By assuming that x = 2 and substituting this into the original equation x^2 + x = 4, we arrive at a contradiction because 4 + 2 ≠ 4. Thus, we conclude through indirect proof that x cannot equal 2.
To give an indirect proof of the statement If x2 + x = 4, then x ≠ 2, we start by assuming the opposite of what we want to prove, which is that x = 2. Our goal is to show that this assumption leads to a contradiction.
Assume that x = 2. Substituting 2 for x in the original equation gives us (2)2 + 2 = 4 + 2 = 6, which is clearly not equal to 4. This contradicts the original equation x2 + x = 4. Since our assumption that x = 2 leads to a false statement, it follows that x cannot be 2, thereby proving the original statement by contradiction.
The method of assuming the negation and arriving at a contradiction shows that the original statement must be true according to the logical principle of indirect proof. Hence, if x2 + x = 4, then indeed x ≠ 2.
sorry wrong problem if ab =58 find the value of x
Answer:
x=12
Step-by-step explanation:
if ab =58 find the value of x
The length of AB= 58
Given : AC= 3x-6
CB= 2x+4
[tex]AC + CB=AB[/tex]
Now replace the expressions
[tex]3x-6+2x+4=58[/tex]
now we solve for x, combine like terms
[tex]5x-2=58[/tex]
Add 2 on both sides
[tex]5x=60[/tex]
Divide both sides by 5
x=12
a speed of limit of 100 kilometers per hour is approximately equal to 62 miles per hour predict the following measures round your answers to the nearest whole number
a. a speed limit in mph for a speed limit of 75 kph
b. a speed limit in kph for a speed limit of 20 mph
Answer:
a. 46.5 mph
b. 32.3 kph
Step-by-step explanation:
If the speed limit is 100 km/hour we and this equals 62 mile per hour we can determine how many kilometers is in miles and vice versa:
WE can do this as:
[tex]62/100=0.62[/tex]
Therefore the 0.62 miles per kilometer
a) For 75 kph we can use the conversion we determine to convert to miles per hour:
[tex]75*0.62=46.5[/tex]
It takes a speed limit of 46.5 mph for a 75 kph limit
b) For 20 mph we can use the conversion we determine to convert to kilometers per hour:
[tex]20/0.62=32.3[/tex]
It takes a speed limit of 32.3 kph for a 20 mph limit
Suppose you invest $400 at an annual interest rate 7.6% compounded continuously. How much will you have in the account after 1.5 years? Round the solution to the nearest dollar
You can expect to have approximately $447 in your account after 1.5 years of continuously compounded interest on your $400 investment.
How much will you have in the account after 1.5 years?
To find out how much you'll have in your account after 1.5 years, we can follow these steps:
1. Formula: Use the formula for continuous compounding:
[tex]Final\ amount = Initial\ amount * (1 + annual\ interest\ rate)^{time}\[/tex]
2. Plug in the values: We know:
Initial amount = $400
Annual interest rate = 7.6% (remember to convert it to a decimal by dividing by 100, so 7.6% becomes 0.076)
Time = 1.5 years
3. Calculation: Substitute the values and calculate:
Final amount = $400 * (1 + 0.076)^{1.5}
[tex]Final\ amount = $400 * (1 + 0.076)^{1.5} = 446.5[/tex]
4. Round the answer: Round the final amount to the nearest dollar:
Final amount = 447
Solve the following equation, answer as a reduced, mixed number. Then place the correct number in the box provided.
15(2 - x) = 13(3 - x)
x=(written as a fraction)
the answer i got was x = - 9/2
hope this helps
Find the following.
a. The side length of a cube with a volume of 125 units^3.
b. The volume of a cube with a side length of 4 units.
If four friends can eat four cakes in four days, then how many cakes can 10 friends eat in 10 days?
A parking lot charges $1.50 for the first hour of parking, and 55 cents for each additional half hour . how much would it cost to park a car from 12:45 pm to 6:15 pm
The parking cost for the specified duration would be $6.70.
Explanation:The parking fee consists of a base charge of $1.50 for the first hour. In this case, the car is parked for 5.5 hours (from 12:45 pm to 6:15 pm). The first hour is covered by the base charge, and the remaining 4.5 hours are billed as subsequent half-hours. For each half-hour, there is an additional charge of 55 cents. So, for the subsequent 4.5 hours, the additional charge is calculated as follows:
[tex]\[4.5 \times \$0.55 = \$2.475.\][/tex]
Adding this to the base charge:
$1.50 + $2.475 = $3.975.
Therefore, the total parking cost for the specified duration is $1.50 (for the first hour) + $2.475 (for the subsequent 4.5 hours), resulting in a final cost of $6.70.
