Polynomial is an expression that consists of indeterminates(variable) and coefficients. The power function of the energy is e=mc².
What are polynomials?Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.
The power function is a polynomial. Given the energy, e, produced in a nuclear reaction is proportional to the mass, m. Therefore, we can write,
e ∝ m
To remove proportionality we need to add a constant of variation which is c², the square of the speed of light
e = m c²
Hence, the power function of the energy is e=mc².
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1. Which shows the factoring pattern for the sum of cubes?
1. (a+b)(a2–ab+b2)
2. (a+b)(a2–ab–b2)
3. (a–b)(a2–ab+b2)
4. (a+b)(a+b)(a+b)
2. Select all the solutions of x3+2x2−9x=18.
1. x=2
2. x=−3
3. x=3
4. x=−2
3. If x=−1 is a root of the polynomial 0=x3+2x2−5x−6, what are the other roots?
1. x=3, x=−2
2. x=−3, x=2
3. x=−1, x=−3, x=2
4. x=0, x=−3, x=2
4. Subtract: (x2–1)–(x3–2x+1)
1. –x^3 – x^2 + 2x
2. –x^3 – x^2 + 2x + 2
3. –x^3 + x^2 + 2x – 2
4. –x^3 + x^2 – 2x – 2
5. What is the largest multiplicity in the factored polynomial y=(x2−1)(x+2)(x+4)?
1. 4
2. 1
3. 0
2. 0
The solution to the questions are:
The expression that represents the factoring pattern is (a + b)(a² - ab + b²)The solutions of the equation x³ + 2x² - 9x = 18 are x = -3, x = 3 and x = -2The other roots are x = -3 and x = 2The result of subtracting the expressions is - x³ + x² + 2x - 2The largest multiplicity is 1Factoring pattern for the sum of cubesAs a general rule, the sum of cubes x³ and y³ is:
x³ + y³= (x+y)(x² - xy + y²)
Replace x with a and y with b
a³ + b³= (a + b)(a² - ab + b²)
Hence, the expression that represents the factoring pattern is (a + b)(a² - ab + b²)
The solutions of the polynomialThe equation is given as:
x³ + 2x² - 9x = 18
Subtract 18 from both sides
x³ + 2x² - 9x - 18 = 0
Factorize the expression
x²(x + 2) - 9(x + 2) = 0
Factor out x + 2
(x²- 9)(x + 2) = 0
Express x²- 9 as a difference of two squares
(x + 3)(x - 3)(x + 2) = 0
Split
(x + 3) = 0 or (x - 3) = 0 or (x + 2) = 0
Remove brackets
x + 3 = 0 or x - 3 = 0 or x + 2 = 0
Solve for x
x = -3, x = 3 and x = -2
Hence, the solutions of the equation x³ + 2x² - 9x = 18 are x = -3, x = 3 and x = -2
The other roots of the polynomialThe polynomial equation is given as:
0 = x³ + 2x² - 5x - 6
Rewrite as:
x³ + 2x² - 5x - 6 = 0
Factorize the expression on the left-hand side
(x + 3)(x + 1)(x - 2) = 0
Split
x + 3 = 0 or x + 1 = 0 or x - 2 = 0
Solve for x
x = -3 or x = -1 or x = 2
Hence, the other roots are x = -3 and x = 2
Subtract the expressionsThe expression is given as:
(x² - 1) - (x³ - 2x + 1)
Expand
x² - 1 - x³ + 2x - 1
Collect like terms
- x³ + x² + 2x - 1 - 1
Evaluate the like terms
- x³ + x² + 2x - 2
Hence, the result of subtracting the expressions is - x³ + x² + 2x - 2
The largest multiplicity of the polynomialThe polynomial is given as:
y = (x² - 1)(x + 2)(x + 4)
Express x² - 1 as a difference of two squares
y = (x - 1)(x + 1)(x + 2)(x + 4)
The power of each factor in the above expression is 1.
This means that the largest multiplicity is 1
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A new amusement park presold discounted tickets for the opening day as well as upon arrival at the park. the opening day ticket sales for the park, including presales, is represented by this function, where is the number of tickets sold h hours after opening at 7:00 a.m. what is the approximate rate of change in the number of tickets sold between 10:00 a.m. and 1:00 p.m.? a. tickets per hour b. tickets per hour c. tickets per hour d. tickets per hour
The approximate rate of change in the number of tickets sold between 10:00 a.m. and 1:00 p.m. -21 tickets per hour
How to determine the rate of change?The missing part of the question is represented by the following function:
[tex]T(h) = \frac{386 + 110h}{h}[/tex]
10:00 a.m is 3 hours after 7:00 am and 1:00 p.m is 6 hours after 7:00 am.
