Can someone please help answer the questions attached - it's on inverse proportion? :)
Answers
Answer:
see explanation
Step-by-step explanation:
(a)
given y is inversely proportional to x³ then the equation relating them is
y = [tex]\frac{k}{x^3}[/tex] ← k is the constant of proportion
to find k use any of the ordered pairs from the table
using (1, 8 ) , then
8 = [tex]\frac{k}{1^3}[/tex] = [tex]\frac{k}{1}[/tex] ⇒ k = 8
y = [tex]\frac{8}{x^3}[/tex] ← equation of proportion
(b)
when y = 64 , then
64 = [tex]\frac{8}{x^3}[/tex] ( multiply both sides by x³ )
64x³ = 8 ( divide both sides by 64 )
x³ = [tex]\frac{8}{64}[/tex] = [tex]\frac{1}{8}[/tex] ( take cube root of both sides )
x = [tex]\sqrt[3]{\frac{1}{8} }[/tex] = [tex]\frac{1}{2}[/tex]
Related Questions
Samples of airline departure times are obtained and compared to the scheduled departure times. Major airlines are compared and their mean delay times are recorded. Identify the null and alternative hypotheses for applying an analysis of variance.
Answers
A null hypothesis is directly opposed by an alternative hypothesis. As a result, if either one of the two theories is accurate, the other is untrue.
What is the difference between null and alternative hypotheses?In statistical hypothesis testing, null and alternate hypotheses are utilized. The null hypothesis of a test always predicts no effect or no association between variables, but the alternative hypothesis reflects the effect or relationship that your research predicts.
A null hypothesis is directly opposed by an alternative hypothesis. As a result, if either one of the two theories is accurate, the other is untrue.
Based on the study question or issue that they are attempting to solve, the analyst or researcher develops a null hypothesis. The null may be distinguished in many ways depending on the question.
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If F, G, and H are the midpoints of the sides of triangle JKL, FG=37, KL=48, and GH=30, find each measure. FH=, JL=, KJ=, FJ=
Answers
DCM, this is the solution:
According to the midpoint theorem, the line connecting the midpoints of two sides is parallel to the third and its length is half of the third side.
Therefore,
KJ = 2 * GH
KJ = 2 * 30
KJ = 60 and FJ = 30
JL = 2 * FG
JL = 2 * 37
JL = 74
jackson bikes 2 miles in 15 mins at that rate how many miles will a bike in 45 mins
Answers
Let's use Cross-multiplication:
2mi ------------------------>15min
x mi------------------------->45min
So:
2/x = 15/45
Solving for x:
Multiply both sides by x:
x*(2/x) = x* 15/45
2 = 15x/45
Multiply both sides by 45:
45*2 = 45*(15x/45)
90 = 15x
Divide both sides by 15:
90/15 = 15x/15
6 = x
x = 6mi
23 < y - 2 solve the inequality of y and simplify your answer as much as possible.
Answers
[tex]23 + 2 < y \\ y > 25[/tex]
ATTACHED IS THE SOLUTION Mind you I swap the positions of the term so that y can be on the left hand side.
Goodluck!!
Answer:
25 < y
Step-by-step explanation:
23 + 2 < y
25 < y
that's as much as it goes
Solve the inequality and graph the solution on the line provided.
3x+17_< 41
Answers
Your answer should be: x _< 8
(The “<“ is on top of the underline btw)
The sign between x & 8, should be: “less than or equal to” sign.
And your point on the graph should go form right to left. Starting on right side “8”, then proceeding to the negative side
Check the graph below that I provided
Which fraction equals \dfrac{4}{7} + \dfrac{3}{8}
7
4
+
8
3
?
Answers
Answer:
[tex]$\frac{53}{56}[/tex]
Step-by-step explanation:
Hello!
Let's first convert the denominator of each fraction to the same number. Multiply the denominator by the whole number formed by the other number's denominator.
[tex]\frac{4}{7} + \frac{3}{8}[/tex][tex]\frac{4}{7}(\frac88) + \frac38(\frac77)[/tex][tex]\frac{32}{56} + \frac{21}{56}[/tex]Now we can add the numerators of the fractions and keep the denominators the same.
[tex]\frac{32}{56} + \frac{21}{56}[/tex][tex]\frac{32 + 21}{56}[/tex][tex]\frac{53}{56}[/tex]The simplified form is [tex]$\frac{53}{56}[/tex].
Find the output when the input is n input 1,2,3,4,n output
-6,-8,-10,-12
Answers
The expression that represents the output value when the input is n is -4 - 2n
How to determine the output value for the input n?From the question, the input parameters are given as
Input 1,2,3,4,n
Similarly, the output parameters are given as
output: -6,-8,-10,-12
So, we have the following table of values
1,2,3,4,n
-6,-8,-10,-12
From the above table of values, we have the following parameters
Sequence type = arithmetic sequenceFirst term, a = -6Common difference, d = -2The output value for the input n is then calculated as
Tn = a + (n - 1) * d
So, we have
Tn = -6 + (n - 1) * -2
Open brackets
Tn = -6 - 2n + 2
Evaluate the like terms
Tn = -4 - 2n
Hence, the output value for the input n is -4 - 2n
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Which graph represents the reflection of AABC over the line y = 0?
-54-3 -2 -1
S ON
CH
-3
LO
*
C
A
2 3
A
B
12
X
Answers
Answer:
The graph represents the reflection of triangle ABC over the line y=0 in graph (C).
The coordinates of the triangle ABC are:
A(1, -1), B(4, -1) and C(3, -3).
The rule of reflection over the line y = 0 is:
(x, y) ⇒ (x, -y)
So, we have:
A(1, -1) ⇒ (1, 1),
B(4, -1) ⇒ (4, 1)
C(3, -3) ⇒ (3, 3).
By comparing the above points to the list of options, the correct graph is a graph (c)
Step-by-step explanation:
hope this helps I hope
The graph C represents the reflection of triangle ABC over the line y = 0
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The coordinates of the triangle ABC are:
A(1, -1), B(4, -1) and C(3, -3).
The rule of reflection over the line y = 0 is:
(x, y) ⇒ (x, -y)
So, we have:
The coordinates after applying rule
A(1, -1) ⇒ (1, 1),
B(4, -1) ⇒ (4, 1)
C(3, -3) ⇒ (3, 3).
By comparing the above points to the list of options, the correct graph is a graph (c)
Hence, the graph C represents the reflection of triangle ABC over the line y = 0
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Given the line 2x +3y =4 what is the y intercept
Answers
Answer:
(0, 4/3)
Step-by-step explanation:
2x +3y =4
3y =4 -2x
y = 4/3 - 2/3x
y = -2/3x + 4/3
y = -2/3(0) + 4/3
y = 4/3
-----------
or just plug in 0 for x from the start
2(0) + 3y = 4
3y = 4
y = 4/3
Susan spent 3/8 on school bag and spend 2/5 of the remaining spend on fountain pen. how much is the school bag cost?
Answers
Answer:
30 dollars
Step-by-step explanation:
3/8 and 2/5 is 31/40 and 300.00
Answer is 30.775
Answer: 30 dollars
Step-by-step explanation: cant put explanation right now in a rush! make the other person brainliest they deserve it! :)
I need help!
Use the given information to select the factors of f(x). f(4)=0 f(-1)=0 f(3/2)=0. Make sure to select all correct answers for full credit.
Answers
The given information of the factors f ( x ) helped to get the following correct options:
( x + 1 ) ⇒ f ( -1 )( x - 4 ) ⇒ f ( 4 )( 2x - 3 ) ⇒ f ( 3/2 )What is a function in math?The term function as used n math refers to a relation consisting of variables. the variables are of two major types which include
The dependent variableThe independent variableSubstituting the functions we have:
f (-1 ) = ( 1 - 1 ) = 0
f ( 4 ) = ( 4 - 4 ) = 0
f ( 3/2 ) = (3 * 2/3 - 3 ) = 0
Other options fail to give the desired result of zero.
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What is the slope of the line through the points (6,5) and (4, 10)?
m=
Answers
The slope of the line through the points (6,5) and (4, 10) exists -5/2.
What is meant by the slope of a line?A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively. where "m" represents a line's slope. So, the slope of a line is tan.
Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.
Let the two points are (6, 5) and (4, 10)
(x1, y1) = (6, 5) and (x2, y2) = (4, 10)
The equation of slope of the line through the points (x1, y1) and (x2, y2) = y2 - y1 / x2 - x1
substitute the values in the above equation, and we get
= 10 - 5 / 4 - 6
= 5 / -2
Therefore, the slope of the line through the points (6,5) and (4, 10) exists -5/2.
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2x+y = -7
-4x -5y =23
Answers
Answer:
x = -2
y = -3
Step-by-step explanation:
If it is a simultaneous equation.
2x+y = -7-----equation 1
-4x -5y =23-----equation 2
5(2x+y = -7)
-4x -5y =23
10x+5y = -35
-4x -5y =23 +5y cancel -5y
10x= -35
-4x=23
6x = -12
x = -2
Solving for Y
Substitute the value of x in equation one or two.
equation two = -4x -5y =23
-4x -5y =23
-4(-2) -5y =23
8-5y=23
-5y = 23-8
-5y = 15
y = -3
PLEASE HELP ME FIND X
Answers
Answer:
28°
Step-by-step explanation:
AB and CD are straight lines, all angles in a straight line add up to 180
Helpppppp x = – 3
y = – 1
Answers
The graphs of the equations are in the attached graph
'
How to plot the equations on the graph?Equation (2)
From the question, the equation is given as
x = -3
In the above equation, we can see that
The equation has only one variable and the highest power of the variable is 1
Since the variable is x, then it means that the line of the graph is a vertical line that passes through point x = -3
See attachment for the graph
Equation (3)
Here, we have
y = -1
Also in this equation, we can see that
The equation has only one variable and the highest power of the variable is 1
Since the variable is y, then it means that the line of the graph is a horizontal line that passes through point y = -1
See attachment for the graph
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4x > 28 solve the inequality for x and simplify your answer as much as possible
Answers
Answer:
x > 7
Step-by-step explanation:
x = 28 ÷ 4
x > 7
that's it
Hey there!
4x > 28
DIVIDE 4 to BOTH SIDES
4x/4 > 28/4
SIMPLIFY it
x > 28/4
x > 7
It is an open circle started at 7 & it’s going to the left of the number line
Therefore, your answer should be:
x > 7
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
30, 32, 37, 54, 67, 38, 44 what are the lower and upper bounds to identify an unusual data point. (use up to the first decimal place for your calculation: example 14.2)
Answers
The lower and upper bounds are 16.7 and 69.5 respectively.
So, the numbers are 30, 32, 37, 54, 67, 38, and 44.
In order to determine the lower bound and upper bound
Mean x' =Σ[tex]\frac{x}{n}[/tex] = 302/7 = 43.1429 = 43.1
Variance [tex]s^{2}[/tex] =Σ[tex]\frac{(x-x')^{2}}{n-1}[/tex] = 1048.86/(7-1) = 174.80952
Standard deviation = √174.80952 = 13.221555 = 13.2
Values that deviate more than two standard deviations from the mean are exceptional.
[tex]x -2s = 43.1 - 2*13.2 = 16.7[/tex] is the lower bound for uncommon values.
The upper bound that is exceptional is equal to
[tex]x + 2s = 43.1 + 2(13.2) = 69.5[/tex]
Therefore, 16.7 and 69.5 are the lower and upper bounds of given data
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To prepare for a bake-Off, Sebastian used 830 grams of flour each day for 4 weeks. How many kilograms did Sebastian use in those 4 weeks?
1 q = 0.001 kg
Answers
If 830 grams = 1 day.
23.24 kilograms = 4 weeks.
23.24 kilograms were used by Sebastian in those 4 weeks.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example: 3x = 4 is an equation.
We have,
830 grams is used each day.
830 grams = 1 day ___(1)
1 week = 7 days
Multiply 4 on both sides.
4 weeks = 28 days ___(2)
From (1) and (2) we get,
4 weeks = 28 days
4 weeks = 28 x 1 day
4 weeks = 28 x 830 grams
4 weeks = 23240 grams ____(3)
1000 grams = 1 kg
Multiply both sides by 23240/1000.
23240 grams = 23.24 kilograms _____(4)
From (3) and 94) we get,
4 weeks = 23.24 kilograms
Thus,
23.24 kilograms were used by Sebastian in those 4 weeks.
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3a. Sketch the line that goes through the points A(4,3) and B( 8, 1)Find the slope and the equation of line AB3b. Find the length of segment AB3c. Find the midpoint of segment AB
Answers
Hello! First, let's remember:
We can write a point as a cartesian coordinate (x, y).
The exercise has given two points, A(4,3) and B(8,1).
a. Slope:To calculate the slope of a line, we can use the formula below:
[tex]\text{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's consider A equal to the first point (4, 3) = (x1, y1), and B will be the second point (8, 1) = (x2, y2). Replacing these values in the formula:
[tex]\text{Slope}=\frac{1_{}-(3)_{}}{8-(4)}=\frac{-2}{4}=-\frac{1}{2}[/tex]b. Lenght of segment AB:To find this length, we have to use another formula. Now we will calculate the distance between two points:
[tex]\text{Distance}=\sqrt[]{(x_2-x_1)^2+(y_2_{}-y_1_{})^2}[/tex]Still considering A (4, 3) = (x1, y1), and B (8, 1) = (x2, y2), let's replace the values in the formula:
[tex]\begin{gathered} \text{Distance}=\sqrt[]{(8_{}-4_{})^2+(1-3_{})^2} \\ \text{Distance}=\sqrt[]{(4_{})^2+(-2_{})^2} \\ \text{Distance}=\sqrt[]{(16^{}+4)^{}} \\ \text{Distance}=\sqrt[]{20} \\ \text{Distance}=2\sqrt[]{5} \end{gathered}[/tex]c. Midpoint of segment AB:This value will be the medium point. To calculate it, we'll use another formula:
[tex]x_m=(\frac{x_1+x_2}{2}+\frac{y_1+y_2_{}_{}}{2})[/tex]Still considering the same values for (x1, y1) and (x2, y2), let's replace them:
[tex]\begin{gathered} x_m=(\frac{8+4_{}}{2},\frac{3+1_{}}{2}) \\ \\ x_m=(\frac{12_{}}{2},\frac{4_{}}{2}) \\ \\ x_m=(6,2) \end{gathered}[/tex]The midpoint of segment AB will be at point X (6, 2).
You can see this line represented in a cartesian plan below:
Dr. Choi just started an experiment. He will collect data for days. How many hours is this?
Answers
The data collected in [n] days is collected in 24n hours.
What is the SI unit of time?
The SI unit of time is Seconds. In 1 second, there are (1/60) minutes.
Given is Dr. Choi who just started an experiment and he will collect data for days.
Assume that he collects the data for [n] number of days. In one day, we have 24 hours. Therefore, in [n] number of days, there will be total of 24n hours.
Therefore, the data collected in [n] days is collected in 24n hours.
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Emma is scrapbooking. She has 9 inches of paper and needs to cut it into 2/5 inch strips of paper. how many whole strips will she be able to make?
Answers
ok
I erased the answer but it is 22 whole strips
General MathematicsProblem:What sum would have to be invested at 9% conpounded annually to provide an ordinary annuity at ₱8,000 per year for 5 years?
Answers
Given that a future value annuity of 8,000 is accrued at 9% compounded annually, the present value of the annuity is evaluated as
[tex]\begin{gathered} PV=P(\frac{1-(1+r)^{-n}}{r})\text{ ----- equation 1} \\ \text{where } \\ PV\text{ }\Rightarrow present\text{ value of the annuity} \\ P\Rightarrow value\text{ of each payment} \\ r\Rightarrow interest\text{ rate} \\ n\Rightarrow period \end{gathered}[/tex]Thus,
[tex]\begin{gathered} P=8,000 \\ r=9\text{\%}=\frac{9}{100}=0.09 \\ n=5 \\ PV\text{ is unknown} \\ \end{gathered}[/tex]Substitute the above value into equation 1, to solve for PV
[tex]\begin{gathered} PV\text{ = 8000(}\frac{1-(1+0.09)^{-5}}{0.09}) \\ \Rightarrow8000\times\frac{1-1.09^{-5}}{0.09} \\ =31117.21 \end{gathered}[/tex]Hence, the sum to be invested is 31117.21
-6/5 k -3/4 = -2 + 1/7 k solve for k
Answers
hello
to solve for k, we'll do it in a stepwise manner
step 1
collect like terms
[tex]\begin{gathered} -\frac{6}{5}k-\frac{3}{4}=-2+\frac{1}{7}k \\ -\frac{3}{4}+2=\frac{1}{7}k+\frac{6}{5}k \end{gathered}[/tex][tex]\begin{gathered} -\frac{3}{4}+2=\frac{1}{7}k+\frac{6}{5}k \\ \text{take LCM} \\ -\frac{3+8}{4}=\frac{5+42}{35}k \\ \frac{5}{4}=\frac{47}{35}k \end{gathered}[/tex]step 2 above was to take LCM
step 3
cross multiply both sides and solve for k
[tex]\begin{gathered} \frac{5}{4}=\frac{47}{35}k \\ 4\times47=(5\times35)k \\ 188=175k \\ k=\frac{188}{175} \\ k=1.074 \end{gathered}[/tex]HOW ARE THESE GRAPHS THE SAME AND HOW ARE THEY DIFFERENT
Answers
In this case, we must analyze the graphs to find the solution.
Step 01:
Graph A
Dollars vs Months
If Months = 4 ===> 400 Dollars
Graph B
Months vs Dollars
If Dollars = 4 ===> 400 Months
If Months = 4 ===> The dollar amount is imperceptible on the graph.
The answer is:
The graphics are different.
In this case, we must analyze the graphs to find the solution.
Step 01:
Graph A
Dollars vs Months
If Months = 4 ===> 400 Dollars
Graph B
Months vs Dollars
If Dollars = 4 ===> 400 Months
If Months = 4 ===> The dollar amount is imperceptible on the graph.
The answer is:
The graphics are different.
A barge is being towed by two tugboats, using ropes with force vectors as shown.
Answers
SOLUTION
From the question, we are given
[tex]\begin{gathered} F_1=(11,000,5000) \\ F_2=(14,500,-8,000) \end{gathered}[/tex]Now, to find the angle between the ropes, we will take the dot product of two vectors. This is given as
[tex]\begin{gathered} a.b=|a||b|cos\theta \\ so,\text{ we have } \\ cos\theta=\frac{a.b}{|a||b|} \end{gathered}[/tex]But writing the forces in vector form, we have
[tex]\begin{gathered} F_1=11,000i+5000j \\ F_2=14,500i-8,000j \end{gathered}[/tex]Applying the formula above, we have
[tex]\begin{gathered} cos\theta=\frac{a.b}{|a||b|} \\ cos\theta=\frac{(11,000)(14,500)+(5000)(-8000)}{\sqrt{11,000^2+5000^2)\sqrt{14500^2+(-8000)^2}}} \\ cos\theta=\frac{159,500,000-40,000,000}{\sqrt{121,000,000+25,000,000}\sqrt{210,250,000+64,000,000}} \\ cos\theta=\frac{119,500,000}{\sqrt{146,000,000}\sqrt{274,250,000}} \\ cos\theta=\frac{119,500,000}{12,083.04579\times16560.4952} \\ cos\theta=\frac{119,500,000}{200,101,221.806675} \\ cos\theta=0.5971977 \end{gathered}[/tex]Now, theta becomes
[tex]\begin{gathered} \theta=cos^{-1}0.5971977 \\ \theta=53.3305 \end{gathered}[/tex]hence the answer is option B, 53 degrees
SOLUTION
From the question, we are given
[tex]\begin{gathered} F_1=(11,000,5000) \\ F_2=(14,500,-8,000) \end{gathered}[/tex]Now, to find the angle between the ropes, we will take the dot product of two vectors. This is given as
[tex]\begin{gathered} a.b=|a||b|cos\theta \\ so,\text{ we have } \\ cos\theta=\frac{a.b}{|a||b|} \end{gathered}[/tex]But writing the forces in vector form, we have
[tex]\begin{gathered} F_1=11,000i+5000j \\ F_2=14,500i-8,000j \end{gathered}[/tex]Applying the formula above, we have
[tex]\begin{gathered} cos\theta=\frac{a.b}{|a||b|} \\ cos\theta=\frac{(11,000)(14,500)+(5000)(-8000)}{\sqrt{11,000^2+5000^2)\sqrt{14500^2+(-8000)^2}}} \\ cos\theta=\frac{159,500,000-40,000,000}{\sqrt{121,000,000+25,000,000}\sqrt{210,250,000+64,000,000}} \\ cos\theta=\frac{119,500,000}{\sqrt{146,000,000}\sqrt{274,250,000}} \\ cos\theta=\frac{119,500,000}{12,083.04579\times16560.4952} \\ cos\theta=\frac{119,500,000}{200,101,221.806675} \\ cos\theta=0.5971977 \end{gathered}[/tex]Now, theta becomes
[tex]\begin{gathered} \theta=cos^{-1}0.5971977 \\ \theta=53.3305 \end{gathered}[/tex]hence the answer is option B, 53 degrees
Which equation has no solution?
Answers
Answer:
The answer is the third one down
Step-by-step explanation:
l5-3xl = -8
Absolute value cannot equal a negative number.
Step-by-step explanation:
l5-3xl = -8
the | | is absolute value to it so it cant be negative number
Greg is at his house he gets in his car drives north 8.9 miles and stops at a store then he turns around and drives south 7.7 miles to his friends house how far is the friends house from Greg’s houses
Answers
The distance of the friends house from Greg’s houses is 1.2 miles.
How to illustrate the information?From the information illustrated, Greg is at his house he gets in his car drives north 8.9 miles and stops at a store then he turns around and drives south 7.7 miles to his friends house how
The distance will be the difference between the miles that are given.
This will be:
= 8.9 miles - 7.7 miles
= 1.2 miles
The distance is 1.2 miles.
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PLS HELP, 50 POINTS + BRAINLY FOR CORRECT ANSWER!!!
Answers
-1 - Slope B
-5/4 - Slope C
Solve the equation 5x = 85 for x.
−17
17
−90
80
Answers
x = 17
Step-by-step explanation:
5x = 85
x = 85/5
x = 17.
Hence, option (b) is correct answer
Answer: x=17 the answer is B
Hope this helped
Step-by-step explanation:
Find the perimeter pf the regular polygon.
5 (x+2)
7x+4
Answers
The perimeter of the regular polygon is 108 units.
How to find the perimeter of a regular polygon?A regular polygon is a polygon that has all its sides equal to each other.
Therefore,
5(x + 2) = 7x + 4
5x + 10 = 7x + 4
5x - 7x = 4 - 10
-3x = -6
x = -6 / -3
x = 2
The perimeter of a regular polygon is the sum of the whole sides of the polygon.
Therefore,
each side of the regular polygon = 7(2) + 4
each side of the regular polygon = 14 + 4
each side of the regular polygon = 18
Hence the regular polygon has 6 sides
perimeter of the regular polygon = 18 × 6
perimeter of the regular polygon = 108 units
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