Choose what the expressions below best represent within the context of the word problem.
The length of a rectangle is 12 inches more than its width. What is the width of the rectangle if the perimeter is 42 inches?
x best represents .
x + 12 best represents .
Answers
The expresssion x best represents the width of the rectangle.
The expression x + 12 best reprents the lenght of the rectangle.
This is because if you call x the width, then the length is 12 more than that, i.e. 12 + x.
If you wanted to solve the problem now you could write
2*(width + length) = perimeter
2(x + 12 + x) = 24 and solve for x.
But the answer to the question is:
x best represents the width of the rectangle.
x + 12 best reprents the lenght of the rectangle.
Related Questions
A bag contains 10 black jellybeans, 12 green ones, 3 orange ones, and 20 blue ones. if you reach in and grab one randomly, what is the probability of picking
Answers
12/45 for green
3/45 for orange (can be simplified to: 1/15)
20/45 for blue
HELPPP! true or false and explain pls!!
22. All kites are quadrilaterals.
24.A kite can have congruent diagonals.
Answers
24.)True, as long as diagonals are orthogonal
What is the mean number of hours that high school students spend on homework per week? It is known that the standard deviation of the population is 2.2 hours. In a random sample of 40 students, it is found that they average 13 hours per week on homework.
a) What is the standard deviation for this sample?
b) What is the critical value for a 90% confidence interval?
c) What is the critical value for a 95% confidence interval?
Answers
The standard deviation for the sample is approximately 0.348 hours.
The critical value for a 90% confidence interval is approximately 1.645, and for a 95% confidence interval, it is approximately 1.96.
To calculate the standard deviation for the sample, we use the formula:
[tex]\[ \text{Standard deviation for sample} = \frac{\text{Population standard deviation}}{\sqrt{\text{Sample size}}} \][/tex]
Given the population standard deviation of 2.2 hours and a sample size of 40, we plug these values into the formula:
[tex]\[ \text{Standard deviation for sample} = \frac{2.2}{\sqrt{40}} \][/tex]
[tex]\[ \text{Standard deviation for sample} \approx \frac{2.2}{6.324} \approx 0.348 \text{ hours} \][/tex]
So, the standard deviation for this sample is approximately 0.348 hours.
For the critical values of confidence intervals, we refer to the z-table or use a calculator.
For a 90% confidence interval, the critical value is approximately 1.645, and for a 95% confidence interval, it is approximately 1.96.
These values represent the number of standard deviations from the mean that encompass the specified confidence level.
how to solve xy''+2y'+xy=0
Answers
Which system has no solutions?
x < 5
x > 1
x < 5
x < 1
x > 5
x > 1
x > 5
x < 1
HELP meh plz!!!
Answers
To determine which system has no solutions, we analyze a set of inequalities to identify the contradictory statement.
To determine which system has no solutions, we need to analyze the given inequalities:
x < 5
x > 1
x < 5
x < 1
x > 5
x > 1
x > 5
x < 1
From the list, the system 'x < 1' and 'x > 1' has no solutions as it creates a contradictory statement.
What value corresponds to the 60th percentile in the following data set?
{12, 28, 35, 42, 47, 49, 50}
1) 47
2) 49
3) 28
4) 42
...?
Answers
To find the 60th percentile, multiply 60/100 by the total number of observations plus one, which equates to 4.8. This falls between the 4th and 5th value, and rounding up means the 60th percentile corresponds to the 5th value, which is 47.
Explanation:To find the value that corresponds to the 60th percentile in the given data set {12, 28, 35, 42, 47, 49, 50}, we need to follow a series of steps.
Arrange the data in ascending order, which is already done in this case.Determine the rank of the percentile using the formula: Rank = (P/100) * (N + 1), where P is the percentile and N is the number of observations in the set.For the 60th percentile, the formula becomes Rank = (60/100) * (7 + 1), which gives us Rank = 4.8. This means the 60th percentile falls between the 4th and 5th values in the set.Since we cannot have a fraction of an observation, we round up to the nearest whole number. The 5th value in the set is 47.Therefore, the value corresponding to the 60th percentile in this data set is 47.
Final answer:
The 60th percentile value in the data set {12, 28, 35, 42, 47, 49, 50} is 47, which is the 5th number in the ordered set after calculating the index.