This means that:
h = 3 at 10:00 am
h = 6 at 1:00 pm
Next, we calculate T(3) and T(6)
[tex]T(3) = \frac{386 + 110*3}{3} =238.7[/tex]
[tex]T(6) = \frac{386 + 110*6}{6} =174.3[/tex]
The average rate of change is then calculated as:
[tex]T'(h) = \frac{T(3) - T(6)}{3 - 6}[/tex]
This gives
[tex]T'(h) = \frac{238.7 - 174.3}{-3}\\[/tex]
Evaluate
T'(h) = -21
This means that the approximate rate of change in the number of tickets sold between 10:00 a.m. and 1:00 p.m. -21 tickets per hour
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What is the range of the function
Answer:
should be the first one -inf < y < inf
Which is the graph of f(x)?
Answer: [tex]fx[/tex]
The slope is 0, and
the y-intercept is (0, 0)
[tex]\left[\begin{array}{ccc}x&y\\0&0\\1&0\end{array}\right][/tex]
In order to find the graph of "f(x)", we need to graph the line using the slope and y-intercept, or two points.
the quotient of a number and three is four. what is the number
Answer:
12
Step-by-step explanation:
12/3=4
4*3=12
Hope this helps!
If not, I am sorry.
Answer:
12
Step-by-step explanation:
The quotient of a number and three is four. What is the number?
The word problem can be written as:
[tex]\sf{\dfrac{x}{3}=4}[/tex]
1. Multiply both sides by 3:
[tex]\sf{3\left(\dfrac{x}{3}\right)=4(3)}\\\\\implies x=12[/tex]
2. Check your work:
[tex]\sf{\dfrac{12}{3}=4}\\\\\implies 4=4 \ \checkmark[/tex]
Therefore, the number is 12.
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Please don’t lie to me and tell the right answer and if you do get it correct I will give you a shout out thanks
Answer:
Part A = 7
Part B = 1
I hope this is right, sorry if it isn't
Answer:
See below
Step-by-step explanation:
5 cups cheese / ( 2/3 cup cheese/plate ) =
5 * 3/2 = 15/2 = 7 1/2 or 7 full plates
2/3 cup cheese / plate * 9 plates =
2/3 * 9 = 6 cups cheese total
she has 5 cups to start.....she will need 1 cup more
Find the least common multiple of 35 and 21
Answer:
105
Multiples of 35:
35, 70, 105, 140, 175
Multiples of 21:
21, 42, 63, 84, 105, 126, 147
Answer:
105
Step-by-step explanation:
Given the following question:
We are given two numbers and we are trying to find the least common multiple (LCM) of the two. In order to find the LCM we have to find the GCM or the greatest common multiple.
[tex]35\div7=5[/tex]
[tex]21\div7=3[/tex]
[tex]GCM=7[/tex]
Now that we have the GCM we multiply 35, and 21 then divide it by the GCM.
[tex]35\times21=735[/tex]
[tex]735\div7=105[/tex]
[tex]LCM=105[/tex]
The least common multiple is "105."
Hope this helps.
The vertex of a parabola is at the point (3,1), and its focus is at (3,5). What function does the graph represent?
A.
B.
C.
D.
When the vertex of a parabola is at the point (3,1), and its focus is at (3,5), the function that the graph represents will be y = 1/16 (x - 3)².
How to illustrate the parabola?From the information given, the vertex of a parabola is at the point (3,1), and its focus is at (3,5). The equation of the parabola will be:
(x - 3)² = 4a(y - 1)
The length is measured along x = 3. The final equation of the parabola will be:
(x - 3)² = 4 × 4(y - 1) = 16(y - 1)
Therefore, rearranging the equation will become:
y = 1/16 (x - 3)².
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Answer:
why would you ask question with no answer options an think to get the same right answer ?
Step-by-step explanation:
I need help on this. & I'll give brainlyest to anyone who can solve it for me. Thank's!!!!
