The expression used to verify whether g(x) is the inverse of f(x) is 6( [tex]\frac{x+1}{6}[/tex])-1 and [tex]\frac{(6x-1)+1}{6}[/tex]
Given that f(x) = 6x-1
and g(x) = [tex]\frac{x+1}{6}[/tex]
If inverse [tex]f^{-1}[/tex] exists for a function f(x), then [tex]f(f^{-1}(x)) = f^{-1}(f(x)) = x[/tex]
So to check if g(x) is the inverse of f(x) we find f(g(x)) and g(f(x))
f(g(x)) = f( [tex]\frac{x+1}{6}[/tex]) = 6( [tex]\frac{x+1}{6}[/tex])-1 = x
and g(f(x)) = g(6x-1) = [tex]\frac{(6x-1)+1}{6}[/tex] = x
So g(x) is the inverse of f(x) and the expressions used to verify this are:
6( [tex]\frac{x+1}{6}[/tex])-1 and [tex]\frac{(6x-1)+1}{6}[/tex]
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There are three grizzly bears in the city zoo. Yogi weighs 400.5 pounds, Winnie weighs 560.35 pounds, and Nyla weighs 628.29 pounds. What is the average weight of the three bears? (Hint: What do they weigh all together?)
a.
502.97 pounds
c.
604.38 pounds
b.
529.71 pounds
d.
794.57 pounds
Answer:
So C
Step-by-step explanation:
Average = all values added up/ how many numbers there are
(400.5+560.35+628.29)/3=Average
Average = 529.71
Now multiply the values to get 14,918,904,000. That is almost 15 billion passwords.
That is a lot of passwords! How many passwords would the website have if users were allowed to reuse the letters and numbers? (Enter the number of successful outcomes in each of the blanks below. Let the first six spaces represent letters and the last two spaces represent numbers)
Someone please help me!!
Using the Fundamental Counting Theorem, it is found that the website would have 30,891,577,600 passwords.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For this problem, the first six spaces of the password are letters, and each can assume 26 values, hence the parameters are:
[tex]n_1 = n_2 = n_3 = n_4 = n_5 = n_6 = 26[/tex]
The last two spaces are composed by digits, and each can assume 10 values, hence the parameters are:
[tex]n_7 = n_8 = 10[/tex]
Hence the number of possible passwords is given by:
N = 26^6 x 10² = 30,891,577,600.
The website would have 30,891,577,600 passwords.
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What is the value of -32+(-4+7)(2)?
O-28
O-3
03
O 15
Answer:
-26Step-by-step explanation:
the answer is -26 but it is not in the choices
-32+(-4+7)*(2)=
-32+3*2=
-32+6=
-26
Hello!
Solve this Quadratic Equation: [tex]x^2 + 4x + 3 = 0[/tex]
Use factoring to solve, then double-check using the Quadratic Formula.
Include all steps and show your work in detail. The best answer gets Brainliest.
Answer:
[tex]x = -1, -3[/tex]
Solve by FactoringTo solve by factoring, we will split up the equation using our factoring rules.
In this particular instance, we will factor out common variables.
We need to ensure that we get two numbers that add to equal 4 and two numbers that multiply to equal 3.
[tex]x^2 + 4x + 3 = 0[/tex]
[tex](x+3)(x+1)=0[/tex]
Set each factor equal to zero and solve.
Root 1
[tex]x+3=0[/tex]
[tex]x=-3[/tex]
Root 2
[tex]x+1=0[/tex]
[tex]x=-1[/tex]
The final answer is [tex]\boxed{x = -1, -3}[/tex].
As requested in the question, we must now check with the quadratic formula.
What is the quadratic formula?To solve this quadratic equation, we will utilize the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
The parent formula for a quadratic equation is [tex]ax^2+bx+c=0[/tex].
We will define our variables:
a: 1b: 4c: 3Now, we will plug these into the equation and solve the equation.
Solve[tex]\displaystyle x=\frac{-4\pm\sqrt{4^2-4(1)(3)}}{2(1)}[/tex]
[tex]\displaystyle x=\frac{-4\pm\sqrt{16-12}}{2}[/tex]
[tex]\displaystyle x=\frac{-4\pm\sqrt{4}}{2}[/tex]
[tex]\displaystyle x=\frac{-4\pm2}{2}[/tex]
Root 1
[tex]\displaystyle x=\frac{-4+2}{2}[/tex]
[tex]\displaystyle x=\frac{-2}{2}[/tex]
[tex]\boxed{x=-1}[/tex]
Root 2
[tex]\displaystyle x=\frac{-4-2}{2}[/tex]
[tex]\displaystyle x=\frac{-6}{2}[/tex]
[tex]\boxed{x=-3}[/tex]
Final AnswerThe final answer is [tex]\boxed{x = -1, -3}[/tex].
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Given the equation, we can start by rewriting:
x^2 + 4x + 3 = 0
Now, let’s write in factored form:
(x + 1) (x + 3) = 0
since x is the only variable and there are 2 numbers, we can make 2 equations:
x + 1 = 0
x + 3 = 0
This forms:
(X + 1) (x + 3) = 0
Now, we can solve:
? + 1 = 0
? + 3 = 0
-1 + 1 = 0 and -3 + 3 = 0
x = -1 AND -3
GEOMETRY The length of a rectangle is twice the
width. Find the area, if the perimeter is 60 centimeters.
Draw a picture, define a variable, write an equation, and
solve the problem.
A survey found the following number of children in various neighborhoods around town. {3, 49, 16, 70, 21, 0, 7, 123} What is the mean absolute deviation for these numbers? Round to the hundredths place (two digits after the decimal). MAD =
4 times the sum of a number and 2 is 20. what is the number
Answer:
The sun of 10 is 2 times much 4.
Answer:
x=3
Step-by-step explanation:
➡️ Let x be the number;
4(x+2)=20
x+2=5
x=3
The number is 3.
log[tex]_e[/tex](x-4)=7
and round it to the nearest decimal and show steps please
The value of x will be 1099.8 when rounded it to the nearest decimals.
㏑(x-4)=7
Taking the exponential (e) both side, we get
[tex]e^{ln(x-4)} = e^{7}[/tex]
since 'e' and 'ln' cancels each other,
therefore
[tex]x-4 = e^{7}[/tex]
[tex]x = e^{7} + 4[/tex] ..eq 1
Exponential 'e' is the Euler's number, which is a constant having the value of around 2.718281828459045235360.
It is an irrational mathematical constant.It do not have a fixed value and hence 2.718 can be considered as its round off valueso putting the value of 'e' in eq 1
[tex]x = (2.718)^{7} + 4[/tex]
x = 1095.838 + 4
x = 1099.838
therefore when ㏑(x-4)=7 is solved the value of x will be 1099.8.
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hi can you help woth this question
Answer:
The point of intersection is the number of gigabytes and the total cost when the two plans cost the same.
Step-by-step explanation:
Company A doesn't charge a fee "per gigabyte", there's just a flat fee and it is $100. Company B only charges a flat fee of $20, BUT there IS a "per gigabyte" charge. These two plans actually cost exactly the same when the customer uses 16 gigabytes.
Write an equation of each line.slope = 5/6 ; through (22,12)
The equation of the line in point-slope form, with slope equal to 5/6 and passing through the point located at (22 , 12), is (y - 12) = 5/6(x - 22).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Using the point slope form, plug in the values to set up the equation.