Explanation:
The 60th percentile value in a data set is found by first arranging the data in ascending order, which is already done in the provided data set. Then calculate the index using the formula Index = P(N + 1), where P is the percentile in decimal form and N is the number of data points. In this case, the 60th percentile index for our 7-point data set is 0.60 × (7 + 1) = 4.8. Since the index is not a whole number, we round up to the next whole number, which here would be 5. Therefore, we take the 5th number in the ordered set, which is 47.
PTG has side lengths of 12 cm, 25 cm, and 19 cm. Which type of triangle is PTG?
right
acute
obtuse
isosceles ...?
Answers
We could calculate at least two angles of the triangle to determine whether it is a right, acute, or obtuse. We need to use the cosine law:
a^2 + b^2 - 2ab * cos C = c^2
cos C = (a^2 + b^2 - c^2) / 2ab
C = arccos((a^2 + b^2 - c^2) / 2ab)
Solving for two angles P and T,
P = arccos((12^2 + 19^2 - 25^2)/(2*12*19))
P = 105.3 degrees.
Since one angle is an obtuse angle, we dont need to compute for the other angle. We can conclude then that the triangle is an obtuse angle.
What are the least common factors of 8 and 12
Answers
Yolanda paid for her movie ticket using 28 coins, all nickels and quarters. The ticket cost $4. Which system of linear equations can be used to find the number of nickels, n, and the number of quarters, q, Yolanda used?
Answers
0.05n + 0.25q = 4
Yolanda paid for her movie ticket using 28 coins, all nickels and quarters. The ticket cost $4.
Let n be the number of nickels
and q be the number of quarters
1 nickels = $0.05 , so n nickels cost = 0.05n
1 quarter = $0.25, so q quarters cost = 0.25q
Total number of coins = 28
number of nickels + number of quarters = 28
n + q = 28 ------- equation 1
Total ticket cost =$4
cost of n nickels + cost of q quarters = $4
0.05n + 0.25q = 4 -------> equation 2
system of linear equations can be used to find the number of nickels, n, and the number of quarters, q, Yolanda used are
n + q = 28
0.05n + 0.25q = 4
Why is the answer to a subtraction problem called the difference...
Answers
Well, 'sum'body said that's what they should be called a long time ago, that's why we're using that term to call them now.
Explain the difference between f and f(x).
Answers
Jasmine wants to organize her books in order of most number of pages to least number of pages. Jasmine's longest book has 396 pages and her shortest book has one-fourth as many pages as the longest. If the book in the middle of her shelf has three times the number of pages of the shortest book. Then how many pages does the middle book have?
Answers
Answer:
297 pages
Step-by-step explanation:
Number of pages of longest book = 396 pages
Now we are given that her shortest book has one-fourth as many pages as the longest.
Number of pages of shortest book = [tex]\frac{\text{Number of pages in longest book}}{4}[/tex]
= [tex]\frac{396}{4}[/tex]
= [tex]99[/tex]
Now we are given that the book in the middle of her shelf has three times the number of pages of the shortest book.
So, Number of pages in middle book:
= [tex]3 \times \text{Number of pages of shortest book}[/tex]
= [tex]3 \times 99[/tex]
= [tex]297[/tex]
Hence the middle book have 297 pages.
The cake store is having a 30 % off sale on all of its cakes. if the cake you want regularly costs $10 how much would you save with the discount?
Answers
15
if 6-x=2(x-6) what is the value of x? need steps!!
Answers
The value of x in the equation 6 - x = 2(x - 6) is 6. To convert this to feet, the calculation shows that 6 miles is equivalent to 31,680 feet.
Explanation:To solve the equation 6 - x = 2(x - 6), follow these steps:
Distribute the 2 on the right side to both terms inside the parenthesis: 6 - x = 2x - 12.Add x to both sides to get x terms on one side: 6 = 3x - 12.Add 12 to both sides to isolate the x terms: 18 = 3x.Divide both sides by 3 to solve for x: x = 6.So, the value of x is 6.
To convert 6 miles to feet, using the equation 1 mile/5280 feet = 6 miles/x feet, we cross multiply to get:
1x = 6 × 5280.x = 31,680 feet.Therefore, 6 miles is equivalent to 31,680 feet.
Find the rate of change for the situation.
A chef cooks 9 lbs of chicken for 36 people and 17 lbs of chicken for 68 people.
A. 9/17lb per person
B. 4 lb per person
C. 1/4 lb per person
D. 36 people ...?
Answers
Final answer:
The rate of change for the chef's cooking scenario is calculated by dividing the lbs of chicken by the number of people for each case. In both situations, the rate of change is 1/4 lb per person.
Explanation:
The question asks to find the rate of change for a situation where a chef cooks a certain amount of chicken for a specific number of people. To calculate the rate of change, we need to divide the amount of chicken by the number of people for each situation, and then compare.
For 9 lbs of chicken for 36 people, the rate is 9 lbs ÷ 36 people = 0.25 lbs/person, which is equal to 1/4 lb per person. For 17 lbs of chicken for 68 people, the rate is 17 lbs ÷ 68 people = 0.25 lbs/person, which is also 1/4 lb per person.
Since the rate of change is the same in both cases, 1/4 lb per person, the correct answer is:
C. 1/4 lb per person
PLEASE HELPPP!!!
1. Choose the equation that could be used to solve the given number problem.
The sum of two consecutive integers is 141. Find the integers.
n + 1= 141
2n + 2 = 141
2n = 141
2n + 1 = 141
2. Choose the equation that could be used to solve the given number problem.
The sum of two consecutive odd integers is 112. Find the integers.
2n + 3 = 112
2n + 2 = 112
2n + 1 = 112
n + 2 = 112
Answers
If their sum is 141 we can write:
n + (n+1) = n + n + 1 = 2n + 1 = 141
2) now this is bit tricky. First integer is:
2n-1
the reason for this is because 2n is always even number for any n. when we subtract 1 we always get odd number. Next consecutive odd number is:
2n-1 + 2 = 2n+1
when we sum these 2 numbers we get:
2n-1 + (2n+1) = 2n - 1 + 2n + 1 = 4n.
Now the important part. 4n and 2n are both always even numbers so it doesnt matter if we write 2n or 4n or 6n. If you give yourself thought experiment you will see that sum of two consecutive odd integers is always even integer.
which means that we can write our formula in multiple ways and one of them is:
2n + 2.
2n is always even number and if we add 2 again we get even number.
answer is 2n+2
The table shows ordered pairs of the function y = 16 + 0.5x
Which ordered pair could be the missing values represented by (x, y)?
a) (0, 18)
b) (5, 19.5)
c) (8, 20)
d) (10, 21.5)
Answers
the answer is C (8,20)
Answer:
c) (8, 20)
Step-by-step explanation:
We must plug in the given value of x in the function and confirm that the value of y that is returned to us is the correct one.
a) (0, 18)
[tex]x=0,y=18[/tex]
[tex]y = 16 + 0.5(0)=16+0=16[/tex]
the values for y do not match, so it is not a solution.
b) (5, 19.5)
[tex]x=5,y=19.5[/tex]
[tex]y = 16 + 0.5(5)=16+2.5=18.5[/tex]
again, the values for y do not match so it is not a solution.
c) (8, 20)
[tex]x=8,y=20[/tex]
[tex]y = 16 + 0.5(8)=16+4=20[/tex]
For this option, the values of y do match, so (8, 20) are the missing values.
A wave traveling in water has a frequency of 250 Hz and a wavelength of 6.0 m. What is the speed of the wave?
Answers
If ef = 6 and eg = 21 what is the value of fg
Answers
e/ef=6 e/eg=21
f=6/e g=21/e
21*6= 126/e²
If EF = 6 and EG = 21 what is the value of FG?
The answer is 15.
how do you derive the lens maker's equation? ...?
Answers
Using Snell’s law ( n1 sin θi = n2 sin θr ) at point A gives
1) sin i1 = n sin r1
2) i1 = n r1
3) i1 = α1 + β1
4) r1 = β1 - γ
5) α1 + β1 = n(β1 - γ)
6) sin i2 = n sin r2
7) i2 = n r2
8) i2 = α2 + β2
9) r2 = β2 + γ
10) α2 + β2 = n(β2 + γ)
11) α1 + α2 = (n - 1)(β1 + β2)
12) 1/s + 1/s' = (n - 1)(1/R1 + 1/R2)13) 1/f = (n - 1)(1/R1 - 1/R2)
14) 1/s + 1/s' = 1/f
The lens maker's equation is derived by considering the image formed by the first refracting surface (left surface) and then using this image as the object for the second refracting surface. The equation takes into account the radii of curvature and the refractive indices of the lens and the surrounding medium.
Explanation:The lens maker's equation is derived by considering the image formed by the first refracting surface (left surface) and then using this image as the object for the second refracting surface.
The equation takes into account the radii of curvature and the refractive indices of the lens and the surrounding medium.
The lens maker's equation can be stated as: 1/f = (n₂ - n₁)((1/R₁) - (1/R₂)), where f is the focal length, n₂ is the refractive index of the lens, n₁ is the refractive index of the surrounding medium (usually air), R₁ is the radius of curvature of the first surface of the lens, and R₂ is the radius of curvature of the second surface of the lens.
Let f be the function defined by f(x) = 3x^5-5x^3+2
a) On what intervals is f increasing
b) On what intervals is the graph of f concave upward.
c) Write the equation of each horizontal tangent line to the graph of f.
Please provide some detail to your response. ...?
Answers
f'(x) = 15x^4 - 15x^2 > 0
15x^2(x^2 - 1)> 0
x^2 - 1 > 0 (The inequality doesn't flip sign since x^2 is positive)
x^2 > 1
Then f is increasing when x < -1 and x > 1.
(b) The f is concave upward when f''(x) > 0.
f''(x) = 60x^3 - 30x > 0
30x(2x^2 - 1) > 0
x(2x^2 - 1) > 0
x(x^2 - 1/2) > 0
x(x - 1/sqrt(2))(x + 1/sqrt(2)) > 0
There are four regions here. We will check if f''(x) > 0.
x < -1/sqrt(2): f''(-1) = -30 < 0
-1/sqrt(2) < x < 0: f''(-0.5) = 7.5 > 0
0 < x < 1/sqrt(2): f''(0.5) = -7.5 < 0
x > 1/sqrt(2): f''(1) = 30 > 0
Thus, f''(x) > 0 at -1/sqrt(2) < x < 0 and x > 1/sqrt(2).
Therefore, f is concave upward at -1/sqrt(2) < x < 0 and x > 1/sqrt(2).
(c) The horizontal tangents of f are at the points where f'(x) = 0
15x^2(x^2 - 1) = 0
x^2 = 1
x = -1 or x = 1
f(-1) = 3(-1)^5 - 5(-1)^3 + 2 = 4
f(1) = 3(1)^5 - 5(1)^3 + 2 = 0
Therefore, the tangent lines are y = 4 and y = 0.
Answer:
a) [-1, ∞-) and [1, ∞+)
b) (√2/2,∞) and (0,-√2/2)
c) y=0, y=2 and y=4
Step-by-step explanation:
a) On what intervals is f increasing?
We need to proceed some steps, to answer it properly. What are the critical points? So
1) Differentiate the original function
[tex]f(x)=3x^{5}-5x^3+2\\ f'(x)=15x^4-15x^{2}[/tex]
2) Turn this into an equation
[tex]15x^4-15x^2=0\\ u=x^{2} and \\u^{2}=x^{4} \\ Then\\ 15u^{2} -15u=0\\ \\15u(u^2 -1)=0\\Therefore\\u=0,u=1[/tex]
Substitute back to x
[tex]x^{2} =u\\ x^{2} =u^4\\ x^{2}=1\\ x= 1,x=-1\\ x^{2} =0\\ x=0[/tex]
Those are x-coordinates of the critical points of [tex]f(x)=3x^{5}-5x^3+2[/tex]
Using the critical points x, to find y-coordinates of those critical points: namely, maximum point, saddle point and minimum point
x=-1 [tex]y=3x^{5}-5x^3+2[/tex]
[tex]y=3(-1)^{5}-5(-1)^3+2[/tex]
y=4
(-1,4) Maximum point
--
x=0 [tex]y=3x^{5}-5x^3+2[/tex]
[tex]y=3(0)^{5}-5(0)^3+2[/tex] y=2
(0,2) Saddle Point
--
x=1 [tex]y=3x^{5}-5x^3+2[/tex]
[tex]y=3(1)^{5}-5(1)^3+2[/tex]
(1,0) Minimum point
f(x) increases when any value of x ∈ (-∞, -1] and x ∈ [1, ∞+) is plugged in the function. Or we can rewrite as x[tex]x\leq -1\\ \\x\geq 1[/tex]
-------------------------------------
b)On what intervals is the graph of f concave upward?
To find out which intervals are these, we need to calculate the 2nd derivative.
[tex]f(x)=3x^{5}-5x^3+2\\ f(x)'=15x^4-15x^{2} \\f(x)''=60x^3-30x\\[/tex]
Since we want the concave upward
f(x)''>0
Then:
[tex]60x^3-30x>0\\ 30x(2x^2-1)>0\\[/tex]
Rewriting
[tex]30x(\sqrt{2x}-1)[/tex]
Then
x=0, x=[tex]\frac{\sqrt{2}}{2} \\-\frac{\sqrt{2}}{2}[/tex]
Studying the sign
The intervals >0, when the graph is concave upwards.
are (√2/2,∞) and (0,-√2/2)
c) Write the equation of each horizontal tangent line to the graph of f.
Generally, every time somebody ask for a tangent line of any given function, they provide an information. A specific point.
But when they do not? Like in this case?
We have to look for where the 1st function's derivative is zero.
As we 've done previously in letter a. x=-1, x=0, x=1
Let's plug them back to the original function
[tex]y=3x^{5}-5x^{3}+2\\ y=3(-1)^{5}-5(-1)^{3}+2\\ y=-3-5+2\\ y=-8+2\\ y=4\\ \\y=3x^{5}-5x^{3}+2\\ y=3(0)^{5}-5(0)^{3}+2\\ y=2\\\\ y=3x^{5}-5x^{3}+2\\ y=3(1)^{5}-5(1)^{3}+2\\ y=0[/tex]
So each horizontal tangent line, tangents the maximum, saddle and the minimum point.
How to solve the formula for Vf in the formula of acceleration?
Answers
Multiply by t on both sides to clear the denominator
at = Vf - Vi
Add Vi to both sides.
at +Vi = Vf
Final answer:
To solve for final velocity (Vf) in acceleration calculations, identify the initial velocity (Vo), acceleration (a), and time (t), then use the formula Vf = Vo + at to find Vf. Substitute the known values into the formula to calculate the final velocity.
Explanation:
To solve for final velocity (Vf) in the formula for acceleration, follow these steps:
Identify the initial velocity, Vo, and any other known variables such as acceleration (a) and time (t).
Determine which equation to use, using the relationship that acceleration is the change in velocity over time (Δv/Δt). The formula to calculate final velocity is v = Vo + at.
Substitute the known values into the equation to solve for Vf. For example, with an initial velocity (Vo) of 30.0 km/h (which converts to 8.333 m/s), an unknown final velocity (Vf), and a time (Δt) of 8.00 seconds, the change in velocity (Δv) would be Vf - Vo.
To find Vf, rearrange the equation: Vf = Vo + (a Δt). Insert the known values into the equation and calculate the result.
As an example, if the initial velocity Vo is 0 and the acceleration is 0.40 m/s² over a time of 100 seconds, then the final velocity Vf is calculated as:
Vf = Vo + at = 0 + (0.40 m/s²) (100 s) = 40 m/s.
This procedure will yield the final velocity of an object assuming constant acceleration over the given time period.
evaluate 3log3^21 ...?
Answers
= 21 x 3 Log 3
= 21 x 1
= 21
Hope this helps
The period of y = cos x occurs every 2pi units.
T/F?
Answers
True, the period of y = cos x occurs every 2pi units.
What are the trigonometric identities?Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.
Given:
Trigonometric function,
y = cosx.
To find the period:
Use formula,
period = 2π/the coefficient of cosx.
Period = 2π
Therefore, the period of y = cosx is 2π.
To learn more about the trigonometric identities;
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How do we find x-intercept of rational function
Answers
An X-intercept in a rational function is the point where the graph intersects the x-axis. It is derived by setting the function equal to zero and then solving for the variable x. This solution, x, represents the x-intercept of the rational function.
Explanation:In Mathematics, the x-intercept of a rational function is the point where the function intersects the x-axis. The x-intercept(s) can be found by setting the function equal to zero and solving for x. When graphing, this point determines where the line crosses the x-axis.
The same principle is applied to the calculation of the x-intercept as other functions. The given rational function is set equal to zero, and then algebraic methods are used to solve for the value of x. For example, if given the rational function y = 2x/3x + 1, setting this function to zero would read as 0 = 2x/(3x + 1). Cross-multiplication can then be applied to find the solution for x, which represents the x-intercept.
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Jenna and her friend, Khalil, are having a contest to see who can save the most money. Jenna
has already saved $110 and every week she saves an additional $20. Khalil has already saved $80
and every week he saves an additional $25. Let x represent the number of weeks and y represent
the total amount of money saved.
So far I've got 110+20x= ??? for jenna because I don't know what goes after the equal sign and 80+25x=???
Answers
which fraction below represents the following statement "in the third game of the season Martha made one of 5 free throws"
Answers
Answer: Which fraction below represents the following statement?“In the third game of the season, Martha made one out of five free throws.” The answer for this questions would be 1/5
Step-by-step explanation: I got it correct on Edge.
The fraction that represents the statement "in the third game of the season Martha made one of 5 free throws is 1/5.
What is a fraction?A fraction is written with a numerator and a denominator where the numerator is less than the denominator.
Example: 1/3 is a fraction.
We have,
Total number of free throws = 5
Number of free throws Martha made = 1
The number of free throws Martha made can be written in fraction form as:
= Number of free throws Martha made / Total number of free throws
= 1 / 5
Thus,
The fraction that represents the statement "in the third game of the season Martha made one of 5 free throws is 1/5.
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A farmer's land is separated into sections of size
2 1/5
acres. Suppose there are
4 4/9
such sections. How many acres of land does the farmer own?
Answers
The farmer owns 8 10/45 acres of land.
Explanation:To find out how many acres of land the farmer owns, we need to multiply the number of sections by the size of each section. The size of each section is 2 1/5 acres.
The number of sections is 4 4/9. Using multiplication, we can calculate the total number of acres:
(2 1/5) x (4 4/9) = 10/5 x 40/9 = 400/45 = 8 10/45
Therefore, the farmer owns 8 10/45 acres of land.
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Box of 12 golf balls costs $45. what is the unit rate
Answers
Find dy/dx by implicit differentiation and evaluate the derivative at the given point.
xy = 35 ...?
Answers
Since that, the first thing you should do is to differentiate with respect to x
(look at the pic. 1), as you can see this is simply 1, which means you have to simplify
Then we need to perform solving for for dy/dx as we are about to get the derivative of y with respect to x. pic.2
Get back to the oroginal function, now we can substitute this for y to get the func which will depend only on x pic.3
Then pic.4
Final answer:
To find dy/dx by implicit differentiation of the equation xy=35, differentiate both sides with respect to x. Use the product rule to obtain x * (dy/dx) + y = 0 and solve for dy/dx, giving dy/dx = -y / x. Evaluate this at a specific point by substituting the x and y values from that point into the derived formula.
Explanation:
To find dy/dx by implicit differentiation of the equation xy = 35, we differentiate both sides of the equation with respect to x. Since y is a function of x, when we differentiate y we must apply the chain rule, resulting in the derivative y with respect to x, or dy/dx.
Starting with the original equation:
xy = 35
We apply differentiation to both sides with respect to x:
Using the product rule for the left side: d/dx (xy) = d/dx (35)
This gives us x * (dy/dx) + y * (1) = 0 because the derivative of a constant, like 35, is 0.
We then solve for dy/dx: dy/dx = -y / x.
To evaluate the derivative at a given point, you substitute the x and y coordinates of that point into the derivative equation. For example, if we are given a point (5,7), we substitute into the dy/dx equation to find the derivative at that point:
dy/dx = -y / x = -(7) / (5)
Therefore, dy/dx at the point (5,7) is -7/5 or -1.4.