Answer:
Because basically, you are multiplying by 1
Step-by-step explanation:
Let me explain this with an example. Rationalize the following expression:
[tex]\frac{5}{\sqrt{7} }[/tex]
In order to rationalize the denominator, the numerator and denominator of the fraction must be multiplied by the root of the denominator. So, what happen if you do that? Well first of all you aren't altering the expression because:
[tex]\frac{\sqrt{7} }{\sqrt{7} } =1[/tex]
Right? Because a certain quantity divided by itself is always equal to 1. So basically you are doing this because you want to rewrite the expression without altering its original value, it is the same when you do this:
[tex]9=3^2=3+3+3=\sqrt{81}[/tex]
Therefore, the only thing you do when you rationalize is remove radicals from the denominator of a fraction. Take a look:
[tex]\frac{5}{\sqrt{7} } *\frac{\sqrt{7} }{\sqrt{7} } =\frac{5*\sqrt{7} }{\sqrt{7}*\sqrt{7} } =\frac{5*\sqrt{7}}{(\sqrt{7} )^2} =\frac{5*\sqrt{7} }{7}[/tex]
You can check this new expression is equal to the original using a calculator:
[tex]\frac{5}{\sqrt{7} } \approx1.8898\\\\\frac{5*\sqrt{7} }{7} \approx1.8898[/tex]
In mathematics, the distance between one point (a) and another point (b), each with coordinates (x,y), can be computed by taking the differences of their x coordinates and their y coordinates and then squaring those differences. the squares are added and the square root of the resulting sum is taken and... voila! the distance. given two variables, p1 and p2 that are of type point -- a structured type with two fields, x and y, both of type double-- write an expression whose value is the distance between the two points represented by p1 and p
The distance between two points can be found using the formula sqrt((x2 - x1)^2 + (y2 - y1)^2).
Explanation:The distance between two points can be found using the formula sqrt((x2 - x1)^2 + (y2 - y1)^2). To find the distance between the two points represented by p1 and p2, we substitute the x and y coordinates of p1 and p2 into the formula:
distance = sqrt((p2.x - p1.x)^2 + (p2.y - p1.y)^2).
Evaluate the integral. (use c for the constant of integration.) sin^2(πx) cos^5(πx) dx
On Saturday, a local hamburger shop sold a combined total of 273 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday?
Final answer:
To determine the number of hamburgers sold on Saturday, we used the given total of 273 burgers and the relationship that cheeseburgers were twice as numerous as hamburgers. By setting up an equation and solving for the number of hamburgers, we found that 91 hamburgers were sold.
Explanation:
The question asks us to determine how many hamburgers were sold on Saturday given that the total number of hamburgers and cheeseburgers sold was 273, and the number of cheeseburgers was two times the number of hamburgers. Let's denote the number of hamburgers as H and the number of cheeseburgers as C. The problem states that C = 2H. The total number of burgers sold was H + C = 273. Substituting C with 2H, we get H + 2H = 273.
Solving for H, we combine like terms to get 3H = 273, and then we divide both sides by 3 to find H = 273 / 3. Therefore, H = 91. So, 91 hamburgers were sold on Saturday.
Felicia invested money at an interest rate of 4%. After six months, she had earned $90.00 interest. How much money did Felicia invest?
Answer:
the answer is 4500 i got it right
Step-by-step explanation:
Consider a game in which player 1 moves first. the set of actions available to player 1 is a1={a,b,c}. after observing the choice of player 1, player 2 moves. the set of actions available to player 2 is a2={a,b,c,d}. at how many information sets does player 2 move?
Nate rides his bike to school every day. From his home he rides 2.5 miles north, and then six miles west. If a straight line is drawn from Nate's house to the school, find the distance between these two locations.
use Pythagorean Theorem
2.5^2 + 6^2 = x^2
6.25 +36 = 42.25
x= sqrt(42.25) = 6.5 miles
Find the half-life of an element which decays by 3.411% each day. Hint: use y = ab^t.
This is about half life of elements with exponential decay.
Half life = 20 years
We are given a decay rate of 3.411% per day.We are given;
y = ab^(t)
Where;
t is the half life
y = a/2 is the amount of substance remaining after decay
a is amount of substance initially
b = 100% - 3.411% = 96.589% = 0.96589
Thus;a/2 = a(0.96589)^(t)
a will cancel out to give;
0.5 = 0.96589^(t)
ln (0.5) = t(ln 0.96589)
t = ln(0.5)/ln(0.96589)
t = 19.968 days
This is approximately 20 days.
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Hours worked: 40 Rate: $3.85 Wages: ?
Answer: $154.00
Step-by-step explanation:
I am assuming you are looking for how much the person made.
