The value of given equation i.e. [tex]m^{3} -\frac{1}{m^{3} }[/tex] is [tex]\frac{63}{8}[/tex]
Given a equation i.e.[tex]\frac{m-1}{m}[/tex]=3 and asked to calculate the value of the equation [tex]m^{3} -\frac{1}{m^{3} }[/tex]
To calculate the value of [tex]m^{3} -\frac{1}{m^{3} }[/tex] , Need to use various operations like subtraction and division)
Given .[tex]\frac{m-1}{m}[/tex]=3
⇒m-1=3m ( cross multiplies 3 and m)
⇒2m=-1( subtraction is used)
⇒m=-[tex]\frac{1}{2}[/tex]( division is used)
Thefore the value of m in the given equation i.e.[tex]\frac{m-1}{m}[/tex]=3 is -[tex]\frac{1}{2}[/tex]
⇒ [tex]m^{3} -\frac{1}{m^{3} }[/tex]
Here the value of m =-[tex]\frac{1}{2}[/tex]
Substituting the value of m in the given equation
⇒[tex](\frac{-1}{2} )^{3}[/tex]-[tex](-2)^{3}[/tex]
⇒[tex]\frac{-1}{8}[/tex]+8(addition is used)
⇒[tex]\frac{64-1}{8}[/tex]
⇒[tex]\frac{63}{8}[/tex]
Therefore, the value of the given equation i.e. [tex]m^{3} -\frac{1}{m^{3} }[/tex] is [tex]\frac{63}{8}[/tex]
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An online store sells old video games and DVDs as a bundle. A bundle of two video games and three DVDs can be purchased for $90.00. A bundle of one video game and two DVDs can be purchased for $51.50. Find the cost of one video game and the cost of one DVD in the bundle.
Using system of equations, the cost of one video game is $25.5; the cost of one DVD is $13.
How to Apply System of Equations to Solve a Problem?Given the problem above, we would do the following:
Video games = vDVDs = dUsing the information given, we would form two equations for the system as shown below:
2v + 3d = 90 ---> equation 1
v + 2d = 51.5 ---> equation 2
Multiply equation 2 by 2 to get equation 3
2v + 4d = 103 ---> equation 3
Subtract equation 1 from equation 3
d = 13
The cost of one DVD = d = $13.00
Substitute d = 13 into equation 2
v + 2d = 51.5 ---> equation 2
v + 2(13) = 51.5
v + 26 = 51.5
v = 51.5 - 26
v = 25.5
The cost of one video game = v = $25.50.
Therefore, using system of equations, the cost of one video game is $25.5; the cost of one DVD is $13.
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A line is perpendicular to y = -x-2
and intersects the point (-5, 10).
What is the equation of this
perpendicular line?
y = x + [?]
The equation of the perpendicular line is y = x + 15.
How to determine the equation of the perpendicular line
In this problem we need to determine the equation of the line perpendicular to another line, that intersects at the point (x, y) = (- 5, 10). The explicit form of the equation of the line is defined by the following first order polynomial:
y = m · x + b
Where:
m - Slopeb - y-Interceptx - Independent variabley - Dependent variableThe first line has a slope - 1 and the slope of the second line is:
m' = - 1 / m
m' = 1
Then, the intercept of the second line is:
b = y - m · x
b = 10 - (- 5)
b = 15
The equation of the perpendicular line is y = x + 15.
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What sentence represents the number of test questions in the problem
below?
A test is worth 50 points. Multiple-choice questions are worth point, and
short-answer questions are worth 3 points. If the test has 20 questions, how
many multiple-choice questions are there?
A. The number of multiple-choice questions plus the number of
short-answer questions is 50.
B. The number of multiple-choice questions minus the number of
short-answer questions is 50.
• C. The number of multiple-choice questions times the number of
short-answer questions iS 20.
D.
The number of multiple-choice questions plus the number of
short-answer questions is 20.
Answer:
D
Step-by-step explanation:
The number of questions is 20; it's the total points that are worth 50 and the question is asking for number of questions
Y is inversely proportional to the square of x. if y=3 when x=3 then y =1/3 when x is _______. help me isuck at proportionals
The following table gives a partial set of values of a polynomial function. x −2 −1 0 1 2 3 g(x) 14 2 0 4 6 −2 Between which two values would a relative minimum most likely occur? (2 points) −2 and 0 0 and 2 −1 and 1 1 and 3
From -1 to 0, the function goes decreases, and from 0 to 1 the function goes increases. Then we will have the minimum between -1 and 1.
Between which two values would a relative minimum most likely occur?Here we have the table:
x: -2, -1, 0, 1, 2, 3g(x): 14, 2, 0, 4, 6, -2You can see that:
g(-1) = 2
g(0) = 0
So the function goes downwards from x = -1 to x = 0.
g(1) = 4
So the function goes upwards between 0 and 4.
Then, from -1 to 0, the function goes decreases, and from 0 to 1 the function goes increases. Then we will have the minimum between -1 and 1.
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Find the center of mass of the wire that lies along the curve r and has density =4(1 sin4tcos4t)
The mass of the wire is found to be 40π√2 units.
How to find the mass?To calculate the mass of the wire which runs along the curve r ( t ) with the density function δ=5.
The general formula is,
Mass = [tex]\int_a^b \delta\left|r^{\prime}(t)\right| d t[/tex]
To find, we must differentiate this same given curve r ( t ) with respect to t to estimate |r'(t)|.
The given integration limits in this case are a = 0, b = 2π.
Now, as per the question;
The equation of the curve is given as;
r(t) = (4cost)i + (4sint)j + 4tk
Now, differentiate this same given curve r ( t ) with respect to t.
[tex]\begin{aligned}\left|r^{\prime}(t)\right| &=\sqrt{(-4 \sin t)^2+(4 \cos t)^2+4^2} \\&=\sqrt{16 \sin ^2 t+16 \cos ^2 t+16} \\&=\sqrt{16\left(\sin t^2+\cos ^2 t\right)+16}\end{aligned}[/tex]
Further simplifying;
[tex]\begin{aligned}&=\sqrt{16(1)+16} \\&=\sqrt{16+16} \\&=\sqrt{32} \\\left|r^{\prime}(t)\right| &=4 \sqrt{2}\end{aligned}[/tex]
Now, use integration to find the mass of the wire;
[tex]\begin{aligned}&=\int_a^b \delta\left|r^{\prime}(t)\right| d t \\&=\int_0^{2 \pi} 54 \sqrt{2} d t \\&=20 \sqrt{2} \int_0^{2 \pi} d t \\&=20 \sqrt{2}[t]_0^{2 \pi} \\&=20 \sqrt{2}[2 \pi-0] \\&=40 \pi \sqrt{2}\end{aligned}[/tex]
Therefore, the mass of the wire is estimated as 40π√2 units.
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The complete question is-
Find the mass of the wire that lies along the curve r and has density δ.
r(t) = (4cost)i + (4sint)j + 4tk, 0≤t≤2π; δ=5
Given mn, find the value of x.
The following dotplot shows the number of songs on each album in Sal's collection. Each dot represents a different album.
A dot plot with an axis labeled "number of songs" and numbered from 0 to 20 in increments of 1, with 19 points. 4, frequency 1. 7, frequency 1. 8, frequency 2. 9, frequency 2. 10, frequency 4. 11, frequency 1. 12, frequency 2. 13, frequency 2. 14, frequency 1. 16, frequency 1. 18, frequency 1. 20, frequency 1.
Here is the five-number summary for these data:
Five-number summary
min \text{Q}_1Q
1
start text, Q, end text, start subscript, 1, end subscript median \text{Q}_3Q
3
start text, Q, end text, start subscript, 3, end subscript max
444 999 101010 131313 202020
According to the 1.5\cdot \text{IQR}1.5⋅IQR1, point, 5, dot, start text, I, Q, R, end text rule for outliers, how many high outliers are there in the data set?
Choose 1 answer:
Using the quartiles of the data-set, it is found that there is one high outlier in the data-set.
What are the median and the quartiles of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set, which is also the 25th percentile.The third quartile is the median of the second half of the data-set, which is also the 75th percentile.The interquartile range is the difference between the third quartile and the first quartile.The dot plot shows the frequency of each observation, hence the complete data-set is given by:
4, 7, 8, 8, 9, 9, 10, 10, 10, 10, 11, 12, 12, 13, 13, 14, 16, 18, 20.
The quartiles are found as follows:
The first half is composed by the first 9 elements, given by 4, 7, 8, 8, 9, 9, 10, 10, 10, hence Q1 = 9.The second half is composed by the last 9 elements, given by 11, 12, 12, 13, 13, 14, 16, 18, 20, hence Q3 = 13.The IQR is given by:
IQR = Q3 - Q1 = 13 - 9 = 4.
The high outliers are the values that are more than 1.5 IQR above Q3, hence the threshold is given by:
13 + 1.5 x 4 = 19.
There is only value greater than 19, which is of 20, hence there is one high outlier in the data-set.
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Answer:
answer was 0
Step-by-step explanation:
The solution set of a linear system whose augmented matrix is [ 1 2 3 ] is the same as the solution set of =, if =[ 1 2 3 ].
x+2x+x=d is solution set of a linear system whose augmented matrix.
What does matrix mean?
A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.First statement
[ 1 2 3 | d][x]
[ 1 2 3]x=d
x+2x+3x=d
Second statement
Ax=d
Given that A = [ 1 2 3]
[ 1 2 3]x=d
x+2x+3x=d
x+2x+x=d
Then, they are going to have the same solution
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The ratio of 6th grade basketball players to 6th grade volleyball players is 5:2 if THERE ARE 30 BASKETBALL PLAYERS HOW MANY VOLLEYBALL AYERS ARE THERE
Answer: There are 12 volleyball players
Step-by-step explanation:
If the ratio of basket to volleyball players is 5:2 and there are 30 known basket ball players that means the ratio can be written as 30:x.
If 30 is 5 parts (5x) and volleyball players is 2 parts (2x) we need to figure out the value of 1 part (x)
This can be done by
5x=30
x=6
Now we know what 1 part is, we can now use that two figure out 2 parts
2x or 2(6)
2(6) = 12
So the ratio is 30:12. This can be confirmed by dividing both sides of the radio by 6 to get 5:2
Two shops each charge a rental fee plus an hourly fee to rent a canoe. How many
hours must a canoe be rented for the total costs at both shops to be the same?
Rental fee
Hourly fee
Shop A Shop B
$2
$8
$5
$4
The time when the two total costs would be equal is 6 hours.
When would the total cost be equal?The equation that can be used to represent the total cost of renting a canoe is a linear function. A linear equation is an equation that has a single variable raised to the power of 1. A linear equation increases by a predetermined constant. An example of a linear equation is 2x + 2.
The form that the equation would be is:
Total cost = rental fee + (cost per hour x number of hours)
Total cost at Shop A = $2 + $5h
Total cost Shop B = $8 + $4h
When the total costs are equal, the two above equations would be equal.
$2 + $5h = $8 + $4h
Combine similar terms: $$5h - $4h= $8 - $2
Add similar terms: h = 6 hours
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Kara earns $8 per hour
plus a $40 one-time bonus.
She works between 16
and 20 hours in a week.
What is the greatest value in
range of this situation?
The greatest value in range of work situation is $200.
What is referred as the inequality?a statement of an order relation between two figures or algebraic expressions (greater than, greater or equal to, less than, or less than as well as equal to).a statement of an order relationship between two numbers or algebraic expressions (greater than, greater than or equivalent to, less than, or less than or equal to).For the given question;
The one time bonus is $40.
Amount earned by Kara per hour is $8.
The range of working hours lies between 16 to 20 hours in a week.
Let 'x' be the number of hours Kara worked.
The the inequality will be;Then, the equation for the amount earned in a week is;
Total pay = one time pay + 8×number of hours
Total pay = one time pay + 8x
The greatest value will be earned by the kara when she will work for 20 hours.
Thus, put x = 20.
Total pay = one time pay + 8×20
Total pay = 40 + 8×20
Total pay = 200
Therefore, the total greatest pay earned by the Kara is $200.
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guys im new and i need help withe some first one
1. -2 2/3 divided by 4/3
2. -2 1/4 divided by (-5/8)
3. 1/2 divided by 2/5
4.11/3 divided by 4/5
Answer:
#1 = -2
Step-by-step explanation:
First, we need to make -2 2/3 an improper fraction. An improper fraction is a fraction whose numerator is bigger than its denominator.
you first multiply the whole number (ignoring the negative sign for now) by the denominator:
2*3=6
then you add the numerator:
6+2=8
finally you put that number over the denominator and then put the negative sign back:
-8/3
Next, you can use keep change flip to solve the division
You keep the first fraction, change the division sign to a multiplication sign, and flip the numerator and the denominator of the second fraction:
-8/3 divided by 4/3 becomes -8/3 x 3/4
finally you multiply across as you would normally and simplify
-8/3 x 3/4= -24/12
-24/12 simplified is -2
:D
if you need help with the rest just comment on this response and I'll try to answer as soon as I can
..........................................................................................................................................................................
Answer:
0.012÷2=12 thousandths ÷ 2
50 PoInts for math homework Waxton
The midpoint of \overline{\text{AB}}
AB
is M(1, -3)M(1,−3). If the coordinates of AA are (-6, -7)(−6,−7), what are the coordinates of BB?
Answer:
the coordinates of BB would be: B(8,1)
Find the distance between (10,6), (1,-4)
Graph the inequality 1
The graph of the combined inequality, 1 < y + 7x ≤ 12, is shown below. The correct graph is graph b.
Graph of InequalitiesFrom the question, we are to graph the given inequality
The given inequality is
1 < y + 7x ≤ 12
First, we will separate the inequality
1 < y + 7x and y + 7x ≤ 12
1 < y + 7x
We will determine two points on the line
1 = y + 7x
When x = 0
1 = y + 7(0)
1 = y
y = 1
(0, 1)
When y = 8
1 = y + 7x
1 = 8 + 7x
1 -8 = 7x
-7 = 7x
x = -7/7
x = -1
(-1, 8)
We can use these two points to plot the line of 1 < y + 7x
Also,
We will determine two points on line y + 7x ≤ 12
y + 7x = 12
When x = 0
y + 7(0) = 12
y + 0 = 12
y = 12
(0, 12)
When y = 5
5 + 7x = 12
7x = 12 - 5
7x = 7
x = 7/7
x = 1
(1, 5)
We can use these two points to plot the line of y + 7x ≤ 12
The graph of the combined inequality, 1 < y + 7x ≤ 12, is shown below. The correct graph is graph b.
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Pls help! shannon is designing a new rectangular flag for the school's color guard and is determining the angles at which to cut the fabric. she wants the measure of 22 to be three times as great as the measure of z1. she thinks the measures of 23 and 24 should be equal. finally, she wants the measure of 26 to be half that of 25. determine the measures of the angles. 3
The angles are: ∠1 = 22.5°, ∠2 = 67.5°, ∠3 and ∠4 = 45°, ∠5 = 135° and ∠6 = 67.5°.
The flag is rectangle; hence, each corner will be 90°. Now, sum of ∠1 and ∠2 and sum of ∠3 and ∠4 will be 90°. We are given ∠2 is three times the ∠3. So, forming the equation -
∠2 = 3 ∠3
∠2 = 3 ∠1
∠1 + ∠2 = 90
∠1 + 3 ∠1 = 90
4 ∠1 = 90
∠1 = 22.5°
∠2 = 90 - ∠1
∠2 = 90 - 22.5
∠2 = 67.5°
According to Shannon, ∠3 = ∠4
∠3 + ∠3 = 90
2 ∠3 = 90
∠3 = 45° = ∠4
∠2 and ∠6 are the opposite angles and hence are also equal. Also, according to Shannon, ∠6 = 1/2 ∠5.
67.5 = 1/2 × ∠5
∠5 = 67.5 × 2
∠5 = 135°
Hence, each angle is: ∠1 = 22.5°, ∠2 = 67.5°, ∠3 and ∠4 = 45°, ∠5 = 135° and ∠6 = 67.5°.
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A+number+is+stored+in+cell+c24.+in+cell+d24,+you+wish+to+calculate+5%+of+the+number+stored+in+cell+c24.+to+accomplish+this,+what+formula+should+be+entered+in+cell+d24?
Answer:
just put out + from the question.
The stock market closed on Tuesday at
-284 points. On Wednesday, it closed at -8
points. Find the change in points from
Tuesday to Wednesday.
-2 9 2 is the change in points from Tuesday to Wednesday in stock market.
What does the term "stock market" mean?
Buyers and sellers can trade equity shares of public firms in stock exchanges. Due to their ability to democratize access to investor trading and capital exchange, stock markets are essential elements of a free-market economy. Prices are discovered and traded in stock markets in an efficient manner.What does the stock market represent?
ETFs, stock index and stock options, equity swaps, single-stock futures, and stock index futures are a few examples. These last two may be traded over-the-counter or on futures exchanges, which are separate from stock exchanges and have a history that may be traced back to commodities futures markets.The stock market closed on Tuesday = -284 points
On Wednesday it closed = -8
the change in points from Tuesday to Wednesday = -284 - 8 = -2 9 2
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-3, -5
a b
Step by step?
The given algebraic equation formula i.e., [tex](a^{2} -b^{2} )=(a+b)(a-b)[/tex] is verified for the given values of a and b of -3 and -5 respectively.
As per the question statement, we are supposed to verify the algebraic equation formula
[tex](a^{2} -b^{2} )=(a+b)(a-b)[/tex]
We are given that a = -3 and b = -5
Now substituting the values of a and b in the algebraic equation formula
[tex](a^{2} -b^{2} )=(a+b)(a-b)\\LHS = (a^{2} -b^{2} )\\LHS= ([-3]^{2} -[-5]^{2} )\\LHS=(9-25)\\LHS = -16[/tex]
LHS = Left hand side of the equation
Now considering RHS i.e., Right hand side
[tex]RHS = (a+b)(a-b)\\RHS = ([-3]+[-5])([-3]-[-5])\\RHS= (-8)(2)\\RHS = -16[/tex]
As Left Hand Side LHS = Right Hand Side RHS
Hence the equation, [tex](a^{2} -b^{2} )=(a+b)(a-b)[/tex] is verified for the given values of a and b and is true for all real values of a and b.
Algebraic Equation: The term "algebraic equation" refers to a formulation of the equality of two expressions using the algebraic operations of addition, subtraction, multiplication, division, raising to a power, root operations.To learn more about algebra and equations, click on the link given below:
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Evaluate the expression 30-14divided by 2
Answer:
23
Step-by-step explanation:
You have to do the division first unless it is a fraction.
14/2 = 7
30 - 7 = 23
If it was a fraction (with 30 - 14 on top and 2 on the bottom) Then the answer would be 8 > 30 - 14 = 16/2 = 8
Hope this helps.
what is the midpoing of (-5,4) and (7,-5)
Answer:
(1,-1/2)
Step-by-step explanation:
Add both x values and divide by 2
Add both y values and divide by 2
( -5+7 )/2 = 1
(4 - 5)/2 = -1/2
(1,-1/2)
What is the value of x − 7 if x = −18?
Answer:
x - 7 = -25
Step-by-step explanation:
The value of x is,
→ x = -18
Then the value of x - 7 will be,
→ x - 7
→ -18 - 7
→ -25
Hence, the answer is -25.
Two customers spent the same total amount of money at a restaurant.
• The first customer bought 8 hot wings and left a $4 tip.
• The second customer bought 10 hot wings and left a $2.80 tip.
• Both customers paid the same amount per hot wing.
How much does one hot wing cost at this restaurant in dollars and cents?
Record your answer in the boxes below. Be sure to use the correct place value.
+/-
Help please I cant figure it out.
PLEASE HELPP!
FIND THE MEASURE OF ANGLE A!!!
Answer:
123
Step-by-step explanation:
supplementary angles add up to 180
(5x - 22) + (x + 28) = 180
5x - 22 + x + 28 = 180
6x + 6 = 180
6x = 180 - 6
6x = 174
x = 174/6
x = 29
<A = 5x - 22 = 5(29) - 22 = 123
twice a number increased by three is between negative three and seven
The number can be -3, -2, -1, 0 ,1
Here, we are given that twice a number is increased by three and the result is between negative three and seven.
Let the number be x
Twice of the number = 2x
Four more than twice the number = 2x + 4
This number is between -3, 7
⇒ -3 < 2x +4 < 7
subtracting 4 from both sides we get
-3 -4 < 2x < 7 - 4
-7 < 2x < 3
Dividing both sides by 2 we get
-7/2 < x < 3/2
- 3.5 < x < 1.5
Thus the original number lies between -3.5 and 1.5
This means that it can take 5 values-
-3, -2, -1, 0 ,1
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Solve the equation −108 = 6x for x.
Answer:
[tex] \sf \large \: x = −18[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
−108 = 6x
Step 1: Flip the equation.
6x = −108
Step 2: Divide both sides by 6.
6x/6 = −108/6
x = −18
