The general formula for a quadratic equation is ax² + bx + c = 0.
To solve
[tex]2x^2+6x=-3[/tex]You can follow the steps.
Step 01: Write the equation in the general formula.
To do it, add 3 to each side of the equation.
[tex]\begin{gathered} 2x^2+6x+3=-3+3 \\ 2x^2+6x+3=0 \end{gathered}[/tex]Step 02: Use the Bhaskara formula to find the roots.
The Bhaskara formula is:
[tex]x=\frac{-b\pm\sqrt[]{\Delta}}{2\cdot a},\Delta=b^2-4\cdot a\cdot c[/tex]In this question,
a = 2
b = 6
c = 2
So, substituting the values:
[tex]\begin{gathered} \Delta=b^2-4\cdot a\cdot c \\ \Delta=6^2-4\cdot2\cdot3 \\ \Delta=36-24 \\ \Delta=12 \\ \\ x=\frac{-6\pm\sqrt[]{12}}{2\cdot2} \\ x=\frac{-6\pm\sqrt[]{2\cdot2\cdot3}}{4} \\ x=\frac{-6\pm2\cdot\sqrt[]{3}}{4} \\ x_1=\frac{-6+2\sqrt[]{3}}{4}=\frac{-3+\sqrt[]{3}}{2} \\ x_2=\frac{-6-2\sqrt[]{3}}{4}=\frac{-3-\sqrt[]{3}}{2} \end{gathered}[/tex]Answer:
Exact form:
[tex]x=\frac{-3-\sqrt[]{3}}{2},\frac{-3+\sqrt[]{3}}{2}[/tex]Decimal form:
[tex]x=-2.37,\text{ -0.63}[/tex]which system of equations can be used to determine how many quarters, x, and how many nickels, y, he has?
Given: Alfred has 12 coins in his piggy bank. Some of the coins are quarters, some are nickels, and have a total of $3.15.
Required: To determine the system of linear equations for the given situation.:
Question 4 of 10 In the function y + 3 = (2x)2+1, what effect does the number 2 have on the graph, as compared to the graph of y=x"? 2 A. It shrinks the graph vertically to 1/2 the original height. B. It stretches the graph vertically by a factor of 2. C. It stretches the graph horizontally by a factor of 2. O OD. It shrinks the graph horizontally to 1/2 the original width
The parental function of the graph is,
[tex]y+3=(x)^2+1[/tex]The transformed function of the graph is,
[tex]y+3=(2x)^2+1[/tex]The transformation between the parent function and the transformed function will be resolved graphically.
From the graph above, the parent function is represented with red while the transformed image is represented with green colour.
We can conclude that the parent function was shrinked horizontally by 1/2.
Hence, it shrinks the graph horizontally to 1/2 the original width.
The correct option is Option
Consider function f, where B is a real number.
f(z) = tan (Bz)
Complete the statement describing the transformations to function f as the value of B is changed.
As the value of B increases, the period of the function
When the value of B is negative, the graph of the function
shy
and the frequency of the function
If the value of B increases, the period of the function decreases, and the frequency of the function increases. When the value of B is negative, the graph of the function reflects over the y-axis.
How to estimate the graph and the frequency of the function?Let the tangent function be f(z) = tan (Bz)
The period exists [tex]$P=\frac{\pi}{|B|}$[/tex]
The frequency exists [tex]$F=\frac{1}{P}=\frac{|B|}{\pi}$[/tex].
The period exists inversely proportional to B, therefore, as B increases, the period decreases.
Frequency exists inversely proportional to the period, therefore, as the period decreases, the frequency increases.
When B is negative, we get f(z) = tan -Bz = f(-z), therefore, the function exists reflected over the y-axis, as the graph at the end of the answer shows, with f(z) exists red(B positive) and f(-z) exists blue(B negative).
As the value of B increases, the period of the function decreases, and the frequency of the function increases. When the value of B exists negative, the graph of the function reflects over the y-axis.
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Helppppppppppppppppppp
Perpendicular line are reciprocals
slope of the original line = -1/9
slope of the perpendicular line = 9
5|x +1| + 7 = -38
Solve for x
Answer: No solutions
Step-by-step explanation:
[tex]5|x+1|+7=-38\\\\5|x+1|=-45\\\\|x+1|=-9[/tex]
However, as absolute value is non-negative, there are no solutions.
Write a sine function that has a midline of 4 , an amplitude of 3 and a period of 2/3
Given a midline of 4, an amplitude of 3 and a period of 2/3 we are asked to write a sine function.
Explanation
The equation of a sine function is given as
[tex]y=Asin(\frac{2\pi x}{T})+B[/tex]Where A is the amplitude, T is the period and B is the midline of the sine function.
Therefore, we will have;
[tex]\begin{gathered} y=3sin(2\pi x\div\frac{2}{3})+4 \\ y=3sin(2\pi x\times\frac{3}{2}_)+4 \\ y=3s\imaginaryI n(3\pi x)+4 \end{gathered}[/tex]Answer:
[tex]y=3s\imaginaryI n(3\pi x)+4[/tex]metres> -21,23Sup10f3: Wandere first rareAnswerTeir wiced data prosto w will be whermerson is us. There will stand er is danfromGoethe type of boundary lineDashedEnter two points on the boundary lineSelect the repon you wish to be shaded:
Given
[tex]\begin{gathered} x>-2 \\ y\ge3 \end{gathered}[/tex]The graph
[tex]\begin{gathered} x>-3\text{ the pink colour} \\ y\ge3\text{ the blue colour} \end{gathered}[/tex]Two boundary points
[tex]\begin{gathered} \lparen-2,3) \\ \lparen-2,0) \end{gathered}[/tex]Function g is defined as g(x)=f (1/2x) what is the graph of g?
Answer:
D.
Explanation
We know that g(x) = f(1/2x)
Additionally, the graph of f(x) passes through the point (-2, 0) and (2, 0).
It means that f(-2) = 0 and f(2) = 0
Then, g(-4) = 0 and g(4) = 0 because
[tex]\begin{gathered} g(x)=f(\frac{1}{2}x_{}) \\ g(-4)=f(\frac{1}{2}\cdot-4)=f(-2)=0 \\ g(4)=g(\frac{1}{2}\cdot4)=f(2)=0 \end{gathered}[/tex]Therefore, the graph of g(x) will pass through the points (-4, 0) and (4, 0). Since option D. satisfies this condition, the answer is graph D.
The cost of renting a bicycle from Dan's Bike Shop is $2 for 1 hour plus $1 for each additional hour of rental time. Which of the following graphs shows the cost, in dollars, of renting a bicycle from Dan's Bike Shop for 1, 2, 3, and 4 hours? Bicycle Rental Cost Bicycle Rental Cost 7 6 Rental Cost (dollars) Rental Cout (dollars) 2. 1 Hetalia A B. Rental Time Chours) Bicycle Rental Cosi Bicycle Rental 7 7 Rental Cost dollars) 1 Rental Time (hours) Rental Tiene Chours) D.
option B
Explanation:The cost of renting per hour = $2
For 1 hour = $2
For each additional hour, it is $1
For 2 hours = First hour + 1(additional hour)
For 2 hours = $2 + $1(1) = 2+1 = $3
For 3 hours = $2 + $1 (2) = 2+2 = $4
For 4 hours = $2 + $1(3) = 2+3 = $5
The graph which shows this rental cost as 2, 3, 4, 5 is option B
The period T(In seconds) of a pendulum is given by T=2PI(Square root of L/32) Where L stands for length (in feet) of the pendulum If pi =3.14 and the period is 6.28 what is the length
Let me check your question
[tex]T\text{ = 2}\cdot\text{ 3.14}\cdot\text{ }\sqrt[]{L/\text{ 32}}[/tex][tex]\frac{T}{2\cdot\text{ 3.14}}\text{ = }\sqrt[]{L/\text{ 32}}[/tex]T= the period = 6.28
[tex]\frac{6.28}{6.28}\text{ = }\sqrt[]{L/\text{ 32}}[/tex][tex]L/32=1^2[/tex][tex]L=32[/tex]_________________
Answer
L= 32
(3x² − 5x + 7) and (2x² + x − 2).
By using polynomial rule we can get 6x^4-7x^3+3x^2+17x-14
What is polynomial rule?
All exponent in the algebraic expressions must be non-negative integer in order for the algebraic expressions to be a polynomial.
A polynomial is defined as per an expression which is the composed of variables, constants and exponents, that are combined using the mathematical operations are such as addition, subtraction, multiplication and division.
Sol- (3x^2-5x+7).(2x^2+x-2)
(3x^2-2x^2+3x^2.x-3x^2.2)-5x.2x^2-5x.x+5x.2+7.2x^2+7.x-14
{polynomial multiplication rule}
=6x^4+3x^2-6x^2-10x^3-5x^2+1x+14x^2+7x-14
{Plus or minus with the same x coefficient}
We are get=
6x^4-7x^3+3x^2+17x-14
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A pancake recipe asked for one and 2/3 times as much milk as flower if two and one half cups of milk is used what quantity of flower would be needed according to the recipe?
Let x be the quantity of flour used
Let y be the quantity of milk used
A pancake recipe asked for one and 2/3 times as much milk as flour:
[tex]y=1\frac{2}{3}x[/tex]If two and one half cups of milk is used what quantity of flower would be needed according to the recipe?
Find x when y=2 1/2:
[tex]2\frac{1}{2}=1\frac{2}{3}x[/tex]Write the quantities as fractions;
[tex]\begin{gathered} 2+\frac{1}{2}=(1+\frac{2}{3})x \\ \\ \frac{4}{2}+\frac{1}{2}=(\frac{3}{3}+\frac{2}{3})x \\ \\ \frac{5}{2}=\frac{5}{3}x \end{gathered}[/tex]Solve x:
[tex]x=\frac{\frac{5}{2}}{\frac{5}{3}}=\frac{15}{10}[/tex]Write the answer as a mixed number:
[tex]\frac{15}{10}=\frac{10}{10}+\frac{5}{10}=1+\frac{5}{10}=1+\frac{1}{2}=1\frac{1}{2}[/tex]Then, for 2 1/2 cups of milk would be needed 1 1/2 cups of flourAnswer: 1 1/2Solve the system by elimination. 2x+3y=06x+9y=0
We have the next system of equations
2x+3y=0 ...(1)
6x+9y=0 ...(2)
I order to solve this system by elimination we will multiply the first equation by -3
So we will have
-6x-9x=0
then we add the equation above with the second equation
-6x-9x=0
+6x+9y=0
As we can see we obtain 0=0 which means that we have infinity solutions
ANSWER
Infinity solutions
Find (fog)(x) and (gof)(-1) for the functions f(x) = 3x² + 5 and g(x) = -x + 1
Answer:
Step-by-step explanation:
fog(x)=3(-x+1)^2+5
=3(x^2+2x+1)+5
=3x^2+6x+3+5
fog(x) =3x^2+6x+8
gof(x)=-(3x^2+5)+1
=-3x^2-5+1
gof(x)=-3x^2-4
gof(-1)=-3(-1)^2-4
=-3-4
gof(-1) =-7
Find the value of M and YZ if Y is between X and Z. XY = 5m YZ =m, and X2 = 25
Notice that XZ = XY + YZ
where XY = 5m
YZ = m and XZ =25
Thus,
25 = 5m + m
25 = 6m
Hence,
[tex]m\text{ = }\frac{25}{6}\text{ = 4}\frac{1}{6}\text{ }[/tex]But YZ = m
Therefore, YZ =
[tex]4\frac{1}{6}[/tex]A solid plastic cube has sides of length 0.5 cm. Its mass is m g. Write a formula for its density in grams per cubic centimetres
The density of the cube is equal to ρ = m / L³.
What is the density of a plastic cube?
The density of the plastic cube (ρ), in grams per cubic centimeter, is equal to the mass of the cube (m), in grams, divide to the volume of the cube. The volume is equal to the cube of the side length (L), in centimeters. Then, the density of the plastic cube is:
ρ = m / L³
By using the definition of density, the density of the element is equal to ρ = m / L³.
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Today, October 20, 2022, seven friends ate lunch together at Chipotle.
Friend #1 eats there every day - including weekends.
Friend #2 eats there every other day - including weekends
Friend #3 eats there every third day - including weekends
Friend #4 eats there every fourth day - including weekends
Friend #5 eats there every fifth day - including weekends
Friend #6 eats there every sixth day - including weekends
Friend #7 eats there every seventh day - including weekends
Assuming that none of them catch Covid or miss any days, what will be the date when the friends again all eat lunch together at Chipotle?
The most appropriate choice for LCM of two numbers will be given by -
All the friends together can eat lunch on 14th December 2023.
What is LCM?
