f(x)=x²−4x−21
The degree is the biggest power of x. That's a polynomial of degree 2, also called a quadratic function. Let's find its zeros.
0 = x²−4x−21 = (x - 7)(x+3)
x=7 or x=-3
The fundamental theorem guarantees every non-constant polynomial with complex coefficients has a complex zero, let's call it r. If we divide the polynomial by x-r there won't be any remainder and we'll get a new polynomial, one degree less. The fundamental theorem again applies and (if it's not a constant polynomial) we are assured of another zero, s. We divide by x-s and get a new polynomial of degree one less. We repeat all this until we get a constant polynomial (degree zero). So we get a zero for every degree. They're not necessarily all different.
Answer:
The degree of f(x) is 2. The Fundamental Theorem of Algebra guarantees that a polynomial equation has the same number of complex roots as its degree. This means that f(x) has exactly 2 zeros. Those zeros are 7 and -3.
In a certain room, there are 28 women and 21 men. What is the ratio of
men to women? What is the ratio of women to the total number of
people?
Answer:
The men to women ratio is 3 : 4The ratio between women to total number of people is 4 : 7Step-by-step explanation:
Men to women ratio = 21 : 28 or 3 : 4
The men to women ratio is 3 : 4
Total people = 21 + 28 = 49 people
The ratio of women to total number of people is
28 : 49 or 4 : 7
The ratio between women to total number of people is 4 : 7
I want help! Please
Pocket allowance of 5 students respectively are:
125, 75, 150, 175, 200
Find out arithmetic mean.
Answer:
145
Step-by-step explanation:
125+75+150+175+200= 725
725÷5=145
Answer:
145
Step-by-step explanation:
(125+75+150+175+200)÷5
725÷5= 145
A chemical is studying the properties of a gas under various conditions. He observes that when the gas is at room temperature and low pressure, it behaves as an ideal gas. When the gas is cooled to 10 kelvin and is placed under high pressure, however, it deviates significantly from an ideal gas.
Answer;
Explanation:
CHECK THE COMPLETE QUESTION BELOW:
chemist is studying the properties of a gas under various conditions. He observes that when the gas is at room temperature and low pressure, it behaves as an ideal gas. When the gas is cooled to 10 kelvin and is placed under high pressure, however, it deviates significantly from an ideal gas. Explain these observations.
ideal gas reffered to as one that has the collisions between its atoms or molecules perfectly eleastic and in which there are no intermolecular attractive forces existing between them. The ideal gas concept is important because it obeys the ideal gas law.
Which is PV=nRT
Where P is the pressure
T is the Temperature
V is the Volume
R is ideal gas constant
n is amount of substance
The ideal gas model assumes that gas particles experience no intermolecular attractions. These are the behavior of gases under different condition
✓At low temperature, gas particles move slowly.
-✓At high pressures, gas particles are very close together.
✓ When the particles of gases are close they have low speed and their low speed allow intermolecular forces to become important at high pressure and low temperature.
OBSERVATION S:
At room temperature which is comfortable ambient temperature, generally taken as about 20°C to 25C
Gases behave non ideally at cold temperatures, So when the gas is cooled to 10Kelvin, molecules are moving relatively slowly past one another, then they give room for the repulsive and/or attractive forces between their molecules giving room for deviation from an Ideal Gas.
The intermolecular forces cause the gas to deviate from ideal behavior So, the reason why a gas deviate from ideal behaviour may be due to some two assumptions of kinetic theory of gases. The forces of attraction between gas molecules are negligible. When the gas is placed under high pressure the gas molecules get more crowded and the amount of empty space between the molecules is reduced.
--
Answer:
Ideal gas explains the property of gas that has no inter-molecular attractions irrespective of temperature and pressure.
Explanation:
Ideal gases assumes that the gases would experience no inter-molecular attraction and collision with other gases.
These gases are perfectly exhibiting elastic collision in nature.
The particle of gases moves slowly at lower temperature and the gases would become close when they exhibit high pressure.
The "closeness of the gas-particle" and "low-speed characteristics" are the important observations noted.
The inter-molecular forces deviate the property of gases from ideal gas behavior.
Step-by-step explanation:
Aunt Patricia has a large farm, which contains a right triangular area where her house and gardens are
located. She also has three square pastures where she keeps her milk cows. Aunt Patricia has written a
will. In the will, she leaves the triangular area with house and garden to a local charity. But she leaves
the three square pastures to her two nieces, Mia and Erika.
The side length of the smallest square pasture is 24 meters, and the area of the middle-size square
pasture is 1,024 square meters.
