Answer:
3 and 4 ==> see work below
[tex]5. \quad\quad f^{-1}(x) = x^{1/7}[/tex]
[tex]6. \quad\quad f^{-1}(x) = -\left(\dfrac{5x}{2}\right)^{1/3}$}\\\text{We can also write this as $-\sqrt[3]{\frac{5x}{2}}$ }\\[/tex]
Step-by-step explanation:
Definition of inverse functions
If f and g are inverse functions, then f(x) = y if and only if g(y) = x
Or, in other words
If f(g(x)) = (g(f(x)) = x
then f and g are inverse functions
Q3
We have f(x) = x + 4 and g(x) = x - 4
To find f(g(x)), substitute g(x) = x - 4 wherever there is an x term in f(x)
f(g(x)) = g(x) + 4
= x - 4 + 4 = x
g(f(x)) = f(x) - 4
= x + 4 - 4 =x
Hence f(x) and g(x) are inverse functions
Q4
[tex]f(x) = \dfrac{1}{4}x^3\\\\g(x) = (4x)^{1/3}[/tex]
[tex]\\\begin{aligned}f(g(x)) &= \dfrac{1}{4} (g(x))^3\\\\\end{aligned}[/tex]
[tex]\begin{aligned}(g(x))^3 &= \left((4x)^{1/3} \right)^3 \\& = (4x)^{\frac{1}{3} \cdot 3}\\& = 4x\end{aligned}[/tex]
Therefore
[tex]\\\begin{aligned}f(g(x)) &= \dfrac{1}{4} (g(x))^3\\&= \dfrac{1}{4} \cdot 4x\\&= x\\\end{aligned}[/tex]
[tex]\begin{aligned}g\left(f(x)\right) & = \left(4f(x)\right)^{1/3}\\&= \left(4 \cdot \dfrac{1}{4}x^3\right)^{1/3}\\& = \left(x^3\right)^{1/3}\\& =x& \end{aligned}[/tex]
So f(x) and g(x) are inverse functions
Q5
[tex]\text{Given $f(x) = x^7 $ we are asked to find inverse $f^{-1}(x)$}[/tex]
[tex]\rm{Let \: y = f(x) = x^7}\\[/tex]
Interchange x and y:
[tex]x = y^7[/tex]
Solve for y:
[tex]y = x^{1/7}[/tex]
The right hand side is the inverse function of f(x)
[tex]f^{-1}(x) = x^{1/7}[/tex]
Q6
[tex]\rm{Given \;f(x) = -\dfrac{2}{5}x^3 \:find\:the\:inverse,\;f^{-1}(x)}[/tex]
Using the same procedure as for Q5
[tex]y=-\dfrac{2}{5}x^3\\\\x=-\dfrac{2}{5}y^3\\\\\text{Solve for y}\\[/tex]
[tex]y^3=-\dfrac{5x}{2}[/tex]
[tex]y=-\left(\dfrac{5x}{2}\right)^{1/3}\\\\\\\text{Inverse of $f(x)$ is $f^{-1}(x) = -\left(\dfrac{5x}{2}\right)^{1/3}$}\\\text{We can also write this as $-\sqrt[3]{\frac{5x}{2}}$ }\\[/tex]
b/8 < 8 help me please I also need the graphic
The solution of the inequality given is b < 64
the graph is attached
How to solve for bIn the equation, let us replace b with x
To solve the inequality x/8 < 8 for x, we need to isolate x on one side of the inequality.
We can do this by multiplying both sides of the inequality by 8, which will cancel out the 8 in the denominator on the left side:
Therefore, the solution to the inequality x/8 < 8 is x < 64.
This means that any value of x that is less than 64 will make the inequality true.
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Triangle ABC is dilated to create triangle A'B'C'. If AB=12 and A'B'=9, what is the scale factor of the dilation?
If the side AB=12 and side A'B'=9, then the scale factor of the dilation is 3/4.
The "Scale-Factor" of a dilation is the ratio of the corresponding side lengths of the two similar figures.
In this case, we can find the scale factor by dividing the length of side A'B' by the length of the corresponding side AB:
So, scale factor = A'B'/AB,
Substituting the values,
We get,
Scale factor = 9/12,
Scale Factor = 3/4,
Therefore, the scale factor of the dilation is 3/4. This means that all corresponding side lengths of the dilated triangle A'B'C' are 3/4 of the length of the corresponding side lengths of the original triangle ABC.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer: C {m | m > 2}
Step-by-step explanation:
write the number in exponential form with the base of 2
2^3m-4 > 2^2
compare the exponents = 3m-4 >2
move the constant to the right and then change the sign
3m> 2+4 add
3m>6 divide
m>2
For the functions f and g find a. (f+g)(x), b. (f-g)(x), c. (f
The value of the given functions are:
(a) (f + g)(x) = (x -8 + 14) = x + 6
(b) (f-g)(x) = (x -8 - 14) = x - 22
(c) (f • g)(x) = (x - 8 (14)) = 14x - 112
(d) (f/g)(x) = (x - 8)/ 14
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
We have the functions are as follows:
f(x)=x - 8,
g(x)=5 + 9
To solve :
a. (f + g)(x),
b. (f-g)(x),
c. (f • g)(x), and
d. (f/g)(x)
Now,
(a) (f + g)(x) = (x -8 + 14) = x + 6
(b) (f-g)(x) = (x -8 - 14) = x - 22
(c) (f • g)(x) = (x - 8 (14)) = 14x - 112
(d) (f/g)(x) = (x - 8)/ 14
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The given question is incomplete, complete question is:
For the functions f and g find a. (f+ g)(x), b. (f-g)(x), c. (f• g)(x), and d. (f/g)(x) f(x)=x - 8, g(x)=5 + 9
Solve for p.
p − 4
2
= 3
The value of p in the expression is 45
What is additive inverse?Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0.
For example a+5 = 2 , by solving this we add the additive inverse of 5 to both sides. The additive inverse of 5 is -5
this means,
a+5-5 = 2-5
a = 2-5
a = -3
Similarly, p-42 = 3 is solved in the same way. we add the additive inverse of -42 which is +42 to both sides,
p-42+42 = 3+42
p = 3+42
p = 45
therefore the value of p is 45
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I really need help please
Valid row operations are:
6R₁+ R₂ → R₃-(1/2) R₁ → R₁R₁ ↔ R₂R₁ ÷ 2 → R₁2R₂ → R₂-1R₃+ R₂ → R₂2R₁ → R₂R₁ + R₂ → R₂What are invalid row operations?Invalid row operations are:
0R₁ → R₁ (this is equivalent to multiplying a row by zero, which is not a valid row operation)
R₃ ÷ 0 → R₃ (division by zero is undefined)
-2 ÷ R₁ → R₁ (division by a variable is not a valid row operation)
2R₁ + R₂ → R₂ (the row operation should be adding multiples of one row to another row, not a combination of multiple rows)
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Hi can someone please help me? Look in the picture. I’ll give brainly if you explain :)
Find each of the following probabilities for a normal distribution.
a. p(z > 1.25)
b. p(z > –0.60)
c. p(z < 0.70)
d. p(z < –1.30)
The solution is: the following probabilities for a normal distribution is:
a. 0.5434
b. 0.5746
c. 0.2957
d. 0.0902
Here, we have,
Explanation:
To find each probability we need to use the normal distribution table that is accumulated to the left, so each probability is equal to
P(-1.80 < z < 0.20) = P( z < 0.20) - P( z < -1.80)
P(-1.80 < z < 0.20) = 0.5793 - 0.0359
P(-1.80 < z < 0.20) = 0.5434
P(-0.40 < z < 1.40) = P( z < 1.40) - P( z < -0.40)
P(-0.40 < z < 1.40) = 0.9192 - 0.3446
P(-0.40 < z < 1.40) = 0.5746
P(0.25 < z < 1.25) = P(z < 1.25) - P(z < 0.25)
P(0.25 < z < 1.25) = 0.8944 - 0.5987
P(0.25 < z < 1.25) = 0.2957
P(-0.90 < z < -0.60) = P(z < -0.60) - P(z < -0.90)
P(-0.90 < z < -0.60) = 0.2743 - 0.1841
P(-0.90 < z < -0.60) = 0.0902
Therefore, the answers are, the following probabilities for a normal distribution is:
a. 0.5434
b. 0.5746
c. 0.2957
d. 0.0902
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Please solve this quickly!!!!
