Answers
=
0
O
r
m
=
23
15
Explanation:
1
3
m
+
6
m
−
9
3
m
=
3
m
−
3
4
m
⇒
1
+
6
m
−
9
3
m
=
3
m
−
3
4
m
⇒
−
8
+
6
m
3
m
=
3
m
−
3
4
m
⇒
(
−
8
+
6
m
)
×
4
m
=
(
3
m
−
3
)
×
3
m
⇒
−
32
m
+
24
m
2
=
9
m
2
−
9
m
⇒
−
32
m
+
24
m
2
−
9
m
2
+
9
m
=
0
⇒
15
m
2
−
23
m
=
0
⇒
m
(
15
m
−
23
)
=
0
m
=
0
Or
15
m
−
23
=
0
⇒
15
m
=
23
⇒
m
=
23
15
The correct answer is option B, as the solution of the equation:
[tex]\frac{1}{3 m}+\frac{6 m-9}{3 m}=\frac{3 m-3}{4 m}[/tex] is [tex]\frac{23}{15}[/tex]
Solving this type of equation containing the fractions involves the mathematical operations like finding a common denominator, combining the fractions, eliminating the fraction denominators, cancelling common terms, distributing, adding/subtracting to both sides, simplifying, and dividing both sides by the same factor.
The Steps of calculation are as follows:
Let's verify the answer:
We had the equation:
[tex]\[\frac{1}{3m} + \frac{6m - 9}{3m} = \frac{3m - 3}{4m}\][/tex]
And we simplified it to:
[tex]\[\frac{6m - 8}{3m} = \frac{3m - 3}{4m}\][/tex]
Next, we cross multiplied:
[tex]\[4m(6m - 8) = 3m(3m - 3)\][/tex]
[tex]\[24m^2 - 32m = 9m^2 - 9m\][/tex]
We then brought all terms to one side:
[tex]\[24m^2 - 9m^2 - 32m + 9m = 0\][/tex]
[tex]\[15m^2 - 23m = 0\][/tex]
Factoring out m:
[tex]\[m(15m - 23) = 0\][/tex]
So, either m = 0 or 15m - 23 = 0.
If 15m - 23 = 0, then [tex]\(m = \frac{23}{15}\)[/tex].
Therefore, the correct answer is: b. [tex]\frac{23}{15}$[/tex].
Related Questions
which situation could be represented by 5 divided by 1/2=10
Answers
See explanation
Step-by-step explanation:
A situation where a farmer needs to divide his 5 acre land into 1/2 an acre to get 10 pieces of land where he can grow ten different crops.
In such a case; you divide 5 by 1/2
5/ 1/2 = 5*2 =10 pieces
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Division :https://brainly.com/question/13063965
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Answer:can someone help
Step-by-step explanation:
asap, please and thank you
Answers
Answer: Here dimension of bigger triangle = 10
Dimension of smaller triangle = 5
Scale factor = 10/5 =2
Therefore
Center C and scale factor 2
Use >, <, and + signs to write inequalities for the relationships among
the sides of the triangles. Show your work below the numbers.
7. 1/2 _______________1/3 _______________1/5
8. 0.1 _______________ 0.15 _______________ 0.2
Answers
Answer:
7. [tex]\frac{1}{2}+\frac{1}{3}>\frac{1}{5}[/tex]
8. [tex]0.1+0.15>0.2[/tex]
Step-by-step explanation:
Given:
Three sides of the triangles are given.
For Question 7
1/2 _ 1/3 _1/5
For Question 8
0.1 _ 0.15 _ 0.2
We need to use >, <, and + signs to write inequalities for the relationships among the sides of the triangles.
Solution:
Part 7.
Property of the triangles.
Sum of two side of triangles must be greater than third side.
So, first, second and third side of the triangle is [tex]\frac{1}{2}, \frac{1}{3}\ and\ \frac{1}{5}[/tex]
[tex]\frac{1}{2}+\frac{1}{3}>\frac{1}{5}[/tex]
[tex]\frac{5}{6}>\frac{1}{5}[/tex]
So, its satisfy the triangle rule.
Therefore, Inequality is [tex]\frac{1}{2}+\frac{1}{3}>\frac{1}{5}[/tex]
Part 8.
Property of the triangles.
Sum of two side of triangles must be greater than third side.
So, first, second and third side of the triangle is [tex]0.1, 0.15\ and\ 0.2[/tex]
[tex]0.1+0.15>0.2[/tex]
[tex]0.25>0.2[/tex]
So, its satisfy the triangle rule.
Therefore, Inequality is [tex]0.1+0.15>0.2[/tex]
Use inequalities to compare sides of triangles with >, <, and + signs.
For 7:
1/2 > 1/3
1/3 > 1/5
1/2 + 1/3 > 1/3 + 1/5
For 8:
0.1 < 0.15
0.15 < 0.2
0.1 + 0.15 < 0.15 + 0.2
The number of hours in d days and 6 hours how to write in algebraic expression
Answers
In a day, there are 24 hours. Then the number of hours in d days and 6 hours is 24d + 6.
What is Algebra?Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.
The number of hours in d days and 6 hours. Then the algebraic expression will be
We know that in a day, there are 24 hours.
Let the number of the days be d. Then the algebraic expression will be
→ 24 d + 6
Then the number of hours in d days and 6 hours is 24d + 6.
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the tempurature is changing every day by -3/16 degree farenheit. what will be the change in temerature after 4 days?
Answers
Answer:
After 4 days, the temperature will be 3/4 Fahrenheit degrees lower than today
Step-by-step explanation:
Let's calculate the change in temperature after 4 days, this way:
Today's temperature = t in Fahrenheit degrees
Tomorrow's temperature = t - 3/16 Fahrenheit degrees
The day after tomorrow's temperature = t - 2 * 3/16 = t - 3/8 Fahrenheit degrees
Therefore, the temperature after 4 days will be = t - 4 * - 3/16 = t - 3/4 Fahrenheit degrees
After 4 days, the temperature will be 3/4 Fahrenheit degrees lower than today
Find the Mid point of (-5,-9) (-7,-4)
Answers
Answer: ( -6 , -6.5 )
Step-by-step explanation:
The formula for calculating Mid - point is given by
M = ([tex]\frac{x_{1}+x_{2}}{2}[/tex] , [tex]\frac{y_{1}+y_{2}}{2}[/tex] )
[tex]x_{1}[/tex] = -5
[tex]x_{2}[/tex] = -7
[tex]y_{1}[/tex] = -9
[tex]y_{2}[/tex] = -4
substituting into the formula , we have
M = [tex]\frac{-5-7}{2}[/tex] , [tex]\frac{-9-4}{2}[/tex]
M = [tex]\frac{-12}{2}[/tex] , [tex]\frac{-13}{2}[/tex]
Therefore : mid point = ( -6 , -6.5 )
A circle has a circumference of 44m. What
is its area?
A. 616m
B. 154m
C. 14m
D. 308m
Answers
================================
Work Shown:
C = 44 is the circumference
in general, the circumference of a circle is
C = 2*pi*r
Plug in C = 44 and solve for r.
C = 2*pi*r
44 = 2*pi*r
2*pi*r = 44
r = 44/(2pi)
r = 7.0028175 which is approximate
--------------------
Now plug this into the formula for the area of a circle
A = pi*r^2
A = pi*(7.0028175)^2
A = 154.061985
A = 154 rounding to the nearest whole number
Answer:
B
Step-by-step explanation:
Circumference = 2πr
And circumference = 44 m
44 = 2πr
so, r = 44/2π
r = 22/π
Radius is 22/π
Area of circle = πr²
Area of circle = π × (22/π)²
Area of circle = π × 22²/π²
Area of circle = 22²/π
Area of circle = 484/π
Area of circle = 154.14m²
Am not good makeing word problems can you help me make one here we go 2/3 x 3 =c now help me make a word problem
Answers
Answer:
Emily decides marbles the ratio of marbles is 2 to 3 she adds 3 times more to that.
Step-by-step explanation:
Answer:
Step-by-step explanation:
I have 2/3 of milk and I need 6/3 so my neighbor gave me 3
Write the polynomial function, in standard form, that has zeros -2, 5, and 0.
Answers
Answer:
f(x) = x³ - 3x² - 10x
Step-by-step explanation:
Given that the zeros are x = - 2, x = 5 and x = 0 then the factors are
(x + 2), (x - 5) and (x - 0) = x
The polynomial is the product of it's factors, thus
f(x) = x(x + 2)(x - 5) ← expand factors using FOIL
= x(x² - 3x - 10) ← distribute parenthesis by x
= x³ - 3x² - 10x
What is the area of a circle with a radius of 15 inches to the nearest 10th use 3.14
Answers
Step-by-step explanation:
The area of a cirkel is calculated with the formula \pi×r^2. Using the 15 inch radius given we get \pi×15^2=706.5 inches squared.
Javier asks his mother how old a tree in their yard is. His mother says, “The sum of 10 and two-thirds of that tree’s age, in years, is equal to 50.”
Javier writes the equation , where a is the tree’s age in years. His equation is not correct. What error did he make?
Answers
Answer:
[tex]10 + (\frac{2}{3}) a = 50[/tex] is the CORRECT equation.
Step-by-step explanation:
The given question is INCOMPLETE.
Javier asks his mother how old a tree in their yard is. His mother says, “The sum of 10 and two-thirds of that tree’s age, in years, is equal to 50.” Javier writes the equation { 10 + 2/3} where a is the tree’s age in years. His equation is not correct. What error did he make?
Now here:
a: The tree’s age in years.
Also, “The sum of 10 and two-thirds of that tree’s age, in years, is equal to 50.”
⇒ 10 + two-thirds of that tree’s age = 50
[tex]\implies 10 + (\frac{2}{3}) a = 50[/tex]
But in the equation written by Javier, the the third fraction is NOT MULTIPLIED by the age of the tree a in Years.
So, the written equation by Javier is Incorrect.
Now, solving the written correct equation for the value of a, we get:
[tex]\implies 10 + (\frac{2}{3}) a = 50\\\implies (\frac{2}{3}) a = 40\\\implies a = 40 \times (\frac{3}{2}) = 60\\\implies a = 60[/tex]
Hence the correct age of the tree = 60 years
If you place a 89-foot ladder against the top of a 80-foot building, how many feet will
the bottom of the ladder be from the bottom of the building?
Answers
Answer:
[tex]\large \boxed{\text{39 ft}}[/tex]
Step-by-step explanation:
Let x be the distance from the foot of the ladder to the base of the building.
We have a right triangle, so we can use Pythagoras' Theorem.
[tex]\begin{array}{rcl}80^{2} + x^{2}& = & 89^{2} \\6400+ x^{2} & = & 7921\\x^{2} & = & 1521\\x & = & \sqrt{1521}\\& = &\mathbf{39}\\\end{array}\\\text{The foot of the ladder will be $\large \boxed{\textbf{39 ft}}$ from the base of the building,}[/tex]
Teo earns 47.25$ in 7 h of work at Beck’s Burgers. How much will he earn in 12 hours?
Answers
Answer:
He will earn $81 in 12 hours.
Step-by-step explanation:
Given:
Teo earns 47.25$ in 7 hours of work at Beck’s Burgers.
Now, to find the money he will earn in 12 hours.
As, given Teo earns 47.25$ in 7 hours of work.
So, to get the money he will earn in 12 hours we solve by using unitary method:
If Teo earns in 7 hours $47.25.
Then, in 1 hour he earns = [tex]\frac{47.25}{7}[/tex]
Thus, in 12 hours he will earn = [tex]\frac{47.25}{7} \times 12[/tex]
= [tex]6.75\times 12[/tex]
= [tex]\$81.[/tex]
Therefore, he will earn $81 in 12 hours.
There are 1,198 souvenir paperweights that need to be packed in boxes. Each box will hold 12 paperweights. How many boxes will be needed?
Answers
Answer:
100 boxes
Step-by-step explanation:
Divide 1,198 with 12 because if there are 1,198 paperweights and each box holds 12 then how many boxes can hold these paperweights. Answer us 100 boxes
-f(x) = 2x + 6 Find f(-4)
Answers
What is the complete factorization of 12x2 + 36x + 27?
A.
(x+3)(12x+ 9)
B. 3(2x + 3)2
C. 6(x + 2)2
D.
(6x + 3)(2x + 9)
Need help please
Answers
Answer:
B) 3(2x+3)^2
Step-by-step explanation:
12x^2+36x+27
factor out the 3 first,
3(4x^2+12x+9)
factor out the trinomial 4x^2+12x+9,
3(2x+3)(2x+3)
3(2x+3)^2
Answer:
B. 3(2x + 3)2
Step-by-step explanation:
chetan makes a necklace for his sister. twelve beads take up 5 inches of strings. how many beads fit on 1 foot of string.
Answers
Answer:
28 beads fit on the string.Step-by-step explanation:
12 inch = 1 ft.
12 inch can be be written as (5 + 5 + 2) inch.
It is given that, 5 inches require for 12 beads.
Hence, (12 + 12) = 24 beads will take up (5 + 5) = 10 inches.
There are 2 inches more to fill.
5 inches required for 12 beads.
1 inch required for [tex]\frac{12}{5}[/tex] beads.
2 inches will be required for [tex]\frac{24}{5}[/tex] beads.
[tex]\frac{24}{5} = 4.8[/tex].
Hence, there will 24 + 4 = 28 beads in total. (Only 4 is added instead of 4.8 because, the number can not be in fraction and there is no space for 29 beads in total).
What is the algebraic equation for this math trick
Pick a number
Add 2
Multiply by 3
Subtract 3
Divide by 3
Subtract the original number
Answers
Answer:
it will always be 1
Step-by-step explanation:
lets make an equation
pick a number : x
add 2 : x+2
multiply by 3 : (x+2)*3
subtract 3 : (x+2)*3-3
divide by 3 : ((x+2)*3-3)/3
if you simplify, you will get 1
step by step simplification
(x+2)*3 = 3x+6
3x+6-3=3x+3
(3x+3)/3 = x+1
x+1-x=1
Final answer:
The algebraic equation for the given math trick is: (((((x + 2) * 3) - 3) / 3) - x).
Explanation:
To represent the math trick you described algebraically, we can use the variable x to represent the initial number you pick. Following the steps you provided, the algebraic equation would be: ((((x + 2) * 3) - 3) / 3) - x. Let's break down each step:
Start with the initial number x.Add 2: x + 2.Multiply by 3: (x + 2) * 3.Subtract 3: ((x + 2) * 3) - 3.Divide by 3: (((x + 2) * 3) - 3) / 3.Subtract the original number x: ((((x + 2) * 3) - 3) / 3) - x.The graphs of f(x) and g(x) are shown below.
On a coordinate plane, a straight line with a positive slope represents f (x) = x minus 3. The line goes through (0, negative 3) and (3, 0). On a coordinate plane, a straight line with a negative slope represents g (x) = negative 0.5 x. The line goes through (negative 4, 2), (0, 0), and (4, negative 2)
For what interval is the value of (f – g)(x) negative?
(negative infinity, negative 1)
(negative infinity, 2)
(0, 3)
(2, infinity)
Answers
Answer:
(negative infinity, 2)
Step-by-step explanation:
The two functions are given by f(x) = x - 3 and g(x) = - 0.5x
So, (f - g)(x) = x - 3 - ( - 0.5x) = 1.5x - 3
Then, for (f - g)(x) to be negative (1.5x - 3) < 0
⇒ 1.5x < 3
⇒ x < 2
Therefore, the interval will be (negative infinity, 2) for which the function (f - g)(x) will be negative. (Answer)
Answer:
negative infinity 2
Step-by-step explanation:
just did the test
what is the solution to this system of equations?
5x-3y=10
3x+3y=3
Answers
Answer:
y = 5/2 , x= 7/2
Step-by-step explanation:
5x - 3y = 10…....(1)
3x + 3y = 3......(2)
solving by elimination, we subtract equation (2) from equation (1)
so, 2x = 7
dividing both sides by 2
x= 7/2
substitute x=7/2 for the value of y in equation (1)
5(7/2) - 3y = 10
multiply both sides by 2
35 - 6y = 20
rearranging
-6y = -15
dividing both sides by -6
y = 5/2
Can someone plz help me with this problem?
Answers
Answer:
option (2)
Step-by-step explanation:
Given the area (A) of a circle is
A = πr² ← r is the radius ( divide both sides by π )
[tex]\frac{A}{\pi }[/tex] = r² ( take the square root of both sides )
[tex]\sqrt{\frac{A}{\pi } }[/tex] = r → option (2)
whats the square root of 49
Answers
Answer:
The square root of 49 is 7. 7*7=49
Hope this helps,
:)
Divide the following polynomials, then place the answer in the proper location on the grid. Use synthetic division. Write the answer in descending powers of x.
(3x2 + 7x - 18) (x - 3)
Answers
The answer for the given polynomial by synthetic division is 3x+16+(30/(x-3)).
Step-by-step explanation:
The given polynomial is (3x^2 +7x -18) divided by (x - 3)
Take (x-3)=0, then x=3
3 | 3 7 -18
9 48
3 16 30
step 1: write the coefficients of x^2, x and constant in first row. The divisor 3 is written separately on outside.
step 2: Write down the coefficient of x^2= 3 in the answer row as it is without any change.
step 3: Multiply each number in the answer row with the divisor and fill the answers in the second row.
step 4: The final step is to add the first row and second row. After addition, the answers are written in answer row and the last number in the answer row is the Remainder.
step 5: The remainder is written by dividing it with the divisor (x-3). The answer in the descending powers of x is 3x + 16 + (30/(x-3)).
The result of the division (3x^2 + 7x - 18) by (x - 3) using synthetic division is obtained as (3x + 16 + 30/(x - 3)).
Explanation:To perform the synthetic division, the divisor (x - 3) is represented by its root '3'. Write down the coefficients from the dividend polynomial (3, 7, -18) at the top of your division setup. Write '3' to the left, leave some space, and then write down '3', '7', -18.
Then, perform the synthetic division: step one, bring the first coefficient (3) straight down. Step two, multiply this number by the root of the divisor (3), which is also 3. Write this product (9) underneath the next coefficient (7). Add these two numbers (7 + 9) to get 16. Write this number under the line. Now, repeat the previous step by multiplying 16 by the root, 3, to get 48. Write this under -18, add to get 30.
The quotient of the division is the polynomials received from the synthetic division which is 3x + 16 with a remainder of 30. So, the result of division (3x^2 + 7x - 18) by (x - 3) is (3x + 16 + 30/(x - 3)).
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Factor and solve the equation x^3-x^2-30x=0
Answers
Answer:
Step-by-step explanation:
If f(x) = 5x + 4, which of the following is the inverse of f(x)
Answers
Answer:
f^-1 (x)=1/5x-4/5
Step-by-step explanation:
y=5x+4
x=5y+4
5y=x-4
y=1/5x-4/5
Answer:
I WOULD SAY THAT THE ANSWER IS C
Step-by-step explanation:
I GOT IT FROM A
P
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X
The main road in Belleville is 7 3/10 Miles long so far 2 3/4 miles have been repaved. How many miles have not been repaved
Answers
Answer:
4 11/20
Step-by-step explanation:
The length of road unpaved is 7 3/10 less 2 3/4 miles The LCD of the fractions is 20 (both 10 and 4 divide evenly into 20).
Thus, the problem becomes 7 6/20 - 2 15/20.
We have to borrow 1 from that 7 because 15/20 is larger than 6/20. This results in
6 26/20 - 2 15/20, or
4 11/20
The total length of the main road in Belleville is [tex]7^{(3/10)}[/tex] miles. So far, [tex]2^{3/4}[/tex] miles have been repaved, leaving [tex]7^{(3/10)}[/tex] - [tex]2^{3/4}[/tex] miles that have not been repaved.
1. The total length of the main road is given as [tex]7^{(3/10)}[/tex] miles. In mathematical notation, [tex]7^{(3/10)}[/tex] represents the cube root of 7, which is then raised to the power of 3. So, the total length of the road is the cube root of 7, and then that result is cubed.
2. The length of the repaved portion is given as [tex]2^{3/4}[/tex] miles. In mathematical notation, [tex]2^{3/4}[/tex] represents the fourth root of 2, which is then raised to the power of 3. So, the repaved length is the fourth root of 2, and then that result is cubed.
3. To find the remaining length that has not been repaved, we simply subtract the repaved length from the total length:
Remaining length = [tex]7^{(3/10)}[/tex] - [tex]2^{3/4}[/tex]
Calculating the values, the total length is approximately 2.262 miles (rounded to three decimal places) and the repaved length is approximately 1.682 miles (rounded to three decimal places). Now, subtracting the repaved length from the total length, we get approximately 0.580 miles (rounded to three decimal places) as the length that has not been repaved.
Therefore, the remaining length that has not been repaved is approximately 0.580 miles (rounded to three decimal places).
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Solve v^2-7v-33=0 by factoring
Answers
What is this ????????
Answers
help please 10 points !!images below
Answers
Answer for Question 1 is option 2
Answer for Question 2 is option 3
Answer for Question 3 is option 3
Step-by-step explanation:
For question 1 by plotting the two points we get the coordinates as (-2, 3) and (2, 1) where the x values are -2, 2 and the y values are 3, 1 respectively. By substituting values of x in the formula given we get that equation 2 satisfies the values of y as in the graph.
For question 2 the plotted line is split into two parts where one half is for values of x <2 and the other half is for values of x>2. By finding out the coordinates we get them as (2,-2), (1,-2.5) and (0,-3) for x<2 and by substituting the values of x in the formula we get option 3 as our answer.
For question 3 we need to find the value of y when x=3 and the first condition is only for values greater than 3 so we take the second condition and substitute the value of x=3 and we get the value of y as 5 so the answer is option 3
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 4 large boxes and 8 small boxes has a total weight of 197 kilograms. A delivery of 2 large boxes and 3 small boxes has a total weight of 83 kilograms. How much does each type of box weigh?
Answers
A large box of fruit weighs 18.25 kilograms and a small box weighs 15.5 kilograms.
Step-by-step explanation:
Let,
Weight of large box = x
Weight of small box = y
According to given statement;
4x+8y=197 Eqn 1
2x+3y=83 Eqn 2
Multiplying Eqn 2 by 2
[tex]2(2x+3y=83)\\4x+6y=166\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 1
[tex](4x+8y)-(4x+6y)=197-166\\4x+8y-4x-6y=31\\2y=31[/tex]
Dividing both sides by 2
[tex]\frac{2y}{2}=\frac{31}{2}\\y=15.5[/tex]
Putting y=15.5 in Eqn 2
[tex]2x+3(15.5)=83\\2x+46.5=83 \\2x=83-46.5\\2x=36.5[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{36.5}{2}\\x=18.25[/tex]
A large box of fruit weighs 18.25 kilograms and a small box weighs 15.5 kilograms.
Keywords: linear equation, elimination method
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