A polynomial function of degree n has at most n real zeros and at most n-1 turning points.
What is polynomial function ?
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only involves non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
What isa Zeros of Polynomials?
Every polynomial will have as many zeros as its degree if we are able to factor it over the entire set of complex numbers, though some of these zeros are repeated and therefore counted more than once. As the function might not be fully factorable over the set of real numbers, if we limit ourselves to the set of real numbers, we might or might not be able to identify this many zeros.
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Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents. Y to the one third power all over y to the one sixth power.
The expression [tex]$\frac{3^{\frac{1}{3}}}{3^{\frac{1}{6}}}$[/tex] represents [tex]$\sqrt[6]{3}$[/tex]as rational exponents as a radical expression.
What is an expression?
"An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation in it."
The given expression is:
[tex]$$\begin{aligned}& \frac{3^{\frac{1}{1}}}{3^{\frac{1}{6}}} \\& =3^{\frac{1}{3}-\frac{1}{6}} \\& =3^{\frac{1}{6}} \\& =\sqrt[6]{3}\end{aligned}$$[/tex]
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function rule to find f(9).
Answer: 12
Step-by-step explanation:
[tex]f(9)=3+9=12[/tex]
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Equivalent expressions are expressions that have the same result.
The expression in this problem is defined as follows:
13 + 4g.
The commutative property is applied in this problem, meaning that the order of the terms is exchanged, hence the equivalent expression is given as follows:
4g + 13.
The numeric values of the expression are given as follows:
g = 2: 13 + 4(2) = 21, 4(2) + 13 = 21.g = 10: 13 + 4(10) = 53, 4(10) + 13 = 53.More can be learned about equivalent expressions at https://brainly.com/question/15775046
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HELP ASAP!!!! 20 PTS
The floor of a new planetarium will be a circle with a 33- diameter. The material for the floor will cot $3. 86 per quare. If no material i wated when making the floor, how could you find how much the floor will cot? How much will the floor cot? Ue 3. 14 for
The cost of the circular floor is $3299.77.
The space a circle takes up in a two-dimensional plane is known as the area of the circle.
For measuring the area occupied by a circular field or plot, use the area of a circle formula. The area formula will allow us to determine how much cloth is required to completely cover a circular table, for example.
Area of circle = [tex]\pi r^{2}[/tex]
Given in question,
[tex]\pi[/tex] = 3.14
Diameter = 33
Radius = Diameter/2
= 33/2
= 16.5
Area = 3.14*16.5*16.5
= 854.865 square
Cost per square = $3.86
Cost for 854.865 square = 3.86*854.865
= 3299.78
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Find the value of the expression 2xy(8x - 3y), when x = 2 and y = 4.
A 48
B 72
C 64
D 24
Answer:
C 64
Step-by-step explanation:
1. 2(2)(4)(8(2)-3(4))
2.2(8)(16-12)
3. 16(4)
4. 64
please help: in the figure, ∆LMN ≅ ∆RST. find the values of x and y
Answer:
X=8, y=19
Step-by-step explanation:
These two triangles are congruent. This means that angle STR = angle MNL, so angle STR = 63°. We know the angles in a triangle must sum to 180°, so we can figure out 3x from this, given that we know the other two angles. 63 + 93 = 156, so 3x = 180-156=24. This gives us that x = 8. Now we can solve for x, because we know that SR = ML, so 3x + y = 43. We know x = 8, so we get that 24 + y = 43, or y = 19.
I hope this helps!
A group of friends were working on a student film that had a budget of $1400. They used 23% of their budget on equipment. How much money did they spend on equipment?
Answer: $322
Step-by-step explanation:
1400x0.23 = $322
thirteen black and six white hexagonal tiles were used to create the figure below. if a new figure is created by attaching a border of white tiles with the same size and shape as the others, what will be the difference between the total number of white tiles and the total number of black tiles in the new figure?
The difference between the total number of white tiles and the total number of black tiles in the new figure is 11.
Thirteen black and six white hexagonal tiles. If a new figure is created by attaching a border of white tiles with the same size and shape as the others
To find the difference between the total number of white tiles and the total number of black tiles in the new figure.
Now, According to the question:
The solution will be:
The first ring around the middle tile has 6 tiles, and the second has 12. From this pattern, the third ring has 18 tiles. Of these, 6+18=24 are white and 1+12=13 are black, with a difference of 24-13 = 11.
Hence, the difference between the total number of white tiles and the total number of black tiles in the new figure is 11.
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Plant A i 5 centimeter tall and growing at a rate of 2. 5 centimeter per month. Plant B i 4 centimeter and growing at a rate of 4. 5 centimeter per month. When will Plant B exceed the height of Plant A. Write an inequality that repreent the ituation
In linear equation, plant b height will exceed the height of plant a after 16 days.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Plant a: 5 cm tall and rate of change = 2.5 cm per month
Plant b: 4 cm tall and rate of change = 4.5 cm per month.
Now we have to form the linear equations.
Plant a:
y = 2.5x + 5, where y is the total height and "x" be the number of months.
Plant b:
y = 4.5x + 4 , where y is the total height and "x" be the number of months.
Now we have to when the height of the plant a and plant b are the same.
To do that, we have to equivate both the equations and find x.
2.5x + 5 =4. 5x + 4
Isolate the variables terms and constants.
4.5x - 2.5x = 5 - 4
2x = 1
Dividing both sides by 2, we get
x = 1 ÷ 2
x = 0.5 months.
So after 15 days, the height of the plant a and plant b are the same.
Therefore, plant b height will exceed the height of plant a after 16 days.
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What is the product of x=8 and 2x^2-5x-3
a 2x^3+16x^2-4x+5
b 2x^3-11x2+43x+24
c 3x^3 2x^2-5x+8
d 2x^3+11x^2-43x-24
Quadratic equation is a type of equation which has the highest power of 2. The product of the given terms is option B. [tex]2x^{3}[/tex] - [tex]11x^{2}[/tex] + 43x + 24
An equation is said to be quadratic if and only if the highest power of the variable in its terms is 2. Thus they can be solved either by completing the square method, graphical method, the use of the quadratic formula etc.
The product of an algebraic term and a quadratic equation involves a stepwise procedure, such that all terms and exponential are considered.
The given question state thus:
what is the product of x - 8 and [tex]2x^{2} -5x-3[/tex]?
Thus using the expansion method, we have:
(x + 8)( [tex]2x^{2} -5x-3[/tex]) = [tex]2x^{3}[/tex] - [tex]5x^{2}[/tex] - 3x + [tex]16x^{2}[/tex] - 40x - 24
= [tex]2x^{3}[/tex] - [tex]11x^{2}[/tex] + 43x + 24
Thus the product of the given question is option B. [tex]2x^{3}[/tex] - [tex]11x^{2}[/tex] + 43x + 24
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The enrollment for a school in 2010 was 1510 students. In 2020, the enrollment was 860 students. Find and interpret the rate of change in enrollment from 2010 to 2020.
Answer:
Step-by-step explanation:
The rate of change is the slope of the line formed by connecting the two data points:
1. (2010,1510). and [enrollment for a school in 2010 was 1510 students]
2. (2020, 860) [In 2020, the enrollment was 860 students]
Slope is the Rise/Run of the line. Lets go from the first point to the second.
The Rise: (1510 - 860) = 650
The Run: (2020-2010) = 10
The slope, or rate of change, is = 65
The interpretation is that "The enrollment at the school increase by an average of 65 students every year since 2010 until 2020."
Which of the following statements is INCORRECT?
A. A triangle with three congruent sides is equiangular.
B. The Isosceles Triangle Theorem can be applied to equilateral triangles.
C. The measure of each angle of an equilateral triangle is 120°.
D. A triangle with three congruent angles is equilateral.
Answer:
C
Step-by-step explanation:
The measure of each angle in an equilateral triangle is [tex]60^{\circ}[/tex], not [tex]120^{\circ}[/tex].
Caroline bike 1,754 mile in ix month. If he bike the ame number of mile each month, about how many mile doe he bike each month
The distance covered in each month = 194.89 miles
What is unitary method ?The unitary method entails figuring out the value of a single unit from which we can extrapolate the values of all the required units.
What is Distance ?Distance. A line or line segment's length between two points along the line or line segment
According to the given information
Using unitary method
Distance covered in 9 months = 1,754 miles
Distance covered in each month = [tex]\frac{1754}{9}[/tex] miles
So,
The distance covered in each month = 194.89 miles
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Put the following equation of a line into slope-intercept form, simplifying all fractions.
2x+4y=-20
Answer: y = -5 - 1/2 x
Step-by-step explanation:
Slope intercept form: y=mx+b
2x+4y=-20
Isolate the y.
4y=-20-2x
Divide by 4.
y=-20/4-2x/4
y = -5 - 1/2 x
x intercept of y = x-7
The x-intercept of the linear equation is (7, 0).
How to find the x-intercept of the linear function?Here we have the following linear equation:
y = x - 7
We want to find the x-intercept, this is the point where the line intercepts the x-axis, it will happen when we take the value of y = 0, then we need to solve.
0 = x - 7
Solving that, we get:
7 = x
Then we conclude that the x-intercept of the linear equation is (7, 0).
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A machine in a factory can assemble 234 units in 3 hours. Matt wants to write an equation to represent this situation. He says that the independent variable is the number of units assembled; the dependent variable is the number of hours, and the constant of proportionality is 78. What mistake did matt make in finding the parts of the equation that represents this relationship?.
Matt should take dependent variable is the number of units assembled; the independent variable is the number of hours to make it correct.
Explain variables.A variable is any qualities, number, or amount that can be estimated or counted. A variable may likewise be known as an information thing. Age, sex, business pay and costs, nation of birth, capital use, class grades, eye tone and vehicle type are instances of factors.
According o question:Considering that a machine in a plant can collect 234 units in 3 hours. Free factor is the no of units gathered and subordinate variable is the time taken.
Let y be number of hours and x be number of units assembled;
So, we can write
y = mx
Slope = y/x = 3/234 = 1/78
constant of proportionality is 78 is inverse, so To make correct we have to take dependent variable is the number of units assembled; the independent variable is the number of hours.
correct equation is, x = 78y
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Slope Item 21025
slope =-
slope=
517
Which is the slope of the line that passes through the points (3, 5) and (8, 7)?
slope =
slope =
vijes
37
CLEAR
C
Answer:
Step-by-step explanation:
Well, the x increases by 5
And the Y increases by 2
So the slope is 5/2
And the equation would be 5/2x + b
Please I need help I need to pass this
Despite what he may have told you, Mr. Robeson is actually quite bad at
making free throws in basketball. On average he makes 35% of the free
throws he takes and he doesn't learn from previous shots. What is the
probability that the first time he makes a free throw is on the 5th shot he
attempts?
Answer:
0.009754
Step-by-step explanation:
(.65)^4 x (0.35)
By saying that he makes a free throw on the fifth show, he did not make the first four, therefore 4 of the times he shot, he did not get it in.
If he makes the shot 35% of the time, he doesn't make it 65% of the time: (1-0.35=.65)
On the last shot he made it, which he makes 35% of the time therefore:
You want to multiply : 0.35 (which is = 35%) by itself four times and then multiply that by 0.65 (since the last shot was made)
0.35 x 0.35 x 0.35 x 0.35 x 0.65 = 0.009754 or 0.9754%
There is a 0.9754% chance he makes it BUT a 0.009754 probability
Is this proportional or not proportional?
Help me please I really need a fast answer because I don’t get the question please help me out!
The Answer is
D) x=3 and x=-4
Answer: it D
x=3 and x=-4
If you want to increase an amount by 15%, what is the multiplying factor?
with a clear explanation
Answer:
multiplying factor = 1.15
Step-by-step explanation:
the original amount is 100%
the increase is 15%
then increasing the original amount by 15% is
100% + 15% = 115% = [tex]\frac{115}{100}[/tex] = 1.15
multiplying factor is 1.15
2x + 2 = 5y
This is needed now!!!
Answer:
x = 2.5y - 1
Step-by-step explanation:
Subtract 2 from both sides
then you get 2x = 5y - 2
then divide everything by 2 for the answer
x = 2.5y -1
Q is the midpoint of PR. If QR = x + 9 and PR = 3x + 9, what is PR?
Therefore, as per the solution from the linear equation in one variable, the line segment PR is 9 units.
What is a linear equation in one variable?A linear equation in one variable is one that is written in the form ax + b = 0, where a, and b are real numbers and the coefficients of x and constant, i.e. a and b, are not equal to zero.
Given :
PR is a line.
Q is the midpoint of PR. So PQ = PR.
QR = x + 9
PR = 3x + 9
According to the question, verification is
PQ = PR
X + 9 = 3x + 9
3x – x = 9 - 9
2x = 0
x = 0
Therefore, as PQ = PR
x + 9 = 3x + 9
0 + 9 = 0(3) + 9
9 = 9
PR = 3(0) + 9
PR = 0 + 9
PR = 9
Therefore, as per the solution from the linear equation in one variable, The line segment PR is 9 units.
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Therefore, as per the solution from the linear equation in one variable, the line segment PR is 9 units.
What is a linear equation in one variable?A linear equation in one variable is one that is written in the form ax + b = 0, where a, and b are real numbers and the coefficients of x and constant, i.e. a and b, are not equal to zero.
Given :
PR is a line.
Q is the midpoint of PR. So PQ = PR.
QR = x + 9
PR = 3x + 9
According to the question, verification is
PQ = PR
X + 9 = 3x + 9
3x – x = 9 - 9
2x = 0
x = 0
Therefore, as PQ = PR
x + 9 = 3x + 9
0 + 9 = 0(3) + 9
9 = 9
PR = 3(0) + 9
PR = 0 + 9
PR = 9
Therefore, as per the solution from the linear equation in one variable, The line segment PR is 9 units.
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8x + 38 = -3(-6 - 4x)
Answer:
x=5
Step-by-step explanation:
step one: distribute to get rid of parentheses. this means multiplying -3 by the numbers inside of the parentheses next to it.
-3(-6)= 18 and -3(-4x)=12x
this makes the equation now 8x+38=18+12x
step two: move x to one side of the equation. we can do this by using inverse operations, so we're going to subtract 8x from both sides.
8x-8x=0, 12x-8x= 4x.
this makes the equation now 38=18+4x
step three: isolate x. this means getting rid of the 18. to do this, we are going to use inverse operations again. this means subtracting 18 from both sides.
18-18=0, 38-18=20.
this makes the equation now 20=4x
step four: divide to get x by itself. we don't want to know what 4x is, we just want to know what plain x is. so we're going to use inverse operations for the last time and divide both sides by 4 because 4x is the same thing as saying "four times x"
20/4= 5, 4x/4=x
this makes the equation now 5=x
that's your answer, x=5. hope this helped!
PLEASE HELP ME! i have been trying for hours
Step-by-step explanation:
The 3 possible solutions for the inequality.
Add (or subtract) a number from both sides. Multiply (or divide) both sides by a positive number. Simplify a side
try this to get your answer
answer
b5
Step-by-step explanation:
If b = 3, then the inequality becomes 17 ≥ 2(3) or 17 ≥ 6, which is true.
If b = 6, then the inequality becomes 17 ≥ 2(6) or 17 ≥ 12, which is not true.
If b = 2, then the inequality becomes 17 ≥ 2(2) or 17 ≥ 4, which is true.
If b = 5, then the inequality becomes 17 ≥ 2(5) or 17 ≥ 10, which is true.
Therefore, the solutions to the inequality 17 ≥ 2b are b = 3, b = 2, and b = 5.
The midpoint of \overline{\text{AB}} AB is M(4, 0)M(4,0). If the coordinates of AA are (3, -1)(3,−1), what are the coordinates of BB?
Answer:
The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the line segment. If the coordinates of one endpoint are (x1, y1) and the coordinates of the other endpoint are (x2, y2), then the coordinates of the midpoint are given by:
M = ((x1 + x2)/2, (y1 + y2)/2)
In this case, the coordinates of the midpoint are (4, 0), and the coordinates of AA are (3, -1). Therefore, the coordinates of BB must be (5, 1).
You can confirm this by calculating the midpoint using the coordinates of AA and BB:
M = ((3 + 5)/2, (-1 + 1)/2)
= (4, 0)
This shows that the point (5, 1) is indeed the other endpoint of the line segment, and the coordinates of BB are (5, 1).
Step-by-step explanation:
What is the value of x?
In which way should the graph of f(x) = x2 be shifted to produce the graph of g(x) = (x - 3)2?
A.
3 units to the left
B.
3 units to the right
C.
3 units down
D.
3 units up
Answer:
g(x) = f(x - 2) + 3 denotes a 2-unit right and 3-unit up in the graph of g(x)
Step-by-step explanation:
Answer:
uh nose
Step-by-step explanation: