For the pair of functions, (g⁰f)(x) is - 6 x ² - 3 x + 22 and (f ⁰g)(x) is - 18 x ² + 7 x - 5
The given questions asks to find (g⁰f)(x) and (f ⁰g)(x), that is, function of g in terms of f(x) and function of f in terms of g(x).
To find : (g⁰f)(x)
Step 1 : Write g (x)
=> g (x) = - 3x -1
Step 2 : Put f (x) in place of x in g (x)
=> g (f(x) = -3 ( 2 x ² + x - 7 ) + 1
=> g (f(x) = - 6 x ² - 3 x + 21 + 1
=> g (f(x) = - 6 x ² - 3 x + 22
=> (g⁰f)(x) = - 6 x ² - 3 x + 22
Similarly,
To find : (f ⁰g)(x)
Step 1 : Write f (x)
=> f (x) = 2 x ² + x - 7
Step 2 : Put g (x) in place of x in f (x)
=> f (g(x) = 2 ( -3 x - 1 ) ² + x - 7
=> f (g(x) = 2 - ( 9 x ² + 1 + 3 x ) + x - 7
=> f (g(x) = - 18 x ² + 2 + 6 x + x - 7
=> f (g(x) = - 18 x ² + 7 x - 5
=> (f ⁰g)(x) = - 18 x ² + 7 x - 5
Therefore, we get for the pair of functions, (g⁰f)(x) as - 6 x ² - 3 x + 22 and (f ⁰g)(x) as - 18 x ² + 7 x - 5
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Suppose that x and y vary inversely. Write a function that models each inverse variation and find y when x=-5 . x=2 when y=12
A function that models each inverse variation is y = 24. 1/x and y when x=-5 is -24/5
What precisely is the inverse of a function?Those with inverse properties cancel each other out. In other words, f(g(x)) = g(f(x)) = x if g(x) is f's inverse (x). We have a great approach we can use to achieve this given an equation for which we desire the inverse.
Not every action has an equivalent. It is obvious that f(x) will never again have the same value if it has an inverse. We designate a unique name for this resource.
Inverse variation is y = k. 1/x
given y = 12
x = 2
So, 12 = k. 1/2
So, the value of k = 24
We can conclude that the value of constant variation is 24
when x = -5, the value of y will be -
y = k.1/x
y = 24 . 1/-5
y = -24/5
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Help for A Brainlist!!! geometry question!!! In the right triangle XYZ, angle X and angle Z are complementary angles. Given ( please see image attached below thank you for the help:) take care)
In the right triangle XYZ, angle X and angle Y are complementary angles, is angle sin z= 36/85, then the value of cos z= 77/85
In the right triangle XYZ, angle X and angle Y are complementary angles.
The complementary angle is either of two angles whose sum is 90 degrees
Therefore,
Angle X + Angle Z = 90 degrees
In trigonometry,
sinθ = Opposite side / Hypotenuse
sin z= 36/85
z= [tex]sin^{-1}(\frac{36}{85} )[/tex]
z= 25.06
Then the value of cos z is
cos 25.06 = 77/85
Hence, in the right triangle XYZ, angle X and angle Y are complementary angles, is angle sin z= 36/85, then the value of cos z= 77/85
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Evaluate each logarithm.
log₁/₂ 1/2
The answer to the given logarithm expression is log₁/₂ 1/2 = 1
Another technique to clarify exponents in mathematics is through logarithms. A base number's logarithm equals another number.
For instance, log10 100 = 2 if 102 = 100. A logarithm is defined as an influence by which variety must be raised to receive another value. this is often the foremost convenient thanks to represent large numbers. Logarithms have several important properties that prove that logarithmic multiplication and division is written because the logarithm of addition and subtraction. The log is named the logarithm of base e. The logarithm is represented by ln or loge. where 'e' represents Euler's constant, approximately capable 2.71828. as an example, the log of 76 is written as ln 76. The log defines what percentage times 'e' must be multiplied to induce the required output.
Using log property logₐ a = 1log₁/₂ 1/2 = 1
Hence , we evaluated the logarithm which is log₁/₂ 1/2 = 1
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WILL GIVE BRAINLIEST
Answer:
y = 85
Step-by-step explanation:
6x - 25 = 4x + 15
(Subtract 4x from both sides)
2x - 25 = 15
(Add 25 to both sides)
2x = 40
(Divide 40 by 2)
x = 20
6(20) - 25 = 4(20) + 15
(Solve)
95 + 95 = 190
(Subtract 360 from 190)
360 - 190 = 170
(Divide 170 by 2)
85
y = 85
3) Find the length of the line on the grid below. Hint: you need to draw a
right triangle with the given line as the hypotenuse!
You are given that f(x)=x²+4 and g(x)=3 x-1 .
b. Find f(x)+g(x) .
The summation of f (x) and g (x) = x ² + 3 x + 3
Given,
f (x) = x ² + 4
g (x) = 3 x - 1
The question states to find the summation of the function f, that is, f (x) = x ² + 4, and function g, that is, g (x) = 3 x - 1
Performing the addition operation on these functions is just like simple addition.
This implies, adding the two functions f (x) and g (x), we get
f (x) + g (x) = x ² + 4 + 3 x - 1
=> f (x) + g (x) = x ² + 3 x + 3
This assumes that the summation or addition of the two functions f (x) and g (x) gives x ² + 3 x + 3
Therefore, we get the summation of f (x) and g (x) as x ² + 3 x + 3
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What values of x and y satisfy the system {y=−2x+3y=5x−4?
Enter your answer as an ordered pair, like this: (42, 53)
If your answer includes one or more fractions, use the / symbol to separate numerators and denominators. For example, if your answer is (4253,6475), enter it like this: (42/53, 64/75)
If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf."
The solution to the given system of equations is x = 1, y = 1. That is, (1, 1)
From the question, we are to solve the given system of equations.
The given system of equations is
y = -2x + 3y ------------- (1)
y = 5x - 4 ------------- (2)
Substitute equation (2) into equation (1)
y = -2x + 3y
5x - 4 = -2x + 3(5x - 4)
5x - 4 = -2x + 15x - `12
Collect like terms
-4 + 12 = -2x + 15x - 5x
Simplify
8 = 8x
∴ x = 8/8
x = 1
Substitute the value of x into equation (2)
y = 5x - 4
y = 5(1) - 4
y = 5 - 4
y = 1
Hence, the solution to the given system of equations is x = 1, y = 1. That is, (1, 1)
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I can type 400 words per hour. How many minutes will it take me
to write a report with 2,000 words
Writing 2,000 words will take about 50 minutes for the average writer typing on a keyboard and 1.7 hours for handwriting.
Answer:
5 hours. the response has to be 20 characters long.
A common race is a 5K race, where runners travel 5 kilometers. Is it more appropriate to report the distance as 5 kilometers or 5×10^6 millimeters?
This version is much shorter, and more simpler, compared to 5 x 10^6 millimeters. It's more appropriate to use millimeters with very small objects or distances.
Note: 5 x 10^6 = 5,000,000 = 5 million
Complete the table and then graph the function.
summing-up the values for equation of line y = x/2 + 1 in table :
x y
-10 -4
-6 -2
-2 0
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
Here, the given equation is :
y = x/2 + 1
Now, computing the value of y corresponding to values of x by substituting values in above equation :
when x = -10 :
y = x/2 + 1
y = -10/2 + 1
y = -5 +1
y = -4
similarly, for :
x = -6 , y = -2
x = -2 , 0
summing-up the above values in table that is attached below :
x y
-10 -4
-6 -2
-2 0
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
Now to draw the line graph of above equation taking any two coordinates let us say (-2,0) and (-2,-6). Now drawing the line joining these two points as shown in figure attached below.
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Yong Quan was trying to access his email account when he could not remember the 4 digit password to the email account. He clicked on the button to reveal a hint. The hint: The biggest even number which can be formed by the numbers 1, 3, 8, 6. What was Yong Quan's password to the email account?
what is the equation for this graph in slope intercept form?
-40 -2 (3m + 1/2) = 7m -2
Answer:
m = -3
Step-by-step explanation:
If f(x) = 2x + 1 and g(x) = x² + 2x + 1, find g(f(x)).
Answer:
g(f(x)) = 4x^2 + 8x + 4
Step-by-step explanation:
If f(x) = 2x + 1 and g(x) = x² + 2x + 1, find g(f(x)).
You are asked to find g of f of x.
This means your x value for the equation g(x) is f(x), hence g(f(x)).
g(2x+1)=(2x+1)^2 + 2(2x+1) +1
g(2x+1) = 4x^2 + 4x + 1 +4x + 2 + 1
Combine like terms.
g(2x+1) = 4x^2 + 8x + 4
g(f(x)) = 4x^2 + 8x + 4
Jack bought 8 drill bits for aed11.22 each, 10 washers for aed10.11 each and 2 hammers for aed 545.59 each. a. calculate the total cost? b. later he bought a box to keep all the items. he paid aed 1500 altogether including box and received aed 12 as balance. find the cost of the box?
Jack spent first a total of AED 1282.04 and when he bought the box it cost AED 205.96
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
No. drill bits = 8 drill bitscost of drill bits = AED 11.22/ drill bitsNo. washers = 10 washers cost of washers = AED 10.11 / washers No. hammers = 2 hammers cost of hammers = AED 545.59 / hammersPaid = AED 1500Balance = AED 12Total cost = ?Box cost = ?Calculating the total cost Jack spend before bought the box:
Total cost = (No. drill bits*cost of drill bits) + (No. washers *cost of washers ) + (No. hammers *cost of hammers)
Total cost = (8 drill bits * AED 11.22/ drill bits) + (10 washers * AED 10.11 / washers) + (2 hammers * AED 545.59 / hammers)
Total cost = AED 89.76 + AED 101.1 + AED 1091.18
Total cost = AED 1282.04
Calculating the box cost:
Balance = Paid - (Total cost + box cost)
Balance = Paid - Total cost - box cost
box cost = Paid - Total cost - Balance
box cost = AED 1500 - AED 1282.04 - AED 12
box cost = AED 205.96
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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3. Noemi's team is working together to write a quadratic equation to model the path of the golf ball question in graphing form.
She calculated the value of `a=-\frac{1}{90}` is she correct?
Include detailed work that supports your answer on the left.
Begin with your equation for this golf ball situation from the previous slide.
The value of a calculated by Noemi is not correct as the correct value is
a = -1/45
We know that the general form of the quadratic equation is given as
y = ax² + bx + c
where, a and b are coefficients of the variable x and c is the constant term.
Now according to the question the path of the golf ball is parabola whose coordinates will be
(0,0) = origin where it starts
(60,80) = vertex or the maximum point
(120,0) = end point
Now putting the value of (x,y) in the above formula to find the value of a,b and c
when (x,y) = (0,0)
0 = a0² + b0 +c
c = 0
when (x,y) = (60,80)
80 = a60² + b60 +c
80 = 3600a + 60b + 0 (1)
when (x,y) = (120,0)
0 = a120² + b120 +c
0 = 14400a + 120b + 0
120b = -14400a
b = -120a
Putting the value of a in equation (1) we get
80 = 3600a + 60(-120a)
80 = 3600a - 7200a
80 = -3600a
a = - 1/45
⇒ b = 8/3
Hence the equation will be y = -1/45x² + 8/3x
and the value of a calculated by Noemi is not correct as the correct value is a = -1/45
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Incorrect Work/Solution
-7x-3y + x + 2y
-7x-3y + 1/2x+y
-5-x-2y
Identify and explain the error (2 points)
Find the coordinate of the midpoint of the segment with the given endpoints. - 16 and - 4 The midpoint is (Simplify your answer.)
Answer:
Step-by-step explanation:
The coordinate of the midpoint of the segment is -10
We have been given,
The coordinate of the endpoints of the segment are , -16 and -4
We need to find the coordinate of the midpoint of the segment.
Using the midpoint formula,
m = (-16-4)/2
= -20/2
= -10
Therefore, the coordinate of the midpoint of the segment is -10
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Using the law of exponents to solve:
A) -i
B) -1
C) 1
D) i
Simplify. Rationalize all denominators. 4+√12 / 4-√12
The simplification of 4+√12 / 4-√12 after rationalizing all denominators
is 7+4[tex]\sqrt{3}[/tex]
We are given the equation;
[tex]\frac{4+\sqrt{12} }{4-\sqrt{12} }[/tex]
The above equation can also be written as;
[tex]\frac{4+\sqrt{4*3} }{4-\sqrt{4*3} }[/tex]
Since our question requires us to rationalize the denominator, we will use the initial equation to rationalize the denominator. That is;
[tex]\frac{4+\sqrt{12} }{4-\sqrt{12} }[/tex] * [tex]\frac{4+\sqrt{12} }{4+\sqrt{12} }[/tex]
We then simplify;
4(4+[tex]\sqrt{12}[/tex])+[tex]\sqrt{12}[/tex](4+[tex]\sqrt{12}[/tex]) / 4(4+[tex]\sqrt{12}[/tex])- [tex]\sqrt{12}[/tex](4+[tex]\sqrt{12}[/tex])
= 16+4[tex]\sqrt{12}[/tex]+4[tex]\sqrt{12}[/tex]+[tex]\sqrt{12*12}[/tex] / 16+4[tex]\sqrt{12}[/tex]-4[tex]\sqrt{12}[/tex]-[tex]\sqrt{12*12}[/tex]
= 16+8[tex]\sqrt{12}[/tex]+12 /16-12
=28+8[tex]\sqrt{12}[/tex] / 4
=28+8[tex]\sqrt{4*3}[/tex] /4
= 28+8*2[tex]\sqrt{3}[/tex] /4
=28+16[tex]\sqrt{3}[/tex] /4
Divide all sides by 4;
= 7+4[tex]\sqrt{3}[/tex]
The final answer is therefore; 7+4[tex]\sqrt{3}[/tex]
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I need help on number 2
The value of the x means hypotenuse according to the Pythagoras is 12.8.
According to the statement
We have to find that the value of the x.
So, For this purpose, we know that the
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse
From the given information:
The perpendicular length is 12.
And The base is a 4.5
And we have to find that the hypotenuse value.
Then
According to the theorem
Perpendicular^2 + base^2 = Hypotenuse^2
And substitute the value then
12^2 + 4.5^2 = Hypotenuse^2
144 + 20.25 = Hypotenuse^2
Then
Hypotenuse^2 = 144 + 20.25
Hypotenuse^2 = 164.25
Hypotenuse = 12.8.
So, The value of the x means hypotenuse according to the Pythagoras is 12.8.
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Find m<1 (1 point each)
Answer:
7°
Step-by-step explanation:
The three angles of a triangle should sum up to 180°
→ m∠1 + 121 + 52 = 180
→ m∠1 + 173 = 180
→ m∠1 = 180 - 173 = 7°
Raul is performing an experiment. He pours water into a glass and measures the temperature of the water at 72.3°F. Then he adds a few ice cubes to the glass of water. He measures the temperature of the water again and finds that it has changed by -39.1°F.
The expression that represents the temperature of the water after Raul added the ice cubes is 72.3°F + (72.3°F)
Writing an expressionFrom the question, we are to write an expression that represents the temperature of the water after Raul added ice.
From the given information,
The initial temperature is 72.3°F
and
The change in temperature was -39.1°F
Thus,
The expression that represents the temperature of the water after Raul added the ice cubes is
72.3°F + (72.3°F)
Hence, the expression written as the sum of two numbers is 72.3°F + (72.3°F)
Here is the complete question:
Raul is performing an experiment. He pours water into a glass and measures the temperature of the water at 72.3°F. Then he adds a few ice cubes to the glass of water. He measures the temperature of the water again and finds that it has changed by -39.1°F. Write an expression that represents the temp of the water after Raul added the ice cubes. Write the expression as the sum of two numbers.
