b = - a · b
- 90 / 84 Multiplication of fractions
- 45 / 42 Simplification of fractions
- 15 / 14 Simplification of fraction / Result
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Graph the equation y= −4x −3
Answer: See attached.
Step-by-step explanation:
We can look at the values given in the equation to graph it.
➜ The -3 shows the line will intercept the y-axis at -3.
➜ The equation has a slope of -4, so for everyone right we move four down.
Find the surface area of the sphere.r= 4 cmFormulas for SpheresS.A. = 4tr2v = frer S.A. = [?] cm2Round to the nearest tenth.Enter
The radius of sphere is r = 4 cm.
Substitute the value in the formula to determine the surface area of sphere.
[tex]\begin{gathered} SA=4\pi\cdot(4)^2 \\ =64\pi \\ =201.061 \\ \approx201.1 \end{gathered}[/tex]So answer is S.A = 201.1
Two numbers are respectively twenty percent and ten percent more than a third number. How
much percent is the first number more than the second?
The first number is 8.33 percent more than the second number.
Let m be the first number, n be the second number and p be the third number.
Two numbers are respectively twenty percent and ten percent more than a third number.
m = (100 + 20)% of p
m = 120 percent of p
m = 120 % of p
m = (120 / 100) × p
m = 1.2 p
And the second number would be,
n = (100 + 10)% of p
n = 110 percent of p
n = (110 / 100) × p
n = 1.1 p
We need to find by how much number the first number more than the second.
Consider the difference,
1.2 p - 1.1p = 0.1 p
So the required percentage noting but the difference is what percent of the first number.
(0.1 p / 1.2 p) × 100 = 8.33%
Therefore, the first number is 8.33 percent more than the second number.
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PART F Write the equation of a line that goes through the coordinate (5, 3) and has a slope of 3
I got y=3x-12 I am not sure if it's right
Your answer is correct.
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
A system of linear equations is given by the tables. One of the tables is represented by the equation y = -x + 7.
X
0
3
6
9
y
5
6
7
8
X
-6
-3
0
3
y
9
8
7
6
The equation that represents the other equation is y=
The solution of the system is (
)
4
X +
Reset
Next
y = 1 / 3 x + 5 is the linear equation for the first table.
The system of equations' answer is (3, 6).
Linear Equation: What Is It?A linear equation is an algebraic equation of the form y= mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The previous equation, which has the variables y and x, is sometimes referred to as a "linear equation with two variables."
based on the available facts;
Equation of a point slope:
y = mx + b,
where m = slope and b = y-intercept
As a result, the equation for the second table is y = - 1 /3 x + 7.
With the help of the table's (0, 5)(3, 6) values, the equation for the first table may be solved. Therefore,
m = 6 - 5 / 3 - 0 = 1 / 3
let's find b using (0, 5)
5 = 1 / 3(0) + b
b = 5
Therefore, the equation of the first table is as follows:
y = 1 / 3 x + 5
The solution to the system of equation can be calculated as follows:
y + 1 /3 x = 7
y - 1 / 3 x = 5
2y = 12
y = 12 / 2
y = 6
6 - 1 / 3 x = 5
- 1 / 3 x = 5 - 6
- 1 / 3 x = - 1
x = 3
Therefore, the solution to the system of equation is (3, 6)
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Scale Word Problems (L1)
Oct 09, 9:51:30 AM
Watch help video
A scale drawing of a rectangur park had a scale of 1 cm = 100 m.
4.1 cm
Answer:
11.9 cm-
What is the actual area of the park in meters squared?
m²
Submit Answer
The actual area of the park when a scale drawing of the park had a scale of 1 cm = 100 m is 4879m².
How to calculate the area?From the information, the scale drawing of a rectangur park had a scale of 1 cm = 100 m.
It should be noted that the dimensions are given as 4.1 cm and 11.9cm. The area of the scale will be:
= 4.1 × 11.9
= 48.79cm²
Therefore, the actual area of the park will be:
= 48.79 × 100
= 4879m²
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Please help I have no idea
A 14 (3/4) inch board is cut from a 34 (1/4) inch board. The saw cut takes (3/8) inch. How much of the 34 (1/4) inch board is left after cutting
(Type an integer, fraction, or mixed)
Integer - 19 (1/8)inch board would be left after cutting from 34(1/4) inch board
What is an Integer ?
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. When expressed in mathematical terms,
34 (1/4) inch board = 137/4 ----(1)
Cut piece = 14 3/4 = 59/4 ----(2)
saw cut 3/8 = 3/8 --------(3)
To calculate the board which is left after cutting will be
= 137 / 4 - 59 / 4 - 3/8
= 137 - 59 / 4 - 3 / 8
= 39 / 2 - 3 / 8
= 312 - 6 / 8
= 306 / 16
= 153 / 8
or, = 19 (1/8)inch
Hence, 19(1/8)inch board will be left after cutting
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In a 30-60-90 triangle, how many sides do you need to know in order to determine the remaining sides?
