step 1: convert to improper fraction
57/7 - 26/7
step 2: subtract numerators
31/7
step 3: change to a mixed number
4 3/7
what’s the inverse function of
f (x) = 2x+3
Answer:
[tex]f^{2} (x) = \frac{1}{2} x + \frac{3}{2}[/tex]Step-by-step explanation:
Answer:
[tex]f^{-1}[/tex] = [tex]\frac{x-3}{2}[/tex]
The inverse of a function is just the opposite of the function.
Which inequality is true when the value of x is -3?
-x+6.5 < 1
-x+6.5 < -1
x + 6.5 < -1
-x+6.5 > 1
Answer:
-x + 6.5 > 1 Is true.
Step-by-step explanation:
The explaination is given in the Picture.
Find the missing values in the given matrix equation. \[ \left[\begin{array}{rr} 5 & a \\ 4 & -5 \end{array}\right]\left[\begin{array}{rr} b & -4 \\ -1 & 5 \end{array}\right]=\left[\begin{array}{rr} 6
$a = -8$ and $b = \frac{-520}{49}$
The matrix equation you provided is:
$$\left[\begin{array}{rr} 5 & a \\ 4 & -5 \end{array}\right]\left[\begin{array}{rr} b & -4 \\ -1 & 5 \end{array}\right]=\left[\begin{array}{rr} 6 \\ -7 \end{array}\right]$$
We can solve for the missing values by using the matrix equation $A \cdot B = C$. In this case, we have $A \cdot B = C$, where $A$ is the matrix on the left, $B$ is the matrix on the right, and $C$ is the matrix on the far right.
We can solve for $a$ and $b$ by using the inverse of $A$. To calculate the inverse of $A$, we use the formula: $$A^{-1} = \frac{1}{\det(A)}\left[\begin{array}{cc} -5 & a \\ 4 & 5 \end{array}\right]$$
The determinant of $A$ is $5 \cdot -5 - 4 \cdot a = -25 - 4a$, so $$A^{-1} = \frac{1}{-25 - 4a}\left[\begin{array}{cc} -5 & a \\ 4 & 5 \end{array}\right]$$
We can then calculate $b$ by multiplying the inverse of $A$ by the matrix $C$. $$\begin{align*}
A^{-1} \cdot C &= \frac{1}{-25 - 4a}\left[\begin{array}{cc} -5 & a \\ 4 & 5 \end{array}\right]\left[\begin{array}{rr} 6 \\ -7 \end{array}\right]\\
&= \frac{1}{-25 - 4a}\left[\begin{array}{rr} -5\cdot 6 + a\cdot (-7) \\ 4 \cdot 6 + 5 \cdot (-7) \end{array}\right]\\
&= \frac{1}{-25 - 4a}\left[\begin{array}{rr} -30 - 7a \\ 24 - 35 \end{array}\right]
\end{align*}$$
Solving for $b$, we have $$\begin{align*}
b &= \frac{-30 - 7a}{-25 - 4a}\\
&= \frac{-30 - 7a}{-25 - 4a}\cdot \frac{25 + 4a}{25 + 4a}\\
&= \frac{25\cdot(-30 - 7a) + 4a\cdot(-25 - 4a)}{25^2 + 4a^2}\\
&= \frac{-750 - 175a - 100a - 16a^2}{625 + 16a^2}
\end{align*}$$
Now, we can solve for $a$ by substituting $b$ into the equation $A \cdot B = C$. $$\begin{align*}
A\cdot B &= \left[\begin{array}{rr} 5 & a \\ 4 & -5 \end{array}\right]\left[\begin{array}{rr} b & -4 \\ -1 & 5 \end{array}\right]\\
&= \left[\begin{array}{rr} 5b + a(-4) & 5(-4) + a(5) \\ 4b - 5(-1) & -5(-1) - 5(5) \end{array}\right]\\
&= \left[\begin{array}{rr} -20 - 4a & 25 + 5a \\ 4b - 5 & 25 - 25 \end{array}\right]
\end{align*}$$
Comparing this to the equation $A\cdot B = C$, we can solve for $a$: $$\begin{align*}
6 &= -20 - 4a\\
-7 &= 4b - 5\\
&= 4\left(\frac{-750 - 175a - 100a - 16a^2}{625 + 16a^2}\right) - 5\\
&= \frac{-3000 - 700a - 400a - 64a^2}{625 + 16a^2} - 5\\
&= \frac{-3500 - 700a - 400a - 64a^2}{625 + 16a^2}\\
\end{align*}$$
By comparing this to the equation $6 = -20 - 4a$, we can solve for $a$: $$\begin{align*}
-3500 - 700a - 400a - 64a^2 &= -20 - 4a\\
64a^2 + 400a + 700a + 3520 &= 0\\
a^2 + 5a + 56 &= 0\\
(a + 8)(a + 7) &= 0\\
a &= -8 \;\text{or}\; -7
\end{align*}$$
Thus, the missing values are $a = -8$ and $b = \frac{-520}{49}$.
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the data is given for 62 students in certain class regarding their mathematics marks out of 100.take the classes 0-10,10-20..and prepare frequency distribution table and cumulative frequency table more than or equal to type 55,60,81,90,45,65,45,52,30,85,20,10,75,95,09,20,25,39,45,50,78,70,46,64,42,58,31,82,27,11,78,97,07,22,27,36,35,40,75,80,47,69,48,59,32,83,23,17,77,45,05,23,37,38,35,25,46,57,68,45,47,49.from the prepared table answer the following question 1.
The frequency and cumulative frequency distribution tables for the given data are below in the solution part.
What is the cumulative frequency of the data?Cumulative frequency is used to calculate the number of observations in a data collection that is above (or below) a specific value.
The data is provided for 62 students in a certain class in terms of their maths marks out of 100.
55, 60, 81, 90, 45, 65, 45, 52, 30, 85, 20, 10, 75, 95, 09, 20, 25, 39, 45, 50, 78, 70, 46, 64, 42, 58, 31, 82, 27, 11, 78, 97, 07, 22, 2 36, 35, 40, 75, 80, 47, 69, 48, 59, 32, 83, 23, 17, 77, 45, 05, 23, 37, 38, 35, 25, 46, 57, 68, 45, 47, 49.
The frequency distribution table for the given data is as follows:
Class Frequency
(Marks obtained) (No. of students)
0 - 10 4
10 - 20 3
20 - 30 8
30 - 40 9
40 - 50 13
50 - 60 6
60 - 70 5
70 - 80 6
80 - 90 5
90 - 100 3
N = 62
The cumulative frequency table more than or equal to the type for the given data is as follows:
Class Frequency Cumulative frequency
(Marks obtained) (No. of students)
0 - 10 4 62
10 - 20 3 58
20 - 30 8 55
30 - 40 9 47
40 - 50 13 38
50 - 60 6 25
60 - 70 5 19
70 - 80 6 14
80 - 90 5 8
90 - 100 3 3
N = 62
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Which graph models function m?
x- 0 1 2 3 4 5
m(x)- -9 -4 -1 0 -1 -4
Use the remainder theorem to find the remainder when
dividing
f(x) = -4x^3 + 2x^3 -3x+5 by x - 2
-17.
According to the remainder theorem, the remainder when dividing a polynomial f(x) by a linear factor x-a is equal to f(a). In this case, we want to find the remainder when dividing f(x) = -4x^3 + 2x^3 -3x+5 by x - 2, so we need to find f(2).
f(2) = -4(2)^3 + 2(2)^3 -3(2) + 5
f(2) = -4(8) + 2(8) -6 + 5
f(2) = -32 + 16 -6 + 5
f(2) = -17
Therefore, the remainder when dividing f(x) = -4x^3 + 2x^3 -3x+5 by x - 2 is -17.
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Man this shi 40 points
The match of the terms and correct locations are:
1. A - Amplitude
2. B is compression
3. C is rarefaction
What are longitudinal waves?A longitudinal wave is a form of wave in which its direction of propagation is similar to the direction of vibration of the particles of the medium through which the wave is travelling. The waves generated by a stretched or compressed spiral spring produces longitudinal waves.
When a spiral spring is streched or compressed, on removal of the force a series of compression and rarefactions of the sections of the spring are produced. This sections vibrates in the direction of propagation of the waves produced.
Thus the match of the terms and correct locations are:
i. A - Amplitude
ii. B is compression
iii. C is rarefaction
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GEOMETRY PLEASEE HELPPP
14 : 25 best represents the number of unshaded squares to total squares. The solution has been obtained by using arithmetic operations.
The four mathematical operations that result from dividing, multiplying, adding, and subtracting are quotient, product, sum, and difference.
We are given a figure in which some squares are shaded and rest are unshaded.
Number of total squares = 10 × 10 = 100
Number of shaded squares = 44
So, Number of unshaded squares = 100 - 44 = 56
Ratio of unshaded squares to total squares is as follows
56 : 100
Reducing to the lowest, we get
14 : 25
Hence, 14 : 25 best represents the number of unshaded squares to total squares.
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4K + 12 = -36
solving 2 step equations
Step-by-step explanation:
[tex]4k + 12 = - 36 \\ 4k = - 36 - 12 \\ 4k = - 48 \\ k = - \frac{48}{4} \\ k = - 12[/tex]
#hope it's helpful to you
Match each number with its name
Answer:
1,254 - whole number; 0.13 - terminating; 0.123456789... - non-terminating/non-repetitive; 0.143143143... - repeating decimal
Step-by-step explanation:
A whole number is a number without any decimals or fractions. A terminating number is one that has an end. A non-terminating number is one that continues on forever. A repeating number is one that has the same pattern and continues on forever.
Please help me! I'm horrible at math!
Answer:
I think the answer is C. 65 m
Step-by-step explanation:
Answer:
L=22
Step-by-step explanation:
For the area of a rectangle you have to multiply the width by the length.
This problem would look like L*W=A. Being that you already have the area and the width, you would just have to fill in for these.
L*6.5=143
Then just follow the rules of PEMDAS to sole for L. In this case this would be dividing 6.5 by both sides.
L=22
Pls help me it’s to go from lease value to the greatest and closest to zero!
According to the information, the expressions that would match the descriptions would be both expressions have the same result, so it doesn't matter which description they are associated with. both are the largest and the smallest value.
How to find the correct expressions for the descriptions?To find the correct descriptions that match the expressions we must look at the graph. In this case q and n represent two numbers on the number line. In this case, to relate them to a description we must find the number to which they refer:
q = -1n = -4The expression q - n would be equal to -1 - 4 = -5The expression n - q would be equal to - 4 - 1 = -5In accordance with the above, we could say that the descriptions would look like this:
Closest to zero = qLeast value = q - nGreatest value = n - qIn this case, both expressions have the same result, so it doesn't matter which description they are associated with. both are the largest and the smallest value.
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Solve the equation in exponential form Y^x = 65 / 177 A. Log 65/177 X= y B. log x 65/177 = y C. Log 65/177 y = x D. Log y 65/177 = X
Therefore, the correct answer is C. Log 65/177 y = x.
The correct answer is C. Log 65/177 y = x.
To solve the equation in exponential form, we need to use the properties of logarithms. The equation Y^x = 65 / 177 can be rewritten in logarithmic form as Log Y (65/177) = x. Using the property of logarithms, Log a^b = b Log a, we can rewrite the equation as Log (65/177) Y = x. This is the same as option C, Log 65/177 y = x.
Therefore, the correct answer is C. Log 65/177 y = x.
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what is the median of 1, 1, 2, 3, 7, 9, 10, 10, 15, 17, 19
Answer:
9
Step-by-step explanation:
The median is the number in the middle of a set of numbers.
Our set of numbers: 1, 1, 2, 3, 7, 9, 10, 10, 15, 17, 19
In this case the median is 9
raina bulit a rectangular fence around her pigpen that had a length of 325 feet and a width of 185 feet. what is the perimeter of raina's pigpen?
The perimeter of Raina's pigpen is 1020 feet.
What is Perimeter?Perimeter is the total distance around the edge of a two-dimensional shape. It is the sum of the lengths of all sides of the shape. Perimeter is typically measured in units such as inches, feet, meters, or centimeters, depending on the system of measurement being used.
To find the perimeter of the rectangular pigpen, we need to add up the lengths of all four sides. The formula for the perimeter of a rectangle is:
perimeter = 2 * length + 2 * width
Plugging in the values we know, we get:
perimeter = 2 * 325 + 2 * 185
perimeter = 650 + 370
perimeter = 1020
Therefore, the perimeter of Raina's pigpen is 1020 feet.
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HELPPP!!!!
What should be reason 2 in the following proof?
The reason that should be used to complete statement 2 "∠2 and ∠3 are supplementary" is linear pair postulate.
What is the linear pair theorem?In Mathematics, the linear pair theorem is sometimes referred to as linear pair postulate and it states that the measure of two angles would add up to 180° provided that they both form a linear pair.
This ultimately implies that, the measure of the sum of two adjacent angles would be equal to 180° when two parallel lines are cut through by a transversal.
According to the linear pair theorem, we have the following supplementary angles:
∠2 + ∠3 = 180°
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pls I need help with this
Answer:34
Step-by-step explanation:
plsssssssss hlp, geometry
Answer:
I believe opposing angles are parallel, so it would be 98
Step-by-step explanation:
Zach's plants grew 2 feet in 7 weeks.
How many centimeters did Zach's plants grow?
1 ft = 0.3 m
1 m = 100 cm
Enter your answer in the box.
( ) cm
Using the unitary method, we found that Zach's plants grew 60cm in 7 weeks.
What is meant by the unitary method?The unitary method is a strategy for problem-solving that involves first determining the value of a single unit and then multiplying that value to determine the required value. Therefore, the goal of this method is to establish values in relation to a single unit. Always write the things that need to be calculated on the right side and the things that are known on the left side to simplify things. The unitary approach must be applied whenever we need to determine the ratio of one quantity to another.
Given that the height the plant grew in 2 weeks = 2 feet
We are asked to convert it into centimetres.
This can be done using the unitary method.
Now, the unitary method can be used to find the value of multiple units when the value of the single unit is known.
Here we are given,
1 ft = 0.3 m
But we need feet and centimetre relation.
So we use the metre and centimetres relation.
1m = 100cm
Using the unitary method,
0.3m = 0.3* 100 = 30 cm
So,
1 feet = 0.3m = 30 cm
Then,
2 feet = 30 * 2 = 60 cm
Therefore using the unitary method, we found that Zach's plants grew 60 cm in 7 weeks.
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Help with a problem I do not understand
If you answer brainliest but must have:
High quality Explanation
And just one link so I could understand
( I do not care is it is verified or not. )
If has
Links that are not ALLOWED
Nonsesne
Spam
Will get DELETED. Thank you for your help.
Answer:
[tex]x^2+5x+4+\dfrac{3x-8}{x^2+5x-4}[/tex]
Step-by-step explanation:
Long Division Method of dividing polynomialsDivide the first term of the dividend by the first term of the divisor and put that in the answer.Multiply the divisor by that answer, put that below the dividend and subtract to create a new polynomial.Repeat until no more division is possible.Write the solution as the quotient plus the remainder divided by the divisor.The dividend is the polynomial which has to be divided.
The divisor is the expression by which the dividend is divided.
Given:
[tex]\textsf{Dividend:} \quad x^2+10x^3+25x^2+3x-24[/tex][tex]\textsf{Divisor:} \quad x^2+5x-4[/tex]Following the steps of long division, divide the given dividend by the divisor:
[tex]\large \begin{array}{r}x^2+5x+4\phantom{)}\\x^2+5x-4{\overline{\smash{\big)}\,x^4+10x^3+25x^2+3x-24\phantom{)}}}\\{-~\phantom{(}\underline{(x^4+\phantom{(}5x^3-\phantom{(}4x^2)\phantom{-b)))))))))}}\\5x^3+29x^2+3x-24\phantom{)}\\-~\phantom{()}\underline{(5x^3+25x^2-20x)\phantom{)))..}}\\4x^2+23x-24\phantom{)}\\-~\phantom{()}\underline{(4x^2+20x-16)\phantom{}}\\3x-8\phantom{)}\end{array}[/tex]
The quotient q(x) is the result of the division.
[tex]q(x)=x^2+5x+4[/tex]The remainder r(x) is the part left over:
[tex]r(x)=3x-8[/tex]The solution is the quotient plus the remainder divided by the divisor:
[tex]\implies q(x)+\dfrac{r(x)}{b(x)}=\boxed{x^2+5x+4+\dfrac{3x-8}{x^2+5x-4}}[/tex]
PNDM got dilated about the origin and formed P' N' D' M'. Write the dilation rule.
(x,y) -->
Since PNDM got dilated about the origin and formed P' N' D' M', the dilation rule is (x, y) → (2x, 2y).
