Answers
If the polynomial function be P(x) = [tex]x^4[/tex] − 3x³ + 2x² then Zeros exists at x = 0, 0, 1, 2.
What is meant by polynomial ?A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
An expression that consists of variables, constants, and exponents that exists combined utilizing mathematical operations like addition, subtraction, multiplication, and division exists directed to as a polynomial (No division operation by a variable).
Let the polynomial function be P(x) = [tex]x^4[/tex] − 3x³ + 2x²
P(x) = x²(x² - 3x + 2)
factoring the above polynomial function, we get
P(x) = x·x(x - 1)(x - 2)
Zeros exists at x = 0, 0, 1, 2
P(x) exists degree 4, so it will contain four roots. You only entered three which exists probably why it came up as wrong. The x² term contains a multiplicity of 2, so it counts twice.
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Related Questions
in ️RST, RS ~=TR and m
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
ΔRST
RS ≅ TR
∠ T = 15
∠ S = ?
Step 02:
We must apply the properties of isosceles triangles.
∠ T = ∠ S = 15
The answer is:
∠ S = 15 °
What transformation would cause the change from ABC to A'B'C'?
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Answer:
D. 1/4
Explanation:
When the coordinates of A, B, and C are multiplying by 1/4 we get A', B', and C'.
For example,
[tex]\frac{1}{4}\times A(-8,4)=A^{}(-\frac{8}{4},\frac{4}{4})[/tex][tex]\therefore A(-8,4)\rightarrow A^{\prime}(-2,1)[/tex]The same goes for B and C.
Hence, the transformation that gives us A'B'C' from ABC is Choice D DIlation using k = 1/4.
Evaluate the expression whenb= 48 c= 7simplify as much as possible
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Given:-
[tex]\frac{b}{3}+2c^2[/tex]To find the simplified value when b=48 and c=7.
So now we simplify the solution by substituting the values of b and c in the given equation and get the required solution.
So now we simplify. so we get,
[tex]\frac{b}{3}+2c^2=\frac{48}{3}+2\times7\times7=16+98=114[/tex]So the simplified solution is 114.
Algebra 2 The answer choices are: A. -3 less then or equal to x less then or equal to 6B. -4 less than x less then or greater to 1C. X greater than or equal to 1D. X greater to or equal to 6
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Given:
A graph is given.
Required:
Find the interval of the domain that the graph of exponential function represents.
Explanation:
The graph of the exponential function is given as:
Based on your knowfedgs of the two data sets described below, would you espect a scatter plot describing the two data sets to have a positive, a negative, or nocorrelationduration of usage and the charge in the battery of a mobile phone
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We expect the variable to have a negative correlation.
This means that the more we use the phone the lower the charge will be.
Rewrite the expression 3(12 - 10) using the distributive property of multiplication over subtraction.
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The resulting expression using the distributive property of multiplication over subtraction is 3(12) - 3(10).
What is distributive property of multiplication?The distributive property of binary operations extends the distributive law, which states that in elementary algebra, equality is always true.
For instance, given the expression;
A(B - C)
We will have to distribute A over B and C to have;
A(B - C) = AB - AC
Applying the rule to the given expression
3 (12 - 10)
3(12) - 3(10)
This shows that the given expression can also be written as 3(12) - 3(10)
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Fill in the table using this function rule. y = 2x+4
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The complete table using the given linear equation is x y
-4 -4
-2 0
0 4
2 8
What are linear equations?A linear equation is one that has the form Ax+By=C. This definition comes from mathematics. It consists of two variables combined with a constant value that exists in each of them.
The values of the variables will be obtained when the system of linear equations is solved; this is referred to as the solution of a linear equation.
Given the linear equation y = 2x + 4
If x = -4
y =2(-4) + 4
y = -4
If x = -2
y =2(-2) + 4
y = 0
If x = 0
y =2(0) + 4
y = 4
If x = 2
y =2(2) + 4
y = 8
Hence the complete table using the function is
x y
-4 -4
-2 0
0 4
2 8
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Complete question
Fill in the table using this function rule. y=2x -4
x y
-4 ?
-2 ?
0 ?
2 ?
A regular hexagon has sides 2 feet long. What is the exact area of the hexagon? What is the approximate area of the hexagon?
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The formula for the area of a hexagon is
[tex]A=\frac{3\sqrt[]{3}}{2}s^2[/tex]where 's' is the length of one side of the regular hexagon.
The side of our regular hexagon is 2 feet, therefore, its area is
[tex]\begin{gathered} A=\frac{3\sqrt[]{3}}{2}\cdot(2)^2=6\sqrt[]{3} \\ 6\sqrt[]{3}=10.3923048454\ldots\approx10 \end{gathered}[/tex]The exact area of the hexagon is 6√3 ft², which is approximately 10 ft².
Point-Slope Form: y + 2 = -7(x − 4)Rewrite the equation in slope-intercept form
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Given the equation of a line in Point-Slope Form:
[tex]y+2=-7(x-4)[/tex]You need to rewrite it in Slope-Intercept Form:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
Then, you have to solve for "y":
1. Apply the Distributive Property on the right side of the equation. Remember the Sign Rules for Multiplication:
[tex]\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ -\cdot+=- \\ +\cdot-=- \end{gathered}[/tex]Then:
[tex]y+2=(-7)(x)+(-7)(-4)[/tex][tex]y+2=-7x+28[/tex]2. Apply the Subtraction Property of Equality by subtracting 2 from both sides of the equation:
[tex]y+2-(2)=-7x+28-(2)[/tex][tex]y=-7x+26[/tex]Hence, the answer is:
[tex]y=-7x+26[/tex]the area of a trapezoid is given by the formula A= h(a+b)/2. solve for the formula for b.
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The formula is
[tex]A=\frac{(a+b)\cdot h}{2}[/tex]To solve for b, first, we multiply the equation by 2
[tex]\begin{gathered} 2A=2\cdot\frac{(a+b)\cdot h}{2} \\ 2a=(a+b)\cdot h \end{gathered}[/tex]Then, we divide the equation by h
[tex]\begin{gathered} \frac{2A}{h}=\frac{(a+b)h}{h} \\ \frac{2A}{h}=a+b \end{gathered}[/tex]At last, we subtract a from each side
[tex]\frac{2A}{h}-a=a-a+b[/tex]Hence, the final expression is[tex]b=\frac{2A}{h}-a[/tex]Please help me ASAP I’ll mark brainly
Answers
1. The scholar made a mistake in the last step
where he said x=3.5
SCHOLA DIVIDED 7 BY 2 INSTEAD OF DIVIDING BY 0.5
[tex]0.5x = 7 \\ \frac{0.5x}{0.5} = \frac{7}{0.5} \\ x = 14
AS A RESULTS GOT WRONG ANSWER . x is supposed to be 14.
There is $1.90 in a jar filled with quarters, dimes, and nickels. There are 2 more quarters than dimes and there are 2 more nickels than quarters. How many of each coin are there? quarters dimes [ ) nickels Enter the number that belongs in the green box.
Answers
5 quarters, 3 dimes, 7 nickels
Explanations:Let the number of quarters in the jar = q
Let the number of dimes in the jar = d
Let the number of nickels in the jar = n
1 quarter = $0.25
1 dime = $0.1
1 nickel = $0.05
The jar is filled with quarters, dimes, and nickels, totaling $1.90
This can be represented mathematically as:
0.25q + 0.1d + 0.05n = 1.90.........(1)
There are two more quarters than dime:
q = d + 2..............(2)
There are two more nickels than quarters
n = q + 2..............(3)
make d the subject of the formula in equation (2)
d = q - 2............(4)
Substitute equations (3) and (4) into equation (1)
0.25q + 0.1(q - 2) + 0.05(q + 2) = 1.90
0.25q + 0.1q + 0.05q - 0.2 + 0.1 = 1.90
0.4q - 0.1 = 1.90
0.4q = 1.90 + 0.1
0.4q = 2.0
q = 2.0/0.4
q = 5
n = q + 2
n = 5 + 2
n = 7
d = q - 2
d = 5 - 2
d = 3
There are 5 quarters, 3 dimes, 7 nickels
Use the formula V=lwh and A=bg to complete the table below by evaluating the expression
Answers
we have that
the formula to calculate the area of a rectangle is equal to
A=L*W
we have
L=8.3 cm
W=4 cm
substitute
A=(8.3)*(4)
A=33.2 cm2
therefore
Formula A=L*W
Expression A=(8.3)*(4)
Solve A=33.2 cm2
Can you please help me with 44Please use all 3 forms of the expression such as : down/up. As _,_ And limits
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Answer:
[tex]\begin{gathered} x-\text{intercept}=-3\text{ and 1} \\ y-\text{intercept}=\text{ -9} \end{gathered}[/tex][tex]\begin{gathered} x=1\text{ multiplicity 3} \\ x=-3\text{ multiplicity 2} \\ \lim _{x\rightarrow\infty}(x-1)^3(x+3)^2=\infty \\ \lim _{x\rightarrow-\infty}(x-1)^3(x+3)^2=-\infty \end{gathered}[/tex]Step-by-step explanation:
To find the x-intercepts factor the function to the simplest form:
[tex]h(x)=(x-1)^3(x+3)^2[/tex]As we can see the zeros to the function would be 1 and -3, then its:
[tex]\begin{gathered} x-\text{intercept}=-3\text{ and 1} \\ y-\text{intercept}=\text{ -9} \end{gathered}[/tex]Zero has a "multiplicity", which refers to the number of times that its associated factor appears in the polynomial. Therefore, this function has multiplicity:
[tex]\begin{gathered} x=1\text{ multiplicity 3} \\ x=-3\text{ multiplicity 2} \end{gathered}[/tex]For the end behavior:
down/up
As x approaches infinity f(x) approaches infinity
As x approaches -infinity f(x) approaches -infinity
[tex]\begin{gathered} \lim _{x\rightarrow\infty}(x-1)^3(x+3)^2=\infty \\ \lim _{x\rightarrow-\infty}(x-1)^3(x+3)^2=-\infty \end{gathered}[/tex]which part of the aldr braiding expresses 3 + 7 D is the c o e f f i n c i e n t
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the coefficient is the number that accompanies the variable, so:
[tex]3+7D[/tex]The coefficient is 7
Fill in the empty spaces to complete the puzzle. In any row, the two left spaces should multiply to equal the right-hand space. In any column, the two top spaces should multiple to equal the bottom space.
Answers
Explanation:
We will find the expression for each space in the following order
To find the first expression, we need to find a number that multiplied by 6 is equal to 18. This number is 3 because
6 · 3 = 18
Then, for the second space, we need to factorize the expression 36x² + 144x + 108 as follows
36x² + 144x + 108 = 8(2x² + 8x + 6)
So, the expression that multiplied to 8 is (36x² + 144x + 108) is (2x² + 8x + 6).
The third space can be calculated by factorizing 2x² + 8x + 6 as
2x² + 8x + 6 = (x + 3)(2x + 2)
Therefore, the expression in the third space is (2x + 2)
Finally, for the fourth and fifth space, we need to multiply the expression to the left, so
6(2x + 2) = 6(2x) + 6(2) = 12x + 12
3(x + 3) = 3(x) + 3(3) = 3x + 9
Answer
Therefore, the answer is
Estimate the difference between 7,472 and 3,827 by rounding each number to the nearest hundred.
Answers
Answer:
The difference is aproximately 3700.
Step-by-step explanation:
First, we'll round each number to the nearest hundred:
[tex]\begin{gathered} 7472\rightarrow7500 \\ 3827\rightarrow3800 \end{gathered}[/tex]Now, we can estimate the difference:
[tex]7500-3800=3700[/tex]This way, we can conlcude that the difference is aproximately 3700.
I am canfusing in this question can you solve it.
Answers
Answer:
Step by step explanation:
what is the GCF of 6x+18/x^2-x-12
Answers
The GCF of the expression 6x+18/x^2-x-12 is (x+3)
How to find the GCF of the expression?The GCF (Greatest Common Factor) of two or more numbers or expressions is the greatest number or expression among all the common factors of the given numbers or expressions
Given 6x+18/x²-x-12
We can write 6x+18/x²-x-12 as:
6x+18/x²-x-12 = 6x+18/x²-4x+3x-12 By factorization:
= 6(x+3) / (x+3)(x-4)
Since (x+3) is common to both the numerator and the denominator. Therefore, the greatest common factor (GCF) is (x+3)
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The directions for a weed spray concentrate state that 3 tablespoons of the concentrate should be mixed with 4 gallons of water. How many tablespoons of concentrate need to be mixed with 5 gallons of water?
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The given information is:
- 3 tablespoons of the concentrate should be mixed with 4 gallons of water.
The ratio of tablespoons to gallons of water is:
[tex]\frac{3\text{ tablespoons}}{4\text{ gallons of water}}[/tex]Then, we can apply proportions to find how many tablespoons of concentrate need to be mixed with 5 gallons of water, so:
[tex]\begin{gathered} \frac{3}{4}=\frac{x}{5} \\ Isolate\text{ x} \\ x=\frac{5*3}{4} \\ x=\frac{15}{4} \\ x=3.75\text{ tablespoons} \end{gathered}[/tex]It is needed 3.75 tablespoons of the concentrate.
-6 subtracted from a number equals -12.What is the number?
Answers
Answer:
The number is -18
Explanation:
-6 subtracted from a number equals -12.
We want to find the value of the number
Let the number be x
We can write the statement mathematically as:
[tex]x-(-6)=-12[/tex]Solving this equation, the value of x is the number we are required to find.
[tex]\begin{gathered} x+6=-12 \\ \text{Subtract 6 from both sides} \\ x+6-6=-12-6 \\ x=-18 \end{gathered}[/tex]The said number is -18
What's the equation of the axis of symmetry of g(x)=x^{2}+4 x+3?A) x=0B) x=-2C) x=2D) x=3
Answers
Given a quadratic equation of the form:
[tex]f(x)=ax^2+bx+c[/tex]The equation of the axis of symmetry is obtained using the formula:
[tex]x=-\frac{b}{2a}[/tex]From the given quadratic equation:
[tex]\begin{gathered} g\mleft(x\mright)=x^2+4x+3 \\ a=1 \\ b=4 \end{gathered}[/tex]Therefore, the equation of the axis of symmetry of g(x) is:
[tex]\begin{gathered} x=-\frac{4}{2\times1} \\ x=-2 \end{gathered}[/tex]The correct option is B.
MOSS 79 grom Volume 10 m
Answers
Mass=79gram
Volume=10ml
density=Mass/Volume
[tex]\text{Density}=\frac{79\text{gram}}{10ml}=7.9\text{ gram/ml}[/tex]HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST
Answers
The rational number between -1/3 and 1/-2 could be; -6 / 18, -6/12.
What are natural numbers, rational numbers, and irrational numbers?Natural numbers are: 1, 2, 3, ..Rational numbers are numbers which can be written in the form of a/b where a and b are integers. Example: 1/2, 3.5 (which is writable as 7/5). Irrational numbers are those real numbers which are not rational numbers.
We are asked to find that rational number between -1/3 and 1/-2.
LCM of 3 and 2
3 x 2 = 6
Then we get;
-1/3 x 6/6 = -6 / 18
1/-2 x 6/6 = -6/12
Hence, the rational number between -1/3 and 1/-2 could be; -6 / 18, -6/12.
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if you're lonely then be lonely with me but I need your help
Answers
Let's use distributive property to simplify:
[tex]-35-5x+2\frac{5}{6}x=0[/tex]Now we add up the x's and take number to another side:
[tex]\begin{gathered} -5x+2\frac{5}{6}x=35 \\ -2\frac{1}{6}x=35 \end{gathered}[/tex]We make 2 and one-sixth into improper fraction and divide to get x:
[tex]\begin{gathered} -\frac{13}{6}x=35 \\ x=\frac{35}{-\frac{13}{6}} \\ x=35\cdot-\frac{6}{13}=-\frac{210}{13} \end{gathered}[/tex]x is "minus 210 over thirteen"
The three sides of a triangle are n, 4n - 2, and 4n - 7. If the perimeter of the triangle is 45 cm, what is the length of each side? Separate multiple entries with a comma.
Answers
6, 22, 17
ExplanationStep 1: writing the equation
We have a triangle with sides n, 4n - 2, and 4n - 7
We obtain its perimeter if we add all its sides:
n + 4n - 2 + 4n - 7
Since the perimeter is 45 cm, then:
n + 4n - 2 + 4n - 7 = 45
combining like terms:
n + 4n +4n = 9n
and
-2 - 7 = -9
then, we have:
n + 4n - 2 + 4n - 7 = 45
↓
9n - 9 = 45
Step 2: finding n
Now we solve the equation:
9n - 9 = 45
↓ taking -9 to the right
9n - 9 + 9 = 45 + 9
9n = 54
↓ taking 9 to the right
n = 54/9 = 6
Then, n = 6
Step 3: sides measure
Since the measure of the first side is given by n,
then its length is
n = 6
SInce the measure of the second side is given by 4n-2,
then its length is
4n - 2 = 4 · 6 - 2
= 24 - 2
= 22
SInce the measure of the third side is given by 4n - 7,
then its length is
4n - 7 = 4 ·6 - 7
= 24 - 7
= 17
That is why the measures are 6, 22 and 17.
How do you find the range in a graph like this?
Answers
Answer
y can take on any real number value except around 1 < y < 3 where none of the graphs have values around this region.
Hence, this is the range of the graph.
Explanation
The range of a function refers to the region of values where the fumction can exist. It refers to the values that the dependent variable [y or f(x)] can take on.
From the graph attached to this question, we can see that the function has different forms at different values of x.
But it is also evident that y can take on any real number value except around
1 < y < 3 where none of the graphs have values around this region.
Hence, this is the range of the graph.
Hope this Helps!!!
2) Use a graph to find the length of DE if D(4, -3) and E(-5, -7) in pythagoras theorem.
Answers
Use a graph to find the length of DE if D(4, -3) and E(-5, -7) in pythagoras theorem.
we know that
Applying the Pythagorean Theorem
DE^2=DEx^2+DEy^2
DEx -----> is the distance in the x-coordinate
DEy -----> is the distance in the y-coordinate
DEx=(-5-4)=-9 ------> subtract the x-coordinates
DEy=(-7+3)=-4 -----> subtract the y-coordinates
substitute in the formula
DE^2=(-9)^2+(-4)^2
DE^2=97
[tex]DE=\sqrt[]{97}\text{ units}[/tex]c^2=a^2+b^2
c -----> is the distance DE
a ----> horizontal leg
b ----> vertical leg
we have
a=(-5-4)=-9 ------> subtract the x-coordinates
b=(-7+3)=-4 -----> subtract the y-coordinates
substitute
c^2=(-9)^2+(-4)^2
c^2=97
[tex]c=\sqrt[]{97}\text{ units}[/tex]320000 in decimal form
Answers
Answer:
320×10³
Step-by-step explanation:
This is the standard form for the number 320000
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Suppose you roll a pair of six-sided dice and add their totals.(a) What is the probability that the sum of the numbers on your dice is 9 or 12?
Answers
We know we're dealing with two dice. Since each die has 6 different possibilities, the outcomes of rolling two dice are given by:
6 × 6, which is 36. This will be our denominator.
How many ways can we get 9 or 12 with two dices?
For a sum of 9:
3 + 6 = 9
4 + 5 = 9
There are two possibilities.
For a sum of 12:
6 + 6 = 12
There is only one possibility.
Summing it up, there are 3 possibilities to get a sum of 9 or 12 with the two dice.
The events are independent events since neither of them can ever occur at the same time.
Thus, the probability will be:
[tex]\text{ Probability = \lparen Probability of getting 9\rparen + \lparen Probability of getting 12\rparen}[/tex]We get,
[tex]\text{ Probability = }\frac{2}{36}\text{ + }\frac{1}{36}\text{ = }\frac{3}{36}\text{ = }\frac{1}{12}\text{ \lparen simplified\rparen}[/tex]Therefore, the probability is 1/12.