Answers
We can draw the conclusion that Sadio and Amir's methods for solving the equation are both valid.
What are equations?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.
As in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, and others.
Equation: A declaration that two expressions with variables or integers are equal.
In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.
So, as we have the equation:
12x + 3 = 3(5x + 9)
Now, as we can see, Sadio took out 3 as common from LHS and RHS and solved the equation.
Which gave her the value of x as -8.
Amir, on the other hand, did not take out anything as common and directly multiply 3 with other terms in the brackets to solve the equation.
He also got -8 as the value of x.
Hence, we can conclude that yes both the ways of solving the equation is correct which is done by Sadio and Amir.
Therefore, we can draw the conclusion that Sadio and Amir's methods for solving the equation are both valid.
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Related Questions
Please answer this with right answer, imma give out 12 points
Answers
Answer:
its not blue.
There are currently 3000 in the state of Colorado their population is increasing at a rate of 2% per year how many years will it be before there are 6000 moose in the state of Colorado. Round your answer to the nearest year
Answers
Answer:
50 years
Step-by-step explanation:
the answer is 50 years bc 2% of 3000 is 60 and to get to 300 from 60 you would multiply by 50 to get 3000 added to the populationg colorado has now you get 6000.
brainliest pls
Question 5 of 10
Which pair of functions are inverses of each other?
O A. f(x) = 2 + 15 and g(x) = 12x - 15
O B. f(x) = √3x and g(x) = () ³
O c. f(x) = 3 - 10 and g(x) = +10
3
D. f(x) = 11x-4 and g(x) = +4
Answers
The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11
To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.
Let's test each option:
Option A:
f(x) = x/2 + 15
g(x) = 12x - 15
f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x
g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x
Option B:
f(x) = ∛3x
g(x) = (x/3)^3 = x^3/27
f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x
g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x
Option C:
f(x) = 3/x - 10
g(x) = (x + 10)/3
f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x
g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x
Option D:
f(x) = 11x - 4
g(x) = (x + 4)/11
f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x
g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x
Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:
D. f(x) = 11x - 4 and g(x) = (x + 4)/11
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Please help me, I dont know this :double s, then subtract t from the result
Answers
Let’s use “x” as the result
“•” is the multiplication symbol
Double s: s•2
Subtract t from result: =x-2
So, s•2=x-2
Then just subtract t
The answer will be 2s - t
Answer ASAP
————————-
Answers
Answer:
it should be 680
Step-by-step explanation:
1 kilogram is 1000 grams
720*6=4320
5000-4320=680
I am a function. My parent function is y = x. My parent function is
mapped onto me by a reflection over the line y = 0, then a horizontal shift
4 units to the right, a vertical shift 3 units up, and finally a horizontal
stretch with a factor of 3. Who am I?
Answers
Answer:
Step-by-step explanation:
If the graph of the parent function is shifted 7 units up and is steeper than the parent function, which of these could represent the function? answer choices.
Identify the prime numbers in the following lists. a. 5, 7, 12, 11b. 14, 6, 3c. 31, 17, 9, 15d. 782, 61, 2
Answers
a. The prime numbers in this list are 5 and 7. b. There are no prime numbers in this list. c. The prime numbers in this list are 31 and 17. d. The prime numbers in this list are 61 and 2.
a. In the list 5, 7, 12, 11, the prime numbers are 5, 7, and 11. Prime numbers are numbers greater than 1 that have only two factors, 1 and themselves.
b. In the list 14, 6, 3, the prime number is 3. The other numbers have more than two factors, making them not prime.
c. In the list 31, 17, 9, 15, the prime numbers are 31 and 17. The numbers 9 and 15 have more than two factors, so they are not prime.
d. In the list 782, 61, 2, the prime numbers are 61 and 2. Number 2 is the smallest prime number, and 61 has only two factors, 1 and 61. The number 782 has more than two factors, so it is not prime.
To summarize, the prime numbers in each list are: a. 5, 7, 11; b. 3; c. 31, 17; d. 61, 2.
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True/False: The critical t-values for a two-tailed, independent samples t-test (with 14 total participants) is +2.145 and -2.145. Assume we are using p = 0.05 as a cutoff. - True - False
Answers
The critical t-values for a two-tailed, independent samples t-test (with 14 total participants) are not +2.145 and -2.145. So it is false.
