Answer:
The equation has one real root and two complex roots.
Step-by-step explanation:
The given equation is
[tex]x^3-3x^2+4x-12=0[/tex]
The above equation is true form x=3, therefore (x-3) is a factor of above equation.
Use long division or synthetic division method to divide the equation by (x-3).
[tex](x-3)(x^2+4)=0[/tex]
Equate each factor equal to zero.
[tex]x-3=0[/tex]
[tex]x=3[/tex]
Therefore 3 is a real root of the equation.
[tex]x^2+4=0[/tex]
[tex]x^2=-4[/tex]
[tex]x=\sqrt{-4}[/tex]
[tex]x=\pm 2i[/tex]
2i and -2i are complex roots of the equation.
Therefore the equation has one real root and two complex roots.
How many possible three-digit passwords can be formed using digits 0 through 9 if digits are repeated?
30 ,
720 ,
1,000 ...?
Answer:
The correct option is 3.
Step-by-step explanation:
Total digits 0 to 9 are
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Total number of digits is 10. It means total possible ways to select the first digit of the password is 10.
Since the reparation is allowed, therefore the possible ways to select the second and third digit of the password is 10.
Total possible ways to form a three-digit passwords is
[tex]10\times 10\times 10=1000[/tex]
Therefore the correct option is 3.
There are 1,000 possible three-digit passwords that can be formed using the digits 0 through 9 when repetition of digits is allowed, calculated as 10 possibilities for each of the three positions (10 x 10 x 10).
To determine how many possible three-digit passwords can be created using the digits 0 through 9 with repetition allowed, we consider each of the three positions in the password separately. For each position, we can use any of the 10 digits (0-9), leading to 10 possibilities for each digit.
Therefore, the total number of combinations for a three-digit password is:
First digit: 10 possibilities (0-9)Second digit: 10 possibilities (0-9)Third digit: 10 possibilities (0-9)By the rule of product, we multiply the possibilities for each digit:
10 imes 10 imes 10 = 1,000
Thus, there are 1,000 possible three-digit passwords when digits can be repeated.
Select Is a Function or Is not a Function to correctly classify each relation.
Title
Is a Function
Is not a Function
{(3, 7),(3, 6),(5, 4),(4, 7)}
{(1, 5),(3, 5),(4, 6),(6, 4)}
{(2, 3),(4, 2),(4, 6),(5, 8
{(0, 4),(3, 2),(4, 2),(6, 5)}
Answer:
{(3, 7),(3, 6),(5, 4),(4, 7)} → is not a Function{(1, 5),(3, 5),(4, 6),(6, 4)} → is a Function{(2, 3),(4, 2),(4, 6),(5, 8)} → is not a Function{(0, 4),(3, 2),(4, 2),(6, 5)} → is a FunctionStep-by-step explanation:
A relation from a set X to a set Y is called a function, if each element of X is related to one and exactly one element in Y. Though many elements of X can be related to one element in Y (many to one).
{(3, 7),(3, 6),(5, 4),(4, 7)} → is not a Function (as (3, 7), (3, 6) share same x)
{(1, 5),(3, 5),(4, 6),(6, 4)} → is a Function
{(2, 3),(4, 2),(4, 6),(5, 8)} → is not a Function (as (4, 2), (4, 6) share same x)
{(0, 4),(3, 2),(4, 2),(6, 5)} → is a Function
Answer: ^^^ that person was correct
Step-by-step explanation:
If f'(x)=g'(x) for all x in an interval I, what is the relationship between f and g ...?
Which of the following is something that will not affect your homeowners insurance premium? a. the distance of the home from a school b. the distance of the home from a flood plain c. the distance of the home from a fire station d. the distance of the home from a fire hydrant
Answer:
a. the distance of the home from a school
Step-by-step explanation:
The distance your home is from a flood plain can potentially increase your homeowner's insurance. If your house is close to a flood plain, your insurance will increase.
The distance your home is from a fire station or a fire hydrant either one can lower your insurance. If your home is within so many feet of a hydrant, you get a discount on your insurance; if it is close enough to a fire station, you get a discount as well.
Since the distance a home is from a school has no bearing on the cost of repairing or replacing the home, this will not affect your homeowner's insurance.
What is the simplified form of 48 over 192??
Answer: The simplified form of 48 over 192 is 1 over 4.
Step-by-step explanation:
Since, A fraction is in its simplest form when the numerator and denominator cannot be any smaller, while still being whole numbers.
Also, for find the simplified form of a fraction,
We divide both numerator and denominator by their H.C.F,
Here, the given fraction is,
[tex]\frac{48}{192}[/tex]
Since, 48 = 2 × 2 × 2 × 2 × 3
192 = 2 × 2 × 2 × 2 × 2 × 2 × 3
H.C.F(48,192) = 2 × 2 × 2 × 2 × 3 = 48
[tex]\implies \frac{48/48}{192/48}=\frac{1}{4}[/tex]
Hence, The simplified form of 48/192 is 1/4.
The simplified form of 48/192 is 1/4.
First, let's find the GCD of 48 and 192.
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
The factors of 192 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192.
The common factors are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
So, the greatest common divisor (GCD) of 48 and 192 is 48.
Now, we divide both the numerator and denominator by 48:
48/48 = 1
192/48 = 4
Therefore, the simplified form of 48/192 is 1/4.
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Which one is the greater quantity 1/3 of a box of corn crinkles or 50% of a box of corn krinkles
During which two time intervals does the particle undergo equal displacement?
Choices:
a) AB & BC
b) AB & DE
c) BC & DE
d) CD & DF
It’s AB and DE so it would be b
A consistent system of equations is a system with __________.
the same line
parallel lines
intersecting lines and lines that have the same slope
intersecting lines and lines that have the same equation
Jasmine wants to use her savings of $1,128 to buy video games and music CDs. The total price of the music CDs she bought was $72. The video games cost $43 each. What is the maximum number of video games that Jasmine can buy with her savings?
24
25
26
27
Answer: 24 video games
Step-by-step explanation: jasmine has 1,128 bucks originally. she gets some megadeth and metallica cd's (cause if she's got taste, that's probably what she got) and that adds up to 72 bucks. now she wants to buy a whole bunch of video games, which cost 43 each (imagine she got fortnite mod's. ew) so we put that in an equation-
$1,128 - $72 = $1,056
$1,056 divided by 43 equals 24.55813953488372.
when dealing with money, you always round down, so the total number of games she bought was 24
please mark brainliest
Emily has a coupon for 20% off her purchase. She finds a backpack on the discount rack. It's original price is $60 but is 30% off. Emily thinks 30% & 20 % make 50% so the backpack will be $30. Is Emily correct? Explain your answer.
lim cos(pi+h)+1 / h
h->0
evaluate the limit
Use you graph to estimate the value of x when y = 2. How would you work that out?
Which equation shows the quadratic formula used correctly to solve 7x2 = 9 + x for x?
Answer:
Quadratic formula for given equation is [tex]x=\frac{-(-1)\pm\sqrt{(-1)-4(7)(-9)}}{2\times7}[/tex]
Step-by-step explanation:
Given Quadratic Equation is 7x² = 9 + x
We need to find correct Quadratic formula for the given quadratic equation.
If the quadratic equation is in standard for,
ax² + bx + c = 0
then quadratic formula is given by,
[tex]x=\frac{-b\pm\sqrt{b-4ac}}{2a}[/tex]
First we rewrite the quadratic equation,
7x² - x - 9 = 0
by comparing with standard form of equation we get,
a = 7 , b = -1 and c = -9
oNw putting these value in quadratic formula we get,
[tex]x=\frac{-(-1)\pm\sqrt{(-1)-4(7)(-9)}}{2\times7}[/tex]
Therefore, Quadratic formula for given equation is [tex]x=\frac{-(-1)\pm\sqrt{(-1)-4(7)(-9)}}{2\times7}[/tex]
I need help on this asap i'll give you so many points!!
what times what equals 429
What is equivalent to 3/4 (3y 15)?
Christian is rewriting an expression of the form y = ax2 + bx + c in the form y = a(x – h)2 + k. Which of the following must be true?
h and k cannot both equal zero
k and c have the same value
the value of a remains the same
h is equal to one half –b
Quadratic equations can be expressed in standard form or in vertex form.
The true statement about [tex]\mathbf{y = ax^2 + bx + c}[/tex] and [tex]\mathbf{y = a(x - h)^2 + k}[/tex] is that: the value of a remains the same
The original expression is given as:
[tex]\mathbf{y = ax^2 + bx + c}[/tex]
He wants to rewrite it as:
[tex]\mathbf{y = a(x - h)^2 + k}[/tex]
Expand the above equation
[tex]\mathbf{y = a(x - h)(x - h) + k}[/tex]
Open brackets
[tex]\mathbf{y = a(x^2 - hx - hx + h^2) + k}[/tex]
[tex]\mathbf{y = a(x^2 - 2hx + h^2) + k}[/tex]
Remove bracket
[tex]\mathbf{y = ax^2 - 2ahx + ah^2 + k}[/tex]
Compare the above equation to: [tex]\mathbf{y = ax^2 + bx + c}[/tex]
[tex]\mathbf{ax^2 = ax^2}[/tex]
[tex]\mathbf{-2ahx = bx}[/tex]
[tex]\mathbf{ah^2 + k = c}[/tex]
Analyzing the above equations
[tex]\mathbf{ax^2 = ax^2}[/tex]
Divide both sides by [tex]\mathbf{x^2}[/tex]
[tex]\mathbf{a = a}[/tex]
The above equation means that, the value of a remains unchanged.
Hence, option (c) is true
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The number 0.1111... repeats forever; therefore, it is irrational. True or False.
The amount of time Ricardo spends brushing his teeth follows a Normal Distribution with unknown mean and standard deviation. Ricardo spends less than one minute brushing his teeth about 40% of the time. He spends more than two minutes brushing his teeth 2% of the time. Use this information to determine the mean and standard deviation of this distribution.
round 0.9874 to the greatest non zero place
y = 3x
x + 2y = -21
Solve the system. Write your answer as an ordered pair (x, y)
Kate ate 1 out of 4 of her orange. ben eat 2 out of 4 of his banana. did kate and ben eat 1 out of 4 add 2 out of 4 equal 3 out of 4 of their fruit? explain
Please solve:
x+y=8.
xy=15. ...?
What is the circumference of the circle in terms of pi? The radius is 2.2
choices are 1.1, 1.21, 2.2 and 4.4
im so confused so could someone please explain what i did wrong?
What is the smallest angle of rotational symmetry for a square
When we rotate a figure and there is no change in the shape of the figure then it has rotational symmetry.
We know that the order of rotation for a square is 4.
Hence, we have [tex]\frac{360}{4} =90^{\circ}[/tex]
Thus, the angle of rotational symmetry of square are
[tex]90^{\circ}, 180^{\circ}, 270^{\circ}[/tex]
Hence, the minimum angle of rotational symmetry is [tex]90^{\circ}[/tex]
Therefore, the minimum angle of rotational symmetry for a square is 90 degrees.
Write9^3 *p without exponents
What is the end behavior of f(x) = (x − 3)2(x + 5)(x − 2)3?
T he end behavior of f(x) can be described as:
As x → -∞, f(x) → +∞
As x → +∞, f(x) → +∞
To determine the end behavior of f(x) = (x − 3)²(x + 5)(x − 2)³, we need to consider the degree and leading coefficient of the polynomial.
1. Degree of the Polynomial:
The degree is the highest sum of exponents of the variable x in any term. In this case:
(x - 3)² contributes a degree of 2 (x² term)
(x + 5) contributes a degree of 1 (x term)
(x - 2)³ contributes a degree of 3 (x³ term)
Adding these degrees, we get a total degree of 2 + 1 + 3 = 6.
2. Leading Coefficient:
The leading coefficient is the coefficient of the term with the highest degree. Since all factors have a leading coefficient of 1, the leading coefficient of the entire polynomial will also be 1 (positive).
3. End Behavior Based on Degree and Leading Coefficient:
Even Degree & Positive Leading Coefficient: When the degree is even and the leading coefficient is positive, both ends of the polynomial will approach positive infinity. In other words, as x approaches both positive and negative infinity, f(x) will also approach positive infinity.
Therefore, the end behavior of f(x) can be described as:
As x → -∞, f(x) → +∞
As x → +∞, f(x) → +∞
Complete question:
What is the end behavior of [tex]f(x) = (x - 3)^{2} (x + 5)(x - 2)^{3}[/tex]?
Is the square root of 100 rational or irrational?
What about the square root of 0.25?
Final answer:
The square root of 100 is rational, as is the square root of 0.25.
Explanation:
The square root of 100 is a rational number. A rational number is a number that can be expressed as a quotient or fraction of two integers, where the denominator is not zero. In this case, the square root of 100 is 10, which can be written as 10/1, making it a rational number.
The square root of 0.25 is also a rational number. The square root of 0.25 is 0.5, which can be expressed as 1/2, making it a rational number.
Cylinder has a height of 14 centimeters and its circle bases have a radius of 10 centimeters. find the surface area of the cylinder.
2(100 ) + 140 square centimeters
1,400 + 140 square centimeters
2(100 ) + 280 square centimeters
2(1,400 ) + 2(140 ) square centimeters
Find the 9th term of the following geometric sequence: 1, –3, 9, –27. PLEASEEEEE HELP!!!!!!
A. –5,661
B. 7,241
C. –2,456
D. 6,561