Answer:
I can helpyou with that but im not sure with it
What is the length of st given s (-3, 4) and t (1, 0)
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{0})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[1 - (-3)]^2 + [0 - 4]^2}\implies d=\sqrt{(1+3)^2 +(-4)^2} \\\\\\ d=\sqrt{32}\implies d\approx 5.66[/tex]
Kayla drew a right triangle. Which could be the lengths of the triangle's sides?
A. 12 cm, 25 cm, 37 cm B. 9 cm, 16 cm, 25 cm
C. 8 cm, 14 cm, 17 cm D. 7 cm, 24 cm, 25 cm
Answer:
A triangle has side lengths 10 feet, V205 feet, and V105 feet
Step-by-step explanation:
Write the expression for the steps "12 increased by 4 and then double it." Then solve.
Erica buys a package of note cards costing $1.44. She gives the cashier
$5.00. The cashier gives her her change using the least number of coins and
bills possible. How many of each coin or bill does she receive?
Answer:
See below.... several options
Step-by-step explanation:
Change is $3.56
3 dollar bills one 50 c piece one nickel one penny
(though 50 cent pieces are uncommon.....this may be 2 quarters)
[For a while , there was $ 2 bills
so it could be one 1 dollar bill and one $ 2 bill instead of three dollar bills]
I need help please help me and thank you :))
Answer:
see explanation
Step-by-step explanation:
∠ CZD = 90° , then
∠ CZF = 90° - ∠ FZD = 90° - 40° = 50°
∠ FZD and ∠ AZG are vertically opposite angles and are congruent , so
∠ AZG = 40°
∠ CZF and ∠ GZE are vertically opposite angles and are congruent , so
∠ GZE = 50°
E
∠ AZB + ∠ BZC = 90° , that is
3x - 2 + 32 = 90
3x + 30 = 90 ( subtract 30 from both sides )
3x = 60 ( divide both sides by 3 )
x = 20
Condense the expression to the logarithm of a single quantity.
Answer:
[tex]\log _3\left(\frac{x^{\frac{1}{2}}}{\left(y+8\right)^2}\right)[/tex]
Step-by-step explanation:
-> Apply log rules
[tex]\log _3\left(x^{\frac{1}{2}}\right)-2\log _3\left(y+8\right)[/tex]
->
[tex]\log _3\left(x^{\frac{1}{2}}\right)-\log _3\left(\left(y+8\right)^2\right)[/tex]
-> Apply basic math rules
[tex]\log _3\left(\frac{x^{\frac{1}{2}}}{\left(y+8\right)^2}\right)[/tex]
A group of 50 mothers were asked how many children they have. the
table shows the results.
number of children
number frequency
1
8
2
12
3
10
4.
14
5
6
what is the experimental probability of a mother having 1
child?
Answer:
4/25
Step-by-step explanation:
total no of children-15
total no of mothers-50
probability that a mother has i child
1/50
=8/50
=4/25
Answer:
0.16
Step-by-step explanation:
A group of 50 mothers were asked how many children they have. the
table shows the results.
number of children 1 2 3 4 5
number frequency 8 12 10 14 6
What is the experimental probability of a mother having 1
child?
Total number of mothers = 8 + 12 + 10 + 14 + 6 = 50
Number of mothers with 1 child = 8
p(1 child) = 8/50 = 0.16
Is LMN = OPQ? If so, name the congruence postulate that applies. N Given: LM = OP PQ = MN P M = 00 O A. Congruent - SAS O B. Congruent - SSS O C. Might not be congruent O D. Congruent - ASA
Based on the sides of LMN and OPQ, the congruence postulate that applies is B. Congruent - SSS.
When is the SSS rule used?It is used when the two triangles given have three equal corresponding sides which also have equal angles.
All three sides of LMN and OPQ are equal sides and have equal angles and so the SSS rule applies.
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Given: ABCD is a parallelogram. Prove: ∠A ≅ ∠C and ∠B ≅ ∠D Parallelogram A B C D is shown. By the definition of a ▱, AD∥BC and AB∥DC. Using, AD as a transversal, ∠A and ∠ are same-side interior angles, so they are . Using side as a transversal, ∠B and ∠C are same-side interior angles, so they are supplementary. Using AB as a transversal, ∠A and ∠B are same-side interior angles, so they are supplementary. Therefore, ∠A is congruent to ∠C because they are supplements of the same angle. Similarly, ∠B is congruent to ∠ .
A parallelogram is a quadrilateral with four sides. The opposite sides of the parallelogram are equal and parallel.
How to illustrate the parallelogram?The parallelogram is a quadrilateral with equal and parallel sides, such that the interior angles present on the same side of the transversal are supplementary.
The sum of supplementary angles is equal to 180-degrees. From the theorem of same-side interior angles, the supplementary angles present on the parallel lines must be intersected by a transversal.
From the property of transversal, the interior angles on the same side of the transversal are supplementary. Therefore, ∠A and ∠D are supplementary and their sum is equivalent to 180-degrees.
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Answer:
D Supplementary BC D
Step-by-step explanation:
did on edgu 2022 !!
period of f(x)=cos(x)+2
Answer:
The period is 2π
Explanation:
The period is 2 times pi because 2 is the standalone-term multiplied by pi to get the period.
can you go 24.3 miles with 15.3 gallons of gas
Answer:
yes you can go 24.3miles with 15.3 gallons of gas
Step-by-step explanation:
Corrine wrote temperatures in degrees Celsius and the equivalent temperatures in degrees Fahrenheit.
Equivalent Temperatures
Celsius
–10
5
10
20
Fahrenheit
14
41
50
68
Which explains how Corrine could determine if the temperatures vary directly?
Compare the equivalent temperatures as a ratio; if the ratios are equivalent, then the temperatures vary directly.
Draw a graph of the temperatures; if the points form a straight line, then the temperatures vary directly.
Write an equation that converts one temperature to another; if the temperatures satisfy the equation, then they vary directly.
Look for a pattern in the table; if the pattern is consistent, then the temperatures vary directly.
Draw a graph of the temperatures; if the points form a straight line, then the temperatures vary directly , Option B is the correct answer.
What is Direct Variation ?When a quantity of one variable is increased and the value of the other also increases then they are said to be in direct variation.
For the data to be in direct variation
Draw a graph of the temperatures; if the points form a straight line, then the temperatures vary directly.
The points in any linear equation can only fluctuate directly, therefore all points will lie on the same line.
Option B is the correct answer.
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Answer:
ez b
Step-by-step explanation:
What is the value of angle C
Answer:
around 190
Step-by-step explanation:
The measure of angle is 0 is 7pi/4. The measure of its reference angle is ___ °, and tan 0 is ____
Answer: pi/4 and -1
Step-by-step explanation:
Please help! This is a problem that is relatively easy but I still need help!
Answer:
Hi,
Step-by-step explanation:
The triangles CBA and DEA are equals ( 3 sides 2 to 2 equals), angles CAB and DAE are also equals:
6t-12=18-4t
10t=30
t=3(°)
angle CAB=6t-12=6*3-12=6(°)=angle(DAE)
angle BCA=(180-6)/2=87(°)=angle CBA=angle (ADE)=angle(DEA)
answer asap!!! please
Answer:
D.
Step-by-step explanation:
You can see it in the graphs after you plot it.
find the value of x and y
Answer:
x= 131
y = 49
Step-by-step explanation:
X and 49 form a straight line so they add to 180
x+49 = 180
x = 180-49
x =131
49 and y are alternate interior angles and alternate interior angles have the same value
y = 49
Step-by-step explanation:
please mark me as brainlest
50 POINTS HELP ME PLEASE ITS GEOMETRY
Answer:
x is the midpoint of a segment in the diahram
Answer:
x is mid point
Step-by-step explanation:
I hope it's helpful for
this is due today. help please
In the triangle represented in the diagram, The value of X is: 23°
Meaning of a TriangleA triangle can be defined as a plain shape that has three sides, three edges and three angles.
A triangle is majorly defined as a shape that possesses three angles and their interior angles sum up to 180°
In conclusion, in the triangle represented in the diagram, The value of X is: 23°
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Considering the sum of the internal angles of a triangle, it is value that the value of x is of x = 23º.
What is the sum of the internal angles of a triangle?A triangle has three angles, and their sum is of 180º.
In this problem, the angles are:
x, 67º, 90º.
Hence:
x + 67º+ 90º = 180º.
x = 23º.
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Helen purchased 3 copies of a book online at a 20% discount. She also paid $10 for shipping that was not discounted. How much was the original price of one copy of the book if her total ended up being $40?
Answer:
The original price of the book was $12.50
Step-by-step explanation:
3x - 0.2(3x) + 10 = 40
30x - 2(3x) + 100 = 400
30x - 6x + 100 = 400
24x + 100 = 400
24x = 300
x = 12.50
High school geometry. help is needed, please and thank you.