1. What is the area of the smallest square pasture? _________________________ square meters
Show how you figured it out.
2. What is the side length of the middle-size square pasture? ______________________ meters
Show how you figured it out.
In Aunt Patricia’s will, she gave the large pasture to Mia and the two smallest pastures to Erika.
3. What is the side length of Mia’s square pasture (large pasture)? ____________ meters
What is the total area of Mia’s pasture? ______________________________ square meters
Show how you figured it out.
4. The nieces don’t think the will is fair. Explain to them why, in this case, it is fair. Justify your
explanation with mathematics.
__________________________________________________________________
Answer:
see below
Step-by-step explanation:
The smallest size has area b^2
A = s^2
A= b^2 = 24^2 =576 m^2
The middle size has area a^2
1024 = a^2
Take the square root of each side
sqrt(1024) =sqrt(a^2)
32 = a
The side length is 32 m
To find the side length of the largest pasture use the pythagorean theorem
a^2 + b^2 = c^2
32^2 + 24^2= c^2
1024+576 = c^2
1600 = c^2
Taking the square root of each side
sqrt(1600) = sqrt(c^2)
40 = c
The side length is 40 m
The area is 1600 m^2
It is fair since the areas are the same.1600 m^2 = 1600 m^2
3 x 4 x 5 x m x n = ???????
what does it equal???
The equivalent expression for the given expression is 60mn.
The given expression is 3×4×5×m×n.
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
Here, 3×4×5×m×n = 60mn
Therefore, the equivalent expression for the given expression is 60mn.
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PLZ HLP MEEEEEEEEEEEEEEE the table below shows what 300 boxer students ate for lunch on friday. what is the ratio of the number of students who ate soup to the number of students who did not eat soup?
Answer:
number of students who ate soup = 60
number of students who didn't ate soup
= 300-60
= 240
60/240 = 1/4
Find the circumference of the circle.
Use 3.14 for Pi
c=2pi r
13 cm
Give your answer to the nearest hundredth.
Answer:
81.64
Step-by-step explanation:
2(3.14)=6.28
6.28*13=81.64
Plug r into the equation provided...
c = 2(3.14)(13)
c = 81.64cm
Simplify this algebraic expression completely.
8y-2(y + 4)
A. 6y + 4
B. 6y + 2
C. 6y-8
D. 6y - 4
Answer:
C.) 6y-8
Step-by-step explanation:
8y-2(y+4)
8y-2y-8
6y-8
So answer is C
Answer:
Option C
Step-by-step explanation:
[tex]8y-2(y+4)\\\\\text{Distribute:}\left \{ {{-2*y=-2y} \atop {-2*4=-8}} \right. \\8y-2y-8\\\text {Combine like terms:}\\8y-2y=6y\\\text {We are left with:}\\\boxed {6y-8}\\\text {This is the simplest form of the equation. Option C should be the correct answer.}[/tex]
Please help! Correct answers only!
Out of 100 tickets in a raffle, one ticket will win a $150 prize, one ticket will win a $130 prize, one ticket will win a $110 prize, and one ticket will win a $40 prize. The rest will win nothing. If you have a ticket, what is the expected payoff?
Answer:
" Expected Payoff " = $ 4.30
Step-by-step explanation:
Consider the steps below;
[tex]Probability of Winning the 150 Dollar Prize - 1 / 100,\\Probability * Money Won = " Expected Payoff " For The 150 Dollar Prize,\\\\1 / 100 * 150,\\" Expected Payoff " - 1.5 Dollars,\\\\Probability of Winning the 130 Dollar Prize - 1 / 100,\\\\1 / 100 * 130,\\" Expected Payoff " - 1.3 Dollars,\\\\Probability of Winning the 110 Dollar Prize - 1 / 100,\\\\1 / 100 * 110,\\" Expected Payoff " - 1.1 Dollars,\\\\Probability of Winning the 40 Dollar Prize - 1 / 100,\\\\[/tex]
[tex]1 / 100 * 40,\\" Expected Payoff " - 0.4 Dollars,\\\\Conclusion ; " Expected Payoff " = 1.5 + 1.3 + 1.1 + 0.4 = 4.30 Dollars[/tex]
Solution ; " Expected Payoff " = $ 4.30
Make a table as shown in the diagram below. X represents the winnings, P(X) is the probability of getting such winnings. The third column X*P(X) represents the product of the first two columns. After you figure out every value in the third column, you add everything up to get the final answer.
A shopkeeper sold a watch for Rs 810 at 10% loss. How much did he pay to buy the watch ?
Answer:
Rupees 891
Step-by-step explanation:
If you multiply 810 times 0.1 which is the decimal of 10%, you get 81 which you can add to 810 to get 891 which is the price the shopkeeper payed to buy the watch.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
Can anyone help me solve this equation? 4b+11=39
Emily convinced her mom to buy a giant box of her favorite cereal. Her mom doesn't think the box will fit on their shelf. The volume of the box is 10,000cm^3 cubed. The base of the box is 25 cm by 10 cm.
Answer:
Complete question:
Emily convinced her mom to buy a giant box of her favorite cereal. Her mom doesn't think the box will fit on their shelf. The volume of the box is 10,000 cm^3 cubed. The base of the box is 25cm by 10cm.
How tall is the box of cereal?
Answer: 40cm
Step-by-step explanation:
Given that :
A box is normally in the shape of a cube
formula of volume of a cube;
We want to find the height(tallness)
Volume=LengthxWidthxHeight
Volume = 10,000cm^3
Base of box = 25cm by 10cm,
Base of box = Length × width
Therefore:
Length = 25cm, Width = 10cm
Volume = Lengh × Width × Height
10,000cm^3 = 25cm × 10cm × Height
10,000cm^3 = 250cm^2 × Height
Height = 10,000cm^3 ÷ 250cm^2
Height = 40cm
Let the polynomials A = 7x² + 3xy e B = -3xy.
Determine A + B
a) 7x²
b) 3xy
c) 7x² + 6xy
d) 14x² + 6xy
e) -3xy
Answer:
The answer is A.
Step-by-step explanation:
You have to add up both polynomials together :
A = 7x² + 3xy
B = -3xy
A + B = 7x² + 3xy + (-3xy)
= 7x² + 3xy - 3xy
= 7x²
What is the length of the side labeled x?
Answer:
AB = 42.15 units
Step-by-step explanation:
In triangle ABD,
By applying Cosine rule in this triangle,
cos(30)°= [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{\sqrt{3} }{2}[/tex] = [tex]\frac{AD}{AB}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{AD}{47}[/tex]
AD = [tex]\frac{47\sqrt{3}}{2}[/tex]
By applying tangent rule in ΔACD,
tan(44)° = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
tan(44)° = [tex]\frac{AD}{x}[/tex]
0.9657 = [tex]\frac{\frac{47\sqrt{3}}{2}}{x}[/tex]
0.9657 = [tex]\frac{47\sqrt{3}}{2x}[/tex]
x = [tex]\frac{47\sqrt{3}}{2(0.9657)}[/tex]
x = 42.15
≈ 42.2 units
in need of help, PLEASEEEE AND THANK YOUUUUUUUUUU <3
Answer:
y = 3/2x - 4
Step-by-step explanation:
Slope-intercept form is y = mx + b
When we count rise over run, we get 3/2
y = 3/2x + b
The line intersects the y-axis at -4
y = 3/2x - 4
I hope this helps :))
Evaluate (x + y)^0for x = -3 and y = 5.
-1/2
2
1 0
Answer: 2
Step-by-step explanation:
[tex](-3+5)^0=2[/tex]
The following pie chart represents how many absences the students of Washington Middle School had during the first quarter. What percentage of the students had less than two absences during the first quarter?
Answer:
68
ignore the rest of this i need 20 charecters
Answer:
68%
Step-by-step explanation:
What is 4+4 will mark as brainliest
Answer:
8
Step-by-step explanation:
if you have 4 books and I add you another 4 books you will have 8 books altogether.
An entry level programmer's annual pay is $58.916 based on 52 weeks per year. Due to the economy, his company is having to cut back on
the number of weeks that it employs its programmers. If the firm cuts the work year to 51 weeks but keeps the same rate of pay, how
much should the programmer expect his annual pay to decrease? Round your answer to the nearest dollar
Answer: $1133
Step-by-step explanation:
Programmer's pay for 51 weeks will be
(51 * 58916) / 52 = 57,783
Loss in salary
= 58916 - 57783 = 1133
A (x+4,y-2)
B (x+2,y-1)
C (x-2,y+1)
D (x-4,y+2)
[tex]answer \\ = (x - 2, y + 1) \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment... \: [/tex]
Please answer correctly !!!!! Will mark brainliest !!!!!!!!!
Answer:
The width is 2x+1
Step-by-step explanation:
10x^2 +5x
Divide this by 5x
10x^2 /5x = 2x
+
5x/5x =1
Add this together
2x+1
The width is 2x+1
Answer:
( 2x + 1 )
Step-by-step explanation:
10x^2 + 5x
it could also be;
5x (2x + 1)
so, the width is( 2x +1)
from this equation, y=12x+1, which of these are true?
the slope is 12
the x intercept is 1
the slope is 1
the y intercept is 12
Answer:
the slope is 12
Step-by-step explanation:
y=12x+1 is from the formula y=mx+b where m is the slope and b is the y-intercept.
Since 12 has replaced m, it is the slope.
Since 1 has replaced b, it is the y-intercept.
"the slope is 12" is the correct answer choice.
Joey is at the pet store wanting to purchase a puppy. The cost of the puppy is $65. He will need to purchase supplies for his new puppy. The puppy food and training pads are the same price. If Joey spends $97 on this total purchase, how much would the puppy food and training pads cost? Explain your answer.
Answer:
97 - 65 = $32 for both the puppy food and training pads
32 / 2 = $16 for the puppy food and $16 for the training pads
somebody help me please i will mark you the brainliest
Answer:
I guess it's the 3rd one as well
Part 3. Identify the X intercepts for
y = (x+4)^2-9
Answer:
x = -1 or x = -7
Step-by-step explanation:
y = (x + 4)^2 - 9
To find x-intercept, set y = 0
=> (x + 4)^2 - 9 = 0
=> ( x + 1)( x + 7) = 0
=> x = -1 or x = -7
To find the x intercepts, plug in y = 0 and solve for x
y = (x+4)^2 - 9
0 = (x+4)^2 - 9 ... replace y with 0
9 = (x+4)^2
(x+4)^2 = 9
x+4 = plus/minus sqrt(9)
x+4 = sqrt(9) or x+4 = -sqrt(9)
x+4 = 3 or x+4 = -3
x = 3-4 or x = -3-4
x = -1 or x = -7 You have the correct answers. Nice work.-----------------------------------------------------------------
Checking each answer:
Plug x = -1 into the original equation. You should get y = 0 as a result
y = (x+4)^2 - 9
y = (-1+4)^2 - 9
y = (3)^2 - 9
y = 9-9
y = 0 .... so this confirms x = -1 as a solution
The same should apply for the other potential solution x = -7
y = (x+4)^2 - 9
y = (-7+4)^2 - 9
y = (-3)^2 - 9
y = 9-9
y = 0 .... this confirms x = -7 as well
what kind of growth model (pattern) is showen in the table x 1, 2, 3, 4, 5 y 5, 25, 125 ,635 ,3,125
Answer:
x= AP, y= GP
Step-by-step explanation:
x = 1, 2, 3, 4, 5 - difference in terms = 1, this is AP
y = 5, 25, 125, 625, 3125 - the ratio of increase= 5, this is GP
Answer:
x= AP, y= GP
Step-by-step explanation:
*I WILL MARK YOU BRAINLIEST!!!* Whose football reaches a greatest height?
Answer:
Austin's football
Step-by-step explanation:
If you graph the equation for James's ball, you will find that the maximum height is at 5.125 feet. For Austin, it is over 8 feet. Therefore, Austin's ball goes higher. Hope this helps!
Answer:
austin's
Step-by-step explanation:
At the end of the first round of a game, Luis has a score of -5 points. At the end of the second round, he has a score of 3 points. How many points did he score in the second round? Complete this model to represent the problem: score at the end + = ? of the first round
Circle O is shown. 2 tangents intersect at a point outside of the circle which is labeled Satellite. The angle formed is 20 degrees and the measure of the first arc formed is x. One tangent intersects the circle at a point labeled Earth.
A satellite views the Earth at an angle of 20°. What is the arc measure, x, that the satellite can see?
Answer:
Your answer is 160
Step-by-step explanation:
Just did this on edg.
The measurement of asked arc is 160°.
What is the arc of a circle?An arc is defined as a portion of the boundary of a circle or a curve. It can also be referred to as an open curve. The boundary of a circle is the perimeter or the distance around a circle, also known as the circumference.
Given that. the two tangents intersect at a point outside the with circle center O
The angle formed between the two tangent = 20°
The first arc formed is measured as x°, which is the arc opposite the point where the two tangents meet = The arc the satellite can see (refer to the attached figure)
The angle x is given by the relationship;
x = 2 × (90 - v/2)
Where;
v = The angle formed at the point where the two tangent meet = 20°
Therefore;
x = 2 × (90 - 20/2) = 2 × (90 - 10) = 2 × 80 = 160°
The arc measure, x, that the satellite can see = 160°.
Hence, the measurement of asked arc is 160°.
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The price of a train ticket consists of an initial fee plus a constant fee per stop. The table compares the number of stops and the price of a ticket (in dollars). What is the initial fee?
Answer:
Initial Fee is $2.
Step-by-step explanation:
