The values in the table represent a linear function with the function rule y = 3x + 6, where x is the input value and y is the output value.
To determine if the values in the table represent a linear function, we can check if there is a constant rate of change between the input and output values. This means that for every increase or decrease in the input value, there is a constant increase or decrease in the output value.
Looking at the input and output values in the table, we can see that for every increase of 1 in the input value, the output value increases by 3. This constant rate of change indicates that the values in the table represent a linear function.
To find the function rule, we can use the slope-intercept form of the equation for a linear function, which is y = mx + b, where m is the slope and b is the y-intercept. In this case, we can find the slope by dividing the change in output values by the change in input values:
slope = change in output / change in input = 3/1 = 3
Therefore, the slope of the function is 3. To find the y-intercept, we can use one of the points in the table. For example, we can use the first row, which gives an input value of 0 and an output value of 6:
y = mx + b
6 = 3(0) + b
b = 6
Therefore, the y-intercept of the function is 6. Combining the slope and y-intercept, we can write the function rule as:
y = 3x + 6
This means that for any input value x, the output value y is equal to three times x plus six.
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2. One of Kara's birthday balloons has a leak. The amount of air in the balloon can be modeled by the
function A(t) = 1.48 (0.87), where A(t) is the number of cubic feet of air in the balloon t seconds
after the leak begins.
a. According to the model, by what percentage is the balloon losing air each second?
Therefore, according to the model, the balloon is losing air at a rate of 13% per second.
What is function?In mathematics, a function is a rule that maps each element in one set, called the domain, to a unique element in another set, called the range. A function can be represented by an equation, a graph, or a table. Functions are commonly used to describe relationships between variables, such as how the area of a square changes as its side length increases. They are a fundamental concept in calculus, linear algebra, and many other branches of mathematics.
Here,
The function A(t) = 1.48(0.87)ⁿ represents the amount of air in the balloon t seconds after the leak begins.
To find the percentage at which the balloon is losing air each second, we need to find the percentage decrease in the amount of air for every one second of time passing.
To do this, we can calculate the ratio of the amount of air at time t=1 second to the amount of air at t=0 seconds, and then find the percentage decrease:
A(1) / A(0) = [1.48(0.87)¹] / [1.48(0.87)⁰] = 0.87
The ratio is 0.87, which means that the balloon is losing 13% of its air each second (since 1 - 0.87 = 0.13, which is 13% expressed as a decimal).
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the marked price of an tv is 45000. after allowing certain percent discount and adding 13% vat, the tv is sold at rs 40680.calculate the selling price of tv without vat (ans=36,000)
Step-by-step explanation:
x = 45000 - (Discount % * 45000/100)
x = 45000 - (Discount % * 450)
Given that the selling price after adding 13% VAT is Rs. 40680, we can write:
x + (13% * x/100) = 40680
Simplifying the above equation, we get:
x = 36000
Therefore, the selling price of the TV without VAT will be x, which is Rs. 36000.
So the final answer is that the selling price of the TV without VAT is Rs. 36000
please mark brainliest
PLEASE PLEASE HELP IT IS DUE TONIGHT!!!
I need help with number 9.
USE MATH WAY IT HELPS ALOT
Abby tosses one penny and Babby tosses two pennies. What is the probability that Babby gets the same number of heads that Abby gets?
The probability that Babby gets the same number of heads that Abby gets is 1/8 + 1/8 = 1/4. To solve this problem, we need to consider all the possible outcomes of Abby and Babby's coin tosses.
There are four possible outcomes for Abby's toss: heads or tails, and two outcomes for Babby's toss: heads or tails. Therefore, there are a total of 4 x 4 = 16 possible outcomes for the two coin tosses.
To determine the probability that Babby gets the same number of heads as Abby, we need to identify the outcomes where this happens. Abby can get either 0 or 1 heads, so we need to consider the outcomes where Babby gets 0 or 1 heads as well.
The possible outcomes where Abby gets 0 heads are:
Abby: tails, Babby: tails tails
Abby: tails, Babby: heads tails
In both of these outcomes, Babby also gets 0 heads, so the probability of this happening is 2/16 = 1/8.
The possible outcomes where Abby gets 1 head are:
Abby: heads, Babby: tails heads or heads tails
Abby: tails, Babby: heads heads
In two of these outcomes, Babby also gets 1 head, so the probability of this happening is 2/16 = 1/8. Therefore, the probability that Babby gets the same number of heads that Abby gets is 1/8 + 1/8 = 1/4.
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Please help me I'm stuck.
[tex]\cfrac{89.40~~ - ~~\stackrel{ \textit{minus the tax of each} }{0.50-0.50-0.50-0.50-0.50-0.50}}{6}\implies \cfrac{86.40}{6}\implies \stackrel{ each }{14.40}[/tex]
Write an equation in point-slope form that has a y-intercept at (0, -3) and also contains the point (4, 5).
Write your answer as an equation with numbers, letters, and symbols - no spaces.
Answer: The point-slope form of an equation of a line is: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
We are given the y-intercept at (0, -3), which means that this point is on the line and that the line crosses the y-axis at y = -3. Therefore, the y-coordinate of the y-intercept is -3.
We are also told that the line passes through the point (4, 5), which means that this point is also on the line. Therefore, x1 = 4 and y1 = 5.
To find the slope of the line, we can use the two points (0, -3) and (4, 5):
slope = (y2 - y1) / (x2 - x1)
slope = (5 - (-3)) / (4 - 0)
slope = 8 / 4
slope = 2
Now that we have the slope and a point on the line, we can use the point-slope form to write the equation of the line:
y - y1 = m(x - x1)
y - 5 = 2(x - 4)
This is the equation of the line in point-slope form that has a y-intercept at (0, -3) and also contains the point (4, 5).
Step-by-step explanation:
PLEASE HELP! NONE OF THE TUTORS ARE ONLINE!
Answer:
4 if x < 3
Step-by-step explanation:
First, find the equation of the line. From the graph we can tell the y-intercept is 4 and the slope is 0. Using y=mx+b, we find that y=(0)x+4 (same as y=4). f(x) is the same as y, so all you have to write is 4.
To find the domain, you must look at where the function is defined. It is only defined to the left of the point (3,4), where x < 3. We know its only defined there because the arrow and line only go in that direction. We know that it should be a < not a ≤ because the point at (3,4) is hollow, so (3,4) is not a point in the function and not included in the domain.
A motor racing circuit has length 55 miles. A straight section of the circuit has length 14 miles. What fraction of the circuit is the straight section? Give your answer in its simplest form.
one angle of a triangle measures 20 and the other two angles are in a ratio of 3:5 what are the measures of the 2 angles
Answer:
60 and 100 degrees.
Step-by-step explanation:
Sum of the other 2 angles = 180-20 = 160 degrees.
3 + 5 = 8
160 / 8 = 20
- so the other 2 angles are:
3*20 = 60 and
5*20 = 100 degrees.
3(x-4)-2>5x solve for x
Answer:
x < -7
Step-by-step explanation:
3(x-4)-2>5x
3x - 12 - 2 > 5x
3x - 14 > 5x
-2x > 14
x < -7
Answer: x<-7
Step-by-step explanation: 3(x-4)= 3x-12
3x-14>5x
5x-3x=2x
-14>2x
-14/2=-7
-7>x
PLS HELP REALLY NEED IT
Answer:
An even function is symmetric about the y-axis. An odd function is symmetric about the origin. As the graphed function is neither symmetric about the origin, nor symmetric about the y-axis, it is neither even nor odd.
Step-by-step explanation:
Even and odd functions are special types of functions.
Even functionf(x) = f(- x) for all values of x.Symmetric about the y- axis.Example even function: y = x²Odd functionf(–x) = –f(x) for any value of x.Symmetric about the origin.Example odd function: y = x³An even function is symmetric about the y-axis. An odd function is symmetric about the origin. As the graphed function is neither symmetric about the origin, nor symmetric about the y-axis, it is neither even nor odd.
in this problem you will solve the nonhomogeneous system a. write a fundamental matrix for the associated homogeneous system 1 1 2 0 b. compute the inverse c. multiply by and integrate (do not include and in your answers). d. give the solution to the system (do not include and in your answers). if you don't get this in 2 tries, you can get a hint.
a. Φ(t)= P.D.[tex]P^{-1}[/tex] is the fundamental matrix of the homogeneous system.
b. [tex]P^{-1}[/tex]= 1/√5 || 1 2 || || -2 1 || is the inverse
c. x(t)= Φ(t)∫ Φ(t)-1.b(t) dt + Φ(t).[tex]x_0[/tex]
d. The solution to the system is x(t)= || e-t/√5 (1-e2t)/2√5 - (2e2t -3)/2√5 || || 1/√5 e-t/√5 +2/√5 (e2t-1)/2√5 ||
In this problem, we will solve the nonhomogeneous system.
Firstly, we will write a fundamental matrix for the associated homogeneous system 1 1 2 0.
a) Fundamental matrix for the homogeneous system
The homogeneous system of equations can be written as:
X'=AX
Here, X is the vector of unknowns, and A is a matrix of constants.
For the given homogeneous system of equations, we have:
1 1 2 0X1' X2'= 1 2 X1X2
X'= AX
Thus, the matrix A can be written as:
A= 1 2 1 0
Now, let us solve the eigenvalue problem for matrix A as follows:
| A - λI |= 0
⇒| 1 - λ 2 || 1 || λ - 0 || 1 || 2 || 0 - λ || 0 |
⇒ (1-λ)(0-λ)-2⋅1=0
⇒ λ2 - λ - 2 = 0
On solving, we get:
λ1 = -1 and λ2 = 2
Thus, the eigenvectors corresponding to these eigenvalues are:
For λ1 = -1, A - (-1)I= 2 2 || x || = 0 1 || y ||
⇒2x+2y = 0y = -2x
Thus, the eigenvector corresponding to λ1 is:
x1= || 1 || and x2 = || -2 ||
The normalized eigenvector corresponding to λ1 is:
x1= || 1/√5 || and x2 = || -2/√5 ||
For λ2 = 2, A - 2I= -1 2 || x || = 0 -2 || y ||
⇒-x+2y = 0y = 1/2x
Thus, the eigenvector corresponding to λ2 is:
x1= || 2 || and x2 = || 1 ||
The normalized eigenvector corresponding to λ2 is:
x1= || 2/√5 || and x2 = || 1/√5 ||
Thus, the matrix P of eigenvectors is:
P= || 1/√5 -2/√5 || || 2/√5 1/√5 ||
Hence, the fundamental matrix of the homogeneous system is:
Φ(t)= P.D.[tex]P^{-1}[/tex]
where D= diagonal matrix of eigenvalues= || -1 0 || || 0 2 ||and [tex]P^{-1}[/tex] is the inverse of matrix P.
We will now find the inverse of matrix P.
b) Computation of inverse of matrix P
The inverse of matrix P is:
[tex]P^{-1}[/tex]= 1/√5 || 1 2 || || -2 1 ||
c) Multiplication by and integration
Multiplying Φ(t) by e
At, we have:e AtΦ(t)= PeDt.
[tex]P^{-1}[/tex].eAt= P.|| e-1t 0 || || 0 e2t ||.[tex]P^{-1}[/tex]
The solution to the system is:
x(t)= Φ(t)∫ Φ(t)-1.b(t) dt + Φ(t).[tex]x_0[/tex]
where b(t) is the vector of inhomogeneous terms, and [tex]x_0[/tex] is the initial condition.
d) Solution to the system
The nonhomogeneous system of equations can be written as:
X'=AX + b
where b= 1 [tex]e^{-t}[/tex]
The solution to the system is:
x(t)= Φ(t)∫ Φ(t)-1.b(t) dt + Φ(t).x0= P.|| e-t/√5 (e2t -1)/2√5 || || -2(e2t-1)/2√5 e-t/√5 ||.P-1 .|| 0 || || 1 ||+ P.|| 1/√5 -2/√5 || || e-t/√5 (e2t -1)/2√5 || || -2(e2t-1)/2√5 e-t/√5 ||.P-1 .|| -1/√5 || || 2/√5 ||= || 1/√5 -2/√5 || || e-t/√5 (1-e2t)/2√5 || || (e2t-3)/2√5 e-t/√5 ||.|| 0 || || 1 ||+ || 1/√5 -2/√5 || || e-t/√5 (e2t -1)/2√5 || || -2(e2t-1)/2√5 e-t/√5 ||.|| -1/√5 || || 2/√5 ||
The final answer is: x(t)= || e-t/√5 (1-e2t)/2√5 - (2e2t -3)/2√5 || || 1/√5 e-t/√5 +2/√5 (e2t-1)/2√5 ||
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Which graph shows the solution to the equation below?
log Subscript 3 Baseline (x + 2) = 1
On a coordinate plane, a curve starts in quadrant 3 and curves up into quadrant 1 and approaches y = 3. It crosses the x-axis at (1, 0). A horizontal straight line is at y = 1.
On a coordinate plane, a curves starts in quadrant 4 and curves up into quadrant 1 and approaches y = 3. It crosses the x-axis at (1, 0). A horizontal straight line is at y = negative 1.
On a coordinate plane, a curve starts in quadrant 3 and curves up into quadrant 1 and approaches y = 1. It crosses the x-axis at (negative 1, 0). A horizontal straight line is at y = 1.
On a coordinate plane, a curves starts in quadrant 3 and curves up into quadrant 1 and approaches y = 2. It crosses the x-axis at (negative 1, 0). A horizontal straight line is at y = negative 1.
Nοne οf the given graphs match this descriptiοn, sο nοne οf them shοw the sοlutiοn tο the equatiοn.
What is the equivalent expressiοn?Equivalent expressiοns are expressiοns that wοrk the same way despite their appearance. If twο algebraic expressiοns are equivalent, then the twο expressiοns have the same value when the variable is set tο the same value.
The equatiοn lοg Subscript 3 Baseline (x + 2) = 1 can be rewritten as 3^1 = x + 2. This simplifies tο x = 1. Therefοre, the sοlutiοn tο the equatiοn is x = 1.
On the cοοrdinate plane, this sοlutiοn is represented by a vertical line passing thrοugh x = 1.
Hence, Nοne οf the given graphs match this descriptiοn, sο nοne οf them shοw the sοlutiοn tο the equatiοn.
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Answer: A
Step-by-step explanation:
b/4 + 2 = -1 please help
Answer : The answer is B= -12
The first three terms of a sequence are given. Round to the nearest thousandth
75, 90, 108, ...
Find the 7th term.
The value of the 7th term of the geometric progression is 223.9488
Based on the information given,
First term = 75
Second term = 90
Common ratio = 90/75 = 1.2
The nth term of a geometric progression is calculated as:
[tex]a_n=ar^{r-1}[/tex]
The 7th term will then be:
[tex]= 75 \times (1.2)^6[/tex]
[tex]=75\times2.985984[/tex]
[tex]=223.9488[/tex]
Therefore, the value of the 7th term of the geometric progression is 223.9488.
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The table represents the equation y=2-4x
The missing value in the table for x = –1 is Y=6 is the value that x=-1 lacks.
Describe equation-An equation is a mathematical statement that two expressions are equal. It consists of two expressions that contain numbers, variables, and/or operators, and is written in a symbolic form. Equations are used to explain a variety of real-world phenomena and also used to describe the behavior of physical systems.An equation can be used to solve for a single unknown variable or to find relationships between multiple variables.
How to resolve the equation?
The equation's unknown value can be obtained by inserting known values for them.
Provided is the equation y=2-4x.
discover y when x=-1
Replace x=-1 in the given equation,
We obtain y=2-4 (-1)
y=6
Therefore, the value of y at x=-1 is 6.
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Complete questions as follows-
The table represents the equation y = 2 – 4x The x-values are the The y-values are the The missing value in the table for x = –1 is y =
A book sold 35,500 copies in its first month of release. Suppose this represents 9.9% of the number of copies sold to date. How many copies have been sold to date?
Round your answer to the nearest whole number.
Answer:
Step-by-step explanation:
smelly a becasue
Use substitution to solve the system 5r+2w=68, r=3w
Answer:
4
Step-by-step explanation:
5r+2w=685(3w)+2w=6815w+2w=6817w=68w=68/17w=4Answer: w=4
Step-by-step explanation:
1). 5(3w)+2w=68
2). 15w+2w=68
3). 17w=68
4). 17w/17=68/17
5). w=4
the base of a right triangular prism is a right isosceles triangle whose equal sides measure 25 cm each. the volume of the prism is 0.075 cubic meters. find the height of the prism.
The height of the right triangular prism is 84.3 cm.
To find the height of the right triangular prism, let's use the formula for the volume of a right triangular prism.
Volume of the right triangular prism = 1/2 × base × height × length
Where, base = 25 cm and height is what we need to find.
We are given that the volume of the prism is 0.075 cubic meters. We first need to convert the volume into cubic cm as the other units are given in cm. 1 cubic meter = 100 cm × 100 cm × 100 cm= 1,000,000 cubic cm
So, 0.075 cubic meters = 0.075 × 1,000,000 = 75,000 cubic cm
Substituting all the known values into the formula, we get:
75,000 = 1/2 × 25 × height × length
Hence, height = 75,000 / (1/2 × 25 × length)
Now, we need to find the length of the prism. As the base of the right triangular prism is a right isosceles triangle, its hypotenuse is the length of the prism. Using the Pythagorean theorem to find the hypotenuse, we have:
Length² = 25² + 25²
Length² = 1,250
Length = √1,250
Length ≈ 35.36 cm
Substituting this length into the equation we found earlier, we get:
height = 75,000 / (1/2 × 25 × 35.36)height ≈ 84.3 cm
So, the height of the right triangular prism is approximately 84.3 cm.
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Myra buys an old cell phone from her friend for $60 and signs up for a phone plan that costs $20
per month. Which graph represents Myra's total expenses, y, for the phone and x months on the
phone plan?
When x = 3, y = 60 + 20(3) = 120. So, we can plot the point (3, 120).
What is equation?An equation is a mathematical statement that uses symbols, numbers, and operations to show that two expressions are equal. It usually contains one or more variables, which represent unknown values that need to be solved for. Equations are used in a wide range of mathematical fields, such as algebra, geometry, calculus, and physics, to model real-world situations and solve problems. Some common examples of equations include:
Linear equation: y = mx + b
he total expenses for Myra's phone plan include the initial cost of buying the phone plus the monthly cost of the phone plan. Therefore, the total cost can be represented by the equation:
y = 60 + 20x
where y is the total cost and x is the number of months on the phone plan.
To graph this equation, we can plot a point at (0, 60) to represent the initial cost of buying the phone. Then, we can plot additional points by plugging in different values of x into the equation and finding the corresponding values of y. For example:
When x = 1, y = 60 + 20(1) = 80. So, we can plot the point (1, 80).
When x = 2, y = 60 + 20(2) = 100. So, we can plot the point (2, 100).
When x = 3, y = 60 + 20(3) = 120. So, we can plot the point (3, 120).
Connecting these points gives us a straight line, since the equation is linear.
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HOW CAN I SOLVE THIS ASAP??
Suppose you trap 255 stickleback fish in a lake and mark them by clipping the first spine of their dorsal fins. One month later you recapture a total of 162 individuals, 78 of them marked. Estimate the total population size.
The estimated total population size of stickleback fish in the lake is approximately 530 individuals.
The mark and recapture method can be used to estimate the total population size of a species in a particular area. Based on the information provided, we can use the Lincoln-Petersen method to estimate the population size.
The formula for the Lincoln-Petersen method is
N = (M x R) / C
Where
N = total population size
M = number of individuals in the first sample (marked individuals)
R = number of individuals in the second sample (recaptured individuals)
C = number of marked individuals recaptured in the second sample
Using the given information, we can plug in the values to the formula
N = (255 x 162) / 78
N = 529.62
N = 530
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Find the Exact answer:
Answer:
-1
Step-by-step explanation:
calculator
:)
6. Match each situation to one of the equations. (4 pts)
A
A whale was diving at a rate of 2 meters per second. How long will it take for
the whale to get from the surface of the ocean to an elevation of 12 meters
at that rate?
B.
A swimmer dove below the surface of the ocean. After 2 minutes, she was
12 meters below the surface. At what rate was she diving?
C.
The temperature was-12 degrees Celsius and rose to 2 degrees Celsius.
What was the change in temperature?
D. The temperature was 2 degrees Celsius and fell to -12 degrees Celsius. What
was the change in temperature?
The equation would be: ΔT = 2 - (-12) = 14 degrees Celsius, ΔT = T2 - T1, where ΔT is the change in temperature, T2 is the final temperature (-12 degrees Celsius)
A. d = rt, where d = 12 meters, r = 2 meters per second (rate), and t is the time it takes for the whale to get to an elevation of 12 meters. The equation would be:
12 = 2t
B. r = d/t, where r is the rate of diving, d = 12 meters (depth), and t = 2 minutes (time). The equation would be:
r = 12/(2 x 60) = 0.1 meters per second
C. ΔT = T2 - T1, where ΔT is the change in temperature, T2 is the final temperature (2 degrees Celsius), and T1 is the initial temperature (-12 degrees Celsius). The equation would be:
ΔT = 2 - (-12) = 14 degrees Celsius
D. ΔT = T2 - T1, where ΔT is the change in temperature, T2 is the final temperature (-12 degrees Celsius), and T1 is the initial temperature (2 degrees Celsius). The equation would be:
ΔT = -12 - 2 = -14 degrees Celsius
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A full glass of water can hold 1/6 of a bottle. How many glasses of water can be filled with 3 1/2 bottles of water?
Answer:
21
Step-by-step explanation:
[tex]\frac{x}{6}=\frac{7}{2} \\x=21[/tex]
Answer:
21 glasses------------------------------
Let the number of glasses be g.
Then g glasses can be filled with 3 1/2 bottles of water.
Set up equation to represent this and solve for g:
(1/6)g = 3 1/2(1/6)g = 7/2g = 7/2 : 1/6 g = 7/2 * 6g = 7*3g = 21can someone helpp please
The center of the specified circle is at (-7, 4). Thus, the updated center will be (-7 - 3, 4 - 4) = (-10, 0).
What are the new equation and circle center?In order to move the circle 3 units to the right and 4 units below, we must subtract 3 from x and 4 from y. Thus, the updated center will be (-7 - 3, 4 - 4) = (-10, 0).
The equation for the resulting circle can be discovered by adding the new center and simplifying. The standard version of the circle's equation is [tex](x - h)^2 + (y - k)^2 = r^2[/tex], with (h, k) denoting the circle's center and r denoting the radius. We can use the new center (-10, 0) and the original equation [tex](x+7)^2+(y-4)^2=36[/tex]to replace the original equation.
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Estimate 15 times 34 by rounding each number to the nearest
Which of the following lines is parallel to the line that goes through the points (5, 8) and (3, 6)? Please help me!!!!!!
Answer:
Any line with the slope 1 or y = x + b
Step-by-step explanation:
Parallel lines by definition have the same slope
Value of the y-intercept or b doesn't matter in this case
You have to find the slope of the line through (3,6) and (5,8)
Slope equation is
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]Plug in values given
[tex]\frac{8-6}{5-3}[/tex]
Evaluate
[tex]\frac{2}{2} =1[/tex]
Any line with the slope of 1 (or no co-efficient in front of x) would be parallel to the line through (3,6) and (5,8)
suppose that a highway is governed by a use fee charged to motorists that is based on congestion, operation and maintenance. the total traffic t is used to determine the cost of 5t2. what is the average cost per motorist?
The average cost per motorist on a highway governed by a use fee based on congestion, operation and maintenance is determined by dividing the total cost ([tex]5t^2[/tex]) by the total traffic (t). So, the average cost per motorist is 5t.
The average cost per motorist for a highway governed by a use fee based on congestion, operation and maintenance can be determined by dividing the total cost ([tex]5t^2[/tex]) by the total traffic (t).
So, the average cost per motorist is 5t.
To better understand how this works, let's look at an example.
Suppose the total traffic is 20.
In this case,
the total cost is 5 × 202 = 2000.
Therefore, the average cost per motorist is 2000/20 = 100.
The cost per motorist is determined by the total traffic because the more cars there are on the highway, the more congested the highway will be.
Consequently, the more congested the highway, the more operation and maintenance is required, and thus the higher the use fee will be.
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Question 1-12
6
Select all the expressions that are equivalent to 9x + 5(6/5x+3)-30
15x-30
16(x-2)
15x-15
15(x-1)
16(x-1)
16(x-1)
The equivalent expressions for the expression 9x + 5(6/5x+3)-30 are (15x-15) and 15(x-1).
Equivalent expressions:
Equivalent expressions are mathematical expressions that have the same value, even though they may look different.
Here are some examples:
2x + 4 and 4 + 2x are equivalent expressions.
(Proof: 2x + 4 = 4 + 2x for any value of x)
3(x + 2) and 3x + 6 are equivalent expressions.
(Proof: Distributing the 3, we get 3(x + 2) = 3x + 6)
Here we have
9x + 5(6/5x+3)-30
The above expression can be simplified as follows
=> 9x + 5(6/5x) +5(3) -30 [ Multiply 5 with (6/5x+3) ]
=> 9x + (6x) + 15 -30
=> 15x - 15 [ Add like terms ]
=> 15(x - 1) [ take 15 as common ]
Hence,
The equivalent expressions for the expression 9x + 5(6/5x+3)-30 are (15x-15) and 15(x-1).
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