(y - y1) = m(x - x1)
where m = 5/6 and (x1 , y1) = (22 , 12)
(y - 12) = 5/6(x - 22)
In slope-intercept form, the equation of the line is:
(y - 12) = 5/6(x - 22)
y - 12 = 5/6 x - 110/6
y = 5/6 x - 19/3
In standard form, the equation of the line is:
y = 5/6 x - 19/3
5/6 x - y = 19/3
Multiplying both sides by 6,
5x - 6y = 38
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A classmate uses the formula for the sum of an infinite geometric series to evaluate 1+1.1+1.21+1.331+ . . . and gets -10 . What error did your classmate make?
What error did your classmate make? This series is divergent so does not have a sum.
How is the divergence of the series proved?
Given:
[tex]a(\text{ the first term })=1\\\\r(\text{ the common difference })=1.1[/tex]
Since, [tex]\vert r \vert > 1[/tex] the infinite series diverges.
What is an infinite geometric series?
The result of an endless geometric sequence is an infinite geometric series.There would be no conclusion to this series.The total of all finite geometric series can be determined.However, if the common ratio of an infinite geometric series is bigger than one, the terms in the sequence will grow steadily larger, and adding the larger numbers together will not yield a solution.To learn more about infinite geometric series, refer:
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295+39x=350+33x
This is based off of solving equations with variables!
.ALGEBRA 1
Answer: x=55 over 6
Step-by-step explanation:
Write a two-column proof.
Given: MS ≅ RQ, MS || RQ
Prove: Δ M S P ≅Δ R Q P
We can conclude that ΔMSP ≅ ΔRQP under SAS conditions.
What do we mean by a triangle's congruency?If all three corresponding sides and angles of two triangles are the same size, they are said to be congruent.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are moved, they will coincide.When two triangles satisfy the five congruence conditions, congruence exists.They are the side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).So,
Given: MS ≅ RQ, MS || RQ
To Prove: ΔMSP ≅ ΔRQP
MS = RQ = (Given)SP = PQ = (Q is the midpoint)So, ∠MSP = ∠RQP (SAS)ΔMSP ≅ ΔRQP is proved.
Therefore, ΔMSP ≅ ΔRQP under SAS condition.
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Do the following side lengths form a right triangle?
51, 68, 85
Answer: Yes
Step-by-step explanation:
If these lengths were to form a right triangle, then 51 and 68 would be the legs and 85 would be the hypotenuse.
[tex]51^2 +68^2 =7225\\\\85^2 =7225\\\\\therefore 51^2 +68^2 =85^2[/tex]
So, the side lengths form a right triangle.
Calculate the electric flux through the cube face in the plane z = 0 and the cube face in the plane z=l. for each face the normal points out of the cube.
Ф2 = E2 L² is the electric flux through the cube face in the plane z = 0.
What exactly are electric flux and unit?
The SI unit for electric flux is newton-meters squared per coulomb (N m 2 /C N m 2 /C), and it is a scalar quantity. It is important to note that N E A 1 N E A 1 can also be represented as N N , proving that the number of field lines crossing a surface is what determines how much electric flux there is.given ,
edge length = L
Area of each surface = L²
Ф = E . A
= E . A Cos θ
Φ1 = E1 A Cosθ
Φ1 = E1 L²
Similarly we get
Ф2 = E2 L²
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Savannah is making pots and plates to sell at a local art fair. Each pot weighs 2 pounds and each plate weighs 1 pound. Savannah cannot carry more than 50 pounds to the fair. She only has enough clay to make 40 plates. In addition, she only has enough clay to make 24 pots. She will make $12 profit on every plate and $25 for every pot that she sells. How many pots and how many plates should Savannah make to maximize her profit?
Answer:
24 pots 2 plates
Step-by-step explanation:
Answer:
24 pots and 2 plates
Step-by-step explanation:
MATH
-2 1/3 + ( -1 3/4) =
In the equation |x| = b, if b>0, then how many solutions are there for x?
O Zero
O Two
O Can't be determined without more information
O One
The value of b (real number) can be anything greater than zero so we cannot be determined with the given information so option (C) will be correct.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
Given the absolute equation,
|x| = b for b >0
b is a set of all positive real numbers and we know that real number goes 0 to infinite means,
b could be 1,2,3... anything.
It means the corresponding solution will also be 1,2,3... anything.
Therefore we cannot determine the solution.
Hence "We cannot predict the number of solutions of the given mode function |x| = b, such that b>0 without more information".
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A school sells tickets to its annual talent show and earns $80 for selling 50 tickets. Each ticket cost the same price. How much does the school earn for one ticket?
Answer:
1 dollar and 6 cents
Step-by-step explanation:
Help with this please!
The numeric values for the functions are given as follows:
(f x g)(-4) = -88.(g/h)(-6) = -1.g(-9)/h(-9) = -18/693.How to find the numeric value of a function?To find the numeric value of a function, we replace each instance of the variable by the desired value.
For the first problem, we have that:
f(-4) = -2(-4) = 8.g(-4) = 4(-4) + 5 = -11.(f x g)(-4) = -88. (8 x -11)For the second problem, we have that:
g(-6) = (-6)² + 4(-6) = 12h(-6) = 2(-6) = -12.(g/h)(-6) = -1. (12/-12).For the third problem, we have that:
g(-9) = -2(-9) = 18.h(-9) = (-9)³ - 4(-9) = -693.g(-9)/h(-9) = -18/693.More can be learned about the numeric values of a function at https://brainly.com/question/28367050
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Two similar spheres have radii of 20 \pi meters and 6 \pi meters. What is the ratio of the surface area of the large sphere to the surface area of the small sphere?
A. 100/3 B. 100/9 C. 10/3 D. 10/9
The ratio of the surface area of the large sphere to the surface area of the small sphere of radius 20π meters and 6π meters, respectively, is B. 100/9.
Surface area refers to the total area covering the outside of a three dimensional shape. The surface area of a sphere is given by the formula:
A = 4πr^2
Solving for the surface area of each sphere:
1. larger sphere, r = 20π meters
A = 4πr^2
A = 4π(20π meters)^2
A = 4π(400π^2 square meters)
A = 1600π^3 square meters
2. smaller sphere, r = 6π meters
A = 4πr^2
A = 4π(6π meters)^2
A = 4π(36π^2 square meters)
A = 144π^3 square meters
Getting the ratio of the surface area of the large sphere to the surface area of the small sphere:
1600π^3 square meters / 144π^3 square meters = 100/9
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In triangle △ABC, ∠C is a right angle and CD is the altitude to AB . Find the angles in △CBD and △CAD if
Applying the triangle sum theorem, the measures of the angles in △CBD are: m∠CDB = 90°; m∠BCD = 65°; m∠CBD = 25°
In △CAD, they are: m∠A = 65°; m∠ADC = 90°; m∠ACD = 25°
What is the Triangle Sum Theorem?All interior angles of a triangle have a total sum of 180 degrees when added together, according to the triangle sum theorem.
Given:
Measure of angle C = 90 degrees
In △CAD, we have the following angle measures:
m∠A = 65° (given)
m∠ADC = 90° [right angle]
m∠ACD = 180 - 90 - 65 [triangle sum theorem]
m∠ACD = 25°
In △CBD, we have the following angle measures:
m∠CDB = 90° [right angle]
m∠BCD = 90 - m<ACD [complementary angle]
m∠BCD = 90 - 25
m∠BCD = 65°
m∠CBD = 180 - m∠BCD - m∠CDB [triangle sum theorem]
m∠CBD = 180 - 65 - 90
m∠CBD = 25°
In summary, applying the triangle sum theorem, the measures of the angles in △CBD are: m∠CDB = 90°; m∠BCD = 65°; m∠CBD = 25°
In △CAD, they are: m∠A = 65°; m∠ADC = 90°; m∠ACD = 25°
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Jorge can run 7 laps in 18 minutes. How many laps can he run in 50 minutes?
answer
3 Laps
Step-by-step explanation:
4(20+12) / (5-3)
What is this
a. What is the solution of the system?
