The required domain of g ( x ) = 3 x - 1 is R ( real nos . ) .
Given : g ( x ) = 3 x - 1
To find : Domain of function
Domain : The set of all possible values of input variable ( x in this case ) is called the domain of the function .
Calculating domain :
g ( x ) = 3 x - 1
Since , it is a polynomial function with degree 1 , therefore it's domain will be real nos .
Hence , domain of g ( x ) = 3 x - 1 is R .
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Write the equations for the lines parallel and
perpendicular to the given line j that passes
through Q. . y = −4x + 1; Q(6, −1)
Answer:
Parallel: y = -4x + 23
Perpendicular: y = (1/4)x - (5/2)
Step-by-step explanation:
Parallel Line:
y = -4x + 1; (6, -1)
(x₁, y₁)
y - y₁ = m (x - x₁)
y - (-1) = -4 (x - 6)
y + 1 = -4 (x - 6)
y + 1 = -4x + 24
y = -4x + 23
----------------------------------------------------------------------------------------------------------
Perpendicular:
y = (1/4)x + 1
y - y₁ = m (x - x₁)
y - (-1) = (1/4) (x - 6)
y + 1 = (1/4) (x - 6)
y + 1 = (1/4)x - (6/4)
-1 -1
y = (1/4)x - (5/2)
I hope this helps!
Find the inverse of each function. Is the inverse a function?
y=3 x+2
The inverse of the fuction y = 3 x + 2 is y = x/3 - 2/3.
What exactly is the inverse variation?Inverse variation refers to a relationship between two variables in which the value of one increases while the value of the other decreases.When two quantities, say X and Y, are related in such a way that increasing X causes a decrease in Y and vice versa, this is known as indirect or inverse variation.So,
All we have to do to find the inverse of an equation is switch the variables x and y.
x = 3y + 2Now, solve for y as follows:
3y = x - 2y = x/3 - 2/3Therefore, the inverse of the fuction y = 3 x + 2 is y = x/3 - 2/3.
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During spring break, Ian studied 3 hours
on the first day, 6 hours on the second
day, and 4 hours on the third day. How
many hours must he study on the fourth
day if he wants to spend an average
(arithmetic mean) of 5 hours each day
studying?
A. 6
B. 7
C. 8
D. 9
Nathaniel is an insurance underwriter. He earns $31.45 per hour, is paid weekly, and works 40 hours per week. His current federal withholding per week is
$106. Nathaniel lives in a state with a flat-rate income tax of 5.3%. He will receive a 5.25% raise and his new federal withholding will be $117. Determine
the following after taxes:
Answer:
Step-by-step explanation:
yyyyyyyyyyyyyyyyyyyyyyyyyyyy
Simplify each expression.
log₃(x+1)-log₃(3 x²-3 x-6)+log₃(x-2)
Simplification of given expression is , -1
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_ax=N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log a . b = log a + log b log a/b = log a - log blog a^x = x log alog a^a = 1According to question,
log₃(x+1)-log₃(3 x²-3 x-6)+log₃(x-2)
applying formula of log a - log b , equation can be written as
[tex]= log_3(\frac{x+1}{3x^{2} -3x-6} ) + log_3(x-2)\\\\=log_3(\frac{x+1}{3{(x+1)(x-2)} } ) + log_3(x-2)\\\\= log_3(\frac{1}{3 {(x-2)} } ) + log_3(x-2)[/tex]
now, applying formula of log a+ log b
[tex]=log_3(\frac{1}{3{(x-2)} } (x-2)) \\\\=log_3(\frac{1}{3} )\\[/tex]
apply, [tex]log_a(\frac{1}{x}) = -log_a x[/tex]
[tex]= - log_33[/tex]
= -1
Thus, Simplification of given expression is , -1
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Write an equation of the line that passes through (-7,9), (-5,3)
Answer:
y = - 3x - 12
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 7, 9 ) and (x₂, y₂ ) = (- 5, 3 )
m = [tex]\frac{3-9}{-5-(-7)}[/tex] = [tex]\frac{-6}{-5+7}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3 , then
y = - 3x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 5, 3 )
3 = 15 + c ⇒ c = - 3 - 15 = - 12
y = - 3x - 12 ← equation of line
Solve each equation. If necessary, round to the nearest ten-thousandth. 4 log₃2-2 log₃x=1
The value of x for the equation 4 log₃2-2 log₃x=1 is 2.30946
What is logarithmic function?The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which a set number, base b, must be increased in order to obtain a specific number x, is represented by the logarithm of that number.
Given,
4 log₃2-2 log₃x=1
log₃ 2⁴ - log₃ x² = 1
using logₐ(m - n) = logₐ(m/n)
log₃(2⁴ / x²) = 1
2⁴ / x² = 3¹
x = 4/√3
x = 2.30946
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1. The table shows the estimated profits y (in dollars) for a concert
when the charge is x dollars per ticket. Write and evaluate a
function to determine the maximum profit.
Ticket price, x
Profit, y
0
-1000
3
4100
6
7400
9
8900
12
8600
15
6500
Please help, dont troll me
The profit function for the concert is presented as follows;
y = -100•x² + 2,000•x - 1,000
The maximum profit is $9,000
What is a profit function?A profit function is one that gives the profit of a business which is the difference between the business's revenue and the costs of the business.
Profit = Revenue - Cost
Revenue = Quantity × Ticket price
Cost = Quantity × unit cost
Which gives;
y = Q•x - Q•c = Q•(x - c)
Given that the quantity, Q, varies, and Q•(x - c) is the product of two variables, a quadratic function is used as follows;
y = a•x² + b•x + c
When x = 0, y = -1000
Which gives;
y = a×0² + b×0 + c = -1000
c = -1000
When x = 3, y = 4,100
Which gives;
4,100 = a•3² + b•3 - 1000 = 9•a + 3•b - 1000
4,100 = 9•a + 3•b - 1000
5,100 = 9•a + 3•b
When x = 6, y = 7,400
Which gives;
7,400 = a•6² + b•6 - 1000 = 36•a + 6•b - 1000
7,400 = 36•a + 6•b - 1000
8,400 = 36•a + 6•b
Solving gives;
a = -100, b = 2,000
Which gives;
y = -100•x² + 2,000•x - 1,000
The profit function is therefore;
y = -100•x² + 2,000•x - 1,000The maximum profit is therefore at point, x = -2000/(2×(-100)) = 10
Which gives;
Max profit = -100×10² + 2,000×10 - 1,000 = 9,000
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Sphere A has radius 2 cm. Sphere B has radius 4 cm. a) Calculate the volume of each sphere.
Given the radius of each sphere, the volume of sphere A and B are 33.49cm³ and 267.95cm³ respectively.
What are the volumes of sphere a and b?A sphere is simply a geometrical object with a three-dimensional analogue to a two-dimensional circle.
The volume of a sphere is expressed as;
V = (4/3) × π × r³
Where r is radius and π is constant pi ( π = 3.14 ).
Given the data in the question;
Radius of Sphere A = rA = 2cmRadius of Sphere B = rB = 4cmVolume of each sphere = ?First, we determine the volume of sphere A.
V = (4/3) × π × r³
V = (4/3) × 3.14 × (2cm)³
V = (4/3) × 3.14 × 8cm³
V = 33.49cm³
Hence, the volume of sphere A is approximately 33.49cm³.
Next, we determine the volume of sphere B.
V = (4/3) × π × r³
V = (4/3) × 3.14 × (4cm)³
V = (4/3) × 3.14 × 64cm³
V = 267.95cm³
Hence, the volume of sphere Bis approximately 267.95cm³.
Given the radius of each sphere, the volume of sphere A and B are 33.49cm³ and 267.95cm³ respectively.
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I thought of a number, subtracted
7/18
from it, added 1 5/6 and got 3 2/3.
What was my number?
Answer:
[tex]\dfrac{20}{9}[/tex]
Step-by-step explanation:
Convert mixed fractions to improper fractionsAnswer
[tex]x = \dfrac{20}{9}[/tex]. So the original number = [tex]\dfrac{20}{9}[/tex]
The original number is 20/9.
What is mean by Fraction?
A number expressed as a quotient in which a numerator is divided by denominator is called a fraction.
Given that;
The numbers are 1 5/6 and 3 2/3.
Now, Let us assume original number 'x'.
Change mixed fraction into improper fraction,
1 5/6 = 11/6
3 2/3 = 11/3
Then by the given condition,
Subtracting 7/18 from x and add 11/6, we get;
x - 7/18 + 11/6
And this is equal to = 11/3
So, we get;
x - 7/18 + 11/6 = 11/3
Add 7/18 both side,
x - 7/18 + 11/6 + 7/18 = 11/3 + 7/18
x + 11/6 = 11/3 + 7/18
Subtract 11/6 both side,
x + 11/6 - 11/6 = 11/3 + 7/18 - 11/6
x = 11/3 + 7/18 - 11/6
x = 66/18 + 7/18 - 33/18
x = 40/18
x = 20/9
Thus, The original number is 20/9.
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6(x - 4y) how to I answer this question
Answer:6x-24y
Step-by-step explanation:You basically distribute the 6 with the x and the you do the same with the 4y. and thats how u get ur answer
Answer:
6x - 24y
Step-by-step explanation:
I'm guessing that they want you to distribute the 6 to each term inside the parentheses...
aircraft a has 136 more seats than aircraft b. if their total number of seats is 606, find the number of seats for each aircraft
Aircraft a has 371 seats and Aircraft b has 235 seats.
What is a linear equation?A linear equation is an algebraic equation that has highest degree of 1.
The total number of seats in both aircraft is 606.
Assuming aircraft b has x number of sheets.
∴ Aircraft a has (x + 136) number of sheets.
From the question itself we can form a numerical expression which is
x + (x + 136) = 606.
2x + 136 = 606.
2x = 606 - 136.
2x = 470.
x = 470/2.
x = 235.
So, Aircraft b has 235 seats and Aircraft a has ( 235 + 136) = 371 seats.
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help me please
show your solution
Hello,
[tex]1) \: - 24[/tex]
[tex] 2) \frac{ - 24}{2} = - 12[/tex]
[tex] 3)\frac{ - 12}{2} = - 6[/tex]
[tex]4) \frac{ - 6}{2} = - 3[/tex]
[tex]5) \frac{ - 3}{2} = - 1.5[/tex]
Answer → -1,5
A number c decreased by 12 is 4 as an equation
Answer:
c - 12 = 4
Step-by-step explanation:
Hello!
Decreasing a number by something is subtracting that number with something.
c decreased by 12 can be represented as c - 12.
When something is something, we set it equal to each other. We can set that equal to 4 to find our equation.
Equation: c - 12 = 4
The equation 9x = 27 has an answer of x = 3.
Write down Pive different equations with an answer of x = 3.
Answer:
5x = 15
2x = 6
10x = 30
8x = 24
21x = 63
Step-by-step explanation:
The equations that can give you an answer of 3 are the following
[tex]3x=9[/tex]
[tex]6x=18[/tex]
[tex]11x=33[/tex]
[tex]10x=30[/tex]
[tex]7x=21[/tex]
The equations above are one step linear equations
and many many more
We know 2×6=12.
So, which of the following statements are also true?
Choose 2 answers:
A, 12 is a multiple of 2
B, 12is a multiple of 6
C, 6 is a factor of 6
fyi kinda bad at factors a multiples...
Answer:
A and C is true statements
hope this helps :)
Step-by-step explanation:
Answer:
C and A
Step-by-step explanation:
4=q+13. Solve the equation using addition or subtraction A. q=4. B.q=17 C.q= -9 D. q= -2
Answer:
C. q= -9
Step-by-step explanation:
4=q+13
-13 -13 (4-13= -9)
q=-9
hope this helps :)
The solution of the given equation 4=q+13 is -9. Thus option C is correct.
The equation is defined as an expression consisting of an equality sign.
let us consider an example :
[tex]2x - 5 = 13.[/tex]
The given equation is:
[tex]4 = q + 13 \rightarrow 1[/tex]
For part A when q = 4 (given)
on substituting the value in equation 1 we get,
On transposing 13 to opposite side we get,
[tex]4 -13 = q[/tex]
[tex]-9 = q[/tex]
rewrite the equation as,
[tex]q =9[/tex]
The solution of the given equation [tex]4=q+13[/tex] is -9.
Thus option C is correct.
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Would Diagonal FH be considered perpendicular to side FE?
Diagonal FH bisect angles EFG and EHG and the angle FEH is congruent to angle FGH.
Why is the triangle congruent?
Congruent triangles are two triangles that are the same size and shape. Two congruent triangles remain congruent even if we flip, turn, or rotate one of them. Two triangles must have the same angles and, as a result, must be congruent if their sides are the same.We need to check all the statements that are applicable for the diagram.
1) EFGH is a rectangle.
The above statements is not true in general. EFGH is a quadrilateral with opposites sides are equal, it may be rectangle in some cases but it is not always be a rectangle.
2). EFGH has 4 congruent sides.
The above statement is also false. EFGH has two opposite sides are congruent.
3). Diagonal FH bisect angles EFG and EHG.
The above statement is true. Triangle EFH and FGH both are isosceles triangles and hence they both have equal angles for the equal sides. Thus, it is true in all cases.
4). Diagonal FH is perpendicular to side Fe.
The above case is not true in general.
5). Angle FEH is congruent to angle FGH.
Yes, the above statement is the correct one, because both the triangles are congruent to each other.
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The complete question is -
Triangle FGH is the image of isosceles triangle FEH after a reflection across line HF. Select all the statements that are a result of corresponding parts of congruent triangles being congruent
What is the midpoint of (3,5) and (6,0)
The midpoint of (3,5) and (6,0) is (9/2, 5/2)
How to calculate the midpoint of (3,5) and (6,0)?The points are given as
(3,5) and (6,0)
The midpoint of the points is calculated using
Midpoint = 1/2 * (x1 + x2, y1 + y2)
So, we have
Midpoint = 1/2 * (3 + 6, 5 + 0)
Evaluate the sum
So, we have
Midpoint = 1/2 * (9, 5)
Evaluate the product
So, we have
Midpoint = (9/2, 5/2)
Hence, the midpoint of (3,5) and (6,0) is (9/2, 5/2)
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Can someone help me please? This is imporant
The solutions for the system of equations: x₁ ≈ - 3.967, x₂ ≈ - 0.622. (Correct choice: B)
How to solve graphically a system of equations
In this question we find a system formed by one nonlinear equation and one linear equation, which can be resolved by using a graphic approach. g(x) = f(x) represents the point of intersection of the two curves. First, we plot the graphs of the two curves and, second, the point of intersection is marked on the Cartesian plane.
According to the result given by the graphing tool, there are two solutions for the system of equations: x₁ ≈ - 3.967, x₂ ≈ - 0.622.
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5. yo-yos the largest yo-yo in the world is 37.8 feet in circumference. the formula for the
circumference of a circle is c = 2tr, where c represents circumference and r represents
radius.
a. solve the formula for r.
b. find the radius of the yo-yo?
The formula for r will be C/2π.
The radius of the yo-yo will be 6.02 feet.
What is circumference?It should be noted that circumference simply means the distance round the circle.
In this case, the circumference is given as 37.8 feet.
The formula is illustrated as:
C = 2πr
r = C/2π
The radius will be:
r = C / 2π
r = 37.8 / (2 × 3.14)
r = 37.8 / 6.28
r = 6.02
Therefore, the radius of the yo-yo will be 6.02 feet.
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At a large university it is known that 30% of the students eat at dinning halls on campus. The director of student life is going to take a random sample of 300 students. What is the probability that less than a quarter of the sampled students eat at dinning halls on campus?.
swer.
At the beginning of the month, Sarah had $600 in her bank account. Within the month she
made two deposits of $40 and $25. She also made three withdrawals of $100, $50, and $20.
How much was in her account at the end of the month?
Sarah have $495 in her account at the end of the month.
Given,
The amount Sarah had in her bank account at the beginning of the month = $600
The deposits she made within the month = $40 and $25
The withdrawals she made = $100, $50 , $20
We have to find the balance amount in Sarah's account after all these transactions made:
The deposits Sarah had = 600 + 40 + 25 = 665
Sarah had $665 in her account in a month.
Withdrawals made by Sarah = 100 + 50 + 20 = 170
Sarah made a total withdrawal of $170 in the month.
Now, we have to find the account balance of Sarah:
Account balance = Total deposits - Total withdrawals
Account balance = 665 - 170 = 495
That is, Sarah have $495 in her account at the end of the month.
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What method can be used to write the equation of a line in slope-intercept form given two points? Find the slope using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept. Find the slope using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept. Find the y-intercept using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope. Find the y-intercept using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope.
The equation of the line y = mx + b can be used to calculate the slope of a line m = ( y₂ - y₁ ) / ( x₂ - x₁ ) that passes through two points.
A line is defined as a curve showing the shortest distance between 2 points.
Here,
The slope of the line passing through two points ( x₁, y₁ ) and ( x₂, y₂ ) is given as :
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
The line that connects two locations has the equation y = mx + b, where m is the slope of the line and b is a constant.
We can find b, using the x, y, and m values in the equation of a line to obtain the y-intercept.
Therefore, the Slope of the line can be given as m = ( y₂ - y₁ ) / ( x₂ - x₁ ) and equation of line y = mx +b.
Hence, option A is correct.
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Answer:
A or Find the slope using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept.
Step-by-step explanation:
What is the employee yearly contribution to the
U.S. Medicare tax on a salary of 40,000 $/year?
A. $2480
C. $1160
FICA Taxes
Social Security
12.4%
employer exployee
6.2%
6.2%
Medicare
2.9%
employer employee
1.45% 1.45%
B. $4960
D. $580
The employee yearly contribution to the
U.S. Medicare tax on a salary of 40,000 $/year is $580.
Medicare is a federal employment tax that helps pay the Medicare insurance program.
The Medicare duty, occasionally known as the" sanitarium insurance duty," is a civil employment duty that contributes to the Medicare insurance program. Medicare duty, like Social Security duty, is taken from an hand's payment or paid as a tone- employment duty.
Part A of the Medicare program, which covers sanitarium insurance for grown-ups 65 and aged, as well as persons with certain impairments or medical conditions, is funded by the Medicare duty. Medicare sanitarium insurance includes hospitalization, lodge care, nursing home care, and certain home healthcare.
Anyone working in the United States is obliged to pay Medicare levies.
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Does this graph represent a function? Why or why not?
Check the picture below.
well, according to the line vertical test, if a vertical line anywhere on the graph hits the graph only once, then yeap, it's a function.
y varies directly with x .
If x=10 when y=3 , find y when x=4 .
After direct variation y = 6/5 when x = 4.
What do we mean when we say "direct variation"?To give the reader a hint, direct variation equations use the same phrase.The phrase could be "directly proportional" or "directly varies."For example, the area of a square is proportional to the square of its side.The variational constant is k = 3 if y varies directly as x and y = 6 when x = 2.As a result, y = 3x is the direct variation equation.So,
The initial statement is y = kx
Then to find y when x = 4.
K constant will be y/x ⇒ 3/10That is y = kx ⇒ y = 4/3 × xWhen x = -3:
y = 3/10 × 4 ⇒ y = 6/5
Therefore, after direct variation y = 6/5 when x = 4.
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Find the real and imaginary solutions of each equation.
125 x³-1=0
A solution that is real in its nature is called the real solution of that equation.
X + 5 = 0
We can solve the above equation as,
X + 5 = 0
X = -5
Now, if we plug the value of X into the equation,
X + 5 = 0
-5 + 5 = 0
0 = 0
The solution is real and is true for this equation.
While the solution of an algebraic expression solution is imaginary if it is the square root of a negative number. It involves the imaginary unit iota.
The complete solution of the expression is given below in the picture.
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Find the gcf of 18a and 20ab
Answer:
the gfc is 1 because of the unknowns which are a and b
Solve each equation. If necessary, round to the nearest ten-thousandth. 12⁴⁻x=20
The solution of the given equation by rounding off it to the nearest ten-thousandth is 20716.0000.
What is a round-off of the digit?
In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.
For eg: 13.58 ~ 13.6
Solving the given equation: 12⁴ - x = 20
We are given that 12⁴ - x = 20 —- 1
We know that 12⁴ = 20736
So, equation 1 becomes,
20736 - x = 20
x = 20736 - 20
= 20716
Hence, the solution of the given equation to the nearest ten-thousandth is 20716.0000.
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