LCM means Lowest Common Multiple. LCM of two numbers a and b is the least number that is divisible by both a and b.
Friend 1 eats lunch together at Chipotle everyday including weekends
Friend 2 eats lunch together at Chipotle every other day including weekends
Friend 3 eats lunch together at Chipotle every third day including weekends
Friend 4 eats lunch together at Chipotle every fourth day including weekends
Friend 5 eats lunch together at Chipotle every fifth day including weekends
Friend 6 eats lunch together at Chipotle every sixth day including weekends
Friend 7 eats lunch together at Chipotle every seventh day including weekends
Number of days after which all the friends together can eat lunch
= LCM of 1, 2, 3, 4, 5, 6, 7 = 420 days
All the friends together can eat lunch after 420 days
All the friends together can eat lunch on =
(31 - 20) + 30 + 31 + 31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 +14 = 14th December 2023
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A remodeling project calls for sanding a chair with a disksander. The sanding disk used on the sander has a radiusof 4.5 Inches. Find the area of the disk. Use 3.14 for
Which value of n makes the following equation true?√n=4020408O 16
Solution
- The solution steps are given below:
[tex]\begin{gathered} \sqrt{n}=4 \\ \text{ Square both sides} \\ n=4^2 \\ n=16 \end{gathered}[/tex]Final Answer
The answer is 16
How do you determine 1 and 2/5 - 6/10 =
[tex]\frac{4}{5}[/tex].
Step-by-step explanation:1. Write the expression.[tex]1+\frac{2}{5} -\frac{6}{10}[/tex]
2. Rewrite the fractions with a common denominator.A common denominator is just a number that can be used as a denominator all fractions when we convert them through multiplications. A common denominator is usually found just by multiplying all denominators of all fractions. In this case, we don't need to go that far, since 5 could be a common denominator.This is how you do it:
[tex]1=\frac{1}{1} *\frac{5}{5}=\frac{5}{5} \\ \\\frac{2}{5}= \frac{2}{5}\\\\\frac{6}{10} =\frac{6/2}{10/2}=\frac{3}{5}[/tex]
3. Take all the rewritten fractions and rewrite the operation.[tex]\frac{5}{5} +\frac{2}{5} -\frac{3}{5}[/tex]4. Solve.[tex]\frac{5}{5} +\frac{2}{5} -\frac{3}{5} =\frac{5+2-3}{5} =\frac{4}{5}[/tex]
5. Express your result.[tex]1+\frac{2}{5} -\frac{6}{10}=\frac{4}{5}[/tex].
[tex]\frac{4}{5}[/tex].
Step-by-step explanation:1. Write the expression.[tex]1+\frac{2}{5} -\frac{6}{10}[/tex]
2. Rewrite the fractions with a common denominator.A common denominator is just a number that can be used as a denominator all fractions when we convert them through multiplications. A common denominator is usually found just by multiplying all denominators of all fractions. In this case, we don't need to go that far, since 5 could be a common denominator.This is how you do it:
[tex]1=\frac{1}{1} *\frac{5}{5}=\frac{5}{5} \\ \\\frac{2}{5}= \frac{2}{5}\\\\\frac{6}{10} =\frac{6/2}{10/2}=\frac{3}{5}[/tex]
3. Take all the rewritten fractions and rewrite the operation.[tex]\frac{5}{5} +\frac{2}{5} -\frac{3}{5}[/tex]4. Solve.[tex]\frac{5}{5} +\frac{2}{5} -\frac{3}{5} =\frac{5+2-3}{5} =\frac{4}{5}[/tex]
5. Express your result.[tex]1+\frac{2}{5} -\frac{6}{10}=\frac{4}{5}[/tex].
Set up the equation for the following word problem and solve the equation. Let x be the unknown number. -26 times a number minus 5 is equal to 56 less than the number. Step 2 of 2: Solve the equation for x. Express your answer as an integer, a reduced fraction, or a decimal number rounded to two pl Answer
Answer:
Step 1 of 2:
-26x - 5 = x - 56
Step 2 of 2:
17/9 or 1.89
Step-by-step explanation:
1. Putting word statement in algebraic form
Step 1:
Let x be the unknown number ==> x is the unknown variable to be used in the equation and to be solved for
Step 2:
-26 times a number minus 5 ==> -26x - 5
Step 3:
is equal to 56 less than the number ==> = x - 56
Putting it all together:
-26x - 5 = x - 56
2. Solving the equation
-26x - 5 = x - 56
1. Subtract x from both sides:
-26x - 5 - x = x - x -56
-26x -x - 5 = -56
-27x - 5 = -56
2. Add 5 to both sides
-27x - 5 + 5 = -56+ 5
-27x = -51
x = -51/-27 (dividing both sides by -27)
x = 51/27 (negative divide by negative results in positive)
Reduce 51/27 by dividing numerator and denominator by 3
x = (51 ÷ 3)/(27 ÷ 3) = 17/9
= 1.88888.... = 1.89 rounded to two decimal places
Text-to-Speech6.For the expression, combine like terms and write an equivalentexpression with fewer terms.4- 2x + 5xВ ІΣSave answer and go to next question
hello
the question given request we write an equivalent expression as the one given which is
[tex]4-2x+5x[/tex]an equivalent expression to the one above would be
[tex]4+3x[/tex]so, we can say
[tex]4-2x+5x=4+3x[/tex]Comment on the similarities and differences for the graph of every polynomial function.
There are different graphs of polynomial functions. In terms of shape, it can go from a straight line, slanting line, parabola, to curvy graphs especially when we are graphing polynomial functions with degrees 3 or higher.
See examples below:
However, what is similar to these graphs is that each graph is continuous or has no breaks and the domain of every polynomial function is the set of all real numbers.
Hi I need help with this thank you! Previous question that may help answer this one : Line of best fit: ^y1=−0.02 x+4.68 ● Curve of best fit: ^y2=−0.09 x2+1.09 x+2.83 Section 2 Question 1 Using a curve to make a prediction of the y value for an x value between two existing x values in your data set is called interpolation. Suppose the year is 2005, where x = 5 years: (a) Use the equation for the line of best fit to predict the number of cell phones sold during that year. Round answers to one decimal place and be sure to include the appropriate units. Your Answer: we have the linear equation: y1=-0.02x+4.68Where x is the number of years since the year 2000, y1 ----> is the number of cell phones sold. So for the year 2005, x=2005-2000=5 years.substitute:y1=-0.02(5)+4.68y1=4.58Therefore, the answer is 4.6 cell phones sold.(b) Use the equation for the non-linear curve of best fit to predict the number of cell phones sold during that year. Round answers to one decimal place and be sure to include the appropriate units. Your Answer: We have the equation y2=-0.09x^2+1.09x+2.83For x=5 yearssubstitute:y2=-0.09(5)^2+1.09(5)+2.83y2=6.03Therefore, the answer is 6.0 cell phones sold.
From the information provided we will have that the predictions will be:
*Line of best fit:
[tex]y_1=0.02(13)+4.68\Rightarrow y_1=4.94\Rightarrow y_1\approx4.9[/tex]So, the extrapolation from the line of best fit is 4.9 sold.
*Curve of best fit:
[tex]y_2=0.09(13)^2+1.09(13)+2.83\Rightarrow y_2=32.21\Rightarrow y_2\approx32.2[/tex]So, the extrapolation for the curve of best fit is 32.2 sold.
If ¼ gallon of paint covers 1/12 of a wall, then how many quarters of paint are needed for the entire wall?
We know that
1 quarter gallon of paint ⇄ 1/12 wall
?? ⇄ 1 wall
Now we just divide both sides of the equivalence
[tex]\begin{gathered} \frac{1}{?}=\frac{\frac{1}{12}}{1} \\ \frac{1}{?}=\frac{1}{12} \end{gathered}[/tex]We clear the equation in order to find the unkown value
[tex]\begin{gathered} \frac{1\cdot12}{1}=\text{?} \\ 12=\text{?} \end{gathered}[/tex]Then, we need 12 quarters of paint3/3=_/21Fill the blank space with the answer
In the expression 3/3=_/21, it can be observed that 7 is multipled by denominator 3 in order to obtain 21 in in denominator. So same number, 7 is also multiplied with the numerator also.
[tex]\frac{3}{3}\times\frac{7}{7}=\frac{21}{21}[/tex]So, 21 is to be filled at blank space.