The correct critical value for a two-tailed test with 14 degrees of freedom at the alpha level of 0.05 is ±2.145.
This means that any calculated t-value greater than 2.145 or less than -2.145 is statistically significant with a 95% confidence level.
The critical t-value for a two-tailed, independent sample t-test (with 14 total participants) is +2.145 or -2.145 is False.
In conclusion, the statement "The critical t-values for a two-tailed, independent samples t-test (with 14 total participants) is +2.145 and -2.145. Assuming we are using p = 0.05 as a cutoff" is False.
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find an equation of the plane. the plane through the points (2, −1, 3), (7, 4, 6), and (−3, −3, −2)
Answers
Answer:
Equation of the plane is 19x - 20y - 15z - 38 = 0.
Step-by-step explanation:
We can find an equation of the plane that passes through the given three points by first finding two vectors that lie in the plane and then taking their cross product to get the normal vector of the plane. Once we have the normal vector, we can use any of the three points to write the equation of the plane in point-normal form.
Let's start by finding two vectors that lie in the plane. We can take the vectors connecting (2, −1, 3) to (7, 4, 6) and from (2, −1, 3) to (−3, −3, −2), respectively:
v1 = <7-2, 4-(-1), 6-3> = <5, 5, 3>
v2 = <-3-2, -3-(-1), -2-3> = <-5, -2, -5>
Now we can find the normal vector to the plane by taking the cross product of v1 and v2:
n = v1 x v2 = det( i j k
5 5 3
-5 -2 -5 )
= < 19, -20, -15 >
Now we can use the point-normal form of the equation of a plane, which is:
n · (r - r0) = 0
where n is the normal vector, r0 is a point on the plane, and r is a generic point on the plane. We can use any of the three given points as r0. Let's use the first point, (2, −1, 3):
n · (r - r0) = < 19, -20, -15 > · ( < x, y, z > - < 2, -1, 3 > ) = 0
Expanding the dot product, we get:
19(x - 2) - 20(y + 1) - 15(z - 3) = 0
Simplifying, we get:
19x - 20y - 15z - 38 = 0
Therefore, an equation of the plane is 19x - 20y - 15z - 38 = 0.
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what is thirty-two and six hundred five thousandths,greater than,less than,or equal to 3×10+2×1+7×110 ?
Answers
32.605
3x10+2x1+7x110= 802.
your answer is less than
negative 4 minus 8 equals
Answers
Answer:
-12
hope this helps!
add me as a friend if u can<3
hope that helps
a class has eight girls and two boys. if the teacher randomly picks eight students, what is the probability that she will pick all girls? find the probability of the event.
Answers
Given that a class has 8 girls and 2 boys. The teacher randomly picks 8 students. We need to find the probability that she will pick all girls.
To find the probability of the event, we need to use the formula for the probability of an event, which is:
P (event) = Number of favorable outcomes / Total number of outcomes Probability of picking all girls out of 10 studentsSince there are 8 girls and 2 boys in the class, the total number of students is 10.
There are only 8 girls, so the only way to pick all girls is if all 8 girls are selected out of the 10 students.
Total number of outcomes = 10 C8 = 45 (number of ways to pick 8 students out of 10) Number of favorable outcomes = 1 (since there is only one way to pick all 8 girls)
Therefore, the probability of the teacher picking all girls is:P (all girls) = 1/45 Thus, the probability of the teacher randomly picking all girls out of 8 girls and 2 boys is 1/45.
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A water tank at Camp Newton holds 1200 gallons of water at time t = 0. During the time interval Osts 18 hours, water is pumped into the tank at the rate
W(t) = 95Vt sin^2 (t/6) gallons per hour During the same time interval water is removed from the tank at the rate R(t) = 275 sin^2 (1/3) gallons per hour a. Is the amount of water in the tank increasing at time t = 15? Why or why not?
b. To the nearest whole number, how many gallons of water are in the tank at time t = 18? c. At what time t, for 0 st 18, is the amount of water in the tank at an absolute minimum? Show the work that leads to your conclusion d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(C) until the tank becomes empty. Write, but do not solve, an equation involving an integral expression that can be used to find the value of k.
Answers
(a)The amount of water in the tank is increasing.
(b)Evaluate \(\int\limits^{18}_0(W(t) - R(t)) dt\) to get the number of gallons of water in the tank at t = 18.
