By using exponent, it can be calculated that
[tex](-2ab)^3 (-a^2b)[/tex] = [tex]8a^5b^4[/tex]
What are exponent?
Exponent tells us how many times a number is multiplied by itself.
For example : In [tex]2^4 = 2 \times 2 \times 2 \times 2[/tex]
Here, 2 is multiplied by itself 4 times.
If [tex]a^m = a \times a \times a .... \times a[/tex] (m times), a is the base and m is the index.
The laws of indices are
[tex]a^m \times a^n = a^{m + n}\\\\a^m\div a^n = a^{m - n}\\\\(ab)^m = a^mb^m\\\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\\\a^0 = 1\\\\(a^m)^n = a^{mn}[/tex]
Now,
The given expression is
[tex](-2ab)^3 (-a^2b)[/tex] =
[tex](-8a^3b^3)(-a^2b)\\[/tex]
[tex]8a^{3+2}b^{3+1}[/tex]
[tex]8a^5b^4[/tex]
So, the expression [tex](-2ab)^3 (-a^2b)[/tex] is simplified [tex]8a^5b^4[/tex]
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Write y=2/3x+7 in standard form
Step-by-step explanation:
y = 2/3x + 7
Multiply both sides by 3 to get rid of the fraction 2/3
3y = 2x +21
subtract 2x from both sides
3y - 2x = 21
Answer ofc is 3x - 2y = 21
Please rate if you get the answer right.
Queuing system A has a utilization of 80 percent, and queuing system B has a utilization of 90 percent. Both have single server. Say, the utilization of both systems increases by 5 percent; that is, A increases from 80 percent to 85 percent while B increases from 90 percent to 95 percent. Which system is likely to experience the smaller increase in the average time in queue?
a) System A
b) System B
c) Time in queue for each system will increase by the same amount.
d) More information is needed to determine which has a bigger change in average time in queue
(b) System B is likely to experience a smaller increase in the average time in queue.
As utilization increases, the length of time in line grows more quickly. So a 5% increase in utilization has a larger effect from 90% to 95% than from 80% to 85%.
When you use something, you use it, whether it's a tool—like when you write something down with a pen—or a talent or skill—like the speed you use when you run a race. Utilization is the act of using something, such as using your voice to sing a song. It may be necessary for a team to use a gym for practices until the rain stops.
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Graph the triangle with vertices X(−3, 2), Y(2, 3), and Z(1,−1) and its image after a dilation with scale factor k=3
The image after a dilation with scale factor k=3, then the vertices of triangle X'Y'Z' are X'(-9, 6), Y'(6, 9) and Z'(3, -3).
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Given that, the triangle with vertices X(−3, 2), Y(2, 3), and Z(1,−1) and scale factor k=3.
Now, X(-3, 2)→3(-3, 2)→X'(-9, 6)
Y(2, 3)→3(2, 3)→Y'(6, 9)
Z(1,-1)→3(1, -1)→Z'(3, -3)
Vertices of X'Y'Z' are X'(-9, 6), Y'(6, 9) and Z'(3, -3).
Therefore, the image after a dilation with scale factor k=3, then the vertices of triangle X'Y'Z' are X'(-9, 6), Y'(6, 9) and Z'(3, -3).
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g ten random numbers are drawn from a standard normal distribution. what is the probability that at least one will exceed 2.66? round your answer to three decimal places.
The probability that at least one of ten random numbers drawn from a standard normal distribution will exceed 2.66 is 0.045.
This can be calculated using the complementary probability formula, which is 1 - P(x ≤ 2.66), where P(x ≤ 2.66) is the probability that all ten numbers are less than or equal to 2.66.
The probability that all ten numbers are less than or equal to 2.66 can be calculated using the normal distribution function, which gives the probability that a random variable x follows a normal distribution with mean μ and standard deviation σ. For a standard normal distribution, the mean is 0 and the standard deviation is 1, so the probability that all ten numbers are less than or equal to 2.66 can be calculated as:
P(x ≤ 2.66) = Φ(2.66)^10where Φ(x) is the normal distribution function.
Substituting this value into the complementary probability formula, we get:
1 - P(x ≤ 2.66) = 1 - Φ(2.66)^10 = 0.045Thus, the probability that at least one of ten random numbers drawn from a standard normal distribution will exceed 2.66 is 0.045.
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Please help me quick !!
A food truck did a daily survey of customers to find their food preferences. The data is partially entered in the frequency table. Complete the table to analyze the data and answer the questions:
Likes hamburgers Does not like hamburgers Total
Likes burritos 39 77
Does not like burritos 95 33
Total 134 205
Part A: What percentage of the survey respondents liked hamburgers but do not like burritos? Show all work. (3 points)
Part B: What is the marginal relative frequency of all customers who like hamburgers? Show all work. (3 points)
Part C: Which category has the lowest joint relative frequency? Show all work. (4 points)
a) The percentage of the survey respondents liked hamburgers but do not like burritos is of: 46.34%.
b) The marginal relative frequency of all customers who like hamburgers is of: 0.6537.
c) The lowest joint frequency is not liking neither of hamburgers or burritos.
How to obtain frequencies and percentages?The relative frequency is obtained as the division of the number of desired outcomes by the number of total outcomes.
The percentage is calculated as the multiplication of the relative frequency by 100%.
From the table given by the image at the end of the answer, the total number of people in the survey is of:
77 + 128 = 134 + 71 = 205.
The percentage for item a is then calculated as follows:
95/205 x 100% = 46.34%.
The relative frequency for item b is then calculated as follows:
134/205 = 0.6537.
The joint frequencies are found completing the table, considering the sums for the rows and columns, as follows:
Like both: 134 - 95 = 39.Like burritos but not hamburgers: 38.Like hamburger and do not like burritos: 95.Do not like both: 71 - 38 = 33. -> lowest.Missing InformationThe table is given by the image shown at the end of the answer.
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What is the equation of the line (in slope intercept form) passing through X(1,-4) perpendicular to line YZ with Y(1,3) and Z(-3,-1)
(Please enter fraction as decimals rounded to the nearest tenth)
The equation for the line we want to get is:
y = -x + 3
How to get the equation of a line?
A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Two lines are perpendicular of the product between the slopes of the two lines is -1.
Here we want to find a line perpendicular to the one that passes through the line with Y(1,3) and Z(-3,-1), the slope of that line is:
a = (-1 - 3)/(-3 - 1) = 1
Then the slope of a perpendicular line, a', is:
a'*1 = -1
a' = -1
Then our line is like:
y = -1*x + b
To find the value of b, we use the fact that this line passes through (1, -4), then we will get:
-4 = -1*1 + b
-4 + 1 = b
-3 = b
So the linear equation is:
y = -x + 3
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Find the value of x in the trapezoid below. Type only the numerical answer.
Check the picture below.
5 plus what equals -6
Answer:
Step-by-step explanation:
-1
Answer:
-11
Step-by-step explanation:
Equation:
5+x=-6
Market reearch firm ha hired operator who conduct telephone urvey. A computer
i ued to randomly dial a telephone number, and the operator ak the anwering peron
whether he ha time to anwer ome quetion. Let Y
= the number of call made until the
firt peron replie that he i willing to anwer the quetion. I thi a binomial e
xperiment?
Explain
The random variable Y does not have a binomial distribution, therefore this is not a binomial experiment
Here, a computer is used to randomly dial a telephone number
Then the operator asks the answering person whether she has time to answer some questions.
Y is the number of calls made until the first person replies that she is willing to answer the questions
There is no independent variable the affect the value of the Y. here the number of trial are not fixed, so there wont be any binomial distribution
Therefore, this is not a binomial experiment, because y does not have a binomial distribution
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What is the average rate of change of the function f(x)= 4x^2 + 3x on the interval [1,5]
Answer:
The average rate of change of f(x)= 4x^2 + 3x on the interval [1,5] is 18.
28% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is (a) exactly three, (b) at least four, (c) less than eight.
The probability distribution that the number of U.S. adults who favor the use of unmanned drones by police agencies is
(a) exactly three :-= 0.251
(b) at least four:-= 0.445
(c) less than eight:-= 0.994
What is probability distribution?
The probabilities of any random occurrence are determined by the probability distribution. It is sometimes described as a collection of potential results from any random experiment depending on the underlying sample space. A set of real numbers, a set of vectors, or a set of any other things might make up these settings. It is a component of statistics and probability.
The outcome of an experiment whose results cannot be anticipated is known as a random experiment. Imagine that we can't foresee whether a coin will land on its head or its tail when we throw one. An outcome is a potential outcome of a random experiment. The collection of results is known as a sample point.
X ~ Bin ( n , p)
Where n = 12 , p = 0.28
Binomial probability distribution is
P(X) = nCx * px * ( 1 - p)n-x .
a)
P(X = 3) = 12C3 * 0.283 * ( 1 - 0.28)9
= 0.251
b)
P(X >= 4) = 1 - P(X <= 3)
= 1 - [ P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) ]
= 1 - [ 12C0 * 0.280 * ( 1 - 0.28)12 +12C1 * 0.281 * ( 1 - 0.28)11 +12C2 * 0.282 * ( 1 - 0.28)10 +12C3 * 0.283 * ( 1 - 0.28)9 ]
= 0.445
c)
P(X < 8) = 1 - P(X >=8)
= 1 - [ P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) ]
= 1 - [ 12C8 * 0.288 * ( 1 - 0.28)4 +12C9 * 0.289 * ( 1 - 0.28)3 +12C10 * 0.2810 * ( 1 - 0.28)2 +
12C11 * 0.2811 * ( 1 - 0.28)1 +12C12 * 0.2812 * ( 1 - 0.28)0 ]
= 0.994
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PLEASE HELP!!!
Which choices are equivalent to the fraction below? Check all that apply.
12/32
A. 4/10
B. 3/8
C. 10/30
D. 6/16
E. 4/9
F. 2/6
PLEASE EXPLAIN HOW TO DO IT‼️‼️‼️
Answer: the answers should be B and D
Step-by-step explanation:
so basically, this is just simplifying
B is the correct answer because the numerator 12, when divided by 4 is 3, and the denominator 32, when also diving by 4, is eight. This makes the two fractions equivalent.
Same goes for D, for if you diving the numerator and denominator by 2, you get answer choice D
it’s kind of a trial and error type problem and you have to test out all possibilities
hope this helps!
Answer:
B and D
Step-by-step explanation:
12/32 (if you divide them both by three) does not equal 4/10
12/32 fully simplified is 3/8
12/32 - subtracting is not simplifying, therefore, 10/30 is not correct
12/32 - both divided by two, a common factor, is 6/16, therefore, this answer is correct
12/32 - both of them divided by three equals 4/10.7 (rounded up to the nearest tenth), therefore, 4/9 is not a correct answer
12/32 - both divided by six equals 2/5.3 (rounded down to the nearest tenth), therefore, 2/6 is not a correct answer
Which of the following is closest to the approximate value of 103√? A 15 B 17 C 18 D 19
The closest to the approximate value of ✓103 is E. 10.
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
It should be noted that the expression is the square root of 103. This will give 10.1
Therefore, this will be 10. The correct option is E
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Complete question
Which of the following is closest to the approximate value of ✓103√? A 15 B 17 C 18 D 19 E. 10
Laney walks 2 1/3 miles to school from her house and rides the bus home. If she attended school five days last week, how many total miles did Laney walk?
The total miles that Laney walked is 11 2/3 miles.
How many total miles did Laney walk?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this situation, Laney walks 2 1/3 miles to school from her house and rides the bus home and she attended school five days last week.
The total miles that Laney walked will be:
= 2 1/3 × 5
= 7/3 × 5
= 35/3
= 11 2/3 miles
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im having trouble again...
its not my day today with math, im so confused i need help :(
Answer:
Answer = 8 books every month
Step-by-step explanation:
Montoya has carefully cut out a perfectly square section of graph
paper. She counts all the blocks in the square, then takes a square root
of this number. Will Montoya's square root equal the number of
blocks in one side of the graph-paper square? Explain.
Answer: Yes, Montoya's square root will equal the number of blocks in one side of the graph-paper square.
Step-by-step explanation: The square root of a number is the number that, when multiplied by itself, produces the original number. For example, the square root of 16 is 4, because 4 * 4 = 16.
If Montoya has cut out a perfectly square section of graph paper, the number of blocks in the square will be the same as the number of blocks in one side of the square multiplied by the number of blocks in the other side of the square. In other words, the number of blocks in the square will be the square of the number of blocks in one side of the square.
Therefore, when Montoya takes the square root of the number of blocks in the square, she will get the number of blocks in one side of the square.
For example, if Montoya's square has 4 blocks on each side, the number of blocks in the square will be 4 * 4 = 16, and the square root of 16 will be 4, which is the number of blocks in one side of the square.
For linear function f,f(2)= 0 and ƒ(4) = -6.
Write function f in slope-intercept form.
Answer:
Step-by-step explanation:
(2, 0), (4, -6)
(-6 -0)/(4 - 2)= -6/2= -3
y - 0 = -3(x - 2)
y = -3x + 6
or
f(x) = -3x + 6
Answer:
Step-by-step explanation:y= -3x + 6
Find part b m of c and m if a. Please explain.
Answer:
Step-by-step explanation:
a) the opposite angles of a quadrilateral inscribed in a circle are supplementary
70 + angle D = 180
angle D = 180 - 70
angle D = 110 degrees
b) DAB is a semicircle, so angle A and angle C are two circumference angles whose sides passes through the extremes of the diameter.
The centre angle of a semicircle is 180 degrees and its circumference angle is half that measure, so its value is 90 degrees
A = 90 degrees
C = 90 degrees
Chase and Alonzo stand next to each other and throw baseballs in the air. The path of chases baseball is described by the equation y= -4x^2+5x+7. The path of Alonzo’s ball is shown by the graph whose baseball reaches a greater height
Quadratic equation :The maximum height reached by Alonzo's ball will be 9m.
What is a quadratic equation?
The equation whose highest degree of the variable used in the equation is 2 and has 2 roots, is called quadratic equation.
Here the quadratic equation of the path of Chase's ball is given by y = - 4x²+ 5x+ 7
To compare the height of both paths followed by the ball
we have to first calculate the height of the path of Chase's ball.
the path of Chase's ball is f(x)=-4x²+ 5x+ 7
The function will have the highest value when f'(x) will be 0.
f'(x)=-8x+5
f'(x)=0
⇒-8x+5=0
⇒-8x=-5
⇒x=5/8
at x=5/8, function value is
f(x)=-4x²+ 5x+ 7
=-4(5/8)²+ 5(5/8)+ 7
=-4(25/64)+(25/8)+7
=(-25/16)+25/8+7
=8.5625
There maximum value of f(x) is 8.5625.
The maximum height reached by Chase's ball will be 8.5625m.
From the graph of the path of Alonzo's ball, it is clear that
The maximum height reached by Alonzo's ball will be 9m.
As 8.5625m < 9m
Alonzo's baseball will reach greater height.
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Complete Question:
Chase and Alonzo stand next to each other and throw baseballs in the air. The path of Chase's ball is described by the equation y = - 4x²+ 5x+ 7. The path of Alonzo's ball is shown by the graph. In each function, x is the horizontal distance the ball travels in meters, and y represents its height. Whose baseball reaches a greater height?
A. Both baseballs reach the same height.
B. Chase's baseball
C. Alonzo's baseball
D) Non of these
Answer:
Alonzo's baseball
whompwhompwhompwhopwhompwhompwhompwhompwhompwhompwhompwhompwhompwhompwhomp
Step-by-step explanation:
Mohal is going to invest $830 and leave it in an account for 8 years. Assuming the interest is compounded daily, what interest rate, to the nearest hundredth of a percent, would be required in order for Mohal to end up with $1,110?
The interest rate, to the nearest hundredth of a percent, that would be required in order for Mohal to end up with $1,110 would be = 4.2%
What is interest rate?The interest rate of an investment is defined as the rate at which an individual receives stipulated amount of money for a period of time over the investment made.
The amount for investment (P) = $830
The time for investment(T) = 8 years
The simple interest yield(SI) = $1,110 -830 = 280
The rate(R) = x%
using the formula;
Simple interest = P×T×R/100
Make R the subject of formula;
R= SI ×100/P×T
R= 280×100/830×8
R= 28000/ 6,640
R= 4.2%
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−5d−5(−0.8d−0.7)??????????????????
Answer: -d + 3.5
Step-by-step explanation:
Expand the brackets to
-5d + 4d +3.5
Add similar elements/ like terms
= -d +3.5
why is y=3x proportional
Answer:
can 3x+3x+3x =9x if so what is the value of x?
It's possible 3x+3x+3x=9
=3*(3x) =9
3^(x+1) =3^(2x)
mike rents a car for a total of$445.
the rental charges are$145 for the first day and $60 for the first day after that
for how many days did mike rent the car?
Answer:
6 days
Step-by-step explanation:
total is 445
first day charge is 145
so, 445-145 = 300
second day onwards its 60.
so, 300/60 = 5 days
so total 5+1 = 6 days.
I hope I helped you
help meeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeee!!!!!
5% of $1100 = 55
Year given = 7
So, 55 × 7 = 385
She would get after 7 years all total = (1100 + 385) = $1485
Simplify 4X•1/x^-5•x^-3
The simplified form of the given expression, [tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }[/tex] is equal to [tex]4x^{9}[/tex]
What are Exponents?
Powers or exponents are quantities that indicate how many times to multiply a base number by themselves.The base is the integer being raised by a power, while the exponent or power is the superscript number above it.For example, in the expression [tex]7^{5}[/tex], 7 is the base and 5 is the exponents, which implies that 7 multiplies 5 times by itself.What is the Product of Powers rule?
The Product of Powers rule is one of the seven major Laws of Exponents.According to this rule, if the bases are the same, then when multiplying two bases with different exponent value, the resulting answer is found by adding the exponents.It can be mathematically expressed using the formula, [tex]x^{m} \times x^{n} =x^{m+n}[/tex]In this question, the expression is [tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }[/tex] ------(1)
Multiplying the values in the numerator, we get
[tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }=\frac{4x}{x^{-5} \times x^{-3} }[/tex]
Now, the values in the denominator can be simplified using the Product of Powers rule.
The formula for the Product of Powers rule is given as, [tex]x^{m} \times x^{n} =x^{m+n}[/tex]
Simplifying the given expression using the Product of Powers rule, we get
[tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }=\frac{4x}{x^{-5+(-3)} }\\\implies \frac{4x \times 1}{x^{-5} \times x^{-3} }=\frac{4x}{x^{-8} }[/tex] -----(2)
The formula for the Quotient of Powers rule is given as, [tex]\frac{x^{m} }{x^{n} } =x^{m-n}[/tex]
Simplifying the expression in (2) using the Quotient of Powers rule, we get
[tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }=4x^{1-(-8)} \\\implies \frac{4x \times 1}{x^{-5} \times x^{-3} }=4x^{9}[/tex]
Therefore, the simplified form of the given expression is [tex]4x^{9}[/tex]
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John is interested in purchasing a multi-office building containing five offices. The current owner provides the following probability distribution indicating the probability that the given number of offices will be leased each year.
Number of Lease Offices 0 1 2 3 4 5
Probability 10/33 1/33 7/33 1/11 4/33 8/33
If each yearly lease is $12,000, how much could John expect to collect in yearly leases for the whole building in a given year?(in dollars)
a) E(X) = $29,130.91
b) E(X) = $29,090.91
c) E(X) = $29,170.91
d) E(X) = $29,070.91
e) E(X) = $29,100.91
AE(X) = $23,333.33 could John expect to collect in yearly leases for the whole building in a given year.
What is probability ?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
The given table is:
Number of Lease Offices : 0 1 2 3 4 5
Probability : 5/18 1/4 1/9 1/18 2/9 1/12
The expected probability is
Expected probability [tex]$=\sum_{i=0}^5 x_i p\left(x_i\right)$[/tex]
Expected probability [tex]$=0 p(0)+1 P(1)+2 P(2)+3 P(3)+4 P(4)+5 P(5)$[/tex]
Expected probability [tex]$=0 \cdot\left(\frac{5}{18}\right)+1 \cdot\left(\frac{1}{4}\right)+2 \cdot\left(\frac{1}{9}\right)+3 \cdot\left(\frac{1}{18}\right)+4 \cdot\left(\frac{2}{9}\right)+5 \cdot\left(\frac{1}{12}\right)=\frac{35}{18}$[/tex]
It is given that the yearly lease [tex]$=\$ 12,000$[/tex].
The yearly leases for the whole building in a given year is
Yearly leases [tex]$=\frac{35}{18} \times 12000=23333.3333333 \approx 23333.33$[/tex]
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You install 402 feet of fencing along the perimeter of a rectangular yard. The width of the yard is 100 feet. What is the length of the yard? The length of the yard is __ feet.
97 divided by 10 and round to the nearest tenth place pleaseeeee
Answer: 9.7
Step-by-step explanation: 97 divided by 10 is 9.7
You and a classmate have been paired to solve an equation. Your partner says they got an answer but the solution they found does not work when they checked it. Here is their work:
6 (8-3x )− 3 (9x−1 )+ 60
54 - 18x = −27x − 3 + 60
54 - 18x = −27x + 57
-18x = -27x + 3
9x = 3
x= 1/3
Explain all of the mistakes your partner made and how to correct them. After correcting the mistakes, write the correct answer for this equation.
Answer: -45x + 111 or -3(15x-37)
Step-by-step explanation:
Instead of :6 (8-3x )− 3 (9x−1 )+ 60
54 - 18x = −27x − 3 + 60
54 - 18x = −27x + 57
-18x = -27x + 3
9x = 3
x= 1/3
Corrected :
6 (8-3x )− 3 (9x−1 )+ 60
First Simplify : 54 - 18x -27x - 3 + 60
Combine Like terms Like 54, - 3, and 60 : 111 - 18x -27x
Combine Like Terms Like -18x and -27x : 111 -45x
Rearrange It So The Variable Is First : -45x + 111
So, the answer is -45x + 111 or if you want you can still simplify it by finding the common factor which you will get -3(15x-37)
Corrections : The friend is wrong because he turned the equation into an inequality instead of simplifying it. He turned the equation into an inequality by adding an equal sign in the middle then he tried to solve it like how you solve inequalities.
P.S : So, correct me if I am wrong but i will try my best to answer. Hope it helps.
Simplify the expression. fraction with negative 4 times the quantity 2 minus the cube root of 8 times 6 end quantity as the numerator and 5 as A.the denominator ten fourths. B.negative ten fourths C.8 D.−8
The expression fraction with negative 4 times the quantity 2 minus the cube root of 8 times 6 end quantity as the numerator and 5 is simplified to give 8
How to simplify the fraction expressionThe fraction: negative 4 times the quantity 2 minus the cube root of 8 times 6 end quantity as the numerator and 5 is written in words
Rewriting the fraction
-4( (2 - ∛8 * 6) / 5)
The equation is simplified as
= -4( (2 - ∛8 * 6) / 5)
= -4( (2 - 2 * 6) / 5)
= -4( (2 - 12) / 5)
= -4( (-10) / 5)
= -4( -2)
= 8
Option C, 8 is the correct answer
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