Multiply 40 hours times $3.85
$154.00
Timothy explains to his brother that the model y=4mt has a constant of variation of 4 and is an example of _____ variation.
Answer:
Joint variation.
Step-by-step explanation:
There are four types of variation,
Direct variation : When a variable varies directly as another variable,
Example : y varies directly with x ⇒ y = kx,
Where, k is the constant of variation,
Inverse variation : When a variable varies inversely as another variable,
Example : y varies inversely with x ⇒ [tex]y=k\frac{1}{x}[/tex]
Joint variation : When a variable varies directly with two or more than two variables,
Example : y varies directly with both x and z ⇒ y = kxz
Combined variation : When a variable varies both directly and indirectly as another variables,
Example : y varies directly with x and inversely with z ⇒ [tex]y=k\frac{x}{z}[/tex]
Now, here the given expression,
y = 4mt,
Where, y, m and t are variables and 4 is the constant of variation,
⇒ y varies directly as both m and t,
⇒ y = 4mt is an example of joint variation.
in the final event of a track meet, 6 runners run a 100 meter dash. A) How many possible arrangements are there for the medal winners (gold, silver and bronze)? B) state whether it is a combination or permutation
Answer:
120 possible arrangements.
It is a permutation
Step-by-step explanation:
Imagine that you are going to give the gold medal to any of the 6 runners. There would be 6 possibilities; now, imagine that you are going to give the gold and the silver medals random in the same way: you could give the gold medal to a person and you would have 5 possibilities to give the silver medal (you can't give both medals to the same person). So, note that for each possibility to give the gold medal there would be 5 possibilities to give the silver one.
Analogously, if you give the three medals random and supposing that you have already given the gold one, for each possibility to give the silver medal you would have 4 possibilities to give the bronze one. That is the reason for the calculation to be a multiplication:
N= Total number possibilities:
[tex]N=6*5*4=120[/tex]
This also can be seen as a permutation. A permutation is a reorganization of elements where the order matters. In this case, it is not just relevant who are the winners (who receive the medal), but their order. A combination just helps us to make groups without taking in mind the order, but the permutation does consider that.
The permutation can be learnt by the formula:
[tex]N=\frac{p!}{(p-n)!}[/tex]
where p is the total ef elements and n is the amount of elements of each subgroup that I want to built. In this case, our population 'p'=6, and we want to organize them in groups of 3 (n=3) where it is important for us the order:
[tex]N=\frac{6!}{(6-3)!}=6*5*4=120[/tex]
last year, Carmen opened an investment account with $7400. At the end of the year, the amount in the account had decrease buy 26.5%. How much is this decrease in dollars? How much money was in her account at the end of the year?
The decrease in Carmen's account was $1961, which is 26.5% of her original investment of $7400. Hence, by subtracting this decrease from the original investment, we find that Carmen had $5439 left at the end of the year.
Explanation:The decrease in Carmen's account over the year is 26.5% of the original investment of $7400. In mathematical terms, we can calculate this value by multiplying the original investment by the percentage decrease, using the formula: Decrease = Original Amount * Percentage Decrease.
In Carmen's case, this would be $7400 * 0.265 (converted from 26.5%). Upon calculating, we find that the decrease is $1961.
Now, to find how much money Carmen had at the end of the year, we subtract this decrease from the original amount invested. Again, using the formula: Final Amount = Original Amount - Decrease, we plug in the numbers to get $7400 - $1961, which equals $5439. This is how much Carmen had left in her account at the end of the year after the decrease.
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find the coefficient of x^6 in the binomial expression of (2x+3)^9
Which set of numbers does 8 2/3 belong to
The excluded values of a rational expression are 2 and 5. Which of the following could be this expression?
Answer: d on eng
Step-by-step explanation:
805 tens in standard form
The sun produces 3.9 x 10^33 ergs of radiant energy per second. how many ergs of radiant energy does the sun produce in 3.25 x 10^3 seconds?
Answer:
1.2675 x 10^37
Step-by-step explanation:
you would have to first multiply 3.9 x 3.25 =12.675. It is not in scientific notation so you would have to change the decimal 1.2675 x 10^37
The ergs of radiant energy produced is: [tex]1.3* 10^{37}[/tex]
The rate of energy is given as:
[tex]Rate = 3.9 * 10^{33}\[/tex] radiant energy per second
The time is given as:
[tex]Time = 3.25 * 10^3[/tex] seconds
The amount of radiant energy produced in this time is:
[tex]Energy = Rate * Time[/tex]
So, we have:
[tex]Energy = 3.9 * 10^{33} * 3.25 * 10^3[/tex]
Multiply
[tex]Energy = 12.675* 10^{36}[/tex]
Rewrite as:
[tex]Energy = 1.2675* 10^{37}[/tex]
Approximate
[tex]Energy = 1.3* 10^{37}[/tex]
Hence, the ergs of radiant energy produced is: [tex]1.3* 10^{37}[/tex]
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A radio telescope has a parabolic surface, as shown below.
If the telescope is 1 m deep and 12 m wide, how far is the focus from the vertex? (5 points)
For a parabolic dish, the focus is at a depth equal to one-fourth of the square of the width of the dish's aperture. Given the width as 12m, the focus of the radio telescope is 36m from the vertex.
Explanation:For a parabolic dish like a radio telescope, the focus (or focal point) is located at the depth equal to one-fourth of the square of the width (i.e., one-fourth of the square of the diameter) of the dish's aperture.
Given the width (diameter) of the dish is 12 meters, we square it to get 144. Quarter of this value is 36 m. So, the focus is 36 m from the vertex of the parabola represented by the dish's surface.
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A math teacher gave her class two tests. 27% of the class passed both tests and 51% of the class passed the first test. What percent of those who passed the first test also passed the second test?
There are 36 girls and 40 boys at a summer camp. The campers will be divided into equal-sized groups. Each group will have the same number of girls and the same number of boys. What is the greatest number of groups that can be formed?
How do you rename 5400
What is next number after 2 7 8 3 12 9
The slope of a vertical line is zero. true or false
The solution is False
The slope of a vertical line is given by the equation Slope m = undefined
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the line be represented as A
Now , the line A is a vertical line
So , the equation of line will be represented as y = mx + c
where m is the slope of the line
And , Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
The slope of a vertical line is infinite or undefined as it has no y-intercept
Because , the change is x is 0
So , the denominator of the fraction is 0 and division by 0 is undefined
Slope m = ( y₂ - y₁ ) / 0
Hence , the slope m is undefined
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The variable Z is directly proportional to X. When X is 5, Z has the value 55.
What is the value of Z when X = 12
What are the solutions to the quadratic equation (5y + 6)2 = 24? y = and y = y = and y = y = and y = y = and y =
For this case we have the following quadratic expression:
[tex] (5y + 6) ^ 2 = 24
[/tex]
From here, we must clear the value of y.
For this, we follow the following steps:
1) We clear the square term:
[tex] (5y + 6) =+/-\sqrt{24} [/tex]
[tex] (5y + 6) =+/-2\sqrt{6} [/tex]
2) Pass the value of 6 by subtracting:
[tex] 5y =-6+/-2\sqrt{6} [/tex]
3) Pass the value of 5 to divide:
[tex] y =\frac{-6+/-2\sqrt{6} }{5} [/tex]
Answer:
The solutions to the quadratic equation are:
[tex] y =\frac{-6+2\sqrt{6} }{5} [/tex]
[tex] y =\frac{-6-2\sqrt{6} }{5} [/tex]
subtract one- fifth from seven times w
Without using a trigonometric ratio, find the distance from the ship to the buoy, B. Round the distance to the nearest tenth of a mile.
The three vertices drawn on a complex plane at represented by 0+0i, 4+0i, and 0+3i. What is the length of the hypotenuse
Henry recorded the number of miles he biked each day for a week. His miles were 25, 40, 35, 25, 40, 60, and 75. Enter the data into the statistics calculator. What is the standard deviation of the miles Henry biked to the nearest tenth?
The standard deviation of the miles Henry biked to the nearest tenth is 17.1. The standard deviation is calculated following the steps below.
Calculation of standard deviationFirst calculate the mean of the numbers that where given which is = 25 + 40 + 35 + 25 + 40 + 60+ 75/7
= 300/7
= 42.9
Then for each number, subtract the Mean and square the result.
(25 - 42.9)² = −17.9² = 320.41
(40-42.9)² = -2.9²= 8.42
(35-42.9)² = -7.9² = 62.41
(25-42.9)² = −17.9² = 320.41
(40-42.9)² = -2.9²= 8.42
(60-42.9)² = 17.1²= 292.41
(75-42.9)² = 32.1²= 1030.41
Then work out the mean of those squared differences. That is,
320.41+ 8.42+62.41+320.41+8.42+292.41+1030.41/7
= 2042.89/7
= 291.8
Take the square root of 291.8 which is,
√291.8 = 17.08215443
= 17.1 to the nearest tenth.
Therefore, the standard deviation of the miles Henry biked to the nearest tenth is = 17.1
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Answer:
17.1
Step-by-step explanation:
got it right
Which expression is equivalent to 3(8 + 7)? 24 + 7 24 + 21 11 + 10 11 + 7
Balcony and orchestra tickets were sold for a Friday night concert last week. The balcony and orchestra tickets sold for $35 and $45, respectively. If 90 tickets were sold, and the total revenue was $3550 for the night, find the number of balcony and orchestra tickets sold.