(c)Solve part (b) to get the absolute minimum from the critical points.
(d)The equation can be set up as \(\int\limits^k_{18}-R(t) dt = 1200\) and solve this equation to find the value of k.
What is the absolute value of a number?
The absolute value of a number is its distance from zero on the number line. It represents the magnitude or size of a real number without considering its sign.
To solve the given problems, we need to integrate the given rates of water flow to determine the amount of water in the tank at various times. Let's go through each part step by step:
a)To determine if the amount of water in the tank is increasing at time t = 15, we need to compare the rate of water being pumped in with the rate of water being removed.
At t = 15, the rate of water being pumped in is given by \(W(t) = 95Vt sin^2(\frac{t}{6})\) gallons per hour. The rate of water being removed is \(R(t) = 275 sin^2(\frac{1}{3})\) gallons per hour.
Evaluate both rates at t = 15 and compare them. If the rate of water being pumped in is greater than the rate of water being removed, then the amount of water in the tank is increasing. Otherwise, it is decreasing.
b) To find the number of gallons of water in the tank at time t = 18, we need to integrate the net rate of water flow from t = 0 to t = 18. The net rate of water flow is given by the difference between the rate of water being pumped in and the rate of water being removed. So the integral to find the total amount of water in the tank at t = 18 is:
\(\int\limits^{18}_0(W(t) - R(t)) dt\)
Evaluate this integral to get the number of gallons of water in the tank at t = 18.
c)To find the time t when the amount of water in the tank is at an absolute minimum, we need to find the minimum of the function that represents the total amount of water in the tank. The total amount of water in the tank is obtained by integrating the net rate of water flow over the interval [0, 18] as mentioned in part b. Find the critical points and determine the absolute minimum from those points.
d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. To find the value of k, we need to set up an equation involving an integral expression that represents the remaining water in the tank after time t = 18. This equation will represent the condition for the tank to become empty.
The equation can be set up as:
\(\int\limits^k_{18}-R(t) dt = 1200\)
Here, k represents the time at which the tank becomes empty, and the integral represents the cumulative removal of water from t = 18 to t = k. Solve this equation to find the value of k.
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Given that 3m=2c-5k,express c in terms of k and m.
Answers
Answer:
The answer is
\(c = \frac{3m + 5k}{2} \)
Step-by-step explanation:
You have to move all the unrelated terms to the other side :
\(3m = 2c - 5k\)
\(3m + 5k = 2c\)
\(2c = 3m + 5k\)
Next you have to divide it by 2 :
\(c = \frac{3m + 5k}{2} \)
uh i need help w this
Answers
Answer:
Its (c) please check if thats correct
Step-by-step explanation:
What is the median of this data set?
Answers
The median of the given data set as required to be determined in the task content is; 4.
What value represents the median of the data set?It follows from the task content that the value which represents the median of the data set is to be determined.
By observation, the number of data values in the data set is; 15. On this note, the median value would be the eighth term in an orderly arrange of the values.
Consequently, the median of the data set as required is; 4.
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assume that your compute completes a 5000 equation back substitution in 0.005 seconds. use the approximate operation counts n 2 for back substitution and 2n 3/3 for elimination to estimate how long it will take to do a complete gaussian elimination of this size.
Answers
In linear equation, 17 seconds it will take to do a complete gaussian elimination of this size.
What are a definition and an example of a linear equation?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.Given that your computer completes a 5000 equation back substitution in 0.005 seconds.
then here Work is: n = 5000 and its rate is = (n2) / 0.005 = 5000000000
and Given formula : The approximate operation counts = ((2n^3)/3) = (2.0 * (n3)) / 3.0 = 83333333333.33
then we can found time = operations / rate = 83333333333.33/5000000000 = 16.67 = 17 seconds
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2 4/5 3.5 4 1/4 5.3 in order greatest to least
Answers
Answer:
5.3, \(4\frac{1}{4}\), 3.5, \(2\frac{4}{5}\)
Step-by-step explanation:
4 intersecting lines are shown. Line m contains points Y, K, and B. Another line contains points C, Y, and W. Another line contains points B, A, and C. The fourth line contains points J, A, K, and W. Points P and X are not on the lines. Points W, K, and are collinear. Line CA and line YK intersect at . Point is not contained on line m.
Answers
Answer:
Points W, K, and
✔ J
are collinear.
Line CA and line YK intersect at
✔ point B
.
Point
✔ W
is not contained on line m.
Step-by-step explanation:
Answer:
Ray C E is contained on line m.
Ray AD is the same as ray AC.
∠ECB is created from Ray C E and Ray C B.
Step-by-step explanation:
i took the test
The linear system shown is equivalent
Answers
The linear system shown is "inconsistent" in nature.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
The given figure is represented linear system represents two parallel lines.
Now, the solution set of the two system of equations could be find by finding their points of intersection.
And when the lines do not intersect then it is said the linear system of the two lines do not have any solution.
Now, we have been given two parallel lines and parallel lines never intersect each other. thus the solution set of both the system of equations represented by these parallel lines is an empty set.
And when the system of linear equation has no solution , then the system is said to be inconsistent.
Hence, The linear system shown is "inconsistent" in nature.
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The complete question is;
The linear system shown is _____.
independent
equivalent
inconsistent
A cyclist bikes a certain distance in 25 minutes,
How long would it take a pedestrian to travel the same distance
if he travels 2 2/5 times slower than the cyclist?
Answers
It would take the pedestrian 50 minutes to travel the same distance that the cyclist covered in 25 minutes, given that the pedestrian travels 2(2/5) times slower than the cyclist.
What is distance?
Distance is a numerical measurement of how far apart objects or points are. It is a scalar quantity that is typically measured in units such as meters, kilometers, miles, etc.
Let's assume that the distance traveled by the cyclist is "d" units. We know that the cyclist takes 25 minutes to cover this distance.
To find how long it would take for the pedestrian to travel the same distance, we need to first determine the speed of the cyclist. We can do this by using the formula:
Speed = Distance / Time
The time taken by the cyclist is 25 minutes, which is equal to 25/60 = 5/12 hours. Therefore, the speed of the cyclist is:
Speed of Cyclist = Distance / Time
= d / (5/12)
= 12d / 5
Now we know that the pedestrian travels 2(2/5) times slower than the cyclist. This means that the speed of the pedestrian is:
Speed of Pedestrian = (5/2) x (2/5) x Speed of Cyclist
= (5/2) x (2/5) x (12d/5)
= 6d/5
To find out how long it would take for the pedestrian to travel the distance "d" at this speed, we can use the formula:
Time = Distance / Speed
Time taken by the pedestrian = d / (6d/5)
= 5/6 hours
We can convert this to minutes by multiplying by 60:
Time taken by the pedestrian = (5/6) x 60
= 50 minutes
Therefore, it would take the pedestrian 50 minutes to travel the same distance that the cyclist covered in 25 minutes, given that the pedestrian travels 2(2/5) times slower than the cyclist.
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Figure ABCD is reflected across the y-axis, translated 5 units left and 3 units down. The resulting figure is then rotated clockwise about
the origin through 90°. Find the coordinates of the vertices of the transformed figure.
D
4
2
O A(-2,-1), B(0, 0), C(-1,-2), and D(1, 1)
O A(-2, 1), B(0, 0), C(1,-2), and D(-1,-1)
O A(2, 11, 810, 0), C(1, 2), and D(1, 1)
O A(0, 0), 8-2, 1), C(-1,-1), and D(1,-2)
Answers
Therefore, OPTION (B) is your answer:
A( 2, 1 )
B(0, 0 )
C(1, -2 )
D(-1, -1 )
Step-by-step explanation:
SOLVE THE PROBLEM:
LEFT:
A(-4, 1 )
B(-5, 3 )
C(-7, 4 )
D(-6, 12 )
REFLECT:
A(4, 1 )
B(5, 3 )
C(7, 4 )
D(6, 12 )
TRANSLATE:
FIVE (5) UNITS and THREE UNITS DOWN
A'(-1, -4 )
B'(0, 0 )
C(2, 1 )
D(1, -1 )
ROTATE CLOCK-WISE DOWN THE ORIGIN THROUGH GOES:
DRAW THE CONCLUSION:
Therefore, OPTION (B) is your answer:
A( 2, 1 )
B(0, 0 )
C(1, -2 )
D(-1, -1 )
I hope this helps you!
In the race for mayor of Columbus, Ohio, in 1999, one poll found that 61.1% of those surveyed would vote for the Democratic candidate. The poll had a 4.1% margin of error at the 95% confidence level. We may correctly conclude that
Answers
We can correctly conclude that the actual percentage of voters who would vote for the Democratic candidate is within 4.1% of the poll's result, with 95% confidence.
Given that the poll had a 4.1% margin of error at the 95% confidence level, we can conclude that the actual percentage of voters who would vote for the Democratic candidate is within 4.1% of the poll's result.
Therefore, we can say that with 95% confidence, the percentage of voters who would vote for the Democratic candidate is between 57% and 65.2% (61.1% ± 4.1%).This means that if we were to conduct the same poll multiple times, 95% of the intervals obtained from the polls would contain the true percentage of voters who would vote for the Democratic candidate.
It is important to note that the margin of error only considers the sampling variability and does not account for other sources of error such as nonresponse bias, measurement error, or sampling bias.
However, assuming that the sample is representative and the assumptions of the statistical test are met, we can use the margin of error to make an inference about the population parameter. This conclusion is valid if the 95% confidence level is correctly used.
The statement is also true when we say that "we may correctly conclude that.
Therefore, we can correctly conclude that the actual percentage of voters who would vote for the Democratic candidate is within 4.1% of the poll's result, with 95% confidence.
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HURRY LAST QUESTION WILL GIVE BRAINLIEST Given l | m || n, find the value of x.
Answers
Answer:
x=19 degrees
Step-by-step explanation:
8x-11=7x+8 b/c of vertical angles, alt. int. angles, vertical angles, and alt. int. angles again.
Which ordered pair could replace the missing value and create a function?
Answers
Given that the ordered pair makes the function and these pairs are
[ (2,5), (7,1), (5,9), (8,0), ( , ) ]
Since the function is the one that has the input having only one output.
Hence, the given options (3,4) is correct.
Therefore the ( 3, 4 ) is the pair.
True or False: For a given mass of rising air, the dry adiabatic rate will always be higher than the wet adiabatic rate.
Answers
Answer:
true
Step-by-step explanation:
because there's less humidity
if each two complementary angles has the same measure, then each angle will equal what?
Answers
Answer:
ok
Step-by-step explanation:
it's ammmmmmmmmmmmmmmmmmmmmost doen
=====================================================
Work Shown:
Let x be the measure of each of the two angles (which is valid because they both have the same measure). Since they are complementary, the angles add to 90
So,
x+x = 90
2x = 90
x = 90/2
x = 45
Each angle is 45 degrees
45+45 = 90
A home improvement store advertises 60 square feet of flooring for $287.00 including an $80.00 installation fee. Write an equation to represent the cost of one square foot of flooring
Answers
60 square feet= $287.00 + $80.00
= $367
1 square feet= $367 / 60
= $6.116666667
= $6.12 (to 2dp)
Hope this helps :))
1. sec x-tanx sinx = 1/sec x2. 1+cosx/sinx = csc x Cot x
Answers
Both of the given equations have no solution.
1. sec x-tanx sinx = 1/sec x
The left-hand side of the equation can be simplified by using the identity that sec(x) = 1/cos(x) and tan(x) = sin(x)/cos(x). So,
sec x - tan x sin x = 1/cos x - sin x/cos x sin x = 1/cos x - sin^2 x/cos x = 1/cos x - (1-cos^2 x)/cos x = 1/cos x - (1/cos x) = 1/cos x - 1/cos x = 0.
On the right-hand side, sec x = 1/cos x, so 1/sec x = cos x. Hence,
0 = cos x
This equation has no solution, which means that the original equation sec x - tan x sin x = 1/sec x has no solution.
2. 1 +cosx/sinx = csc x Cot x
We can simplify the left-hand side of the equation by using the identity that csc(x) = 1/sin(x) and cot(x) = cos(x)/sin(x). So,
1 + cos x/sin x = 1/sin x * cos x/sin x = cot x.
Hence,
1 + cot x = cot x
This equation has no solution, which means that the original equation 1 +cosx/sinx = csc x Cot x has no solution.
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A rectangular prism has a width of 2/3 inches, a length of 5/7 inches, and a height of 9/12 inches. What is the volume of the rectangular prism?
Answers
Answer:
125 is the recangular prism
Step-by-step explanation: