The domain of y equals two divided by the quantity x minus three squared all minus one [y = (2)/(x - 3)² - 1] is: all real numbers.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.
This ultimately implies that, a domain is the set of all possible input numerical values or numbers (x-values) to a function and the domain of a graph comprises all the input numerical values which are located on the x-coordinate.
Translating the word problem into an algebraic equation, we have;
y = (2)/(x - 3)² - 1
When x = 3, we have:
y = (2)/(3 - 3)² - 1
y = 2/-1 = -2
When x = 1, we have:
y = (2)/(1 - 3)² - 1
y = 2/3
In conclusion, the domain of this function is all real numbers.
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I need help me thank you
Step-by-step explanation:
s = 17b
when b =2:
s = 17b
s = 17(2)
s = 34
when b = 4
s = 17b
s = 17(4)
s = 68
2
Select the correct answer.
Which interval describes where the graph of the function is positive?
-8
O
O
O
B.
A. -∞ <<∞
C.
A
D.
N
-∞ < x < -1
-8∞ < < -2
-2 < < -1
Ň
-6
-8
-N
6 8
Option B is the correct answer, the interval in which the graph of the function is positive is -∞ < x < -1.
What do mean by interval?
In mathematics, a (real) interval is a collection of real numbers that includes all real numbers that fall inside any two of the collection's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1. The set of all real numbers, the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton are additional examples of intervals.
As we can see in the graph provided in the question, the graph of function reach the positive side of the y-axis at x = -1, it means one of the two end point of the interval is going to be -1. And, the graph is constantly and slowing increasing it's value as increase in the x-axis therefore, the other endpoint of the interval cab be considered as negative infinity.
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HELP ME!!! Need a new answer for this so it’s my “own”!!!
Question 1 (Essay Worth 10 points)
(06.01, 06.02 HC)
Part A: Create a fourth-degree polynomial in standard form. How do you know it is in standard form? (5 points)
Part B: Explain the closure property as it relates to polynomials. Give an example. (5 points)
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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Can anyone write the equation of the graph?
Answer:
use absolute value
Step-by-step explanation:
absolute of x +5
What are the like terms in the expression 8 + x squared minus 4 x cubed + 5 x + 2 x squared?
8, 5 x
x squared, 2 x squared
8, 5 x 2 x squared
x squared, Negative 4 x cubed, 2 x squared
In the expression, 8 + x squared minus 4 x cubed + 5 x + 2 x squared.
2x^2 and x^2 are the like terms
How to find the like terms in the expressionThe given expression is 8 + x squared minus 4 x cubed + 5 x + 2 x squared
This is rewritten as
8 + x^2 - 4x^3 + 5x + 2x^2
The terms in the expression are grouped as
constant terms: 8
terms with x variable : 5x
terms with x^2 variables: 2x^2 and x^2
terms with x^3 variables: 4x^3
Like terms refers to terms that are similar either as a constants or have same variables
Hence the like terms in the expression is 2x^2 and x^2
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f(x)=x²-5x - 9
Find f(-9)
Answer:
117
Step-by-step explanation:
f(-9)=-9^2-5(-9)-9
f(-9)=81+45-9
f(-9)=126-9
f(-9)=117
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help
Simplify the ratio of 0,5 kg: 250 g
Answer:
2:1
Step-by-step explanation:
.5 kg : 250g
the units must be same at both sides
500g : 250g
{as 1 kg = 1000g}
by simplifying both sides
10g : 5g
2g : 1g
2:1
6) In Jim’s school, there are 3 girls for every 2 boys. There are 800 students in total. Using this information, how many students are girls?
A. 260
B. 320
C. 480
D. 390
Answer:
C) 480
Step-by-step explanation:
Ratio:
[tex]\sf \dfrac{3}{5}*800 = 3 * 160[/tex]
= 480
Antonio has read at most 8 more books than Benji. If Benji has read 38 books, at most how many books has
Antonio read?
Solve x² + 5x - 14 = 0
By solving the equation x² + 5x - 14 = 0 get the value of x is 2 or -7.
Given,
In the question:
To solve the equation:
x² + 5x - 14 = 0
Now, According to the question:
x² + 5x - 14 = 0
Split the middle term into two terms :
x² - 2x + 7x - 14 = 0
Factor the first two terms and the last two terms separately
x(x - 2) + 7 (x -2) = 0
Factor out
(x - 2) (x + 7) = 0
Apply Zero Product Property
x - 2 = 0 or x + 7 = 0
x = 2 or x = -7
Hence, By solving the equation x² + 5x - 14 = 0 get the value of x is 2 or -7.
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(DUE IN 2 HOURS PLEASE HELP) Find an equation for the line that passes through the points (5, 2) and (-4, 5).
Answer:
Y= -1/3x+11/3
Step-by-step explanation:
24.15 as a two significant figures?
24.15 as two significant figures is 24.
What are significant figures?All significant figures are those that enhance the overall worth of the number's meaning. Numbers are frequently rounded to avoid repeating quantities that are not significant. When rounding, one must be careful not to lose precision. Sometimes the purpose of rounding numbers is simply to make them simpler.
What are the significant figure's rules?Use the following guidelines to decide which numbers are important and which are not:
1) A decimal number less than 1 is not affected by the zero to the left of it.
2) The placeholders for all trailing zeros are all insignificant.
3. There should be significance between non-zero numbers.
4) Every non-zero number has meaning.
5) A number is rounded if it has more digits than the necessary number of significant ones. For instance, 432,500 is rounded up to 433,000 to three significant digits using the half-up (regular) method.
6) Zeros at the end of numbers that are not important but are left in because eliminating them would change the number's value. The 000 in 433,000 in the example above cannot be removed without converting the number to scientific notation.
Given the number, 24.15
We have to convert it to two significant figures, so we will consider the only two figures before the decimal point. So, the number up to two significant figures is 24.
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First, complete the story below so that it can be represented by the equation 5000-50x=4800-30x
Pool A started with 5000 liters of water, and 50 liters per minute are being (Drained out or Pumped back in)
Pool B started with 4800 liters of water, and 30 liters per minute are being (Drained out or Pumped back in)
The amount of water after x minutes is more in which pool? Pool A or Pool B?
The amount of water after x minutes is equal in both pools.
What is a Linear equation in one variable?
A univariate linear equation is an equation of the form ax + b = 0, where a and b are two integers, x is a variable, and there is only one solution.
For example, 2x+3=8 is a linear equation in one variable.
The given equation is 5000 - 50x = 4800 - 30x.
solving for 'x',
5000 - 50x = 4800 - 30x
5000 - 4800 = 50x - 30x
200 = 20x
x = 200/20
x = 10
The amount of water after 10 minutes in Pool A will be = 5000 - 50(10)
= 5000 - 500
= 450 liters
The amount of water after 10 minutes in Pool B will be = 4800 - 30(10)
= 4800 - 300
= 450 liters.
Hence, the amount of water will be the same in both pools.
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Find where the line 2y - 3x - 7=0 intersects the:
i y-axis
ii x-axis
Answer:
i = 7/2
ii = -7/3
Step-by-step explanation:
The line intersects one of the two axis when the vale of the other axis is 0
When x=0:
2y - 7 = 0
2y = 7
y = 7/2
When y = 0
-3x - 7 = 0
-3x = 7
x= -7/3
rearrange the formula below to make 'a' the new subject:
[tex]c + \frac{1}{2}a^{2}b = d[/tex]
is the bottom answer correct for this question? :
[tex]a = \sqrt{2(\frac{d-c}{b} )}[/tex]
Step-by-step explanation:
c + 1/2 × a²b = d | - c on both sides
1/2 × a²b = d - c | ×2 on both sides
a²b = 2(d - c) | /b on both sides
a² = (2/b) × (d - c) | sqrt on both sides
a = sqrt(2(d - c)/b)
yes, the given answer is correct.
the probability that a visitor to an animal shelter will adopt a dog is 0.10. out of 9 visits, what is the probability that at least (equal to or more than) 1 dog will be adopted?
The probability of having at least one dog adopted is 0.6126
It is given that the probability to adopt a dog is 0.1
The adoption of the dog here clearly follows a Binomial distribution
ⁿCₓ X pˣ X (1 - p)ⁿ⁻ˣ
where,
n = no. os sample
p = probability of success
x = random variable.
Here the success would be the adoption of a dog, We are given here there were 9 visits
Hence,
n = 9
p = 0.1
1 - p = 0.9
we need to find the probability of the adoption of at least one dog
= P(X ≥ 1)
= 1 - P(X = 0)
Hence we get
P(X = 0)
= ⁹C₀ X 0.1⁰ X 0.9⁹
= 0.3874
Hence,
P(X ≥ 1)
= 1 - 0.3874
= 0.6126
Therefore the probability that at least one dog will be adopted is 0.6126
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reimond needs to order crushed rock for a courtyard what is the cost of 4.5 t at $12.50 per tonne?
The cost of 4.5 tonnes of rock is $56.25
Given,
cost of 1 tonne of rock=$12.50
then
to find cost of 4.5 tonnes of rock, multiply 12.50 with 4.5,
cost of 4.5 tonnes of rock = 4.5* 12.50 = $56.25
Thus ,the cost of 4.5 tonnes of rock is $56.25.
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Are you local grocery store? You can buy 3 pounds of rice for 9 dollars use this information to fill in the missing parts
The proportional relationship that gives the cost of x pounds of rice is given as follows:
y = 3x.
What is a proportional relationship?A proportional relationship is a special case of a linear function, with slope represented by k and intercept of 0, hence the output variable y is obtained with the multiplication of the input variable x and the slope k, as follows:
y = kx.
In this problem, the input and the output are given as follows:
Input: pounds of rice.Output: cost.You can buy 3 pounds of rice for 9 dollars use, hence the constant representing the cost per pound is given as follows:
k = 9/3 = 3.
Hence the equation is:
y = 3x.
Missing InformationThis problem is incomplete but we suppose that it asks for a proportional relationship giving the cost of x pounds of rice.
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Evaluate the numerical expression.
7.5 × 6.6 ÷ 0.6 − 15.3
Responses
A 67.2
B 97.8
C −32.25
D 197.25
The required numerical expression is evaluated as 67.2. Option A is correct.
Given that,
An expression is given 7.5 × 6.6 ÷ 0.6 − 15.3, we have to evaluate the given expression.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
= 7.5 × 6.6 ÷ 0.6 − 15.3
Simplify,
= 7.5 × 11 - 15.3
= 82.2 - 15.3
= 67.2
Thus, the required numerical expression is evaluated as 67.2. Option A is correct.
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Solve for v. Write your answers in simplified, rationalized form.
64v^3+1=0
Answer: v=-.25
Step-by-step explanation:
Step 1: Subtract 1 from both sides.
64v^3+1−1=0−1
64v^3=−1
Step 2: Divide both sides by 64.
64v^3 64 = −1 64
v^3= −1 64
Step 3: Take cube root.
v=( −1 64 )^(1/3 )
Step 4: There is no step 4 lol
v=−0.25
Solve for A in terms of I and P.
I=A–P
Answer:
I+P=A
Step-by-step explanation:
isolate a on 1 side
I=A—P
+P. +P
I+P=A
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Answer:
A=P+I
Step-by-step explanation:
make A the subject of formula
giving A= P+I
a line with slope 2 intersects a line with slope 6 at the point (40, 30). what is the distance between the x-intercepts of these two line
The distance between the x-intercepts of these two line is 10 units.
Given that,
These two lines' x-intercepts are separated by 10 units.
Equation of the line with slope 2 is
y-30/x-40 = 2
For x intercept put y = 0,
then
-30/x-40 =2
x =25
Equation of the line with slope 6 is
y-30/x-40 =6
For x intercept put y = 0,
then
-30/x-40 =6
x =35
Distance between x-intercepts of these two lines is difference of the two intercepts i.e,
D = 35-25 = 10.
Thus, the distance between the x-intercepts of these two line is 10 units.
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Write 95% as a fraction or mixed number in simplest form.
Use estimation or fraction multiplication to determine if your answer is reasonable. Calculate the product. 78.93 x 32.45
Answer:
2561.2785
Step-by-step explanation:
All you gotta do is calculate and times 78.93 x 32.45
Find x and m
Giving brainlist to fastest reply that’s correct! Also liking answers for trying to answer <3
Answer:
x=21, m<s=95
Step-by-step explanation:
85+5x-10=180
75+5x=180
5x=105
x=21
m<S= 5(21)-10
m<S= 105-10
m<s=95
A polygon has 7 sides. The interior angle measures are 131°, 119°, 125°, 133°, 125°, 138°, and x°. Find the value of x.
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Your faucet in your kitchen starts leaking. You put a bucket under it. The faucet is leaking at a constant rate. After 5 minutes, there is 300 mL of water in the bucket. What is the pattern rule?
Answer: 60mL per minute
Step-by-step explanation:
300/5=60
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Please Help!
Solve for x:
-18x = 108
Show your work
Answer:
x=-6
Step-by-step explanation:
-18x=108
/-18. /-18
x=-6
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Divide both sides by −18.
x = 108/-18Divide 108 by −18 to get −6.
x=−6You are asked to write an equation for the line of best fit for the scatter plot shown at the right without the use of a graphing calculator. What should you do first? Explain
Answer:
Find the slope between the points (1,2) and (9,12).
Step-by-step explanation:
If I was going to draw the line of best fit without a calculator, I would draw it including these two points. Once I had these two points, I would find the slope using these points.
Your Spanish club is selling T-shirts for $20 each. The club has $400 in its account left over
from last year and needs to have a total of $2000 for a trip. How many T-shirts does your club
need to sell to reach its goal of $2000.
Had:
T-shirts:
otal:
Answer:
80
Step-by-step explanation:
first you need to substract 400 from 2000, then you divide the remaining by 20