Part A: polynomial in Standard form;-
bluef(x) = ax⁴ + bx³ + cx²+ dx + e
Part B: Closure property relates to polynomial;-
The polynomial's closer property for subtraction. When two polynomials of identical degrees with different leading coefficients are subtracted, a polynomial of the same degree is produced.
What is Polynomial?
A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x.
A.
Any of the following can be the fourth degree polynomial with two terms:
f1(x) = ax⁴ + bx³
f2(x) = ax⁴ + cx²
f3(x) = ax⁴ + dx
f4(x) = ax⁴ + e
a ≠ 0 in all four instances.
Explanation. Because each of the aforementioned polynomials fi(x)-s can be written in the form of f(x) by setting blue0 equal to (c,d,e), (b,d,e), (b,c,e), and (b,c,d), respectively, each of the aforementioned polynomials is in standard form.
B.
The polynomial's closer property for subtraction. When two polynomials of identical degrees with different leading coefficients are subtracted, a polynomial of the same degree is produced.
Example.
Let r(x) be defined as a₁x³ + a₂x² + a₃x + a₄
s(x) is equal to b₁x³ + b₂x² + b₃x + b₄
where a ≠ 0 ≠ b and a ≠ b both belong to a set of real or complex numbers called ai and bi.
If this is how subtraction is defined, then
r(x) - s(x) = [a₁x³ + a₂x² + a₃x + a₄] - [b₁x³ + b₂x² + b₃x + b₄]
r(x) - s(x) = (a₁ - b₁)x³ + (a₂ - b₂)x² + (a₃ - b₃)x + (a₄ - b₄)
Given that (a₁ - b₁) ≠ 0, r(x) - s(x) is similarly a polynomial of fourth degree in this situation.
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According to a report for veterinarians in the united states, 36. 5 percent of households in the united states own dogs and 30. 4 percent of households in the united states own cats. If one household in the united states is selected at random, what is the probability that the selected household will own a dog or a cat?.
The probability of the selected household will own a dog or a cat can't be determined because there is not enough information to determine the probability
How to calculate probility?Probability is counted by dividing the event number with the total number of outcomes. In this case, the probability of the selected household will own a dog or a cat will have a formula like this:
P(A ∨ B)=P(A)+P(B)+P(A ∧ B)
Annotation:
P(A ∨ B) = probability own a dog or a cat
P(A) = probability own a dog
P(B) = probability own a cat
P(A ∧ B) = probability own a dog and a cat.
Based on question, we cant find value of the probability own a dog and a cat. Therefore, the best answer for this question there is not enough information to determine the probability
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Logan just became a personal trainer and is finalizing his pricing plans. One plan is to charge $18 for the initial consultation and then $88 per session. Another plan is to charge $39 for the consultation and $87 per session. Logan realizes that the two plans have the same cost for a certain number of sessions. What is that cost? How many sessions is that?
Answer: The 2 Plan will have same cost of $2149 after 64 sessions.
Let the Two plan be Plan A and Plan B.
Also let the number of session be
According to given detail
Plan A =
Plan B =
We need to find the value of when both are equal.
Plan A = Plan B
=
Solving above equation we get;
Number of session are 64.
Cost after 64 session will be,
Plan A =
Plan B =
Hence The 2 Plan will have same cost of $2149 after 64 sessions.
Step-by-step explanation:
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The equation of the parabola is f(x) = 7(x-3)^2+5.
Given:
The equation of the parabola that has the same shape has f(x) = 7x^2 but with vertex(3,5) in the form of f(x) = a(x-h)^2 + k.
If the parabola has same shape then its a values are same.
so f(x) = 7x^2
here a = 7
so the equation with vertex (3,5) also has a value is 7.
(h,k) = (3,5)
f(x) = a(x-h)^2+k
= 7(x-3)^2 + 5.
Therefore the equation of the parabola is f(x) = 7(x-3)^2+5.
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-13 > 2x -5 or 2x-5>17
The solution set for the pair of inequalities as given in the task content is; (-∞, -4) U (11, ∞).
What is the solution set for the pair of inequalities given?It follows from the task content that the solution set of the pair of inequalities is to be determined.
Therefore, each inequality can be solved as follows;
-13 > 2x - 5;
-13 + 5 > 2x
-8 > 2x
-4 > x.
Also, the inequality 2x - 5 > 17 can be solved as follows;
2x > 17 + 5
2x > 22
x > 11.
Therefore, the solution set of the inequalities as given in the task content in interval notation is;
(-∞, -4) U (11, ∞).
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I need help with this question ASAP
Answer:
X = 14
Hope this helps!
Step-by-step explanation:
The small red square means the angle is 90°.
( 2x + 22 ) + ( 3x - 2 ) = 90°
2x + 22 + 3x - 2 = 90
( 2x + 3x ) + ( 22 - 2 ) = 90
5x + 20 = 90
5x + 20 - 20 = 90 - 20
5x = 70
x = 14
Answer: x = 14
Step-by-step explanation:
When you have a right angle, they add up to 90 degrees
So you add up the two angles that you have that equal a total of 90 degrees
2x+22 + 3x-2 = 90
5x+20 = 90
5x = 70
x = 14
I hope this helps :D
The volume of a cylinder does not change
if you slant the (fill in the blank)
the cylinder but keep the
of(fill in the blank)
the same. The
volume of an oblique cylinder is the same
as the volume of an upright cylinder with
the same base and height.
If you slant the height of the cylinder but keep the radius the same then the volume of an oblique cylinder is the same.
What is an oblique cylinder?
When a cylinder "leans over," that is when its sides are not parallel to its bases, then the cylinder is said to be an oblique cylinder. The bases (ends) of an oblique cylinder stay parallel to one another, while the sides tilt outward at an angle that isn't quite 90°.
An oblique cylinder will have the same volume as a right cylinder with the same radius and height. As long as the radius and height are the same, the volume does not vary, but the height must equal the perpendicular height.
From the above observations, we can say that If you slant the height of the cylinder but keep the radius the same then the volume of an oblique cylinder is the same.
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Solve the following exponential equation
[tex]3 {}^{2x } - 9 = 0[/tex]
Answer:
x = 1
Step-by-step explanation:
Given exponential equation:
[tex]3^{2x}-9=0[/tex]
Add 9 to both sides of the equation:
[tex]\implies 3^{2x}-9+9=0+9[/tex]
[tex]\implies 3^{2x}=9[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies \left(3^2\right)^{x}=9[/tex]
[tex]\implies9^{x}=9[/tex]
[tex]\textsf{Apply exponent rule} \quad a=a^1:[/tex]
[tex]\implies9^{x}=9^1[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]
[tex]\implies x=1[/tex]
Describe the transformation of
f(x) = -2|x + 1 + 5
Shift Up__units.
Shift Down__units.
Shift Right__units.
Shift Left__units.
Compress by a factor of__
Stretch by a factor of__
Reflect over__axis.
The transformation of the equation f(x) = -2|x + 1| + 5 is
Shift Left 1 units
Shift Up 5 units
Compress by a factor of 2
Reflect over x axis
Interpretation of the transformationsTransformation involves movements of image or object usually described in a cartesian plane
starting from |x| at the origin
|x + 1| is a shift to the left 1 unit
|x + 1| + 5 is a shift on the y axis, it represents a shift up 5 units
2|x + 1| + 5 is a vertical compression by a factor of 2
-2|x + 1| + 5 the negative sign shows reflection over x axis turning the graph over
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6. According to Statistics Canada, the number of cable television subscribers increased from about 1 151 000 in 2002 to about 1 393 000 in 2003. What was the mean number of new subscribers per month during that year?
The mean number of new subscribers per month during that year is 242000.
What is a mean?A mean simply means the average of the numbers given.
The number of cable television subscribers increased from about 1 151 000 in 2002 to about 1 393 000 in 2003.
The mean number of new subscribers will be:
= Change in numbers / Number of years
= (1393000 - 1151000) / 1
= 242000 / 1
= 242000
Therefore, the mean is 242000.
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Which equation is parallel to x-y=3 passes through (2,-4)
The equation of the line parallel to x - y = 3 and passes through pint (2,-4) is y = x - 6.
What is the equation of line that passes through the given point and parallel to the given equation?The equation of line is expressed as;
y = mx + b
The point-slope formula is expressed as;
y - y₁ = m( x - x₁ )
Where m is slope and b is the y-intercept.
Given the data in the question;
Equation: x - y = 3Point: (2,-4)
x = 2y = -4First, reorder the given equation in slope-intercept form and determine the slope.
x - y = 3
x = 3 + y
3 + y = x
y = x - 3
Hence,
The slope m = 1
To find the line parallel to the equation, the slope must be equal.
Find the line using point-slope formula.
y - y₁ = m( x - x₁ )
Plug in slope m = 1 and point: (2,-4)
y - ( -4 ) = (1)( x - 2 )
Simplify and convert to slope intercept form.
y + 4 = x - 2
y = x - 2 - 4
y = x - 6
Therefore, the equation of line is y = x - 6.
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Suppose that y varies directly with x, and y=-4 when x=10. what is
y when x=2.
[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies with "x"}}{y=kx}\hspace{5em}\textit{we know that} \begin{cases} y=-4\\ x=10 \end{cases}\implies -4=k(10) \\\\\\ \cfrac{-4}{10}=k\implies -\cfrac{2}{5}=k\hspace{10em}\boxed{y=-\cfrac{2}{5}x} \\\\\\ \textit{when x = 2, what is "y"?}\qquad y=-\cfrac{2}{5}(2)\implies y=-\cfrac{4}{5}[/tex]
Which point is collinear with points A and B?
As stated in the preceding statement the point R is collinear with points A and B.
What is a collinear?An axis is a term used to describe a line upon whatever points are located, particularly if that line is connected to a triangle or other geometric shape. Since two factors determine a line, two points become trivially collinear.
How are collinear points discovered?Two lines may coincide if they have a same point and have the same slope. To put it another way, if A, B, as well as C are three points there in XY plane, they will all lie on a line, or three points will be collinear, but only if AB's slope and BC's slope are both equal.
then
m A B = m BC ( = m AC ).
The point is collinear with points A and B.
Therefore, the correct answer is option (d) R.
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Which units are used to measure both velocity and speed? Select three options.
m/s
d/t
km/h
mph
m2
Answer:
M/s, km/h, and mph
Step-by-step explanation:
M/s = meters (travelled) per second
km/h = kilometers (travelled) per hour
mph= miles (travelled) per hour
Answer:
m/s
km/h
mph
Step-by-step explanation:
: )
The corporate team-building event will cost $1,376 if it has 86 attendees. If there are 94 attendees, how much will the corporate team-building event cost?
Angel bought a plant and planted it in pot near a window in his house. The plant
grew at a rate of 3 inches per month and its height at the time of purchase was 15
inches. Write an equation for H, in terms of t, representing the height, in inches, of
the plant t months after Angel bought the plant.
The required equation for height H of the plant t months after Angel bought the plant is,
H = 15 + 3t
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
t = time in months
H = total height
H= initial height+ rate of growth * time
H = 15 + 3t
So, the required equation for height H of the plant t months after Angel bought the plant is,
H = 15 + 3t
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answer the questions below about the following function
what is the domain of f(x)
what is the range of f(x)
what is the x-intercept of f(x)? enter your answer as an ordered pair. if no x-intercept exists, enter none
what it the equation of the vertical asymptote
Domain of the function is, (0, ∞).
Range of the function is, (-∞, ∞).
x - intercept of the function is, (1, 0).
Vertical asymptote of the function is, None.
What is domain and range?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).
A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
First to find the domain of the function,
Since, all input values shown on the x-axis make up a graph's domain.
We can see that values of x values are from 0 to ∞.
Hence, the domain is (0, ∞).
Now to find the range.
Since, the y-axis on a graph represents the possible output values, or range.
The y - axis having the values from -∞ to ∞.
Hence, the range of the function is, (-∞, ∞).
x - intercept is the point where function crosses the x - axis.
Here function crosses x - axis at (1, 0).
Hence, the x - intercept is (1, 0).
A graph's vertical asymptote is the vertical line at x = a where the graph trends toward positive or negative infinity as the inputs go closer to a.
So, the vertical asymptote is x = 0.
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Determine the value of any unknown GIVE REASONS
The value of angle b is 60 degrees. The reason is angle b is a supplementary angle to angle 120 degrees
angle b is equal to angle c the reason id that they form alternate internal angles
What are linear pairs?A linear pair is a situation where two adjacent angles are on a straight line, hence their sum is 180 degrees.
Linear pair is special cases of supplementary angles involving only two angles that are adjacent
How to solve for angle b
b + 120 = 180
b = 180 -120
b = 60
c = b (alternate internal angles)a = 80 degrees vertical anglesLearn more about linear pair here
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a closed right circular cylinder is to have a volume of 128pi cubic inches. find the radius r and height h of the cylinder with minimal surface area
∛128 is the radius r and height h of the cylinder with minimal surface area .
What is Surface Area?
The term "area" refers to the area occupied by a flat, two-dimensional surface. In square units, it is calculated. A three-dimensional object's surface area is the space it takes up when viewed from the outside.V = πr²n
128π = πr²n
n = 128/r²
s = 2πrn + 2πr²
s = 2πr 128/r² + 2πr²
s = 256π/r + 2πr²
ds/dt = - 256π/r² + 2πr
d²s/dt² = -256/(-2) r³ + 2π
d²s/dt² = 128/r³ + 2π
for maxima or minima
ds/dt = 0
- 256 π/r² + 2πr = 0
256 = 2r³
r = ∛128
d²s/dt² = 128/(∛128)³ + 2π
= 2π + 1
d²s/dt² > 0
so surface area is minimum
a + r = ∛128
n = 128(∛128)²
n = ∛128
r = ∛128 , n= ∛128
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Marlee is making jewelry for a class craft show. She began with 115 inches of wire. She used 25.75 inches for rings. Then her teacher gave her 3014 inches of wire to make more jewelry. She then used 3812 inches for the bracelets and 60.2 inches for necklaces. How much wire does Marlee have left? Write your answer as a mixed number in simplest form.
Marlee is in short of -768.95 inches of wire for making jewelry.
Given that, Marlee is making jewelry for a class craft show. She began with 115 inches of wire.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The numerical expression for the given situation is
115-25.75+3014-(3812+60.2)
= 89.25+3014-3872.2
= 3103.25-3872.2
= -768.95 inches
Therefore, Marlee is in short of -768.95 inches of wire for making jewelry.
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I NEED A AND B OF THIS QUESTION!!
Answer: Part A : it is a function
Step-by-step explanation: once its on a graph it will only cross the line once
Find the range for the measure of the third side of a
triangle given the measures of two sides.
8, 13
By using properties of triangle, it can be inferred that
The value of c lies between 5 and 21 and also 5 and 21 are not included
What is a triangle?
A triangle is a three sided two dimensional figure. A triangle has three sides and three interior angles. The sum of the interior angles of a triangle is 180°
Let a = 8, b = 13 and let the third side be c
We know sum of two sides of a triangle is always greater than the third side
a < b + c
8 < 13 + c
c > 8 - 13
c > -5, which is obvious
b < c + a
13 < c + 8
c > 13 - 8
c > 5
c < a + b
c < 8 + 13
c < 21
5 < c < 21
The value of c lies between 5 and 21 and also 5 and 21 are not included
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what is the notation used for a vector pointing into the page? what about a vector pointing out of the page?
The notation used for a vector pointing into the point is X.
A quantity with a magnitude and direction is called a vector. A vector quantity will be identified in these annotations by a bold letter (such as the electric field vector E). Vectors appear graphically as straight arrows. The magnitude of the vector is commonly represented by the length of the arrow, and both the arrow and the vector point in the same general direction.
Arrows are drawn on the page to represent vectors in the page's plane. Typically, circles with an X engraved on them are used to represent vectors that enter the screen's plane. A vector that deviates from the screen's plane is often represented by circles with dots in the center.
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Write an equation for the nth term of the arithmetic sequence, then find the a10
-3,-1,1,3
An equation for the nth term of the arithmetic sequence is aₙ=a+(n-1)d and a₁₀ of sequence -3,-1,1,3 is 15.
What is Sequence?A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given,
-3,-1,1,3 is a sequence.
An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same.
We know that nth term of arithmetic sequence is aₙ=a+(n-1)d
-3,-1,1,3
First term a=-3
Common difference d=-1-(-3)=-1+3=2
We need to find the 10th term
a₁₀=-3+(10-1)(2)
a₁₀=-3+9(2)
a₁₀=-3+18
a₁₀=15
Hence, an equation for the nth term of the arithmetic sequence is aₙ=a+(n-1)d and a₁₀ of sequence -3,-1,1,3 is 15.
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Which of the following would be a good estimate for -7.94 - 2.31?
-10
-5
-9
-6
will mark brainiest
Answer:-10.25
Step-by-step explanation:
Just because ;) -10.25= -10.00
Answer:
-10
Step-by-step explanation:
Estimate between the two numbers?
Add them together first
Which equals -10.25
The closest would be -10
In the diagram, ABGH = CDEF.
Find the value of x.
X = ___
The value of x is 25
What is congruent polygons ?
A polygon is said to be congruent if it has the same shape as the polygon it is compared to, as well as the identical side lengths and interior angles. In order to meet the condition, congruent shapes must all have the same kind of shape. Because they are different shapes, a rectangle and a pentagon cannot be congruent.
Two squares or two hexagons can be considered congruent polygons since they both have equal-length sides and angles. However, it's crucial to keep in mind that the length of the sides must also be equal. A square is not congruent if it is larger than another square.
1. Pairs of congruent corresponding parts
∠A = ∠C AB = CD
∠B = ∠D AH = CF
∠H = ∠F HG = FE
∠G = ∠E GB = ED
To find the value of x
4x + 5 = 105
4x = 105 - 5
4x = 100
x = [tex]\frac{100}{4}[/tex]
= 25
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Bridgette has 9 dogs. Every day, she feeds them a total of 9/10 of a can of food, where each dog is fed the same amount of food. How many cans of food does Bridgette give to each dog?
Bridgette gives 1/10 cans of food to each dog.
According to the question,
We have the following information:
Bridgette has 9 dogs. Every day, she feeds them a total of 9/10 of a can of food, where each dog is fed the same amount of food.
Now, we have the following expression:
9 dogs = 9/10 can
Now, we can easily find the cans given to each dog using division. We will divide the total number of cans of food by the number of dogs.
1 dog = 9/(10*9) cans
1 dog = 1/10 cans of food
Hence, Bridgette gives 1/10 cans of food to each dog.
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Radioactive elements decrease (or decay) exponentially. Suppose that 120 mg of an unknown radioactive
element decays down to 99 mg after 11 days.
(a) What is the half-life of the element? That is, how many days will it take before half of the original sample
has decayed?
half-life:
days (rounded to at least 2 decimal places)
(b) How long will it take for a sample of 99 mg in this scenario to decay to 40 mg?
days (rounded to at least 2 decimal places)
time needed:
Considering an exponential function, it is found that:
a) The half-life of the element is of 39.63 days.
b) The time needed is of 51.82 days.
What is an exponential function?A decaying exponential function is modeled by the equation presented as follows:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which the variables of the equation are:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem, the parameters are given as follows, from the text:
A(0) = 120, A(11) = 99.
Hence the decay rate r is obtained as follows:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]120 = 99(1 - r)^{11}[/tex]
[tex](1 - r)^{11} = \frac{99}{120}[/tex]
[tex]1 - r = \sqrt[11]{\frac{99}{120}}[/tex]
[tex]1 - r = \left(\frac{99}{120}\right)^{\frac{1}{11}}[/tex]
1 - r = 0.98266367982
Hence the equation is:
[tex]A(t) = A(0)(0.98266367982)^t[/tex]
The half-life is the value of t for which:
A(t) = 0.5A(0).
Hence:
[tex]A(t) = A(0)(0.98266367982)^t[/tex]
[tex]0.5A(0) = A(0)(0.98266367982)^t[/tex]
[tex](0.98266367982)^t = 0.5[/tex]
[tex]\log{(0.98266367982)^t} = \log{0.5}[/tex]
[tex]t\log{(0.98266367982)} = \log{0.5}[/tex]
[tex]t = \frac{\log{0.5}}{\log{(0.98266367982)}}[/tex]
t = 39.63 days.
For item b, the time is obtained as follows:
[tex]A(t) = 99(0.98266367982)^t[/tex]
[tex]40 = 99(0.98266367982)^t[/tex]
[tex](0.98266367982)^t = \frac{40}{99}[/tex]
[tex](0.98266367982)^t = 0.40404040[/tex]
[tex]t = \frac{\log{0.40404040}}{\log{(0.98266367982)}}[/tex]
t = 51.82 days.
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Find the x- and y-intercepts of the graph of 2x+8y=122x+8y=12. State each answer as an integer or an improper fraction in simplest form.
Answer:
x,y [tex]( \frac{2}{61})(\frac{91}{61} )[/tex]
The variable y has a proportional relationship with x as suggested by the graph. Use the graph to find the constant of proportionality.
Answer: THE ANSWER IS 26
4 - 3x = 8 - 4x please help
Step-by-step explanation:
we switch the like terms across the equation and when we do that we change the signs