This calculation ensures that the parking fee is accurately determined based on the initial hourly rate and subsequent half-hourly charges. The approach allows for a clear breakdown of the cost structure, providing transparency for users and ensuring fairness in the billing process.
A parking lot implements a fee structure of $1.50 for the first hour of parking and an additional charge of 55 cents for each subsequent half-hour. If a car is parked from 12:45 pm to 6:15 pm on the same day, how much would the parking cost for this duration?
elise took out a payday loan for $500 due in 2 weeks that charged an $80 fee. what the periodic interest rate of the loan?
Answer:
16%Step-by-step explanation:
The periodic interest rate refers to the rate that it's charged after certain fixed period, can be yearly, monthly, daily. In this case, the periodic interest rate is due in 2 weeks.
Now, to find this interest rate, we just have to divide the fee by the loan and see what percentage represents
[tex]\frac{\$80}{\$500}=0.16[/tex]
Then, we multiply by 100 to obtain the percentage
[tex]0.16(100)= 16\%[/tex]
Therefore, the interest rate is 16%
WILL GIVE BRAINLIEST!!! 12 POINTS!!!!
The table below shows the quiz grades for two students.
Drew 90 81 86 79 97 84 92
Nancy 96 68 91 94 69 99 92
Which statement is true about the data above?
* The students have the same mean, but Nancy's quiz grades have a higher interquartile range.
* The students have the same mean, but Drew's quiz grades have a higher interquartile range.
* The students' grades have the same interquartile range, but Drew has a higher mean.
* The students' grades have the same interquartile range, but Nancy has a higher mean.
Solve (4 - x ≤ -1) ∩ (2 + 3x ≥ 17). Click on the graph until the solution set appears.
The solution set appears at x ≥ 5 for (4 - x ≤ -1) ∩ (2 + 3x ≥ 17).
What are sets and subsets?A set is a collection of well-defined objects.
A subset contains all the elements or a few elements of the given set.
The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.
The symbol ∩ represents an intersection or common between them.
Given, (4 - x ≤ -1) ∩ (2 + 3x ≥ 17).
( x ≥ 5) ∩ ( x ≥ 5).
So, x ≥ 5.
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Which table represents a linear function that has a slope of 5 and a y-intercept of 20?
Table 4 represents the linear function that has slope of 5 and a y-intercept of 20.
Further explanation:
The linear equation with slope [tex]m[/tex] and intercept [tex]c[/tex] is given as follows.
[tex]\boxed{y = mx + c}[/tex]
Given:
The y-intercept is [tex]\left( { - 9, - 3} \right).[/tex]
The slope of the linear function is [tex]- 6.[/tex]
Explanation:
The linear function can be expressed as follows,
[tex]y = 5x + 20[/tex]
In table 1,
Substitute [tex]-60[/tex] for [tex]x[/tex] and 8 for [tex]y[/tex] in linear function to check whether the point satisfy the linear function.
[tex]\begin{aligned}8&= 5\left({ - 60} \right) + 20\\8&= - 300 + 20\\8&= - 280\\\end{aligned}[/tex]
Table 1 is not correct.
In table 2,
Substitute 20 for [tex]x[/tex] and [tex]0[/tex] for [tex]y[/tex] in linear function to check whether the point satisfy the linear function
[tex]\begin{aligned}0&= 5\left( {20} \right) + 20\\0&= 100 + 20\\&0\ne120\\\end{aligned}[/tex]
Table 2 is not correct.
In table 3,
Substitute [tex]-20[/tex] for [tex]x[/tex] and 0 for [tex]y[/tex] in linear function to check whether the point satisfy the linear function
[tex]\begin{aligned}- 20&= 5\left( 0 \right) + 20\\- 20 &\ne 20\\\end{aligned}[/tex]
Table 3 is not correct.
In table 4,
Substitute [tex]-4[/tex] for [tex]x[/tex] and 0 for [tex]y[/tex] in linear function to check whether the point satisfy the linear function
[tex]\begin{aligned}0&= 5\left( { - 4} \right) + 20\\0&= - 20 + 20\\0&= 0\\\end{aligned}[/tex]
Table 4 is correct.
Table 4 represents the linear function that has slope of 5 and a y-intercept of 20.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear equation
Keywords: linear function, numbers, slope 5, y-intercept of 20, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation.
