Answer:
A. 34 millimeters.
B. 118 millimeters.
Step-by-step explanation:
We have been given that after m months the height of a plant is [tex]10+3m[/tex] millimeters.
To find the height of plant after 8 months we will substitute m=8 in our given expression.
[tex]\text{The height of plant after 8 months}=10+3\times 8[/tex]
[tex]\text{The height of plant after 8 months}=10+24[/tex]
[tex]\text{The height of plant after 8 months}=34[/tex]
Therefore, the height of plant after 8 months will be 34 millimeters.
B. Now let us find height of plant after 3 years.
First of all we will convert 3 years into months by multiplying 3 by 12 as 1 year equals to 12 months.
[tex]\text{3 years}=3*12\text{ months}=36\text{ months}[/tex]
Now let us substitute m=36 in our given expression.
[tex]\text{The height of plant after 36 months}=10+3\times 36[/tex]
[tex]\text{The height of plant after 36 months}=10+108[/tex]
[tex]\text{The height of plant after 36 months}=118[/tex]
Therefore, the height of plant after 3 years (36 months) will be 118 millimeters.
50 POINTS + BRAINLIEST:
Are the two triangles below similar?
Triangles GHI and JKL are shown. Angle G equals 46 degrees, Angle I equals 27 degrees, Angle K equals 108 degrees, Angle L equals 27 degrees, side GH equals 4, side HI equals 5, side KJ equals 2, side JL equals 4.
Yes; they have congruent corresponding angles.
No; they do not have congruent corresponding angles.
Yes; they have proportional corresponding sides.
No; they do not have proportional corresponding sides.
Answer: No; they do not have congruent corresponding angles.
What is the end behavior of [tex]f(x)=-x^6+2[/tex] ?
Answer:
A. As x→-∞ f(x) →-∞ and as x→∞ f(x) →-∞
Step-by-step explanation:
f(x) = -x^6 +2
As the numbers get very large, the 2 doesn't matter
Let x go to - ∞
f(-∞) = - (- ∞)^6
Anything to an even power is positive
f(-∞) = - ∞
As x →-∞ f(x) →-∞
Let x go to ∞
f(∞) = - ( ∞)^6
Anything to an even power is positive
f(∞) = - ∞
As x →∞ f(x) →-∞
Together, Tran and Luis take 6 hours to deliver newspapers. If Tran works alone, it takes him 9 hours. How long would it take Luis, working alone, to deliver all the newspapers?
Options:
12 hours
15 hours
18 hours
16 hours
Answer:
18 hours
Step-by-step explanation:
We work in fractions of the job done per hour.
So in the case of Tran alone he does 1/9 of the job per hour.
We have the equation 1/9 + 1/x = 1/6 where x is the time taken for Luis to deliver the newspapers.
1/9 + 1/x = 1/6
Multiply through by the LCM 18x:-
2x + 18 = 3x
18 = x
the answer is:
18 hours !
What is the first step when rewriting y=6x^2+18x+14 in the form y=a(x-h)^2+k?
Factor 6 from the first two terms.
Step-by-step explanation:By factoring out "a", you can better see what "h" needs to be.
y = 6(x^2 +3x) +14 . . . . 6 factored from first 2 termsadd the square of half the x-coefficient inside parentheses; add the opposite outside: y = 6(x^2 +3x +2.25) +14 -6(2.25)rewrite as a square; combine the constants: y = 6(x+1.5)^2 +0.5Janine is packing carrots. Each large box holds 20 2-pound bags of carrots. If Janine has 800 bags of carrots, how many boxes can she fill?
Answer: 40 Boxes
Step-by-step explanation: All you need to do is divide 800 by 20.
Answer:
40
Step-by-step explanation:
The product of the roots of $2x^2 - 7x + N = 0$ is $-5.$ Find $N.$
By the fundamental theorem of algebra, we can factorize the quadratic as
[tex]2x^2-7x+N=2(x-r_1)(x-r_2)[/tex]
so that expanding the right hand side gives
[tex]2x^2-7x+N=2x^2-2(r_1+r_2)x+2r_1r_2[/tex]
[tex]\implies\begin{cases}-2(r_1+r_2)=-7\\2r_1r_2=N\end{cases}[/tex]
We're told that the product of the roots is -5, or [tex]r_1r_2=-5[/tex], so we get
[tex]2(-5)=N=-10[/tex]
The value of N for given conditions is -10. It can be calculated as shown below.
Given that:The quadratic equation given is: [tex]2x^2 -7x + N = 0[/tex]
The product of roots of given equation is: -5
To find: Value of N
Explanation for product of roots and Calculations:For quadratic equation [tex]ax^2 + bx + c = 0[/tex], we have:
[tex]\text{Product of roots} = \dfrac{c}{a}\\\\\text{Sum of roots} = \dfrac{-b}{a}[/tex]
For given quadratic equation, we have:
a = 2, b = -7, c = N
Thus, by above formula:
[tex]\text{Product of roots} = \dfrac{c}{a} = \dfrac{N}{2} = -5\\\\N = -5 \times 2 = -10[/tex]
Thus, value of N for given conditions is -10.
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Graphs of Polynomial Functions Gizmo
5 Answer Review
1. What are the degree and leading coefficient of the function y=4x2-3x+7?
A. degree=4 leading coefficient=2
B. degree=2 leading coefficient=4
C. degree=2 leading coefficient=7
D. degree=3 leading coefficient=4
2. What is the lowest degree of the function graphed here? (image is attached to this)
A. 1
B. 2
C. 3
D. 4
3. what is the maximum of x-intercepts that can be found on a graph with equation y=ax5+cx2+f? (the values a, c, and f are real numbers)
A. 2
B. 3
C. 4
D. 5
4. Which polynomial function has a y-intercept of 3?
A. y=2x4+x2-3
B. y=3x2+4
C. y=-4x7-5x+3
D. y=9x3+3x2
5. What is the end behavior of y=-2x13+25x8-3 as x approaches infinity?
a. y=-3
b. y=13
c. y approaches infinity
d. y approaches negative infinity
Answer:
degree=2 leading coefficient=4
lowest degree = 3
maximum of 5 x-intercepts
[tex]y=-4x^7-5x+3[/tex] has y intecept 3
y approaches negative infinity
Step-by-step explanation:
(1) [tex]y=4x^2-3x+7[/tex]
Highest exponent is the degree of the function
Highest exponent =2 so degree =2
Coefficient of x^2 is 4, so leading coefficient is 4
(2) from the graph we can see that
As x approaches infinity, the graph goes down
As x approaches -infinity, the graph goes up
The value of y goes on the opposite direction. So it is a odd degree function. If degree =1 then the graph should be a line
Here the graph is like a curve. Also we have 2 x intercepts . Hence lowest possible degree of the function is 3
(3) y=ax^5+cx^2+f
Here , the degree of the equation is 5
So we will get maximum of 5 x-intercepts
(4) To find the function that has y intercept of 3, we plug in 0 for x in each function
[tex]y=-4x^7-5x+3[/tex]
[tex]y=-4(0)^7-5(0)+3= 3[/tex]
[tex]y=-4x^7-5x+3[/tex] has y intecept 3
(5) [tex]y=-2x^{13}+25x^8-3[/tex]
Here degree is 13 that is odd and leading coefficient is -2 ( negative)
Degree is odd and leading coefficient is negative so the graph of y goes down on the right side.
the graph of y approaches negative infinity when x approaches infinity
The degree and leading coefficient of the polynomial function y=4x2-3x+7 are 2 and 4 respectively. The maximum of x-intercepts for a polynomial graph y=ax5+cx2+f is 5. The polynomial function y=-4x7-5x+3 has a y-intercept of 3 and as x approaches infinity in the function y=-2x13+25x8-3, y approaches negative infinity.
Explanation:1. The degree of the function y=4x2-3x+7 is 2 and the leading coefficient is 4. Therefore B. degree=2 leading coefficient=4 is correct.
2. As the image of the function graphed is not provided, it is impossible to definitively say what the lowest degree of the function is.
3. The maximum number of x-intercepts that can be found on a graph with the equation y=ax5+cx2+f is 5, matching the degree of the polynomial, so D. 5 is correct.
4. The polynomial function y=-4x7-5x+3 has a y-intercept of 3, therefore C. y=-4x7-5x+3 is correct.
5. Since the polynomial y=-2x13+25x8-3 has an odd degree and the leading coefficient is negative, as x approaches infinity, y approaches negative infinity. Therefore D. y approaches negative infinity is correct.
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Mario purchases a prepaid phone plan for $50 at $0.13 per minute. How many minutes can Mario talk on this plan
Mario can talk for 384 minutes on his prepaid phone plan, calculated by dividing his plan's cost, $50, by the per-minute rate of $0.13.
To determine how many minutes Mario can talk on his prepaid phone plan, you would divide the total amount of the plan by the cost per minute. Mario has $50 and the cost per minute is $0.13. To calculate the total minutes, use the formula:
Total Minutes = Total Plan Cost / Cost Per Minute
Let's do the math:
Total Minutes = $50 / $0.13
Total Minutes = 384.6154
Since we cannot have a fraction of a minute in this context, we round down to the nearest whole minute.
Therefore, Mario can talk for 384 minutes on his prepaid plan.
In a survey of music preference, 82 out of 450 student said that they preferred country music . What percent of the students preferred country music ?
[tex]\frac{82}{450}\cdot100\%=\frac{164}{9}\%=18\frac{2}{9}\%[/tex]
Identify the holes, vertical asymptotes and horizontal asymptotes of f(x)=x²+7x+12/-x²-3x+4
The function factors as ...
... f(x) = -(x+3)(x+4)/((x-1)(x+4)) = -(x+3)/(x-1) . . . . x ≠ -4
and the quotient is ...
... f(x) = -(1 +4/(x-1))
... f(x) = -1 -4/(x-1) . . . . . x ≠ -4
This has a hole at x = -4 (where the denominator factor cancels the numerator factor), a vertical asymptote at x=1 (where the denominator is zero), and a horizontal asymptote at y = -1 (the value of the function for large values of x).
The rectangle below has an area of x^2-11x+30x 2 −11x+30x, start superscript, 2, end superscript, minus, 11, x, plus, 30 square meters and a length of x-5x−5x, minus, 5 meters. what expression represents the width of the rectangle?
Answer:
[tex](x-6)[/tex] meters
Step-by-step explanation:
We have been given that the area of a rectangle is [tex]x^2-11x+30[/tex] square meters and a length of [tex](x-5)[/tex] meters.
Since the area of a rectangle is product of its width and length.
[tex]\text{Area of rectangle}=\text{Width of rectangle*Length of rectangle}[/tex]
We can find width of our rectangle by dividing area of rectangle by length of rectangle.
[tex]\text{Width of rectangle}=\frac{\text{Area of rectangle}}{\text{Length of rectangle}}[/tex]
Let us substitute our given values in above formula.
[tex]\text{Width of rectangle}=\frac{x^2-11x+30}{x-5}[/tex]
Let us factor out numerator by splitting the middle term.
[tex]\text{Width of rectangle}=\frac{x^2-6x-5x+30}{(x-5)}[/tex]
[tex]\text{Width of rectangle}=\frac{x(x-6)-5(x-6)}{(x-5)}[/tex]
[tex]\text{Width of rectangle}=\frac{(x-6)(x-5)}{(x-5)}[/tex]
Upon cancelling out x-5 from numerator and denominator we will get,
[tex]\text{Width of rectangle}=(x-6)[/tex]
Therefore, the expression [tex](x-6)[/tex] meters represents width of the rectangle.
Answer:
the answer is x - 6, have a nice day
This set of points is on the graph of a function.
{(−2, 5), (−1, 2), (0, 1), (2, 5)}
Which points are on the graph of the inverse?
Select each correct answer.
(−5, 2)
(2, −1)
(0, 1)
(5, 2)
Answers: (B) (2, -1) and (D) (5, 2)
Step-by-step explanation:
Inverse is when the x's and y's are swapped
Given: (-2, 5), (-1, 2), (0, 1), (2, 5)
Inverse: (5, -2), (2, -1) (1, 0), (5, 2)
The correct answer would be options (B) (2, -1) and (D) (5, 2)
What is an inverse function?The inverse function is defined as a function obtained by reversing the given function.
To determine the inverse of a function, all you have to do is switch where x and y are and resolve for y.
Given that the set of points is on the graph of a function.
{(−2, 5), (−1, 2), (0, 1), (2, 5)}
We have to find the inverse of the function below :
{(−2, 5), (−1, 2), (0, 1), (2, 5)}
When the values of x and y are switched, the inverse is true.
(-2, 5) ⇒ (5, -2),
(-1, 2) ⇒ (2, -1),
(0, 1) ⇒ (1, 0),
(2, 5) ⇒ (5, 2)
Hence, the points {(5, -2), (2, -1) (1, 0), (5, 2)} are on the graph of the inverse.
The correct answer would be options (B) (2, -1) and (D) (5, 2)
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During a sale atthe book store sold for 3$ and magazinssold for2.50. Jan spent 16$ and bought a total of 6 books and magazines. How many of each did she buy.
Answer:
6 books and 10 magazines
Step-by-step explanation:
Blueberries are on sale for $2.80 per pint. The regular price is $3.50 per pint. What is the percent of decrease? Select from the drop-down menu to correctly complete the statement.
0.2
0.25
0.7
20
25
70
Answer:
it is 20% can you mark me brainless
Step-by-step explanation:
Show you work for full credit Use the SUBSITUTION method or ELIMINATION method to solve this system of equations:
Will give brainliest!!
Answer:
continuous.
Step-by-step explanation:
Given function is [tex]f(x)=5x^4-9x^3+x-7[/tex].
and value of a = 7.
Now we need to find if the given function [tex]f(x)=5x^4-9x^3+x-7[/tex] is continuous or not.
By definition of continuity, we know that a function is continuous at a given point if both left and right hand limits are equal.
Left Hand Limit = LHL
[tex]LHL=\lim_{x\rightarrow 7^-}f(x)=5(7)^4-9(7)^3+(7)-7=8918[/tex]
Right Hand Limit = RHL
[tex]RHL=\lim_{x\rightarrow 7^+}f(x)=5(7)^4-9(7)^3+(7)-7=8918[/tex]
Since both limits are equal at a=7 so we can say that given function is continuous at a=7
This is the sum of all the results included in the sample divided by the number of observations. It is the same as the average.
Answer:
Mean is the sum of all the results included in the sample divided by the number of observations.
Explanation:
Suppose we have the score of 5 randomly selected students in a class.
The scores are:
[tex]45,48,52,65,78[/tex]
Now the mean of the 5 randomly selected students will be:
[tex]Mean = \frac{Sum-of-scores-of-five-students }{Number-of-students}[/tex]
[tex]=\frac{45+48+52+65+78}{5}[/tex]
[tex]=\frac{288}{5}[/tex]
[tex]=57.6[/tex]
Therefore, the mean is 57.6
What is the explicit rule for this geometric sequence?
a1=4; an=13·an−1
an=4(1/3)n−1
an=1/3⋅4n
an=1/3⋅4^n−1
an=4(1/3)n
[tex]\text{The explicit rule of geometric sequence}\\\\a_n=a_1 r^{n-1}\\------------------------------\\\text{We have the recursive form}\ a_1=4,\ a_n=\dfrac{1}{3}\cdot a_{n-1}.\\\\\text{Therefore}\ r=\dfrac{1}{3}.\ \text{Substitute:}\\\\\boxed{a_n=4\left(\dfrac{1}{3}\right)^{n-1}}[/tex]
Answer:
Anne found the 10th term of the following sequence. Her steps are shown below.
3, 7, 11, 15, …
1. common difference = 4, a1 = 3
2. an = 3 + (n - 1)4
3. an = 3 + 4n - 4
4. an = 4n - 1
5. a10 = 4(10) – 1
6. a10 = 39
Analyze Anne’s work. Is she correct? If not, what was her mistake?
Yes, she is correct.
No, she needed to find the common ratio because it is a geometric sequence.
No, she substituted the wrong values into the rule to find the equation that represented the sequence.
No, she solved for the 10th term incorrectly.
Step-by-step explanation:
A line has a slope of -4/5. Which ordered pairs can be points on the line is perpendicular to this line
Answer:
Any ordered pairs which have a slope of 5/4.
Step-by-step explanation:
The line has a slope of -4/5 which means the y values have a difference of -4 and the x values have a difference of 5. If the line is perpendicular to this line then its slope must be the negative reciprocal which is 5/4. Any points which have a difference in y values of 5 and a difference of x values of 4 will be on some line perpendicular to the original.
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!!
(5 - 3i)(6 + 2i)
Multiply and simplify.
Answer:
Step-by-step explanation:
(5 - 3i)(6 + 2i)
30 + 10i - 18i - 6i²
i² = - 1
30 - 8i - 6 - (- 1)
30 - 8i + 6
- 8i + 36
36 - 8i
Alternative D
I hope I helped you.
Answer: D
Step-by-step explanation:
(5 - 3i)(6 + 2i)
= 5(6 + 2i) -3i(6 + 2i)
= 30 + 10i -18i - 6i²
= 30 - 8i -6(-1) because i² = -1
= 30 - 8i + 6
= 36 - 8i
Please help me simplify this! I have no idea how to solve this question! Thank you if you do!
If property damage due to erosion along the coast is $60 million each year, how many money would be spent in 4 years?
Consider the scatter plot.
Consider the scatter plot. The line of best fit is
The line of best fit is y = 0.75x + 5.
Choose the best representation for the y-intercept.
The y-intercept of the line of best fit shows that when time started, the distance was 0.75 feet.
The y-intercept of the line of best fit shows that after 0.75 minutes, the distance was 5 feet.
The y-intercept of the line of best fit shows that when time started, the distance was 5 feet.
The y-intercept of the line of best fit shows that when time started, the distance was 0 feet.
Answer:
The correct answer option is: The y-intercept of the line of best fit shows that when time started, the distance was 5 feet.
Step-by-step explanation:
We are given a scatter plot with a best fit line as shown on the given graph.
The equation of the best fit line is given by:
y = 0.75x + 5
So with the help of the equation and by looking at the given graph, we can conclude about the representation of the y intercept that the the y-intercept of the line of best fit shows that when time started, the distance was 5 feet.
Since the distance shown on the y axis is already 5 when the time started at 0 minutes.
Jaime has 6 quarters and some dimes in his pocket . The total value of the coins in 4.50. How many dimes does he have in his pockets
Hi there! :)
Answer:
Jaime has 30 dimes in his pocket.
Step-by-step explanation:
First off, you need to know that:
A quarter is equal to = $0.25
A dime is equal to = $0.10
Jaime has 6 quarters, which means that he has 6 times $0.25:
6 × 0.25 = $1.50
Jaime has a total of $4.50 → Subtract the amout of money represented by the quarters and you'll be left with the amout of money represented by the dimes:
4.50 - 1.50 = $3
Jaime has $3 worth of dimes in his pocket. In order to know how many dimes $3 represents, you'll need to divide "3" by 0.10, which is what 1 dime is worth:
3 ÷ 0.10 = 30 → YOUR ANSWER
There you go! I really hope this helped, if there's anything just let me know! :)
How to solve
3 log 2x=4
Answer:
= 5 * 10 ^ 1/3
Step-by-step explanation:
3 log 2x=4
Divide each side by 3
3/3 log 2x=4/3
log 2x=4/3
Raise each side to the power of 10
10 ^(log 2x)=10 ^(4/3)
2x = 10 ^(4/3)
Divide by 2
2/2x = 1/2 * 10 ^(4/3)
x = 1/2 * 10 ^4/3
10 ^ 4/3 = 10 * 10 ^ 1/3
x = 1/2 ( 10) 10 ^ 1/3
= 5 * 10 ^ 1/3
(r3 +6r2 −21r−18)÷(r−3) solve using synthetic division
Answer:
y = x^2 + 9x + 6 No remainder.
Step-by-step explanation:
The divisor will be 3 The sign on the divisor switches.
3 || 1 + 6 - 21 - 18 ||
3 27 + 18
================================
1 9 6 0
The answser is x^2 + 9x + 6
Suppose there are 10 green, 8 brown, 3 yellow, 8 blue, and 6 red candies in a bag. If you randomly pick out one candy, what is the probability it is red or yellow?
Answer:
9/35, 0.257 or 25.7%Step-by-step explanation:
The basic and simple way to calculate the probability of an event happening is by using this equation:
Number of desired outcomes------------------------------------------------- = Probability Number of all possible outcomesOur desired outcomes are picking either red or yellow candies. The number of desired outcomes in this case is the total number of red and yellow candies. 6 red + 3 yellow = 9
Number of desired outcomes = 9
Number of all possible outcomes in this case is the total number of candies in the bag. 10 green + 8 brown + 3 yellow + 8 blue + 6 red = 35
Number of all possible outcomes = 35
Use the formula and we get that the probabbility of drawing out a yellow or red candy is: 9/35, 0.257 or 25.7% (those are 3 different ways to write the probability)
A square of area 36cm is cut to make two rectangles a and b the ratio of area a to b is 2:1 work ou the dimensions of rectangles a and b
Answer:
The dimensions of rectangle a are 6x4 and dimensions of rectangle b are 6x2.
Step-by-step explanation:
We are given a square with area 36 squared cm. Therefore, dimension of the square will be 6 cm.
The square is cut into two rectangles with areas in the ratio 2:1.
Let the dimensions of the rectangles be 6*a and 6*b. Therefore, we can set up the ratio of areas as:
[tex]\frac{6a}{6b}=\frac{2}{1} \\a=2b[/tex]
Moreover, we can set the combined area of rectangles equal to the area of square to form another equation:
[tex]6a+6b=36\\a+b=6[/tex]
Using substitution method, we can solve for 'a' and 'b' as shown below:
[tex]2b+b=6\\3b=6\\b=2[/tex]
And
[tex]a=2b\\a=2(2)\\a=4[/tex]
Therefore, dimensions of the two rectangles are 6x4 and 6x2, respectively.
Jenny starts a scarf knitting business. She spends $160 on supplies to start the business, and she spends $4.50 to make each scarf. She sells each scarf for $12. Write and solve an inequality that can be used to determine the number of scarves jenny must sell in order to make a profit. What is the minimum number of scarves jenny must sell in order to make a profit
Answer:
Minimum 22 scarves Jenny has to sell in order to make a profit.
Step-by-step explanation:
Let the number of scarves knitted be 'x'.
Then cost price of the scarves = $ (160+4.5x)
Total selling price of the scarves = $ 12x
In order to attain a profit selling price > cost price
Therefore 12x > 160+4.5x
⇒12x - 4.5x > 160
⇒7.5x > 160
⇒ x >160÷7.5
⇒x > 21.33
SO minimum number of scarves should be 22 a whole number.
To find the minimum number of scarves Jenny must sell to make a profit, set up the inequality 12s > 160 + 4.50s, which represents her earnings from selling scarves being greater than her expenses. Solve for s to obtain s > 21.3. As scarves are sold in whole numbers, Jenny must sell at least 22 scarves to make a profit.
Explanation:To determine the number of scarves that Jenny must sell in order to make a profit, we can set up and solve an inequality. The inequality will represent Jenny's total expenses compared to her total earnings.
Jenny's initial expenses are $160 and it costs $4.50 to make each scarf. This means her total expenses can be represented as 160 + 4.50s, where s is the number of scarves.
Jenny sells each scarf for $12, so her earnings from selling scarves can be represented as 12s.
To establish a profit, Jenny's earnings should be greater than her expenses, so:
12s > 160 + 4.50s
We can solve this inequality by first subtracting 4.50s from each side to isolate the variable:
7.5s > 160
Then, divide both sides by 7.5 to solve for s:
s > 21.3
Since scarves are sold in whole numbers, Jenny needs to sell at least 22 scarves to make a profit.
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What is the justification for each step in solving the inequality?
3x+5/8≥4x−1/2
Select from the drop-down menus to correctly justify each step.
3x+5/8≥4x−1/2 Given
3x≥4x−9/8 ?????
−x≥−9/8 ?????
−x/−1≥−9/8/−1 ?????
x≤9/8 ?????
Chose from
Multiplication or Division property of order
Distributive property
Addition or Subtraction property of order
Step-by-step explanation:
[tex]3x+\frac{5}{8}\geq 4x-\frac{1}{2}[/tex]
Subtract 5/8 on both sides
To subtract 5/8 we make the denominators same
[tex]3x\geq 4x-\frac{1*4}{2*4}-\frac{5}{8}[/tex]
Addition or Subtraction property of order is used
[tex]3x\geq 4x-\frac{9}{8}[/tex]
Subtract 4x on both sides
Addition or Subtraction property of order is used
[tex]-x\geq -\frac{9}{8}[/tex]
Now divide both sides by -1
Multiplication or Division property of order is used
[tex]\frac{-x}{-1} \geq \frac{-\frac{9}{8}}{-1}[/tex]
Multiplication or Division property of order is used
[tex]x\leq \frac{9}{8}[/tex]
Final answer:
The justification for solving the inequality involves using the Addition or Subtraction property of order to combine like terms and isolate the variable, and the Multiplication or Division property of order to solve for the variable, with an important note that dividing both sides by a negative number reverses the inequality symbol.
Explanation:
The justification for each step in solving the inequality 3x + 5/8 ≥4x − 1/2 can be broken down as follows:
3x + 5/8 ≥4x − 1/2 Given
3x ≥4x − 9/8 Addition or Subtraction property of order, subtracting 5/8 from both sides
−x ≥ − 9/8 Addition or Subtraction property of order, subtracting 4x from both sides
−x / −1 ≥ −9/8 / −1 Multiplication or Division property of order, dividing both sides by −1
x ≤9/8 Multiplication or Division property of order, understanding that dividing by a negative number reverses the inequality symbol
Each step involves manipulating the inequality while maintaining the balance, and the direction of the inequality changes when both sides are multiplied or divided by a negative number.