A. 1
B. 2
C. 0
D. 3
Answer:
Step-by-step explanation:
d
Simplify fully 24a^2 + 8a
Answer:
8a(3a + 1)
Step-by-step explanation:
24a² + 8a
8a(3a + 1)
I hope this helps!
Find the value of x
It’s the green one pls help me
PLS ANSWER THIS MATH PROBLEM!!
Answer:
See picture
Step-by-step explanation:
You are offered two different furniture sales jobs. The Furniture Barn offers you a job that pays straight commission of 5% of the sales. The Furniture Warehouse offers you a job that pays a salary of $350 per week plus 1% of the sales. How much would you have to sell in a week in order for the job at The Furniture Barn to pay as well as the job at The Furniture Warehouse? Round the answer to the nearest cent.
A = amount of sales
so hmmm The Furniture Barn gives only 5% of "A" then, that means
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of A}}{\left( \cfrac{5}{100} \right)A}\implies 0.05A[/tex]
whilst The Furniture Warehouse gives you 350 bucks per week and only 1% of "A", well, that means you gross pay there will 350 + 0.01A.
hmmm how much will "A" be for both offers to pay the same amount?
[tex]\stackrel{Furniture~Barn}{0.05A}~~ = ~~\stackrel{Furniture~Warehouse}{350 + 0.01A} \\\\\\ 0.04A=350\implies A=\cfrac{350}{0.04}\implies \boxed{A=8750}[/tex]
Find the area of a rectangle that is 2 7/9 m long and 4 4/5 m wide. Enter your answer as a mixed number and reduce if possible.
Answer:
13 ⅓.
Step-by-step explanation:
The area of a rectangle is given by
Area = Length × Breadth
Length = 2 7/9 = 25/9 and breadth = 4 4/5 = 24/5
.: Area = 25/9 × 24/5 = 600/45 (15 can go to both the numerator and denominator)
We have 40/3 but to convert it to a mixed fraction we get 13 ⅓ as your area.
Given f(x) = 2x² -x+3
Find f(x)
The function f(x) = 2x² - x + 3 equals to 9 when x is equal to 2.
What is function in mathematics?
In mathematics, a function is an expression, rule, or law that establishes the connection between an independent variable and another variable (the dependent variable). In mathematics, functions exists everywhere, and they are crucial for constructing physical links in the sciences.
The function given in the question is:
f(x) = 2x² - x + 3
We have to find f(x) when x = 2,
We are replacing x with 2 in given function, we get:
f(x) = 2(2)² - 2 + 3
f(x) = 2(4) -2 + 3
f(x) = 8 -2 +3
f(x) = 9
Hence the given function equals to 9 when x is equal to 2.
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Complete question
Given f(x) = 2x² -x+3
Find f(x) when x = 2
Tickets for the monster truck rally cost $12 for children and $20 for adults. Last
night 400 total tickets were sold for a total of $6000. Use c for the child tickets and
a for adult tickets. If one of the equations for this system is a + c = 400, write
the second equation for this system below.
Answer:
20a + 12c = 6000
Step-by-step explanation:
a = adult tickets
c = child tickets
$20 for adults, $12 for children, for a total of $6000
20a + 12c = 6000
a + c = 400
Which of the following statements is true?
A. The diagonals of a quadrilateral are always congruent.
B. The diagonals of a parallelogram always bisect each other.
C. The diagonals of a rectangle are always perpendicular to each other.
D. The diagonals of a rhombus are always congruent and perpendicular to each other.
12.03 km = _________ m ______ cm
1km = 1000 m
12.03 km = 12.03 x 1000
12.03 km = 12030 m
1km = 100000 m
12.03 km = 12.03 x 100000
12.03 km = 1203000 cm
Zeke learned that he could make another
$2,000 a year if he became fluent in Spanish.
If he intends to learn the language and work another 10 years at that job, how much is learning Spanish worth to him?
If Zeke learned that he could earn another $2000 a year if he become fluent in Spanish and he intended to learn the language and work another 10 years at that job, then the amount is learning Spanish worth to him is $20000
The extra amount he could make if he learn Spanish = $2000
The number of years he works = 10 years
To find the extra amount, we have to use multiplication
The extra amount he could make if he learn Spanish = The extra amount he could make if he learn Spanish × The number of years he works
Substitute the values in the equation
= 2000×10
Multiply it
= $20000
Hence, if Zeke learned that he could make another $2000 a year if he become fluent in Spanish and he intended to learn the language and work another 10 years at that job, then the amount is learning Spanish worth to him is $20000
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HELP pleasee
A. 15
B. 5
C. 10
Answer:
the answer has to be b
Step-by-step explanation: