Answer:
[tex](x^2 - x)[/tex] will always have an even value.
Step-by-step explanation:
We are given an integer x.
Let x be even, then it can be written in the form x = 2n, where n is an integer.
If we evaluate,
[tex](x^2 - x) = (2n)^2 - 2n = 4n^2 - 2n = 2(2n^2 - n)[/tex]
Thus, it have an even value.
If we take x to be an odd integer, then,it can be written in the form x = 2n+1, where n is an integer.
[tex](x^2 - x) = (2n+1)^2 - 2n = 4n^2 + 2n = 2(2n^2 + n)[/tex]
Thus, it have an even value.
Thus,
[tex](x^2 - x)[/tex] will always have an even value.
how many gallons of 80% antifreeze solution must be mixed with 100 gallons of 10% antifreeze to get a mixture that is 70% antifreeze? use the six step method
To get a mixture that is 70% antifreeze, you would need 600 gallons of 80% antifreeze solution mixed with 100 gallons of 10% antifreeze solution.
Explanation:To solve this problem, we will use the six step method. Let's assign variables to our unknown quantities:
Let x be the number of gallons of 80% antifreeze solution.Now we can set up the equation using the information given:
0.8x + 0.1(100) = 0.7(100 + x)Simplifying the equation:
0.8x + 10 = 70 + 0.7x0.8x - 0.7x = 70 - 100.1x = 60x = 600Therefore, you would need 600 gallons of the 80% antifreeze solution to mix with 100 gallons of the 10% antifreeze solution to get a mixture that is 70% antifreeze.
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How would you write the name of a segment differently than the name of a line
Segments and lines can be named using the letters that represent the points on them, such as AB or line AB.
Explanation:In geometry, segments and lines are fundamental elements. A line is an infinite set of points extending in opposite directions, while a segment is a finite portion of a line with two distinct endpoints. These concepts are essential for understanding geometric shapes, angles, and spatial relationships in mathematics.
In mathematics, the name of a segment and the name of a line can be written differently by using the letters that represent the points on the segment or the line. For example, a segment between points A and B can be written as AB, while a line passing through points A and B can be written as line AB or simply AB. It is important to note that in both cases, the order of the points does not matter, as AB is the same as BA.
If decking cost $5.75 per square feet, how much would it cost to build a deck that is 22 feet by 18.5 feet
It would cost $2338.75 to build a deck that is 22 feet by 18.5 feet at a rate of $5.75 per square foot.
To calculate the cost of building a deck, we need to find the total area of the deck and then multiply it by the cost per square foot.
The area of a rectangle (deck) is given by the formula:
Area = length * width
Given that the deck has a length of 22 feet and a width of 18.5 feet, we can calculate the total area:
Area = 22 feet * 18.5 feet
Area = 407 square feet
Now, to find the total cost of building the deck, we multiply the area by the cost per square foot:
Total cost = Area * Cost per square foot
Total cost = 407 square feet * $5.75/square foot
Total cost = $2338.75
So, it would cost $2338.75 to build a deck that is 22 feet by 18.5 feet at a rate of $5.75 per square foot.
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How do I solve this equation? I need a refresher on Algebra.
Jane is having difficulty deciding whether to put her savings in the Mystic Bank or in the Four Rivers Bank. Mystic offers a 12% rate compounded quarterly, and Four Rivers offers 14% compounded semiannually. Jane has $40,000 to invest and expects to withdraw the money at the end of five years. Using the tables in the Business Math Handbook that accompanies the course textbook, determine which one of the following is the best deal.
A. Four Rivers
B. Mystic
C. Mystic for last two years
D. Four Rivers for first two years
which of the following is a solution set to 4|x+3|
The number n(t) of people in a community who are exposed to a particular advertisement is governed by the logistic equation. initially, n(0) = 500, and it is observed that n(1) = 1000. solve for n(t) if it is predicted that the limiting number of people in the community who will see the advertisement is 50,000. (round all coefficients to four decimal places.)
