Given the quantity of 3 x squared plus x minus 4, all over x minus 1, what are the domain and range?
domain is x is all real numbers where x does not equal negative 1 comma range is y is all real numbers where y does not equal 1
domain is x is all real numbers where x does not equal 1 comma range is y is all real numbers where y does not equal negative 1
domain is x is all real numbers where x does not equal negative 1 comma range is y is all real numbers where y does not equal negative 7
domain is x is all real numbers where x does not equal 1 comma range is y is all real numbers where y does not equal 7
Answers
The domain of the given quantity is all the real numbers except 1.
And range of the function is all the real numbers.
What is domain and range ?All the potential values of the independent variable, x, for which y is specified, constitute the domain and range of a function. Every possible value of the dependent variable y falls inside a function's range.
We have the given quantity
\(\frac{3x^{2} +x-4}{x - 1}\)
So, we can say that now we have a function, let f(x) be the function such that
f(x)= \(\frac{3x^{2} +x-4}{x - 1}\)
As from the fact that, the set of all input values for which this function is defined is called the domain of the function.
And the set of values for the input values is called the range of the given function.
Here, function is not defined for x = 1.
Because if we put x = 1, we get denominator 0. And (something / 0) is not defined.
So, we can input any real numbers for x in function f(x) except 1. Because at x = 1 our function is not defined.
Therefore, the domain of given function f(x) is all the real numbers except 1.
And, if we input all the real numbers in function f(x) we get only real numbers as the output. Therefore, the range of the given quantity or function is real numbers.
Hence, the domain of the given quantity is all the real numbers except 1.
And range of the function is all the real numbers.
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Related Questions
if a^2 = 3a + 1, find the value of (a+1/a)^2
Answers
Answer:First, we can simplify the equation a^2 = 3a + 1 by subtracting 3a and 1 from both sides, to get:
a^2 - 3a - 1 = 0
Now we can factor the left side:
(a-1)(a+1) = 0
This equation tells us that either a-1 = 0 or a+1 = 0. So, a = 1 or a = -1.
Next, we can substitute these values into the expression (a+1/a)^2
For a = 1, (1+1/1)^2 = 2^2 = 4
For a = -1, (-1+1/(-1))^2 = 0^2 = 0
So, the value of (a+1/a)^2 is 4 when a = 1, and 0 when a = -1
Step-by-step explanation:
What is the meaning of "\( \varphi (x,y)\) be \( y\wedge \phi (x)\) "?
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Answers
The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.
The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.
The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.
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Use the cosine of a sum and cosine of a difference identities to find cos (s +t) and cos (s – t).
COS S = -4/5
and sint = 1/5
s and t in quadrant II
Answers
The cosine of a sum and cosine of difference identities are (8√6-3)/25 and (8√6+3)/25 respectively
Given the trigonometry functions:
cos s = -4/5 and sint = 1/5
To find cos(s - t):
cos (s +t) = cos s cost - sins sint
cos(s - t) = cos s cost + sins sint
Get the value of cost and sins
According to SOH CAH TOA identity;
cos s = -4/5 = adj/hyp
hyp^2 = opp^2 + adj^2
5^2 = 4^2 + opp^2
opp^2 = 25 - 16
opp^2 = 9
opp = 3
sin s = opp/hyp
sin s = 3/5
Similarly for cos t
sin t = 1/5 = opp/hyp
ad^2j = 5^2 - 1^2
adj^2 = 25 - 1
adj^2 = 24
adj = 2√6
Get cost:
cost = adj/hyp = -2√6/5 (quadrant II)
Recall that cos (s +t) = cos s cost - sins sint
cos (s +t) = -4/5(-2√6/5) - (3/5)(1/5)
cos(s+t) = 8√6/25 - 3/25
cos(s+t) = (8√6-3)/25
Similarly, cos(s-t) = (8√6+3)/25
Hence the cosine of a sum and cosine of difference identities are (8√6-3)/25 and (8√6+3)/25 respectively
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can i have ten dollahairs
Answers
maybe if you ask politely
PLEASE HELP ASAP ITS TIMED
Which inequality represents all possible solutions of −3(x+5)>12
?
A
x>1
B
x −9
D
x<−9
Answers
Answer:
D. x<-9
Step-by-step explanation:
-3(x+5)>12
x+5<12/-3
x+5<-4
x<-4-5
x<-9
A gardener wants to know if soaking seeds in water before planting them increases the proportion of seeds that germinate. To investigate, the gardener will assign 50 seeds to be soaked before planting and 50 seeds to be planted without being soaked. After two weeks, the gardener will record how many seeds in each group germinated and construct a 95 percent confidence interval for the difference in proportions. Which of the following conditions for inference should be met?
a. The seeds should be randomly assigned to a treatment.
b. The group sizes should be less than 10 percent of the population sizes.
c. The number of successful seeds and unsuccessful seeds in each group should be at least 10.
Answers
Answer:
The condition for inference that should be met is (c) The number of successful seeds and unsuccessful seeds in each group should be at least 10. This condition is related to the assumption of the normal approximation to the sampling distribution of the difference in proportions.
In order to construct a confidence interval for the difference in proportions between the two groups, we need to assume that the difference in proportions follows an approximately normal distribution. This assumption holds if the number of successful and unsuccessful seeds in each group is at least 10. If this condition is not met, the normal approximation may not be valid, and other methods may need to be used to construct a confidence interval.
Condition (a) The seeds should be randomly assigned to a treatment, is important for minimizing bias in the assignment of seeds to the treatment and control groups, but it is not directly related to the conditions for inference.
Condition (b) The group sizes should be less than 10 percent of the population sizes, is related to the assumption of independence between the two groups, but it is not directly related to the conditions for inference.
3.3019 rounded to one decimal places
Answers
Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.
What is the Cubed root of -108
Answers
Answer:
about -4.7622
Step-by-step explanation:
You want the cube root of -108.
CalculatorYour calculator will tell you the cube root of -108 is about -4.7622.
__
Additional comment
Some calculators compute roots using logarithms. Since the logs of negative number are not real, they will give you an error if you try to do this directly. You have to know that the odd index root of a negative number is the opposite of the same root of its absolute value.
The prime factoring of 108 is 2²·3³. Factoring out the perfect cube gives the simplified form ...
∛-108 = -3∛4
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Find the slope of the tangent line to the curve defined by 4x2+5xy+y4=370
at the point (−9,−1)
Answers
Answer:
The slope of the tangent line to the curve at the given point is -11/7.
Step-by-step explanation:
Differentiation is an algebraic process that finds the gradient (slope) of a curve. At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.
Given function:
\(4x^2+5xy+y^4=370\)
To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.
Begin by placing d/dx in front of each term of the equation:
\(\dfrac{\text{d}}{\text{d}x}4x^2+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=\dfrac{\text{d}}{\text{d}x}370\)
Differentiate the terms in x only (and constant terms):
\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=0\)
Use the chain rule to differentiate terms in y only. In practice, this means differentiate with respect to y, and place dy/dx at the end:
\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)
Use the product rule to differentiate terms in both x and y.
\(\boxed{\dfrac{\text{d}}{\text{d}x}u(x)v(y)=u(x)\dfrac{\text{d}}{\text{d}x}v(y)+v(y)\dfrac{\text{d}}{\text{d}x}u(x)}\)
\(\implies 8x+\left(5x\dfrac{\text{d}}{\text{d}x}y+y\dfrac{\text{d}}{\text{d}x}5x\right)+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)
\(\implies 8x+5x\dfrac{\text{d}y}{\text{d}x}+5y+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)
Rearrange the resulting equation in x, y and dy/dx to make dy/dx the subject:
\(\implies 5x\dfrac{\text{d}y}{\text{d}x}+4y^3\dfrac{\text{d}y}{\text{d}x}=-8x-5y\)
\(\implies \dfrac{\text{d}y}{\text{d}x}(5x+4y^3)=-8x-5y\)
\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8x-5y}{5x+4y^3}\)
To find the slope of the tangent line at the point (-9, -1), substitute x = -9 and y = -1 into the differentiated equation:
\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8(-9)-5(-1)}{5(-9)+4(-1)^3}\)
\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{72+5}{-45-4}\)
\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{77}{49}\)
\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{11}{7}\)
Therefore, slope of the tangent line to the curve at the given point is -11/7.
y+z+z; use y-3, and z=3
Answers
(-3) + (3) + (3) =
Step 2: break it apart
(-3) + (3) = 0
0 + (3) = 3
Step 3: answer
(-3) + (3) + (3) = 3
Given sin thata = 2/5 and 0° < thata < 90°. find sin 2 thata
Answers
Recall the double angle identity:
\(\sin2\theta=2\sin\theta\cos\theta\)
With \(\theta\) measuring between 0º and 90º, we know \(\cos\theta>0\). So from the Pythagorean identity, we get
\(\sin^2\theta+\cos^2\theta=1\implies\cos\theta=\sqrt{1-\sin^2\theta}=\dfrac{\sqrt{21}}5\)
Then
\(\sin2\theta=2\dfrac25\dfrac{\sqrt{21}}5=\dfrac{4\sqrt{21}}{25}\)
Answer:
C
Step-by-step explanation:
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136⁰
2
S
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R
Find the measure of the arc or angle indicated
Answers
Answer:
224
Step-by-step explanation:
360.-136.