Find the probability that a randomly chosen point is the figure lies in the shaded region. Give all answers in fraction and percent forms.help with number 5 or all of them if u can pls
NUMBER 5:
INFORMATION:
We have a trapeze and, we need to find the probability that a randomly chosen point is the figure lies in the shaded region
STEP BY STEP EXPLANATION:
To find the probability, we must divide the area of the shaded region by the total area of the trapeze
[tex]\text{ Probability}=\frac{Shaded\text{ area}}{Total\text{ area}}[/tex]- Total area:
To calculate the total area, we must use the formula for the area of a trapeze
[tex]A_{trapeze}=\frac{(b_1+b_2)h}{2}[/tex]Where, b1 and b2 are the bases and h is the height
Then, analyzing the trapeze we can see that b1 = 20, b2 = 14 and h = 12
[tex]A_{total}=A_{trapeze}=\frac{(20+14)12}{2}=204[/tex]So, the total area is 204 square units
- Shaded area:
To find the shaded area, we must subtract the no shaded area from the total area.
We can see that the no shaded area is a rectangle with width = 14 and height = 12
Now, using the formula for the area of a rectangle
[tex]A_{rectangle}=\text{ width}\times\text{ height}=14\times12=168[/tex]Then, subtracting the area of the rectangle from the total area
[tex]A_{\text{ no shaded}}=204-168=36[/tex]So, the no shaded are is 36 square units.
Finally, the probability would be
[tex]\begin{gathered} \text{ Probability}=\frac{36}{204} \\ \text{ Simplifying,} \\ \frac{3}{17}\approx17.65\text{ \%} \end{gathered}[/tex]ANSWER:
the probability that a randomly chosen point is the figure lies in the shaded region is
[tex]\frac{3}{17}\approx17.65\text{ \%}[/tex]i432--5-4-3-2-1(3.1)2 3 45 X(0,-1)What is the equation of the line that is parallel to thegiven line and has an x-intercept of -3?Oy=x+3Oy=x+2Oy=-x+3Oy=-³x+2
Explanation:
Step 1. We are given the graph of a line and we need to find the equation of the line parallel to it that has an x-intercept of -3.
Since the new line will be a parallel line it means that it will have the same slope. Therefore, our first step is to find the slope of the current line.
Given any line, we find the slope as shown in the following example diagram:
Step 2. Using the previous method, the slope of our line is:
The new line will have the same slope of 2/3.
Step 3. We are also told that the x-intercept of the new line is -3, which means that the new line will cross the y-axis at x=-3, that point is:
(-3,0)
We will label that point of our new line as (x1,y1):
[tex]\begin{gathered} (x_1,y_1)\rightarrow(-3,0) \\ \downarrow \\ x_1=-3 \\ y_1=0 \end{gathered}[/tex]Step 4. So far, we know that the new line will have a slope of 2/3:
[tex]m=\frac{2}{3}[/tex]And that it includes the point (-3,0) where x1=-3 and y1=0.
To find the equation, we use the point-slope equation:
[tex]y-y_1=m(x-x_1)[/tex]Step 5. Substituting the known values into the formula:
[tex]y-0=\frac{2}{3}(x-(-3))[/tex]Solving the operations:
[tex]\begin{gathered} y=\frac{2}{3}(x+3) \\ \downarrow \\ \boxed{y=\frac{2}{3}x+2} \end{gathered}[/tex]Answer:
[tex]\boxed{y=\frac{2}{3}x+2}[/tex]i am supposed to find the volume of this pyramid
For this type of problems we use the formula for the volume of a pyramid:
[tex]\begin{gathered} V=\text{ }\frac{1}{3}A_bh \\ A_b\text{ is the area of the base} \\ h\text{ is the height of the pyramid} \end{gathered}[/tex]Substituting h=12 yd and knowing that the area of a square is side*side we get that:
[tex]\begin{gathered} A_b=\text{ 10yd }\cdot10yd=100yd^2 \\ V=\frac{1}{3}100yd^212yd=100yd^24yd=400yd^3 \end{gathered}[/tex]Are they inverses?f(x) = 6x - 6, g(x) = 1/6x + 1
Given function,
f(x) = 6x - 6
or
y = 6x -6
The inverse of a function is calculated by replacing the values of x and y
therefore
Inverse (y = 6x - 6)
x = 6y - 6
x + 6 = 6y
6y = x + 6
y = x/6 + 6/6
y = 1/6*x + 1
or
g(x) = 1/6*x + 1
Hence, both are inverse of each other.