True or false: when comparing two populations, the larger the standard deviation, the more dispersion the distribution has, provided that the variable of interest from the two populations has the same unit of measure. choose the correct answer below.
a. false, because the larger the standard deviation is, the less dispersion the distribution has.
b. true, because the standard deviation is the difference between the largest and smallest observation. when the standard deviation is larger, there is more distance between the largest and smallest observation, and therefore, more dispersion in the distribution.
c. true, because the standard deviation describes how far, on average, each observation is from the typical value. a larger standard deviation means that observations are more distant from the typical value, and therefore, more dispersed.
d. false, because the standard deviation measures the spread of the distribution, not the dispersion of the distribution.
The larger the standard deviation, the more dispersed the distribution is, because the standard deviation measures how far each observation is from the mean value of the distribution.
The correct option is C. The typical value being referred to in the option is the mean. The standard deviation measures how far each observation in a distribution is to the mean value of the distribution. Option D is wrong, because, the spread is also the degree of dispersion. The difference between the largest and smallest value in a distribution is the range and not the standard deviation . Hence, option B is wrong. The larger the standard deviation, the greater the dispersion. Hence, option A is wrong.Learn more : https://brainly.com/question/12402189?referrer=searchResults
is 1 over 3 rational
At the city museum, child admission is $5.20 and adult admission is $8.90 . on friday, 159 tickets were sold for a total sales of $1100.60 . how many adult tickets were sold that day?
Convert 59 degrees in Fahrenheit to Celsius temperature using the formula . 27°C 15°C 12°C 8°C
59 degrees Fahrenheit is equivalent to 15 degrees Celsius.
We have,
To convert a temperature in Fahrenheit to Celsius, you can use the formula:
°C = (°F - 32) x (5/9)
Let's apply this formula to convert 59 degrees Fahrenheit to Celsius:
°C = (59 - 32) x (5/9)
Simplifying the equation:
°C = 27 x (5/9)
°C = 135/9
°C = 15
Therefore,
59 degrees Fahrenheit is equivalent to 15 degrees Celsius.
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Which ordered pairs are solutions to the inequality 2x+3y>-1?
Select each correct answer.
(0,1)
(0,-1)
(-2,1)
(-6,0)
(2,-1)
The ordered pairs are (0, 1), and (2, -1) which are solutions to the inequality 2x+3y>-1 option first and fifth are correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have an inequality:
2x+3y>-1
The above inequality is a straight line and represents a region.
After plotting the inequality on the graph.
The points are in the region of the inequality:
(0, 1)(2, -1)These points satisfy the inequality.
Thus, the ordered pairs are (0, 1), and (2, -1) which are solutions to the inequality 2x+3y>-1 option first and fifth are correct.
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algebra 2 function operations (link)
A pendulum has 887 J of potential energy at the highest point of its swing. How much kinetic energy will it have at the bottom of its swing?
find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule A(n)=-6+(n-1)(1/5)
The formula that represents the nth term of a arithmetic sequence is given by:
[tex]A(n)=-6+(n-1)(\dfrac{1}{5})[/tex]
Now, we are asked to find the first, fourth, and tenth terms of the arithmetic sequence.
i.e. we are asked to find the value of A(n) when n=1 ,4 and 10
when n=1 we have:[tex]A(1)=-6+(1-1)(\dfrac{1}{5})\\\\i.e.\\\\A(1)=-6+0\\\\i.e.\\\\A(1)=-6[/tex]
now when n=4 we have:[tex]A(4)=-6+(4-1)\times (\dfrac{1}{5})\\\\i.e.\\\\A(4)=-6+3\times \dfrac{1}{5}\\\\i.e.\\\\A(4)=-6+\dfrac{3}{5}\\\\i.e.\\\\A(4)=\dfrac{-6\times 5+3}{5}\\\\i.e.\\\\A(4)=\dfrac{-30+3}{5}\\\\i.e.\\\\A(4)=\dfrac{-27}{5}[/tex]
when n=10 we have:[tex]A(10)=-6+(10-1)\times (\dfrac{1}{5})\\\\i.e.\\\\A(10)=-6+9\times \dfrac{1}{5}\\\\i.e.\\\\A(10)=-6+\dfrac{9}{5}\\\\i.e.\\\\A(10)=\dfrac{-6\times 5+9}{5}\\\\i.e.\\\\A(10)=\dfrac{-30+9}{5}\\\\i.e.\\\\A(10)=\dfrac{-21}{5}[/tex]
What is the point of maximum growth rate for the logistic function f(x) ?
Melissa needs to memorize words on a vocabulary list for Russian class. She has memorized 30 of the words, which is five-sixths of the list. How many words are on the list?
Gina paints beach scenes on notecards. She sells packages of 8 notecards for $8 for one package, $16 for 2 packages, and $24 for 3 packages. Which equation is the rule for the pattern if n is the number of packages and d is the selling price in dollars?