What is the measure of angle 3?
1
Answers
Answer:
129
Step-by-step explanation:
Every angle would be similar to each other with having only TWO different degrees...
Each line ( <----------------------> ) equals 180 (never 360, b/c that would be a circle)
Now with you only having 51 as a degree, you need to do 180-51 which gives you 129, with that given, this tells you number 1 and 3 is both 129, and angle 2 is 51.
How to solve: -x=14.
Answers
Answer:
x=-14
Step-by-step explanation:
Multiply each term in − x = 14 by − 1
Answer:
-14
Step-by-step explanation:
I need to do this fast
Answers
you can use photo-math it solves equations with steps
I don’t understand stand this question someone please help me with work shown
Answers
Answer:
8.9 miles
Step-by-step explanation:
well, you got 2 points with their coordinates on the grid if the city. to make it easy, the origin = point (0,0) is also the center of the city.
the school is 4 miles east = 4 units plus to the right in positive x direction.
and 2 miles south = 2 units down in negative y direction.
so, the point school is (4, -2).
the pool is 8 miles east = 8 units plus to the right in positive x direction.
and it is 6 miles north = 6 units up in positive y direction.
so, the point pool is (8, 6).
now we need to find the distance between both points to see how far they need to travel.
just one remark : this is flawed, as we can usually not make a beeline in a city from one place to another. we have to go along streets. but let's ignore that and just find the air distance.
now, to find the direct distance between 2 points, we need Pythagoras for right-angled triangles
c² = a² + b²
c = the Hypotenuse, the baseline opposite of the 90 degree angle. = the direct distance between the 2 points.
a and b are the sides of a right-angled triangle, which are nothing else than the differences of the x and y coordinates of the 2 points.
the x difference between school and pool is 8-4 = 4.
the y difference between school and pool is 6 - -2 = 6 + 2 = 8.
don't worry, if you did it the other way around and got negative numbers. remember that in the Pythagoras formula everything has to be squared first (and that turns also negative numbers into positive ones).
so, we get
c² = 4² + 8² = 16 + 64 = 80
c (the distance) = sqrt(80)
"sqrt" is the usual abbreviation of "square root".
sqrt(80) ≈ 8.9 miles
Please please help!!!!!!!!
Answers
Explication:
Multiply 3 with 8 to turn the 3 whole points into parts.
3 x 8 = 24
Add the 7 pieces you already have,
24 + 7 = 31
Put it over 8 then you have your answer.
Answer = 31/8
(Now you know how to do it!)
5. 14,5.13) 1. Amelia has 16 ounces of perfume to divide equally among 3 bottles. How many ounces of perfume will she pour into each bottle?
Answers
Answer:
-16/3 = -5.3333333333
Step-by-step explanation:
In order to win a prize, Heather randomly draws two balls from a basket of 40. There are 25 blue balls, and the rest are green balls. Of the blue balls, 12% are winning balls. Of the green balls, 20% are winning balls. Calculate the expected number of winning balls that Heather draws.
Answers
Answer:
The expected number of winning balls that Heather draws is 0.3.
Step-by-step explanation:
The balls are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
Expected value of the hypergeometric distribution:
The expected value is given by:
\(E(X) = \frac{nk}{N}\)
Expected number of blue and green balls:
40 balls, which means that \(N = 40\)
2 are chosen, which means that \(n = 2\)
25 are blue, which means that \(k = 25\)
So
\(E(X) = \frac{nk}{N} = \frac{25(2)}{40} = 1.25\)
1.25 balls are expected to be blue and 2 - 1.25 = 0.75 green.
Of the blue balls, 12% are winning.
Of the green balls, 20% are winning.
Calculate the expected number of winning balls that Heather draws.
\(E_w = 1.25*0.12 + 0.75*0.2 = 0.3\)
The expected number of winning balls that Heather draws is 0.3.
After Ted's birthday party, there was 1/5 of his cake left over. He and his 2 brothers decided to split the left over cake. What size piece did each brother have?