Rounding the coefficients to four decimal places:
[tex]\[ n(t) = 50000 \times \left(1 - e^{-20.2020t + 0.0101}\right) \][/tex]
The logistic equation governing the number of people exposed to the advertisement in the community is given by:
[tex]\[ \frac{{dn}}{{dt}} = kn \left(1 - \frac{n}{M}\right) \][/tex]
Where:
n(t) is the number of people exposed to the advertisement at time t
k is the growth rate constant
M is the limiting number of people who will see the advertisement
Given:
[tex]\( n(0) = 500 \)[/tex]
[tex]\( n(1) = 1000 \)[/tex]
[tex]\( M = 50000 \)[/tex]
We first need to find the growth rate constant \( k \):
[tex]\[ 1000 = 500 \times \left(1 - \frac{500}{50000}\right) \times k \][/tex]
[tex]\[ 1000 = 500 \times \left(1 - \frac{1}{100}\right) \times k \][/tex]
[tex]\[ 1000 = 500 \times \frac{99}{100} \times k \][/tex]
[tex]\[ k = \frac{1000 \times 100}{500 \times 99} \][/tex]
[tex]\[ k = \frac{2000}{99} \][/tex]
Now, we integrate to find [tex]\( n(t) \)[/tex]:
[tex]\[ \int \frac{{dn}}{{n(1 - \frac{n}{50000})}} = \int \frac{{2000}}{{99}} dt \][/tex]
[tex]\[ -\ln|1 - \frac{n}{50000}| = \frac{{2000}}{{99}}t + C \][/tex]
Using the initial condition [tex]\( n(0) = 500 \)[/tex], we find[tex]\( C \)[/tex]:
[tex]\[ -\ln|1 - \frac{500}{50000}| = 0 + C \][/tex]
[tex]\[ -\ln\left(\frac{99}{100}\right) = C \][/tex]
So, the equation becomes:
[tex]\[ -\ln|1 - \frac{n}{50000}| = \frac{{2000}}{{99}}t - \ln\left(\frac{99}{100}\right) \][/tex]
Solving for n(t) :
[tex]\[ |1 - \frac{n}{50000}| = e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)} \][/tex]
[tex]\[ 1 - \frac{n}{50000} = e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)} \][/tex]
[tex]\[ \frac{n}{50000} = 1 - e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)} \][/tex]
[tex]\[ n(t) = 50000 \times \left(1 - e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)}\right) \][/tex]
This is the solution for [tex]\( n(t) \)[/tex]. Now, rounding the coefficients to four decimal places:
[tex]\[ n(t) = 50000 \times \left(1 - e^{-20.2020t + 0.0101}\right) \][/tex]
A homeowner plans to hang wallpaper on one wall of a bedroom that is 10 feet long
The figure illustrates the apparatus for a tightrope walker. Two poles are set y = 50 feet apart, but the point of attachment P for the rope is yet to be determined. (a) Express the length L of the rope as a function of the distance x from P to the ground.
Equation for the length L of the rope as a function of the distance x from P to the ground is,
⇒ L = √((x-2)²+50²)
Since L is to the second pole, not x, we can't simply say that;
⇒ x² + y²= L² using the Pythagorean Theorem.
Since, due to that we simply increase the original height by 2, decreasing x by 2.
We can, however, say that ;
⇒ (x-2)² + y² = L²
Plugging 50 as y in, we get ;
⇒ (x-2)² + 50² = L².
Square rooting both sides, we get;
⇒ L = √((x-2)²+50²)
Thus, Equation for the length L of the rope as a function of the distance x from P to the ground is,
⇒ L = √((x-2)²+50²)
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1.5x - 3y = 6 (solve for y)
An equation is formed of two equal expressions. The value of y for the given equation is (1.5x - 6)/3.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
1.5x - 3y = 6
Subtract 1.5x from both the sides of the equation,
1.5x - 3y - 1.5x = 6 - 1.5x
-3y = 6 - 1.5x
Divide both the sides of the equation by -3,
-3y/(-3) = (6 - 1.5x)/(-3)
y = (1.5x - 6)/3
Hence, the value of y for the given equation is (1.5x - 6)/3.
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If Dave drives at a steady speed of 50 mph, how long will it take him to drive 10 miles?
For football tryouts at the local school 12 coaches and 42 players will split into groups each group will have the same number of coaches and players what is the greatest number of groups that can play that can be formed how many coaches and players will be in each of these group
highest common factor of 92 and 42
The Greates Common Factor (GCF) is: 2
You can always share this solution
Find the distance between the points on a number line -7, -54
since they are both negative numbers just subtract 7 from 54
54-7 = 47
in a mayoral election Jane received 213 more votes than Jack. If Jack received N votes how many votes did Jane receive?
Object a has less thermal energy than object b but heat flows from object a to object begat conditions make this possible
How do you rewrite 4x24 using the distributive property
The expression 4 × 24 in distributive form will be 4 × ( 20 + 4 ) and the value of 96.
An expression 4x24 is given.
We have to write it using distributive property.
What is the distributive property of multiplication ?
The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.
As per the question ;
Expression is 4x24.
Let's rewrite it in form of distributive property ;
4 × 24
= 4 × ( 20 + 4 )
So ,
It is now in form A ( B + C ) , where ; A = 4 , B = 20 and C = 4
⇒ 4 × ( 20 + 4 )
= 80 + 16
= 96
Thus , the expression 4 × 24 in distributive form will be 4 × ( 20 + 4 ) and the value of 96.