Which is the focus of a parabola with equation y2=-12x
How might your life insurance premiums depend upon when you initially purchase the policy?
Answer:
The age you are when you purchase life insurance is the biggest factor in how much you will have to pay. The premium amount typically increases about 8% to 10% for every year of age. The older you are, the more expensive you are to insure. When you are in your 40s, your rates increase from 5%-8% and when you are over 50, your rates increase by 9%-12% each year.
Step-by-step explanation:
Answer:
The Life insurance premium totally depends on your age when you will be purchasing it.
Step-by-step explanation:
Age is a significant factor in purchasing the policy. Age can be directly related to the rate of premium in the term plan or in the insurance. The average increase in the rate when it is calculated per year is about 8 to 10 percent. {Told by Ted Bernstien}.
According to the common theories, when you are in your 40's, then the rate will be increased around 5 to 8 percent, and when you are in your 50's it will be about 9 to 12 percent if you calculated it yearly.
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riangle ABC is a right triangle. What is the relationship between angles A and B? They are congruent. They are complementary. They are supplementary. There is no relationship between them.
Answer:
50 square units.
Step-by-step explanation:
Eng2021
Which graph shows the solution to the inequality -x + 2 > 1
devise a plan for simplifying th fourth root of a number that is not a perfect fourth power.
Final answer:
To simplify the fourth root of a non-perfect power, use a calculator to raise the number to the power of 0.25, or calculate the square root twice. For non-integer powers, calculate roots with corresponding fractional exponents. Request assistance from your instructor if necessary.
Explanation:
Simplifying the Fourth Root of Non-Perfect Powers
When simplifying the fourth root of a number that is not a perfect fourth power, you can utilize the power function on a calculator. This involves raising numbers to the power of 0.25, which equates to calculating the fourth root. For example, using the y* button (or equivalent) you can calculate the fourth root of any number by raising it to the power of 0.25. This is analogous to how raising a number to the 0.5 power gives us the square root of that number. If your calculator doesn't have this function, another technique is to calculate the square root of the number twice, since the fourth root is essentially the square root of the square root.
To work through a non-integer power, like 31.7, you can find the tenth-root of 3 by raising it to the power of 0.1 and then raise the result to the 17th power. Similarly, for expressions with fractional exponents like x0.5, you can interpret this as the square root of x. Understanding that fractional powers represent roots can help in simplifying complex expressions without a calculator as well.
If you are dealing with equilibrium problems or other scenarios that require finding roots of numbers, it's crucial to be comfortable with these techniques. If you are unsure about how to perform these operations, don't hesitate to ask for assistance from your instructor. Developing a natural and forgiving relationship with numbers, and only representing precision as needed, is also an important aspect of working with mathematical problems.
Easy question, decent amount of points! 25 points, if you're curious!
Be quick or it is gone.
Avi's pet hamster Chubby loves to run in his hamster wheel. During one "race", Avi counts 100 rotations of the wheel. She wants to know how far Chubby ran, so she measures the diameter of the wheel and finds that it 8 inches.
how far did chubby run?
i need the answer in terms of pi
How many ways can you choose the 5 cards out of a 52 card deck?
There are 2,598,960 ways to choose 5 cards out of a 52-card deck.
Explanation:To determine the number of ways to choose 5 cards out of a deck of 52 cards, we can use the concept of combinations. In this case, order doesn't matter, so we use the formula for combinations. The formula is:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of items to choose from and r is the number of items to be chosen.
For this question, n = 52 (number of cards in the deck) and r = 5 (number of cards to choose). We can plug these values into the formula to calculate the number of ways:
C(52, 5) = 52! / (5!(52-5)!) = 2,598,960
So, there are 2,598,960 ways to choose 5 cards out of a 52-card deck.
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The number of ways to choose 5 cards from a deck of 52, irrespective of order, is 2,598,960. This number is calculated using the combination formula in combinatorics.
Explanation:This question relates to the field of Mathematics known as combinatorics, specifically the concept of combinations. When we choose 5 cards out of a 52-card deck, we're not interested in the order in which the cards are drawn, so we use combinations. We use the notation C(n, k), where n is the total number of items, and k is the number of items to choose.
The formula for finding combinations is C(n, k) = n! / [k!(n-k)!]. In this case, n=52 (the total number of cards in the deck) and k=5 (the number of cards we are selecting). Plug these values into the formula to get C(52, 5) = 52! / [5!(52-5)!] = 52! / (5!47!) = 2,598,960
So, there are 2,598,960 ways to choose 5 cards out of a 52 card deck. This number takes into account all possible combinations of cards, without consideration of order or repetition.
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