The sum expression [tex][2(4 + \frac9n)^4](\frac9n) + ... + [2(4 + \frac{9n}n)^4](\frac9n)[/tex] using the sigma notation is [tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]
Writing the sum using the sigma notationFrom the question, we have the following parameters that can be used in our computation:
[tex][2(4 + \frac9n)^4](\frac9n) + ... + [2(4 + \frac{9n}n)^4](\frac9n)[/tex]
From the above expression, we can see that the different expression in each term is
9/n
So, we introduce a variable
Assuming the variable is i, the i-th term of the expression would be[tex]t(i) = [2(4 + \frac{9i}n)^4](\frac9n)[/tex]
When represented using the sigma notation, we have
[tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]
Hence, the sum expression using the sigma notation is [tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]
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Here are five spinners with orange and white sectors. Each spinner is divided into equal sectors. A a) b) a) For one of the spinners, the probability of spinning orange is Which spinner is this? B A b) For two of the spinners, the probability of spinning orange is more than 40%. Which two spinners are these?
Spinner B is the spinner that has a probability of 1/3 of spinning orange.
How to find the he probability of spinning orange is more than 40%a) For one of the spinners, the probability of spinning orange is 1/3. To identify which spinner this is, we need to find the spinner that has exactly one orange sector out of three total sectors.
From the given spinners, Spinner B is the only spinner that has one orange sector out of three, so Spinner B is the spinner that has a probability of 1/3 of spinning orange.
b) For two of the spinners, the probability of spinning orange is more than 40%. To find these spinners, we need to look for the spinners that have at least three orange sectors out of a total of eight sectors (since 3/8 is greater than 40%).
From the given spinners, Spinner A and Spinner C both have three orange sectors out of eight total sectors, so they are the two spinners for which the probability of spinning orange is more than 40%.
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PLEASE SOMEONE HELP ME DO THIS MATH PROBLEM
i am having a mental breakdown rnn :(.
Check the picture below.
Andy has $100 in an account. The interest rate is 6% compounded annually.
To the nearest cent, how much will he have in 2 years?
The amount that will be in Andy's account in 2 years after the addition of interest is $112.36
How to calculate the amount in Andy's account after 2 years ?Andy has $100 in an account
An interest rate of 6% is compounded annually
The amount that will be present in the account after 2 years can be calculated as follows
= 100(1+ 6/100)²
= 100(1 + 0.06)²
= 100(1.06)²
= 100(1.1236)
= 112.36
Hence the amount that will be present in the account after 2 years with the addition of interest is $112.36
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a group of students were asked if they are in the math club and if they are in the literature club. Partial results are shown in the table. What is the value of x+y?
Hence Option A. 22 is correct.
How to solveOf the students in the maths club , 67% are not in the literature club.
So the number of students in Maths club =
[ ( Number of students in maths club but not in the literature club) / 67 ] * 100 % = [ 16 / 67 ] * 100% = 24 (Rounded)
Hence, Number of students in maths club and in the literature club =
x = Total Number of students in Maths club - Number of students in maths club but not in the literature club
x = 24 - 16 = 8
Of the students not in the maths club , 78% are not in the in the literature club.
So, Of the students not in the maths club , 100% - 78% = 22% are in the literature club.
So the number of students not in the Maths club =
[ ( Number of students not in the maths club and in the literature club) / 22 ] * 100 %
= [ 4 / 22 ] * 100% = 18.18 = 18 (Rounded)
Hence, Number of students not in the maths club and not in the literature club =
y = Total Number of students not in the Maths club - Number of students not in the maths club and in the literature club
y = 18 - 4 = 14
So, x + y = 8 + 14 = 22.
Hence Option A. 22 is correct.
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What are the values of x
X =
The product of the two external segments and the sum of the lengths of each segment in the circle are equal if two secants are drawn to the circle from a single shared exterior point. The x has a value of 2 units.
What is intersecting secants theorem?If two secant segments are drawn to a circle from an exterior point, the product of the measurements of one secant segment and its external secant segment is equal to the product of the measurements of the second secant segment and its external secant segment.
So, we know that:
BE * AE = CE * DE
Now, insert the values as follows:
(x+1) * (x+12) = (x+4) * (x+5)
x² + x + 12x + 12 = x² + 4x + 5x + 20
13x + 12 = 9x + 20
4x = 8x
x= 2
Then: x = 2 units
Therefore, the product of the two external segments and the sum of the lengths of each segment in the circle are equal if two secants are drawn to the circle from a single shared exterior point. The x has a value of 2 units.
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Find the value of linear correlation coefficient r (statistics)
Answer:
r=1
Step-by-step explanation:
The Pearson correlation coefficient is used to measure the strength of a linear association between two variables, where the value r = 1 means a perfect positive correlation and the value r = -1 means a perfect negataive correlation. So, for example, you could use this test to find out whether people's height and weight are correlated (they will be - the taller people are, the heavier they're likely to be).
what is the surface area of 11cn and 14cm
The surface area of the shape will be 46 yards².
What is the surface area?Surface area refers to the total area that the surface of a three-dimensional object covers. It is measured in square units, such as square meters (m²), square centimeters (cm²), square feet (ft²), etc.
The formula for the surface area of the 2 bases is just b*h
12*8=96 yd²
Finding the lateral area:
(10*10)+(10*10)+(12*10)=
100+100+120=
320 yd²
Add the lateral surface area and the surface area of the 2 bases for the total surface area:
320+96=416 yd²
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At 10.30 a.m, a van left Town X travelling at an average speed of 64 Km/h.
At 11.15 a.m., a car left Town X, travelling on the same road at an average speed of
80 Km/h.
a) At what time did the car catch up with the van?
b) How far from Town X did each vehicle travel when they passed each other?
Answer:
a) 2:15 pm
b) 240 km
Step-by-step explanation:
You want to know the time and place where a car leaving at 11:15 a.m. at 80 km/h catches up with a van leaving at 10:30 a.m. at 64 km/h.
Head startThe van travels for 11:15 -10:30 = :45, or 3/4 hour, before the car starts. This gives it a distance advantage of (3/4 h)(64 km/h) = 48 km.
Closing speedThe speed at which that distance is reduced is the difference between the car speed and the van speed:
80 km/h -64 km/h = 16 km/h
Closing timeThe time it takes for the head-start distance to be reduced to zero is ...
time = distance/speed
time = (48 km)/(16 km/h) = 3 h
a) Meeting timeThree hours after the car leaves, it will catch up with the van. That time is ... 11:15 +3:00 = 14:15 = 2:15 p.m.
b) Meeting distanceIn 3 hours, the car travels (3 h)(80 km/h) = 240 km.
Note that the van has been traveling 3 3/4 hours, so will have also traveled (3 3/4 h)(64 km/h) = 240 km. The two vehicles need to be in the same place at the same time if they are to pass each other.
__
Additional comment
The attached graph shows the two vehicles will have traveled 240 km when they mean at 2:15 pm. The horizontal axis is hours after midnight. The vertical axis is kilometers from town X. The relation graphed is distance = speed × time.
need help please
here is the picture is about Row Ops
The result of adding -3 (row 1) to row 2 is determined as (0 10) |-14.
What is the result of the row multiplication?The resultant of the row multiplication in the Matrice is calculated by applying the following method;
row 1 in the given matrices = [1 -4] | 8
To multiply row1 by -3, we will multiply each entity by 3 as shown below;
= -3(1 -4) | 8
= (-3 12) | -24
To add the result to 3;
(-3 12) | -24 + (3 -2)|10
= (0 10) |-14
Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 3.
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3.4 MIXED FACTORING
1. Utilize all of the strategies for factoring in order to factor the following polynomials.
Reminder: Combine like-terms prior to factoring.
a. x² - 4x-2x+8
Answer:
(x -2)(x -4)
Step-by-step explanation:
You want to factor x² - 4x -2x +8.
Factor by groupingWe recognize that the product of the coefficients of the two linear terms is equal to the contant, so this is more easily factored by not combining like terms prior to factoring.
Grouping the terms in pairs, we find we can factor each pair:
(x² -4x) + (-2x +8)
= x(x -4) -2(x -4) . . . . . these terms have a common factor of (x -4)
= (x -2)(x -4) . . . . . . . factored form of the expression
Factor Completely
n^4 − 4n^3 − 17n^2 − 36n + 108
Answer:
It can't be factor
Step-by-step explanation:
n^4 − 4n^3 − 17n^2 − 36n + 108
The GCF of this is 1, so the equation can't be factor.
y= +- 3/5 is equivalent to?
The equivalent value of the expression is y = + 3/5 and y = -3/5
Given data ,
Let the expression be represented as A
Now , the value of A is
y = ±3/5
On simplifying the equation , we get
y = +3/5
And, y = -3/5
Now , the decimal values of y are
y = ±0.6
Hence , the expression is y = ±0.6
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Find cos B. a. Cosine B = StartFraction 41 Over 40 EndFraction c. Cosine B = StartFraction 40 Over 41 EndFraction b. Cosine B = StartFraction 9 Over 41 EndFraction d. Cosine B = StartFraction 9 Over 40 EndFraction
The answer choice which correctly represents the value of cos B as required is; Cosine B = StartFraction 40 Over 41 EndFraction.
Therefore Choice B is correct
What is the cosine rule?The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles and it states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
we know that from the trigonometric ratios that the cosine of an angle is the ratio of its opposite and hypothenuse.
Hence, we can say that:
cos B = 80 / 82
cos B = 40 / 41.
Inn conclusion, the cosine of angle B following from trigonometric ratios as requested is; cos B = 40 / 41.
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#complete question:
Evaluate the function requested. Write your answer as a fraction in lowest terms.
Triangle A B C. Angle C is 90 degrees. Hypotenuse A B is 82, adjacent B C is 18, opposite A C is 80.
Find cos B.
a.
Cosine B = StartFraction 9 Over 41 EndFraction
c.
Cosine B = StartFraction 9 Over 40 EndFraction
b.
Cosine B = StartFraction 40 Over 41 EndFraction
d.
Cosine B = StartFraction 41 Over 40 EndFraction
What does the circled portion represent in the confidence interval formula?
p±z.
O Sample proportion
O Margin of error
p(1-p)
n
Confidence interval
O Sample Size
The circled portion in the confidence interval formula p ± z represents the Margin of Error, which plays a crucial role in interpreting the range of plausible values for the population parameter.
In the confidence interval formula p ± z, the circled portion represents the Margin of Error.
The Margin of Error is a critical component of a confidence interval and quantifies the level of uncertainty in the estimate.
It indicates the range within which the true population parameter is likely to fall based on the sample data.
The Margin of Error is calculated by multiplying the critical value (z) by the standard deviation of the sampling distribution.
The critical value is determined based on the desired level of confidence, often denoted as (1 - α), where α is the significance level or the probability of making a Type I error.
The Margin of Error accounts for the variability in the sample and provides a measure of the precision of the estimate.
It reflects the trade-off between the desired level of confidence and the width of the interval.
A larger Margin of Error indicates a wider confidence interval, implying less precision and more uncertainty in the estimate.
Conversely, a smaller Margin of Error leads to a narrower confidence interval, indicating higher precision and greater certainty in the estimate.
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Find the measure of EB
The measure of angle subtended by the arc EB is 96 ⁰.
What is the measure of arc angle EB?The measure of angle subtended by the arc EB is calculated by applying the following formula.
Based on the angle of intersecting chord theorem, the theory states that, the angle formed by the intersection of two chords at the circumference of a circle is equal to half of the difference between the arc angles of the two chords.
We will have the following equation;
m∠ECB = ¹/₂( 7x + 6 - (4x + 16))
25 x 2 = 7x + 6 - 4x - 16
50 = 3x - 10
60 = 3x
x = 60/3
x = 20
The measure of arc angle EB is calculated as follows;
m∠EB = 4x + 16
m∠EB = 4(20) + 16
m∠EB = 96 ⁰
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Please help!!!!!!!!!
Answer: I did not do the math, I just tell people how to do it
Hope I helped.
Step-by-step explanation:
Multiply the number of triangles you created by 180.
help me solve this please 2x+5y
Answer:
35
Step-by-step explanation:
Simply plug in the value of your 'x' and 'y':
x = 4.5
y = 5.2
[tex]2(4.5)+5(5.2)=9+26=35[/tex]
Write the equation of a line perpendicular to y = −5/9x + 4 and that passes through point (-5,-4) in slope intercept form.
Answer: y = (9/5)x + 5.
Step-by-step explanation:
The slope of the given line is -5/9. The slope of a line perpendicular to it would be the negative reciprocal of -5/9, which is 9/5. Using the point-slope form of a line, we can write the equation of the line as y - (-4) = (9/5)(x - (-5)). Simplifying this equation gives y + 4 = (9/5)x + 9. Solving for y, we get y = (9/5)x + 5. This is the equation of the line in slope-intercept form.
In summary, the equation of a line perpendicular to y = −5/9x + 4 and that passes through point (-5,-4) is y = (9/5)x + 5.
On a sample tray, 3 out of 6 cake samples are chocolate.
What is the probability that a randomly selected piece of cake will be chocolate?
Write your answer as a fraction or whole number.
The probability that a randomly decided piece of cake maybe chocolate is 1/2 or half of or 0.
The proportion of chocolate cakes to all other cakes can be used to calculate the probability that a person will pick a chocolate cake from the pattern tray.
In this case, there are 3 chocolate cakes out of a total of 6 cakes.
So the probability of selecting a chocolate cake is:
3/6 = 1/2 (Dividing the numerator and denominator by their greatest common factor, in this case, 3 will simplify the fraction 3/6.)
Therefore, the probability of selecting a chocolate cake is 1/2 or 0.5 when expressed as a decimal.
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Miguel is 3 years older than Katrice. In 9 years the sum of their ages will be 51. How old is Miguel now?
PLEASE HELP ME!
LaNiyah uses 2 eggs to make brownies, 3 eggs to make a cake, and 6 eggs to make a soufflé. In all, she has one gross of eggs (that’s 144 eggs). If she only makes brownies and soufflés and she uses all the eggs, write an equation to model the eggs used.
An equation that models the eggs used by LaNiyah is 2b + 6s = 144.
What is an equation?An equation is a mathematical statement that shows that two or more mathematical expressions are equal or equivalent.
Equations contain the equal symbol (=), unlike mathematical expressions that combine variables with numbers, and constants using mathematical operands only.
The number of eggs used to make brownies per unit = 2
The number of eggs used to make cakes per unit = 3
The number of eggs used to make soufflés per unit = 6
The total number of eggs used = 144
Let the total number of brownies made = b
Let the total number of soufflés made = s
Equation:2b + 6s = 144
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