Divide miles ran by speed to get time:
2 miles / 8 miles per hour = 0.25 hours = 15 minutes.
2 miles / 6 miles per hour = 0.33 hours = 20 minutes.
20 minutes - 15 minutes = 5 minutes longer.
Final answer:
After calculating the time taken by each runner to complete the 2-mile race, we find that Arif took 5 minutes longer than Sharif to finish.
Explanation:
To determine how many minutes longer Arif took to complete the race compared to Sharif, we need to calculate the time each runner took to complete the 2-mile race. First, we calculate Sharif's time. Since speed is distance divided by time, we can rearrange the formula to find time: time = distance/speed.
For Sharif:
Distance = 2 miles
Speed = 8 miles per hour
Time = 2 miles / 8 mph = 0.25 hours
Convert Sharif's time from hours to minutes by multiplying by 60 minutes per hour (0.25 hours * 60 minutes/hour = 15 minutes).
For Arif:
Distance = 2 miles
Speed = 6 miles per hour
Time = 2 miles / 6 mph = 0.333... hours
Convert Arif's time from hours to minutes (0.333... hours * 60 minutes/hour = 20 minutes).
Now, to find the difference in time, subtract Sharif's time from Arif's time:
Difference = Arif’s time - Sharif's time = 20 minutes - 15 minutes = 5 minutes
Arif took 5 minutes longer than Sharif to complete the race.
What is the instataneous rate of change at x=2 of the function f given by f(x)= x^2-2÷x-1
Answer:
4.5
Step-by-step explanation:
To find the instantaneous rate of chance, take the derivative:
[tex]f(x) = {x}^{2} - \frac{2}{x} - 1 \\ \frac{d}{dx} f(x) = 2x + \frac{2}{ {x}^{2} } [/tex]
Remember to use power rule:
[tex] \frac{d}{dx} {x}^{a} = a {x}^{a - 1} [/tex]
To differentiate -2/x, think of it as:
[tex] - 2 {x}^{ - 1} [/tex]
Then, substitute 2 for x:
[tex]2(2) + \frac{2}{ {2}^{2} } \\ 4 + \frac{2}{4} = 4.5[/tex]
Answer:
2
Step-by-step explanation:
Assuming the function is:
f(x) = (x² − 2) / (x − 1)
Use quotient rule to find the derivative.
f'(x) = [ (x − 1) (2x) − (x² − 2) (1) ] / (x − 1)²
f'(x) = (2x² − 2x − x² + 2) / (x − 1)²
f'(x) = (x² − 2x + 2) / (x − 1)²
Evaluate at x=2.
f'(2) = (2² − 2(2) + 2) / (2 − 1)²
f'(2) = (4 − 4 + 2) / 1
f'(2) = 2
if the rate of change for one linear function is positive and for another is negative can they both be either increasing or decreasing?
Answer:
They can never be both either increasing or decreasing.
Step-by-step explanation:
If the rate of change i.e. the slope of one linear function is positive, that means the graph of the linear function makes angle which varies between 0° to 90° with respect to the positive direction of the x-axis.
Therefore, the function must be increasing.
Again, if the rate of change i.e. the slope of one linear function is negative, that means the graph of the linear function makes angle which varies between 90° to 180° with respect to the positive direction of the x-axis.
Therefore, the function must be decreasing.
Hence, if the rate of change of one linear function is positive and for another is negative, they can never be both either increasing or decreasing. (Answer)
Renata wins a $20 gift card to an online music site. After Renata purchases 16 songs, the gift card has a remaining
balance of $0. Which equation represents the relationship between y, the remaining balance on Renata's gift card,
and x, the number of songs purchased?
The equation that represents the relationship between the remaining balance on Renata's gift card and the number of songs purchased is y = 20 - 1.25x, where x represents the number of songs purchased.
Explanation:The equation that represents the relationship between the remaining balance on Renata's gift card and the number of songs purchased is y = 20 - 1.25x.
Here's how we get to this equation:
Let x represent the number of songs purchased.Since Renata starts with a $20 gift card, the initial balance is $20.For each song purchased, $1.25 is deducted from the balance, so the remaining balance can be represented as y = 20 - 1.25x.For example, if Renata purchased 16 songs, the equation becomes y = 20 - 1.25(16) = 20 - 20 = 0, which matches the given information that the gift card has a remaining balance of $0 after 16 songs are purchased.
Which point could be removed in order to make the relation a function?
{ (-4,3),(-5,6),(1,0),(-4,5),(9,5),(0,-7)}
A. (1,0)
B.(-4,5)
C.(-5,6)
D.(9,5)
Answer:
B. (-4,5)
Step-by-step explanation:
a function cannot have any repeating x values....it can have repeating y values, just not the x values
so..going by ur answer choices, u can remove (-4,5) and it would be a function. The reason is because u have two sets of points with the same x value...so it is not a function unless u take out either (-4,5) or (-4,3)...because they both have the same x value.
pls help
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Answer:
Linear functions can be represented by a straight line, with an intercept and a constant slope. They are formed by a dependent varible (y) and an independent varible (x) whose power equals one, which means that y is related to x in a linear way (they have both power equal to one). The general equation of a linear function can be written as follows: y= a + b x, with a equal to a constant known as the intercept, and b equal to the slope.We can rewrite the equations you have attached as follow, by rearranging terms in order to clear y as a function of x (in order):[tex]y=-19+\frac{1}{2}x[/tex], is a linear function: y is linked to x in a linear way, the curve has the form y= a + b x, where a=-19 and b=1/2.[tex]y=\frac{1}{3} x^{2}[/tex], it is NOT a linear function, because y is linked to x in a way that is not linear (the power of x is different from zero, in this case the power of x equals 2 ), and the graph of this expression would not be linear.[tex]y=\frac{1}{39}x +\frac{5}{13}[/tex] is a linear function: y is linked to x in a linear way (the power of x equals one), the curve in this case has the form y= a + b x, where a=1/39 and b=5/13.[tex]y=x+\frac{25}{5}[/tex] is a linear function: y is linked to x in a linear way (the power of x equals one), and the curve has the form y= a + b x, where a=25/5 and b=1.[tex]y=\sqrt[3]{x}[/tex] is NOT a linear function, because y is linked to x in a nonlinear way, specifically, y is linked to the squared root of x, which means that is linked to [tex]x^{\frac{1}{3} }[/tex], then x has not power equal to one in this case.What times what equals 3.75
Answer:
1\times 28=28\\2\times 14=28\\4\times 7=28
Step-by-step explanation: To obtain number 28, we will find the factors of this number.
Factors of this number are: 1, 2, 4, 7, 14, 28
From the given factors, we can find the combinations which will givs us the product as 28
We are asked to find the multiplication ( times) of two number that will yield a number 28. So, the combinations will be
1\times 28=28\\2\times 14=28\\4\times 7=28
Step-by-step explanation:
Final answer:
To find numbers that multiply to 3.75, we can identify factor pairs like 1.5 and 2.5, or 1 and 3.75. Multiplying these pairs will result in 3.75.
Explanation:
To find which numbers multiplied together equal 3.75, we can look for factor pairs of the number 3.75. A factor pair is a set of two numbers that, when multiplied together, result in the given number. Since 3.75 can also be expressed as the fraction ⅓75/100 (or 15/4 in simplest form), we can find factor pairs by considering both whole numbers and decimals that multiply to give us the fraction equivalent.
For example, one obvious pair is 1.5 and 2.5. If we multiply 1.5 by 2.5, we get 3.75:
1.5 × 2.5 = 3.75
Another pair could be 1 and 3.75 as any number multiplied by 1 equals the number itself.
1 × 3.75 = 3.75
These are just two examples of factor pairs for 3.75, but there can be other combinations as well, particularly if we consider fractions or more decimal places.
Can anyone pls help me I really need help pls help me I will mark them as brainiest pls!!! Can u do it in a paper and then send it to me
(ﾉ◕ヮ◕)ﾉ*:･ﾟ✧ ✧ﾟ･: *ヽ(◕ヮ◕ヽ)
Answer:
see them bellow
Step-by-step explanation:
A crayon company recently changed its labels it currently has a total of 2,776 crayons in stock 1,174of which have new label How many crayons with the old labels does the company have in stock
Answer: 1,602 Crayons with old labels that the company has in stock
Step-by-step explanation:
The total is 2,776 and 1,174 of the total have new labels so you would have to subtract 1,174 from 2,776. Your welcome
what's the equation in point slope form of the line that passes through the point (3, 1) and has a slope of -2
Answer:
equation: y = -2x + 7
Step-by-step explanation:
y = mx + b M: slope b: y intercept
m = -2
x = 3 and y = 1
b = y - mx = 1 - (- 2) x 3 = 7
equation: y = -2x + 7
check: ( 3,1) -2 x 3 + 7 = 1
Answer:
The equation of the required line is,
y = -2x + 7
Step-by-step explanation:
We know that equation of a line passing through the point (x₁, y₁) and having slope 'm' is given by
(y - y₁) = m(x - x₁)
Now, the required line passes through the point (3, 1) and has a slope of -2.
So, (x₁, y₁) = (3, 1) and m = -2
So, equation of the line passing through (3, 1) and having a slope of -2 is given by,
y - 1 = -2(x - 3)
⇒y - 1 = -2x + 6
⇒y = -2x + 6 + 1
⇒y = -2x + 7
So, the required equation of line in point-slope form is,
y = -2x + 7
I NEED HELP WITH THESE QUESTIONS!!DOES ANY ONE KNOW HOW TO DO PROOFS?
Problem 1
Answer: v = 8--------------
Work Shown:
For any convex polygon, the sum of the exterior angles is always 360 degrees
Add up all the angles shown, set the sum equal to 360, then solve for v.
9v+(19v-21)+45+(v+48)+7v = 360
36v+72 = 360
36v+72-72 = 360-72
36v = 288
36v/36 = 288/36
v = 8
===============================================
Problem 2
Answer: D. None of these--------------
Explanation:
Segment WU is not an altitude because we have no angle markers to show if WU is perpendicular to VT.
Segment WU is not a median since we dont know if TU = UV or not.
Segment WU is not an angle bisector. If it were an angle bisector, then the two angles marked (33 and 40) should be equal angles. In other words, an angle bisector cuts an angle into two equal halves.
X^2 + 1/4 or 7 or 7/2 x + 49
Answer:
14
Step-by-step explanation:
Squaring a number (a+b) for example is a^2+2ab+b^2. So you square root x^2 and 49, you get x and seven respectively. you multiply them together and on top of that multiply the product by 2. so 7x*2 is 14x and ye
please solve really stuck much appreciated
Answers:
a) [tex]t=\sqrt{\frac{d}{4.9}}[/tex]
b) 0.299 s
Step-by-step explanation:
a) We are given the following equation:
[tex]t=\sqrt{\frac{2d}{9.8}}[/tex]
If we divide by 2 both the numerator and the denominator, we will have:
[tex]t=\sqrt{\frac{2d/2}{(9.8)/2}}[/tex]
[tex]t=\sqrt{\frac{d}{4.9}}[/tex]
b) From this equation:
[tex]t=\sqrt{\frac{2d}{9.8}}[/tex]
[tex]t[/tex] is the reaction time in seconds
[tex]d=44 cm \frac{1 m}{100 cm}=0.44 m[/tex] is the distance
[tex]9.8 m/s^{2}[/tex] is the acceleration due gravity
Solving:
[tex]t=\sqrt{\frac{2(0.44 m)}{9.8 m/s^{2}}}[/tex]
[tex]t=0.299 s[/tex] This is the reaction time
Find percentage:
3/4% of 9.6
Answer:
0.072
Step-by-step explanation:
3/4 percent of the number 9.6 is 0.072.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, 3/4% of 9.6.
Now, 0.75% of 9.6
= 0.0075×9.6
= 0.072
Therefore, 3/4 percent of the number 9.6 is 0.072.
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In a competitive exam 84% of candidate passed and 780 failed find the number of candidates appeared for the examination
Answer:
4875
Step-by-step explanation:
100%-84%=16%
16%x=780
x=4875
Santa and his elves are
making toys in Santa's
workshop for all the good
little girls and boys. If there
are twice as many wooden
cars as wooden trains and
there are 228 wooden vehicles
made, how many wooden
trains did they make?
Step-by-step explanation:
Wooden Cars = 2 × Wooden Trains
Ratio is
2 : 1
In total there are 3 parts
228 ÷ 3 = 76 (1 part)
Wooden Cars = 2 × 76 = 152
Wooden Trains = 1 × 76 = 76
To find the number of wooden trains made, we can set up an equation and solve for 'x'.
Explanation:To solve this problem, let's represent the number of wooden trains as 'x'.
According to the given information, there are twice as many wooden cars as wooden trains. So, the number of wooden cars can be represented as '2x'.
We are also given that the total number of wooden vehicles made is 228.
Therefore, the equation that represents the given information is: x + 2x = 228
Simplifying the equation, we get: 3x = 228
Dividing both sides by 3, we find that x = 228/3 = 76
So, they made 76 wooden trains.
Find the missing factor. Does anybody know the answer 8b*2+7b-1= (b+1) ( )
Answer:
[tex]8b^2+7b-1=(b+1)(8b-1)[/tex]
The missing factor is: [tex](8b-1)[/tex]
Step-by-step explanation:
Given expression:
[tex]8b^2+7b-1=(b+1)(_-)[/tex]
To find the missing factor of the given expression.
Solution:
In order to factor the given term, we will split the middle term into two terms such that the product of the two terms is equal to the product of the first and last term of the expression.
The product of first and last term for the expression is = [tex](8b^2)(-1)=-8b^2[/tex]
The middle term = [tex]7b[/tex] which can be split into [tex](8b-b)[/tex] as their product = [tex]-8b^2[/tex]
Thus, the expression can be rewritten as:
⇒ [tex]8b^2+8b-b-1[/tex]
We will factor in pairs by taking GCF.
⇒ [tex]8b(b+1)-1(b+1)[/tex]
Factoring the whole expression by taking the common factor.
⇒ [tex](b+1)(8b-1)[/tex]
Thus, the missing factor is: [tex](8b-1)[/tex]
15'
The angle 01 is located in Quadrant I, and cos(01) = = .
What is the value of sin(01)?
Express your answer exactly.
sin(01) =(
Answer:
[tex]sin(\theta_1)=3\frac{\sqrt{21}}{17}[/tex]
Step-by-step explanation:
The complete question is
The angle θ1 is located in Quadrant 1, and cos (θ1)=10/17.
What is the value of sin(θ1)?
we know that
[tex]sin^2(\theta_1)+cos^2(\theta_1)=1[/tex] ---> trigonometric identity
we have
[tex]cos(\theta_1)=\frac{10}{17}[/tex]
The angle [tex]\theta_1[/tex] is located in Quadrant I, that means the sine of angle [tex]\theta_1[/tex] is positive
substitute the given value in the trigonometric identity
[tex]sin^2(\theta_1)+(\frac{10}{17})^2=1[/tex]
[tex]sin^2(\theta_1)+\frac{100}{289}=1[/tex]
[tex]sin^2(\theta_1)=1-\frac{100}{289}[/tex]
[tex]sin^2(\theta_1)=\frac{189}{289}[/tex]
take square root both sides
[tex]sin(\theta_1)=\pm\frac{\sqrt{189}}{17}[/tex]
Remember that the sine is positive (Quadrant I)
so
[tex]sin(\theta_1)=\frac{\sqrt{189}}{17}[/tex]
Simplify
[tex]sin(\theta_1)=3\frac{\sqrt{21}}{17}[/tex]
Widget Wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.
The company also discovered that it costs $29 to produce 2 widgets, $115 to produce 4 widgets, and $757 to produce 10 widgets.
How much does it cost to make 3 widgets?
Answer:
The total cost to make 3 widgets is $64.
Step-by-step explanation:
As cost is give by quadratic function such as [tex]c(x) = ax^2 + bx + d[/tex]
As it costs $29 to produce 2 widgets. So,
[tex]c(2) = a(2)^2 + b(2) + d[/tex]
[tex]29= 4a+2b+d ....[A][/tex]
As it costs $115 to produce 4 widgets. So,
[tex]c(4) = a(4)^2 + b(4) + d[/tex]
[tex]115= 16a+4b+d ....[B][/tex]
As it costs $757 to produce 10 widgets. So,
[tex]c(10) = a(10)^2 + b(10) + d[/tex]
[tex]757= 100a+10b+d ....[C][/tex]
In order to find the values of a, b, c and d, we have to equations [A], [B] and [C]
Subtracting Equation [A] from [B] and [B] from [C]
12a + 2b = 86 ........[D]
84a + 6b = 642 ........[E]
Multiplying Equation [D] by 3 and subtracting from [E]
84a + 6b + 3(12a + 2b) = 642 - 86
48a = 384
a = 8
Putting value of a = 8 in equation [D]
12(8) + 2b = 86
96 + 2b = 86
2b = -10
b = -5
Substituting the value of a = 8 and b = -5 in Equation [A].
29= 4a+2b+d
29 = 4(8) + 2(-5) + d
29 = 32 - 10 + d
d = 29 + 10 - 32
d = 7
The required form of equation can be obtained by substituting a = 8, b = -5 and d = 7 in the cost equation. So,
[tex]c(x) = 8x^2 - 5x + 7[/tex] is the required form of equation.
Therefore, the total cost to make 3 widgets will be:
Putting x = 3 in [tex]c(x) = 8x^2 - 5x + 7[/tex]
[tex]c(3) = 8(3)^2 - 5(3) + 7[/tex]
[tex]c(3) = 72 - 15 + 7[/tex]
[tex]c(3) = 64[/tex]
Hence, the total cost to make 3 widgets is $64.
Keywords: quadratic equation, cost
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PLEASE HURRY I NEED HELP ON MY EXAM! 15PTS!
In which quadrants do solutions for the inequality y is greater than one fifth times x plus 3 exist?
I and II
I, II, and III
I, III, and IV
All four quadrants
The solutions for the inequality y > (1/5)x + 3 exist in Quadrants I and II.
Explanation:The inequality y > (1/5)x + 3 represents a line with a positive slope of 1/5.
The solutions for this inequality exist in the quadrants where y is greater than the value of (1/5)x + 3.
When x is positive and y is positive, the solutions exist in Quadrant I. When x is negative and y is positive, the solutions exist in Quadrant II.
Since the inequality is y > (1/5)x + 3 and not y >= (1/5)x + 3, the solutions do not exist in Quadrant III or IV where y would be negative.
Therefore, the solutions for the inequality y > (1/5)x + 3 exist in Quadrants I and II.
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An airplane's velocity is represented by the vector p = 30i-492j+42k. There is a crosswind of velocity t=19j-45k. Use this information to determine the vector which represents the velocity of the airplane when it is affected by the wind.
Answer:[tex]30 i -473 j -3 k[/tex]
Step-by-step explanation:
We are given two velocity vectors with its three components in unit notation:
Airplane's velocity:
[tex]\vec{p}=30i-492j+42k[/tex]
Crosswind velocity:
[tex]\vec{t}=0i+19j-45k[/tex]
Now, if we want to know the velocity of the airplane when it is affected by the wind, we have to add these two velocity vectors:
[tex]\vec{p} + \vec{t}=(30i-492j+42k) + (0i+19j-45k)[/tex]
Adding both vectors:
[tex]\vec{p} + \vec{t}=30i-473j-3k[/tex]
Answer:
D edge
Step-by-step explanation:
round 4,279 to the nearest thousand
Answer:
it is 4,000
Step-by-step explanation:
since you are rounding it to the nearest thousand, you loo at the 4, and the 2, the 2 is blow five, so it doesn't change the thousands place, but everything else becomes a 0
Answer: 4,000
Explanation: To round 4,279 to the nearest thousand, we first locate the digit in the rounding place which in this case is the 4 in the thousands place.
Next, we look at the digit to the right of the 4 which is 2. The rules of rounding tell us that if the digit to the right of the rounding place is less than 5, we round down and if the digit to the right of the rounding place is greater than or equal to 5, we round up.
In this problem, the digit to the right of the rounding place is less than 5 so we round down. This means that the 4 in the rounding place stays the same and all digits to the right of the 4 become zero.
Therefore, 4,279 rounded to the nearest thousand is 4,000.
If f(x) equals (1/7)(fx) , what is f(3)
Answer:
f(3)=3/7
Step-by-step explanation:
In slope-intercept form, what is the equation of the line passing through the points (-4.26) and (6-4)?
y=-3x - 14
y = 3x - 14
y = -3x - 14
y=-x
-2
Answer:
y=-3x+14
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-4-26)/(6-(-4))
m=-30/(6+4)
m=-30/10
m=-3
y-y1=m(x-x1)
y-26=-3(x-(-4))
y-26=-3(x+4)
y=-3x-12+26
y=-3x+14
what is the equation, in slope-intercept form, of the line that passes through (9, 2) and is perpendicular to y= -1/2x + 7
Answer:
y-2=2(x-9)
Step-by-step explanation:
Perpendicular means negative reciprocal of the slope.
y-y1=m(x-x1)
y-2=2(x-9)
What is the slope of the line represented by 5x - 12y = 24?
Answer:
5/12x
Step-by-step explanation:
Answer:
y = 5/12x - 2
Step-by-step explanation:
5x - 12y = 24
We get -12y = -5x + 24
Divide all of the equation by -12
You get y = 5/12x -2
Find the missing number so that the equation has infinitely many solution -2x-10=-2x+
To find the missing number so that the equation has infinitely many solutions, subtract -2x from both sides to eliminate x and find that the missing number can be any real number.
To find the missing number so that the equation has infinitely many solutions, we need to look at the given equation: -2x - 10 = -2x + c. Since the variable x is present on both sides, we can subtract -2x from both sides to get rid of it. This leaves us with -10 = c. In order for this equation to have infinitely many solutions, the missing number c can be any real number.
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The path of a model rocket can be represented by the equation h(t) = - t ^ 2 + 20t + 12 where h(t) is the height , in feet of the rocket at any given time, t. What is the height of the model rocket after 3 seconds from launch?
Answer:
The height of the rocket after 3 seconds is 63 feet.
Step-by-step explanation:
The path of a model rocket is represented by:
[tex]h(t)=-t^2+20t+12[/tex]
where [tex]h(t)[/tex] represents the height in feet of rocket and [tex]t[/tex] represents time in seconds.
To find the height of the model rocket after 3 seconds from launch.
Solution:
In order to find the height of the model rocket after 3 seconds from launch, we will plugin [tex]t=3[/tex] in the given function of path of rocket.
Thus, we have
[tex]h(3)=-(3)^2+20(3)+12[/tex]
[tex]h(3)=-9+60+12[/tex]
[tex]h(3)=63[/tex]
Thus, height of the rocket after 3 seconds is 63 feet.
Loren and Julie have different part time jobs after school. They are both paid at a constant rate of dollars per hour. The table below show Loren and Julie's total income (amount earned) for working a given amount of time.
Loren
Hours
2
4
6
8
10
12
14
16
18
Dollars
18
36
54
72
90
108
?
?
162
Julie
Hours
3
6
9
12
15
18
21
24
27
Dollars
36
?
108
144
180
216
?
288
324
Who makes more per hour?
Answer:
Julie made $3 /hour more than Loren
Step-by-step explanation:
Loren makes 18 /2 = 9 ($9 / hour constant ratio)
Julie: 36 /3 = 12 ($12 / hour)
Julie - Loren = 12 -9 = 3
? in Loren's : 126, 144
? in Julie's : 72, 252
The value of y varies inversely as the square of x, and y=4, when x=3.
Find the value of x when y=9
The value of x when y = 9 is x = 2 or x = -2
Solution:
Given that value of y varies inversely as the square of x, and y=4, when x=3.
Therefore the initial statement is:
[tex]y \propto \frac{1}{x^{2}}[/tex]
To convert to an equation, multiply by k, the constant of variation
[tex]y = k \times \frac{1}{x^2}[/tex]
[tex]y = \frac{k}{x^2}[/tex] --- eqn 1
Given that,
y = 4 when x = 3
Now find value of k
[tex]4 = \frac{k}{3^2}\\\\4 \times 9 = k\\\\k = 36[/tex]
Find the value of x when y = 9
x = ?
y = 9
From eqn 1,
[tex]9 = \frac{k}{x^2}\\\\9 = \frac{36}{x^2}\\\\x^2 = 4\\\\x = \pm 2[/tex]
Thus value of x is found
Final answer:
To find the value of x when y=9 for a scenario where y varies inversely as the square of x, and given y=4 when x=3, we first determine the constant of variation and then solve for x, resulting in x=2.
Explanation:
The student's question concerns an inverse variation where the value of y varies inversely as the square of x, with an initial condition that when x=3, y=4. To find the value of x when y=9, we recall that an inverse variation can be expressed as y = k/x², where k is a constant. Using the given condition, we can solve for k: 4 = k/3², leading to k = 36. To find x when y=9, we set up the equation 9 = 36/x² and solve for x, yielding x = 2.
you have a list of 7 numbers. the average of the numbers is 9. if you take away one of the numbers, the average of the numbers is 8. what number did you take away?
Answer:
There was a 15 among the 7 numbers. That is the number you removed.
Step-by-step explanation:
x/7 = 9 (1)
(x - y)/6 = 8 (2)
Multiply 1 by 7
x/7 * 7 = 9*7
x = 63
Put 63 for x into equation 2
(63 - y)/6 = 8 Multiply by 6
6*(63-y)/6 =8*6
63 - y = 48 Add y to both sides
63-y+y = 48+y
63 = 48 + y Subtract 48 from both sides
63-48=48-48+y
y = 15
Final answer:
The number removed from the list to change the average from 9 to 8 is 15, calculated by finding the difference between the total sum of the original and remaining lists.
Explanation:
To find the number that was taken away from a list when the average changes, you can first calculate the total sum of the original list, then the sum of the list after the number is removed.
Initially, the average of the 7 numbers is 9. To find the total sum of all 7 numbers, you multiply the average by the number of values.
Total sum of original list = 7 (number of values) × 9 (original average) = 63
After removing one of the numbers, the average of the 6 remaining numbers is 8.
Total sum of the remaining list = 6 (remaining values) × 8 (new average) = 48
The number that was removed can be found by subtracting the sum of the remaining list from the sum of the original list.
Number removed = Total sum of original list - Total sum of the remaining list = 63 - 48 = 15
Therefore, the number that was taken away from the list is 15.