Answers
Answer:
Step-by-step explan
decimal answer: 0.06
fraction: 1/15
(edited)
Answer: 1/15
1/5*1/3 = 1/15
Step-by-step explanation:
what is the slope of the line given by the equation, y=6x-2
Answers
The slope of the line given by the equation, y=6x-2 is 6.
How can the slope intercept be discovered?When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). B is used in the equation to indicate the y value of the y intercept point.
A line equation whose slope and y-intercept may be determined directly is the slope-intercept form, or y = m x + b. The slope's value is m, while the y-value intercept's is b.
Assumed: y = 6 x + 2
The supplied equation, y = m x + b, is already in its slope-intercept form, allowing us to easily determine the slope's value, m.
y = 6 x + 2
m = 6
Consequently, the line's slope is 6.
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The surface area of the prism below is 292 square meters. What is the value of X? Show your work.
Please try to show steps.
Answers
Answer:
x= 14 meters
Step-by-step explanation:
Given
length=x
width=4 meters
height=5 meters
SA= 292 meters
Formula for rectangular prism surface area:
SA=2(lw+lh+wh)
Substitute values and add like terms
292=2(4x+5x+4*5)
292=2(9x+20)
Distribute and solve for x
292=19x+20
292-20=19x
272=19x
x=272/19
x = 14 meters
Question 13
Which of the following best describes the rule for the input-output table
below?
O A P(h) -
B. P(b)-4+h
C. P(h)-4.h
D. P(h)-3-h
h
157
9
11
13
115
17
P(h)
20
28
36
8831
44
52
60
68
G
Answers
The linear function that describes the data in the table for this problem is given as follows:
C. P(h) = h + 11.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope.b is the intercept.From the table, we have that when h increases by 1, P(h) also increases by 1, hence the slope m is given as follows:
m = 1/1 = 1.
Hence:
P(h) = h + b.
When h = 4, P(h) = 15, hence the intercept b is given as follows:
15 = 4 + b
b = 11.
Hence the rule is:
P(h) = h + 11.
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Find value of b and A
Answers
Answer:
Hi
Step-by-step explanation:
Please paste your question so I can solve it
Thanks
find the indicated side of the right triangle. 45 degrees, 45 degrees, 6, y, x, x = ?
Answers
3√2 and 3 are the values of x and y respectively from the figure.
Trigonometry identitiesThe given diagram is a right triangle with an acute angle of 45 degrees
We need to determine the values of variables x and y.
Applying the trigonometry identity, we will have:
sin 45 = opposite/hypotenuse
sin45 = 3/x
x = 3/sin45
x = 3/(1/√2)
x = 3√2
Similarly:
tan 45 = opposite/adjacent
tan 45 = 3/y
1 = 3/y
y = 3
Hence the values of x and y from the figure is 3√2 and 3 respectively
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Shana bought 6.2 pounds of pecans and paid $56.00. About how much per pound did the pecans cost?
$5.00
$6.00
$8.00
$10.00
Answers
$56/6.2=$9.032
Answer:
D
Step-by-step explanation:
What does an equal sign mean mathematically?
Answers
Answer:
It means that the both sides of the expression in the given equation must be/are congruent.
Hope this helps!
foreign direct investment helps improve the economic situation of a recipient country by increasing —- opportunities in the country that the company invests in.
Answers
Foreign direct investment helps improve the economic situation of a recipient country by increasing employment opportunities in the country that the company invests in.
When foreign companies invest in a recipient country, they often establish or expand their operations, which requires hiring local workers. This leads to job creation and reduces unemployment rates in the recipient country.
Increased employment opportunities result in more individuals having access to income and improved standards of living.
Foreign direct investment also contributes to the transfer of technology, knowledge, and skills to the recipient country. Multinational companies often bring advanced technologies, production techniques, and management practices that may not have been available or widely adopted in the recipient country.
Furthermore, foreign direct investment stimulates domestic investment and encourages the growth of local businesses. When foreign companies invest in a recipient country, they often form partnerships or engage in supply chain relationships with local firms.
Overall, foreign direct investment increases employment opportunities, fosters technology transfer, and stimulates domestic investment, all of which contribute to improving the economic situation of a recipient country.
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Simplify: −3 • −26
A. −78
B. −68
C. 68
D. 78
Answers
meaning the answer is D.
The reason the answer is D, is because two negatives when multiplied or divided become positive. Only when multiplied or divided does this occur.
Which of the following are NOT factors of 24?
Answers
Answer:
5,7
Step-by-step explanation:
Answer:
5 and 7
Step-by-step explanation:
If 24 is divided by 5 and 7, the quotient wouldn't be a whole number.