The inverse function of the given function is [tex]\mathbf{= \dfrac{28+7x}{x-1}}[/tex]
What is the inverse of a function?A function g is the inverse of a function f, if and only if the values of y= f(x), x = g(y).
From the formula given:
[tex]\mathbf{y=f(x) = \dfrac{x+28}{x-7}}[/tex]
Let's substitute x with y;
[tex]\mathbf{y= \dfrac{x+28}{x-7}}[/tex]
[tex]\mathbf{x=\dfrac{y+28}{y-7}}[/tex]
Solve for y;
[tex]\mathbf{= \dfrac{28+7x}{x-1}}[/tex]
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What is the name for a line that intersects two or more lines?
Answer:
line that intersects two or more lines at a distinct points is known as transversal line.
Answer:
A Transversal
Step-by-step explanation: A transversal is a line that intersects two or more lines in the same plane.
Write an equation of the line that passes through (−6, 0)
and (0, −24)
.
The equation of the line will be y = -4x - 24.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that the line is passing through the point (−6, 0) and (0, −24).
Ther slope of the point is calculated as,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( -24 - 0 ) / (0 - (-6)
Slope = -4
The y-intercept will be calculated as,
y = mx + c
y = -4x + c
0 =-4 x - 6 + c
c = -24
The equation of the line will be,
y = mx + c
y = -4x - 24
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Which function represents the graph of f (x) = 1/2 (3)^x
The vertical line test can be used to determine whether a graph represents a function. A vertical line includes all points with a particular x value.
How do you find the function of a graph?The graph of a relation is said to reflect a function if a vertical line drawn anywhere on the graph only intersects the graph once. A graph does not reflect a function if a vertical line can cross it at two or more places. Linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal function graphs fall under this category. Write the equation in the form y = mx + b to determine the slope m and the y-intercept. This will allow you to graph the equation using the slope and y-intercept (0, b). Plot the y-intercept next. 3) Depending on whether the slope is positive or negative, go up, down, or left or right from the y-intercept.To learn more about function refer to:
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Identify the percent of change in increase 25 songs to 78 songs
The percent increase in the number of songs is 212%.
How to find the percent increase?The general formula to find the percent increase is:
P = 100%*( final value - initial value)/(initial value).
Here we know that the initial value is 25 songs, and the final value is 78 songs, replacing these numbers of the formula above, we will get:
P = 100%*(78 - 25)/25
P = 100%*53/25
P = 212%
So there was an increase of 212% in the number of songs.
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The area of a trapezoid with bases b₁ and b₂ and height his (b₁
+ b₂)h. Mrs. Barker's
classroom has a table with a trapezoid-shaped top. The trapezoid has bases 4 feet and 2 feet
and height 3 feet.
What is the area of the tabletop?
Therefore , the area of such field is 7725 square feet as a result, which is the answer to the given trapezoid problem.
Explain the trapezoid.A trapezoid is a quadrilateral that has at least one connected pair of sides. It has the name trapezium. By definition, a trapezoid in Euclidean geometry is a convex quadrilateral. The trapezoid's base is made up of its parallel sides. A closed, flat shape having two neighboring sides and four consecutive sides is called a trapezoid. The parallel walls and base of the trapezoid are commonly referred as as the parallel sides and the legs, respectively.
Here,
We can solve the problem using the clue and formula provided.
Since the question asks for the number of square feet of grass, we are certain that we are solving for area,
Additionally,
it mentions that the two stands are 125 feet and 81 feet apart and that the stadium is 75 feet high (facing downhill) (b1 and b2).
Thus, the equation can be resolved.
=>A = 75((125+81)/2)
=> A = 75(206/2)
=> A = 75(103) (103)
=> A= 7725
The field measures 7725 square feet in size.
The area of such field is 7725 square feet as a result, which is the answer to the given trapezoid problem.
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Can you solve this?
A savings account is opened with an initial deposit of $425.00. Determine the account balance after 9 years if the account earns 2.7% simple interest annually.