Use substitution.
x-2y+z = -4
-4x+y-2z = 1
2x+2y- z = 10
By substitution, the solution of the system of equations, x - 2y + z = -4, -4x + y -2z = 1 and 2x + 2y - z = 10, is (x , y , z) = (2 , 1 , -4).
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given three equations in x, y, and z,
x - 2y + z = -4 (equation 1)
-4x + y -2z = 1 (equation 2)
2x + 2y - z = 10 (equation 3)
Using the equation 1, find the value of one variable, lets say x, in terms of the other variables.
x - 2y + z = -4 (equation 1)
x = 2y - z - 4 (equation 4)
Substitute the equation 4 to equation 2 and 3 and find the value of another variable, lets say y, in terms of the other variable.
-4x + y -2z = 1 (equation 2)
-4(2y - z - 4) + y -2z = 1
-8y + 4z + 16 + y -2z = 1
-8y + y = 2z - 4z + 1 - 16
-7y = -2z - 15
y = -(2z + 15)/-7
y = (2z + 15)/7 (equation 5)
2x + 2y - z = 10 (equation 3)
2(2y - z - 4) + 2y - z = 10
4y - 2z - 8 + 2y - z = 10
4y + 2y = 2z + z + 10 + 8
6y = 3z + 18
y = (1/2)z + 3 (equation 6)
Substitute the value of y from equation 5 to equation 6 and solve for z.
y = (1/2)z + 3 (equation 6)
(2z + 15)/7 = (1/2)z + 3
2z + 15 = 7[(1/2)z + 3]
2z + 15 = (7/2)z + 21
2z - (7/2)z = 21 - 15
(-3/2)z = 6
z = -4
Substitute the value of z in either equation 5 or 6.
y = (1/2)z + 3 (equation 6)
y = (1/2)(-4) + 3
y = -2 + 3
y = 1
Finally, substitute the value of y and z to equation 4 and solve for x.
x = 2y - z - 4 (equation 4)
x = 2(1) - (-4) - 4
x = 2 + 4 -4
x = 2
Hence, the solution of the given system of equations is (x , y , z) = (2 , 1 , -4).
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chuck cut an entire length of rope into 28 peices each 1 1/2 feet long what was the length of the rope before chuck cut it ?
Answer:
42 feet
Step-by-step explanation:
1 1/2 * 28 = 42
5x - 29.4 + 1/2x when x = -11/5
Answer: -41.5
Hope that helped.
Write an explicit formula for each sequence. 1,4,7,10, . . . . .
According to the arithmetic progression, explicit formula for this sequence can.be depicted by:
aⁿ = a + ( n -1 ) d.
This sequence is in arithmetic progression, and an explicit formula for this sequence is
aⁿ = a + ( n -1 ) d
where n is the number of terms, d = the difference between two-term, and a is the first term of this sequence.
For example, We have to determine the 8th term of this sequence, so n = 8, and the difference between two correspondent numbers, ( 7 - 4 = 3 )
a⁸ = 1 + ( 8 - 1 ) 3 = 1 + 21 = 22.
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find the missing angle
Answer:
x= 42°
Step-by-step explanation:
The missing angle can be found by using the property '∠ sum of Δ'. The sum of the interior angles in a triangle is 180°.
The square symbol in the triangle represents a right angle, i.e. 90°.
Form an equation:
x +90° +48°= 180° (∠ sum of Δ)
x +138°= 180°
x= 42°
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Write an equation of a circle with the given center and radius. Check your answers.
center (2,3) , radius 4.5
The equation of the circle with radius 4.5 and center at (2 , 3) is (x - 2)^2 + (y - 3)^2 = 20.25.
The general form of the equation of circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (2 , 3)
r = 4.5
(x - 2)^2 + (y - 3)^2 = 4.5^2
(x - 2)^2 + (y - 3)^2 = 20.25
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