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)
Substituting the given parameters into the scale factor formula, we have the following;
Scale factor = Dimension of image/Dimension of pre-image
Scale factor = 4/2
Scale factor, k = 2.
Therefore, the dilation rule is given by:
(x, y) → (kx, ky)
(x, y) → (2x, 2y)
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2) Consider the list(9,2,5,4, 12, 10). a) Compute the mean of the list. b) Compute the standard deviation of the list. 3) The Math and Verbal SAT scores for the entering class at a certain college is summarized below: average Math SAT = 570, SD = 85 average Verbal SAT = 525, SD = 105 r=0.80 The investigator wants to use the Verbal score(x) to predict the Math score(y). a) Find the linear regression equation and use it to predict the Math score of a student who receives a 720 on the Verbal portion of the test.
b) (8 pts) If a student's Verbal percentile rank is 80%, he, his score is higher than 80% of the students taking the test, what is his percentile rank on the Math portion?
The mean of the list is 7
The standard deviation of the list is 4/69
The linear regression equation is y = 227.5 + 0.65*x
The percentile rank on the Math portion for a student with a Verbal percentile rank of 80% is approximately 73.5%.
2a) The mean of the list can be computed by adding all of the numbers in the list together and dividing by the number of items in the list.
Mean = (9+2+5+4+12+10)/6 = 42/6 = 7
2b) The standard deviation of the list can be computed by finding the difference between each number in the list and the mean, squaring these differences, finding the average of these squared differences, and then taking the square root of this average.
Standard deviation = sqrt(((9-7)^2 + (2-7)^2 + (5-7)^2 + (4-7)^2 + (12-7)^2 + (10-7)^2)/6) = sqrt(22) = 4.69
3a) The linear regression equation can be found using the formula:
y = b0 + b1*x
Where b0 is the y-intercept and b1 is the slope. The slope can be found using the formula:
b1 = r*(SDy/SDx)
Plugging in the given values:
b1 = 0.80*(85/105) = 0.65
The y-intercept can be found using the formula:
b0 = meany - b1*meanx
Plugging in the given values:
b0 = 570 - 0.65*525 = 227.5
So the linear regression equation is:
y = 227.5 + 0.65*x
To predict the Math score of a student who receives a 720 on the Verbal portion of the test, plug in x = 720 into the equation:
y = 227.5 + 0.65*720 = 693
So the predicted Math score is 693.
3b) To find the percentile rank on the Math portion for a student with a Verbal percentile rank of 80%, use the formula:
z = (x-mean)/SD
Where z is the z-score, x is the score, mean is the mean of the scores, and SD is the standard deviation of the scores.
Plugging in the given values for the Verbal scores:
z = (x-525)/105
Solving for x:
x = 105*z + 525
Since the Verbal percentile rank is 80%, the z-score is 0.84 (from a z-table). Plugging this into the equation:
x = 105*0.84 + 525 = 613.2
So the Verbal score corresponding to the 80th percentile is 613.2.
To find the Math score corresponding to this Verbal score, plug in x = 613.2 into the linear regression equation:
y = 227.5 + 0.65*613.2 = 623.6
So the Math score corresponding to the 80th percentile on the Verbal portion is 623.6.
To find the percentile rank on the Math portion for this score, use the formula:
z = (x-mean)/SD
Plugging in the given values for the Math scores:
z = (623.6-570)/85 = 0.63
Using a z-table, the corresponding percentile rank is approximately 73.5%.
So the percentile rank on the Math portion for a student with a Verbal percentile rank of 80% is approximately 73.5%.
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15.F(x)=−529, F(x)=x^2+33; h(x)=∣x∣−233 ; g(x)=2x
The values of F(x), h(x), and g(x) when x=3 are 42, -230, and 6, respectively.
The given functions are F(x)=−529, F(x)=x^2+33, h(x)=∣x∣−233, and g(x)=2x.
To find the value of F(x) when x=3, we can substitute x=3 into the equation F(x)=x^2+33 and solve for F(x):
F(x)=x^2+33
F(3)=3^2+33
F(3)=9+33
F(3)=42
Similarly, to find the value of h(x) when x=3, we can substitute x=3 into the equation h(x)=∣x∣−233 and solve for h(x):
h(x)=∣x∣−233
h(3)=∣3∣−233
h(3)=3−233
h(3)=-230
And to find the value of g(x) when x=3, we can substitute x=3 into the equation g(x)=2x and solve for g(x):
g(x)=2x
g(3)=2(3)
g(3)=6
Therefore, the values of F(x), h(x), and g(x) when x=3 are 42, -230, and 6, respectively.
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The product of two functions, (fg)(x), is defined as f(x)*g(x). We are given f(x)=6x-7 and g(x)=5-x. Find the product of these functions.
The product between f(x) and g(x) is equal to -6x² + 37x - 35.
The product of two functions, (fg)(x), is defined as f(x)*g(x). Therefore, to find the product of the given functions, we simply need to multiply them together:
(fg)(x) = (6x -7)(5 - x)
Using the distributive property, we can simplify this expression:
(fg)(x) = (6x)(5) - (6x)(x) - (7)(5) + 7(x)
(fg)(x) = 30x - 6x² - 35 + 7x
Combining like terms, we get:
(fg)(x) = -6x² + (30x + 7x) - 35
(fg)(x) = -6x² + 37x - 35
So the product of the two functions is (fg)(x) = -6x² + 37x - 35.
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What is the domain and range of y = log(-x + 3) - 1?
Answer:
The argument of the logarithmic function should be greater than zero.
Thus, for y = log(-x + 3) - 1 to be real-valued, we need:
-x + 3 > 0
or
x < 3
So, the domain of the function is all real numbers less than 3.
To find the range, let's consider the behavior of the logarithmic function.
As x approaches 3 from the left, the argument of the logarithm approaches zero from the negative side, which means the logarithm approaches negative infinity.
As x approaches negative infinity, the argument of the logarithm becomes very large and negative, which means the logarithm approaches negative infinity.
Therefore, the range of the function y = log(-x + 3) - 1 is all real numbers.
Step-by-step explanation:
Write a quadratic function f whose zeros are -2 and 9 .
To write a quadratic function f whose zeros are -2 and 9 , we have to factor the function by (x+2) and (x-9).
How to find the quadratic function of f?A quadratic function is a second-degree mathematical function whose graph is a parabola. The general form of a quadratic function is given by f(x) = ax² + bx + c, where a, b and c are constants and a cannot be equal to zero. The variable x represents the input of the function and f(x) represents the output or result of the function. To find the quadratic function of f we first need to multiply these factors, like this:
f(x)= (x+2) (x-9)Expanding the product, we have:f(x)= x²-7x-18So the quadratic function whose zeros are -2 and 9 is:
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Help I don't understand.
Tim sells two types of pizza. He charges $10 for a cheese pizza and $15 for a pepperoni pizza. Yesterday he sold 64 pizzas in all. For every cheese pizza he sells 3 pepperoni pizzas. How much money did he make selling pizzas yesterday?
Answer:$880
Step-by-step explanation:
1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3
4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64
55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55
so to explain 1 cheese pizza to 3 pepperonis(1/3) that is 4 pizzas together, and we do that until 64. If pepperoni pizza is 15 each, we time that by 3 which is 45, plus the 10 for cheese pizza which makes it 55. we do 55 dollars until we equal the 64 pizzas, which is 16 together. so 55 x 16=880 dollars selling pizza
Curtis wants to save money for the future. Curtis invests $700 in an
account that pays interest rate of 6.25%.
How many years will it take for the account to reach $15,900? Round
your answer to the nearest hundredth.
A = = P(1+r)t
five students each wrote an expression to represent the perimeter of the given rectangle [3x+3x) +(4x+4x)+( 3+3)
Answer:
The given rectangle is not fully defined, as it is missing some measurements such as the length and width. Without this information, it is not possible to accurately calculate the perimeter of the rectangle.
However, assuming that the missing measurement is the width of the rectangle, then the expressions given by the five students would be:
2(3x + 4x + 3) = 14x + 6
2(6x + 6) + 2(4x + 6) = 20x + 24
2(3x + 3) + 2(4x + 3) = 14x + 12
2(6x + 3) + 2(4x + 3) = 20x + 12
2(6x + 3x) + 2(3 + 4x) = 18x + 10
Note that all expressions follow the formula for the perimeter of a rectangle, which is P = 2l + 2w, where l is the length and w is the width of the rectangle.