$3,928.28
$1,457.75
$528.28
$103.28
Find The First Partial Derivatives Of The Function. W = Ev U + V8
The first partial derivatives of the function [tex]w=e^v/u+v^2[/tex] are:
∂w/∂u = [tex]-e^v/(u+v^2)^2[/tex]
∂w/∂v = [tex](e^v + 2ve^v)/(u+v^2)[/tex]
First partial derivatives are used to find the rate of change of a function with respect to one variable while holding the other variables constant. They are represented by the symbol ∂f/∂x or ∂f/∂y, where f is the function, x and y are the variables, and ∂ is the partial derivative. They are used to calculate the slope of a surface at a point in a multi-variable function.
The first partial derivative with respect to u is the derivative of w with respect to u, holding v constant.
To find this we can use the chain rule:
∂w/∂u = [tex]-e^v/(u+v^2)^2[/tex]
The first partial derivative with respect to v is the derivative of w with respect to v, holding u constant.
To find this we can use the chain rule:
∂w/∂v = [tex]e^v/(u+v^2)[/tex] + 2v [tex]e^v/(u+v^2)[/tex] = [tex](e^v + 2ve^v)[/tex]/[tex](u+v^2)[/tex]
So the first partial derivatives of the function [tex]w=e^v/u+v^2[/tex] are:
∂w/∂u = [tex]-e^v/(u+v^2)^2[/tex]
∂w/∂v = [tex](e^v + 2ve^v)[/tex]/[tex](u+v^2)[/tex]
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The complete question is -
Find the first partial derivatives of the function. [tex]w=e^v/u+v^2[/tex]
Here is a completed box challenge puzzle. If you look at it closely, you'll see that the umber at the top is the product of the two numbers on the left and right, and the number at the bottom is the sum of the two numbers on the left and right. *** 18 15 3x15=45 3+15= 18
The product of the two numbers 45, is the highest number, and the sum of the two numbers 18, is the lowest number follow symmetry .
what is symmetry ?When an object is split into two identical, mirrored components, it is said to have symmetry in mathematics. What does "axis of symmetry" refer to? An "axis of symmetry" is a fictitious line that has the ability to fold or split a thing into two identical mirror parts. Any object is symmetrical if two parts fit together. To determine the shape's symmetry, draw a mirror line across the center, making sure that all parts are identical. Another way of putting it is that symmetry is when two objects are facing one another or when two items have mated components that circle around an axis.
given
The two numbers on the left and right are multiplied together to create the number at the top.
The two digits on the left and right add up to the number at the bottom.
middle number + top number = 3 * 15 = 45 ( top number )
3+15 Equals 18 ( lowest number ) ( bottom number )
The product of the two numbers on the left and right, 45, is the highest number, and the sum of the two numbers on the left and right, 18, is the lowest number.
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The complete question is :-
Here is a completed box challenge puzzle. If you look at it closely, you'll see that the number at the top is the product of the two numbers on the left and right, and the number at the bottom is the sum of the two numbers on the left and right.
-2x+3=-7x-37
Solve for x
Answer:
x=-8
Step-by-step explanation:
Follow the steps in the image.
-Hope this Helped
The maximum resistance for a new spark plug wire is 840 ohms per inch. A 25-in. wire had a resistance of 20,250 ohms. Does this fall within the acceptable limit?
Answer:
Yes
Step-by-step explanation:
Let's calculate the resistance of one inch for our wire and compare it with the maximum:
20250 / 25 = 810 Ohm
810 < 840 ? Yes!
Yes, this is within the acceptable limit. Wire can be used.
3(x + 2) + 4 = 3x + 9 prove this is not an identity
The linear equation has no solutions, thus, it is not an identity.
How to prove that the equation is not an identity?An equation is an identity if it is true for any value of x.
So, if here we can find a unique solution ( or not solutions at all) for the linear equation, then we will prove that the equation is not an identity.
The linear equation is:
3*(x + 2) + 4 = 3x + 9
If we simplify the left side, we will get:
3*(x + 2) + 4 = 3x + 9
3*x + 3*2 + 4 = 3x + 9
3x + 6 + 4 = 3x + 9
3x + 10 = 3x + 9
Subtracting 3x in both sides we will get:
10 = 9
This equation has no solutions, then it is not an identity.
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Help I don’t how to do it
Levi spends all of his free time surfing. Today he was out on the waves for 7.1 hours. That is 0% more time than yesterday. How many hours did he spend surfing yesterday?
Round your answer to the nearest tenth.
HELPPPP IVE BEEN STUCK ON THIS FOREVER!!
Find the balance in the account after the given period
$8000 principal earning %7 compounded annually,5 years
The account has a $10.720.77 balance after 6 years.
Find the compound interest?Compound interest can be calculated by using the formula P(1 + r)t, where P stands for principal (the original sum), r for rate (the interest rate), and t for time (in years).
Let's first round up the percentage rate to the nearest whole number by adding 1. In decimal form, 5% is 0.05. 1 + 0.05 is 1.05.
We'll raise that decimal to the power of six now that we're trying to find the amount after six years. 1.05^5 is 1.34009564062. Do not remove this long decimal from your calculator despite its length.
It must be multiplied by the primary, which is equal to 8,000. When the numbers are added together, the result, rounded to the nearest hundredth, is 10,720.765125, or 10,720.77. There.
The account has a $10.720.77 balance after 6 years.
The complete question is,
Following the specified time, determine the balance in each account. After six years, $8000 in principal has earned 5% yearly compound interest.
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Subtract.
(5y − 3) - (-2y - 7) =
ANSWER THESE QUESTIONS PLEASE. (picture provided)
Answer: oh easy its 1220703250
Step-by-step explanation:
Greatest common factor 10x2+28x-6
Answer:
The equation 10x2+28x-6 can be simplified using a few steps. Firstly, the greatest common factor (GCF) needs to be identified. The GCF of this equation is 2, which can be identified by factoring out the coefficient of the first term, 10. After factoring out 2, the equation becomes -3 + -14x + 5x2.
The next step is to factor the remaining polynomial. This can be done by multiplying the coefficient of the first term by the constant and then finding two factors whose sum equals the coefficient of the middle term. In this case, the multiplication of the coefficient of the first term (5) and the constant (-3) gives -15. Then, two factors of -15 whose sum adds up to -14 must be found. These factors are -15 and 1. Therefore, the equation can be rewritten as 5x2 - 15x + 1x - 3.
Afterwards, the four terms in the equation can be added up in pairs, pulling out like factors. This results in (5x+1)(x-3), which is the desired factorization. Finally, the expression can be written as 2(x-3)(5x+1). Thus, the GCF of 10x2+28x-6 is 2.
Step-by-step explanation:
Answer:
2 is the answer .
if u r not sure u can try doing it yourself
the answer will be the same as I told
sing the variables from the problem statement together with the acceleration due to gravity, g , write an equation for the magnitude of the acceleration of the system. hint: based upon the numeric choices, block 1 will accelerate up the incline while the suspended block, block 2, accelerates vertically downward.
The equation for the magnitude of the acceleration of the system is equals to the
a = g (m₂ - m₁μ꜀ cosθ - m₁sinθ )/(m₁ + m₂ ).
We have, two blocks with masses say m₁ = 3.8 kg and m₂ = 8.6 kg inclined on the plane at angle θ=39° above the horizontal. Also, cofficient of friction, μ=0.39. According to problem, In case of block 1 , accelerate up the inclined plane, Then forces along y-axis,
mass m₁gcosθ , where g is gravity constant moves vertically downward normal force Fₙ moves upwardNet force during vertical motion = 0
=> Fₙ - m₁gcosθ = 0 --(1)
On horizontal direction,
Tension T acts upward acceleration, "a" upward motionforce of friction, f꜀ acts downward m₁gsinθ moves downwardAgain net force = 0
=> T - f꜀ - m₁gsinθ = m₁a --(2) ( using Newton's second law)
For block 2, Vertical motion
mass m₂g moving downward T acting upward Acceleration, " a"acting downwardSo, net vertical force = 0
=> - T + m₂g = m₂a --(3)
Now, f꜀ = μ꜀ Fₙ= μ꜀ m₁g cosθ
so, T - μ꜀ m₁g cosθ - m₁gsinθ = m₁ a --(4)
Using the equation (4) and (3), we have to determine the equation for acceleration, a.
Adding (3) from (4),
m₁ a + m₂a = -μ꜀ m₁g cosθ - m₁gsinθ + m₂g + T - T
=> (m₁ a + m₂a) = g ( -m₁cosθ - m₁ sinθ + m₂)
=> a ( m₁ + m₂ ) = g (-m₁μ꜀ cosθ - m₁ sinθ + m₂)
=> a = g (- m₁μ꜀ cosθ - m₁sinθ + m₂)/(m₁ + m₂ )
by plugging all the above values we can calculate the magnitude of acceleration.
Hence, required equation is a = g (m₂ - m₁μ꜀cosθ - m₁sinθ)/(m₁ + m₂) .
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Complete question:
Referring to the image to the above figure , the mass of block 1 is m1=3.8 kg while the mass of block 2 is m2=8.6 kg. The coefficient of friction between m1 and the inclined surface is μ=0.39. The inclined surface is at an angle θ=39∘ above the horizontal. Using the variables from the problem statement together with the acceleration due to gravity, g , write an equation for the magnitude of the acceleration of the system. hint: based upon the numeric choices, block 1 will accelerate up the incline while the suspended block, block 2, accelerates vertically downward.
Determine the dimensions of Nul A and Col A for the matrix shown below. A = [1 0 0 0 4 0 0 0 -5 1 0 0 2 -4 1 0 -4 -3 -3 0 6 -1 -4 0 -1 -6 6 0] The dimension of Nul A is and the dimension of col A is
The dimension of Nul A = 0 and the dimension of Col A = 4. means that the matrix A has no solutions for the homogeneous equation A × x = 0, which means that its null space is trivial, and it has 4 linearly independent columns, which means that its column space is 4-dimensional.
In other words, it is the number of linearly independent vectors x that satisfy the equation Ax = 0.
The dimension of Col A, also known as the column space of the matrix A, is the dimension of the subspace spanned by the columns of the matrix A. In other words, it is the number of linearly independent columns of matrix A.
In general, it is not possible to determine the dimensions of Nul A and Col A of a matrix just by looking at its elements. In order to find the dimensions, we need to perform the row echelon form or reduced row echelon form of the matrix to find the rank and the nullity which is the difference in the number of columns and rank.
For the specific matrix A provided, the rank of the matrix is not provided, thus we can not determine the dimension of the Nul A and Col A.
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Find the x intercepts of the graph y= 2/pie squared
The x-intercept is the point where the graph of a line intersects the x-axis. The y-intercept is the point where the graph of a line intersects the y-axis.
What is the formula for x-intercept form?Take into account a line with the slope intercept form y = mx + c, an intercept of (c, 0), and a slope of m. To find the x-intercept, enter y = 0 in the equation.Yb = m (xa), where m is the line's slope and (a,b) is a point on the line, is the point-slope form of a straight line. You may find the line's x-intercept by entering y = 0 and x-intercept = (amb)/m.Where the line crosses the x-axis is known as the x-intercept. Because the point won't be on the x-axis if y doesn't equal 0, you must always use a value of 0 for y when calculating the x-intercept.Given data :
y = ( 2 / π )²
y = 2² / π²
y = 4 / π²
Here i attached the graph of x interception
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Find the number of ways of arranging the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 in a row so that the product of any two adjacent numbers is even or a multiple of 3
Answer:
3,10,8,5,4,1,7,2,9,6
Step-by-step explanation:
PLEASE HELPP
Which is an irrational number?
A
317, because it cannot be rewritten as an integer.
B
−6, because it is less than 0.
C
13−−√, because it cannot be expressed as either a terminating or a repeating decimal.
D
0.2971¯¯¯¯, because it is a repeating decimal.
Use a graph to find the value of f(x) when x = -2 for each function
f(x) = -x + 7
Answer:
9
Step-by-step explanation:
X= -2, substitute -2 for X in the function
-(-2)+7, = 2+7
=9
how many linear factors does a polynomial function f of degree n have, where n > 0?
There will be n linear factors of a polynomial function f of degree n
We derive the above answer based on the following explanation,
The Linear Factorization Theorem states that . . . if f(x) is a polynomial of degree n, where n > 0, then f has precisely n linear factors f(x) = an(x – c1)( x – c2) . . . (x – cn) where c1, c2, . . . , cn are complex numbers.
Let us assume f to be a polynomial function with real coefficients and suppose a+bi, b≠0, is a zero of f(x). Then, by the Factor Theorem, x−(a+bi) is a factor of f(x). For f to have real coefficients, x-(a−bi) must also be a factor of f(x). This is true because any factor other than x−(a−bi) when multiplied by x−(a+bi), will leave imaginary components in the product. Only conjugate pair multiplication will get rid of the imaginary components and produce real coefficients.
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Given an isosceles triangle with base length 32 cm and altitude 12 cm, find the length of the congruent
sides.
Answer:
32
Step-by-step explanation:
Which of the following sets of numbers could represent the three sides of a triangle? { 12 , 27 , 39 } {12,27,39} { 12 , 18 , 29 } {12,18,29} { 5 , 9 , 16 } {5,9,16} { 9 , 24 , 33 } {9,24,33}
The sets of numbers that could represent three sides of a triangle is given as follows:
{12, 18, 29}.
What is the condition for 3 lengths to represent a triangle?In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.
Hence the set in this problem is given as follows:
{12, 18, 29}.
The larger measure is of:
29.
The sum of the two smaller measures is given as follows:
12 + 18 = 30.
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hello! can someone please help me? i'll give brainly. Thanks a lot! :)
Answer:
Brand z
Step-by-step explanation:
Answer:
X
Step-by-step explanation:
for W its 20/12 which is 5/3 or roughly 1.66. for X its 1500/1125 which is 4/3 or around 1.33. for Y its 100/65 which is 20/13 or around 1.54. and for Z its 50/25 or just 2.
Solve equation 7x+8=43
x = 5
7x+8=43
First, we want to separate the variable, so we subtract 8 from both sides:
7x=35
Then we divide both sides by 7 to get x all by itself:
x=5
This is because 35/7=5
1. What is the measure of 21? (1 point)
047°
037⁰
074⁰
053⁰
2. What is the measure of 22? (1 point)
047⁰
074°
037⁰
053⁰
Answer:
The measure of 21 and 22 doesn't make sense as they are not specific angles and they are not defined as to what angle you are refering to.
Without proper context and information, I am unable to provide an accurate answer to your question. Can you please provide more context, or explain what exactly you are trying to ask ?
Step-by-step explanation:
Figure B BB is a scaled copy of Figure A AA. Figure AFigure B What is the scale factor from Figure A AA to Figure B BB?
The requried scale factor from Figure A to Figure B is given as 1 / 3.
What is the scale factor?The scale factor is defined as the ratio of the modified change in length to the original length.
here,
The measure of the one side of triangle A = 6 units
The measure of the one side of triangle B = 2
Scale factor = length of the side of B / A
Scale factor = 2 / 6 = 1/3
Thus, the requried scale factor from Figure A to Figure B is given as 1 / 3.
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Answer: 2
Step-by-step explanation: Hope this helped