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Solve each equation. If necessary, round to the nearest ten-thousandth. logB(2 x-1)=1/3
The solution of the given equation by rounding off it to the nearest ten-thousandth is 0.0872.
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 log 8(2x - 1) = 1/3
We are given a logarithmic expression: log 8(2x - 1) = 1/3
We know that e^(log b) = b
a log b = (log b)^a
log a + log b = log (ab)
Using exponential on both sides, we have
e^(log 8(2x - 1)) = e^(⅓)
8(2x - 1) = 1.3956
(2x - 1) = 1.3956 / 8
2x = 0.17445
x = 0.0872
Hence, the solution of the given equation rounded off to the nearest ten-thousandth is 0.0872.
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1) what is the answer to this
Answer:
Slope: 2/1
equation: y=2/1x+2
z -3y + 5y combining like terms?
Answer:
z+2y
Step-by-step explanation:
z is the only z there so dont have to change
-3y+5y=2y
so u get z+2y
Hey there!
z - 3y + 5y
= 1z - 3y + 5y
COMBINE the LIKE TERMS:
= (-3y + 5y) + (1z)
= -3y + 5y + 1z
= 2y + 1z
= 2y + z
Therefore, your answer should be:
2y + z
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Find all the zeros of each function. f(x)=x⁴-5 x²+6
According to the question, to calculate the zeros of each function. The given function is f(x) = [tex]x^{4}-5x^{2} +6[/tex]
Now, let us assume [tex]a=x^{2}[/tex]. Therefore, the above equation can be written as:
[tex]f(x)=a^{2}-5a+6[/tex]
Calculate the factors of the given equation and it can be re-written as:
[tex]f(x) = (a+2)(a+3)[/tex]
To calculate the final solution, equate it to zero.
[tex](a+2)(a+3)=0\\a=-2,-3[/tex]
Now, substitute these values in the original assumed equation:
The zeros function values are [tex]-\sqrt{2i};\sqrt{2i},-\sqrt{3i} ,\sqrt{3i}[/tex]
What is zero functions?
A zero function is a function which is almost zero everywhere on the graph. It is also known as a constant function.
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Multiply. Write your answer in scientific notation.
8.8 (1 x 10^3
)
Answer:
8.8 x 10^3
Step-by-step explanation:
8.8 * 1 x 10^3 = 8.8 x 10^3 <===== done
A computer is rendering two scenes. The computer has already rendered 540540540 thousand pixels (\text{kpx}kpxstart text, k, p, x, end text) of a kitchen scene and renders another 90\,\text{kpx}90kpx90, start text, k, p, x, end text each minute. The computer has rendered 960\,\text{kpx}960kpx960, start text, k, p, x, end text of a garden scene and renders 60\,\text{kpx}60kpx60, start text, k, p, x, end text more pixels each minute.
Answer: 14 min
Step-by-step explanation:
After 14 minutes more the scene will have the same amounts rendered if the computer is rendering two scenes.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
A computer is rendering two scenes. The computer has already rendered 540 thousand pixels (kpx) of a kitchen scene and renders another 90kpx each.
Let after t minutes the scene will have the same amounts rendered.
The linear equation in one variable can be framed as:
540 + 90t = 960 + 60t
After solving the above linear equation in one variable:
90t - 60t = 960 - 540
30t = 420
t = 14 minutes
Thus, after 14 minutes more the scene will have the same amounts rendered if the computer is rendering two scenes.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
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Which expression represents the solution of the equation x/y = c/ a+b solved for a ?
(A) c/b - x / y (B) yc / a+b (C) yc /x+b (D) y c-x b / x
The solution of the equation solved for a is (D) y c-x b / x
As it is given that
x / y = c / a + b
Calculating for a
(a + b)x = cy
a + b = cy / x
a = (cy / x) - b
a = (cy - bx) / x
a = (yc - xb) / x
The solution of the equation solved for a is (D) y c-x b / x
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