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what is -2/3 - (1 1/3)
if f(x)=4-x^2 and g(x)=6x, which expression is equivalent to (g-f)(3)?
To find (g-f)(3), evaluate g(3) and f(3), then subtract f(3) from g(3).
Explanation:To find (g-f)(3), we need to subtract the function f(x) from g(x) and then evaluate the result at x = 3. Let's first simplify the expressions for f(x) and g(x):
f(x) = 4 - x^2
g(x) = 6x
Now substitute these into (g-f)(3) and simplify:
(g-f)(3) = g(3) - f(3)
= 6(3) - (4 - 3^2)
= 18 - (4 - 9)
= 18 - (-5)
= 23
Therefore, (g-f)(3) is equivalent to 23.
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A baker uses 3/4 cup of honey in one of his cakes. There are 60 calories in 1/8 cup of honey. How many cups of honey will the baker use for 15 cakes.
what is the answer to 72-(-58)-62
The answer to [tex]72 - (-58) - 62[/tex] is 68.
Understanding Double Negatives: When we subtract a negative number, it is equivalent to adding that number. Therefore, [tex]-(-58)[/tex] becomes [tex]+58[/tex].
So, the expression can be rewritten as:
[tex]72 + 58 - 62[/tex]
Performing the Addition: Now we add [tex]72[/tex] and [tex]58[/tex]:
[tex]72 + 58 = 130[/tex]
Performing the Final Subtraction: Next, we subtract [tex]62[/tex] from [tex]130[/tex]:
[tex]130 - 62 = 68[/tex]
Therefore, the final answer is [tex]68[/tex].
The Changs updated their bedroom by purchasing a new lamp for $89.95 and a comforter set for $239.99. They paid 2007-03-04-00-00_files/i0120000.jpg% sales tax on their purchases. If the Changs paid $351.72 total, determine if they paid the correct amount. a. The Changs family paid $0.33 too much for their purchases. b. The Changs family paid $0.99 too much for their purchases. c. The Changs family paid $5.94 too much for their purchases. d. The Changs family paid the correct amount for their purchases
In this exercise we will use the knowledge of finance to calculate the total value of the purchase, we have:
Letter D
First, let's organize the information given in the statement as:
$89.95 = New Lamp $239.99 = Comforter 6.6% = Sales Tax $351.72 = Total amount the Chang's paidTaking the percentage over the total amount, we find:
[tex]6.6\% \ of \ 329.94\ is\ \$21.78\\Total= \$351.72[/tex]
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is -8 a solution of -9f=64-f
For student spent $12 on school lunch at this rate find the amount 10 students would spend on the same school lunch?
. Which is equivalent to a drink made with 3 ounces of 80-proof vodka?
describe a situation in which a formula could be used more easily if it were rearranged. Include the formula in your description.
Is the line y = 3x – 7 parallel or perpendicular to 3x + 9y = 9? Explain your answer. Intro Done Go Left Go Right Frame 2 Frame 2 Frame 2 Frame 2 Frame 2 Frame 2 Frame 2 Frame 2 Frame 2 Frame 2 10 of 10
Answer:
the answer is 6.
Step-by-step explanation:
on edge i got my question wrong and the answer was 6 <33.
The graph of f(x) = log x + 3 is the graph of
g(x) = log x translated 3 units a)up b)down c)left D) right
Answer:
A)up
Step-by-step explanation:
Given : f(x)=log x +3
g(x)= log x
To Find :
The graph of f(x) = log x + 3 is the graph of g(x) = log x translated 3 units
a)up
b)down
c)left
d) right
Solution:
Rule: f(x)→f(x)+b
So, the graph f(x) is translated up by b units
So, on comparing given f(x) with rule , we can say that the graph g(x) is translated up by 3 units
Thus option A is correct.
Hence The graph of f(x) = log x + 3 is the graph of g(x) = log x translated 3 units up
om class we learned that in 2010 the federal debt (in millions) was $13,561,623 and the population of the U.S. was 309 million. Use this information to compute the federal debt per capita in 2010.
Answer:
$43888.75
Step-by-step explanation:
We have been given that in 2010 the federal debt (in millions) was $13,561,623 and the population of the U.S. was 309 million.
[tex]\text{The federal debt per capita}=\frac{\text{Total debt}}{\text{Total population}}[/tex]
[tex]\text{The federal debt per capita}=\frac{\$13,561,623}{309}[/tex]
[tex]\text{The federal debt per capita}=\$43888.74757[/tex]
[tex]\text{The federal debt per capita}\approx \$43888.75[/tex]
Therefore, the federal debt per capita in 2010 was $43888.75.
how many more kilometers in 4320 than 7200