If f(x)=2x^2sqrt(x-2), complete the following statement f(6)
The value of f(6) in the function [tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex] is 82
How to determine the function value?The function is given as:
[tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex]
Substitute 6 for x
[tex]f(6)=2 * 6^2 + 5\sqrt{6-2}[/tex]
Evaluate the difference
[tex]f(6)=2 * 6^2 + 5\sqrt{4}[/tex]
Evaluate the exponents
f(6)=2 * 36 + 5 * 2
Evaluate the sum of products
f(6) = 82
Hence, the value of f(6) in the function [tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex] is 82
Read more about functions at:
https://brainly.com/question/13136492
#SPJ2
If f(x) = 2x2 + 1 and g(x) = x2 – 7, find (f – g)(x).
Answer: The required value is
[tex](f-g)(x)=x^2+8.[/tex]
Step-by-step explanation: The given functions are:
[tex]f(x)=2x^2+1,\\\\g(x)=x^2-7.[/tex]
We are given to find the value of [tex](f-g)(x).[/tex]
We know that, if s(x) and t(x) are any two functions of a variable x, then we have
[tex](s-t)(x)=s(x)-t(x).[/tex]
Therefore, we have
[tex](f-g)(x)\\\\=f(x)-g(x)\\\\=(2x^2+1)-(x^2-7)\\\\=2x^2+1-x^2+7\\\\=x^2+8.[/tex]
Thus, the required value is
[tex](f-g)(x)=x^2+8.[/tex]
Answer:
3x2 - 6 its the answer
Susan invests
2
times as much money at
8%
as she does at
4%
. If her total interest after
1
year is
$800
, how much does she have invested at each rate?
Final answer:
To find how much Susan has invested at each rate when she invests 2 times as much money at 8% as she does at 4%, create and solve an equation based on the total interest earned.
Explanation:
Susan has invested $x at 4% interest rate and $2x at 8% interest rate.
Given that the total interest after 1 year is $800, we can create the equation: $x(0.04) + $2x(0.08) = $800.
Solving the equation, we find that Susan has $3,000 invested at 4% and $6,000 invested at 8%.
Consider a line l with positive x- and y- intercepts. Suppose l makes an angle of with the positive x- axis. What is the slope of l in terms of theta?
What is the integral of 1/x?
Final answer:
The integral of 1/x is the natural logarithm of the absolute value of x, plus an integration constant C. This expression is central to calculations in many areas of science and mathematics.
Explanation:
The integral of 1/x is known as the natural logarithm of the absolute value of x, plus a constant of integration, commonly referred to as C. In mathematical terms, this is expressed as:
[tex]\( \int \frac{1}{x} dx = \ln(|x|) + C \)[/tex]
The natural logarithm arises due to the fundamental properties of the integral, and it's significant as it appears frequently across various fields of science and mathematics. While the basic form of integration of 1/x involves the natural logarithm, in applied examples like the cases mentioned above, where one works with additional functions or domain restrictions, the integral may lead to more complex expressions or even vanish under certain symmetry conditions.
What is the next number in the series? 71 62 53 44 35 ?
The scores on a final exam were approximately normally distributed with a mean of 82 and a standard deviation of 11. If 85 students took the exam, and above a 60 is a passing grade, how many students failed the exam?
In this case, we can use the z statistic to find for the proportion of students who failed the exam. The formula for z score is given as:
t = (x – u) / s
where,
x = the sample score = 60
u = sample score mean = 82
s = standard deviation = 11
Substituting all given values into the equation:
t = (60 – 82) / 11
t = - 2
Based from the standard proportion distribution tables for z, this corresponds to:
P = 0.0228
This means that 2.28% of the students failed the exam or equivalent to:
failed students = (0.0228) * 85 = 1.938
approximately 2 students failed the exam
Answer:
2 students failed the exam
Step-by-step explanation:
Each canvas bag will hold exactly 5 pounds of kings tomatoes. How many bags will be necessary to hold 5 kg worth of these same tomatoes? (1 kg = 2.25 pounds)
1 kg = 2.25 pounds
5*2.25 = 11.25 pounds
11.25/5 = 2.25 bags
so you would need 3 bags
In a certain grocery store, strawberries cost $5.92 per pound ( 5.92 dollars/lb ). what is the cost per ounce?
Answer:
$,37 dollars per ounce of strawberries
Step-by-step explanation:
We have to remember that there are 16 ounces in one pound so in order to calculate the cost per ounce, we just divide the cost per pound by 16:
5,92/16= ,37
SO the cost per ounce of strawberries when the price per pound is 5,92 dollars will be 0,37 dollars.
The upper leg length of 20 to 29-year-old males is normally distributed with a mean length of 43.7 cm and a standard deviation of 4.2 cm. a random sample of 9 males who are 20 to 29 years old is obtained. what it the probability that the mean leg length is less than 20 cm? 0.1894 pratically 0 0.2134 0.7898
The probability that the mean leg length is less than 20 cm is practically 0.
Explanation:To find the probability that the mean leg length is less than 20 cm, we can use the sampling distribution of the sample mean. The sampling distribution of the sample mean is approximately normal when the sample size is large enough. In this case, the sample size is 9, which is smaller than 30 but still reasonably large, so we can assume that the sampling distribution of the sample mean follows a normal distribution.
We can standardize the sample mean using the formula:
z = (x - μ) / (σ / sqrt(n))
Where:
z: the z-scorex: the value of the sample meanμ: the population meanσ: the population standard deviationn: the sample sizeSubstituting the given values:
z = (20 - 43.7) / (4.2 / sqrt(9))
z = -23.7 / (4.2 / 3)
z = -23.7 / 1.4
z ≈ -16.93
Looking up the z-score in a standard normal distribution table, we find that the probability of getting a z-score less than -16.93 is practically 0. Therefore, the probability that the mean leg length is less than 20 cm is practically 0.
What is the answer to this question?
Poisson suppose you have 5 cakes made ready to sell. what is the probability that you will sell out?
find the equation of a line containing the given point and slope (10,5); m=9/20
How do you solve this
PLEASE HELP!!!!!! The line of symmetry for the quadratic equation y = ax 2 - 8x - 3 is x = 2. What is the value of "a"?
A) -2
B) -1
C) 2
What is after 100,99,07,94,90
A medium sized apple weighs 130 grams. How many apples are there in 1 kilogram?
Answer:
7
Step-by-step explanation:
Calculator Reference A mountaineer climbed 1,000 feet at a rate of x feet per hour. He climbed an additional 5,000 feet at a different rate. This rate was 10 feet per hour less than twice the first rate. Which expression represents the number of hours the mountaineer climbed?
Answer: The expression that represents the number of hours the mountaineer climbed is given by
[tex]\dfrac{1000}{x}+\dfrac{2500}{x-5}[/tex]
Step-by-step explanation:
Since we have given that
Distance covered by mountaineer = 1000 feet
Speed at which he climbed = x feet per hour
Time taken by him would be
[tex]\dfrac{1000}{x}[/tex]
Additional distance covered by him = 5000 feet
Speed at which he climbed this time = 2x-10
So, Time taken is given by
[tex]\dfrac{5000}{2x-10}\\\\\\=\dfrac{5000}{2(x-5)}\\\\\\=\dfrac{2500}{x-5}[/tex]
Hence, the expression that represents the number of hours the mountaineer climbed is given by
[tex]\dfrac{1000}{x}+\dfrac{2500}{x-5}[/tex]
The leader of the group brought 8.03 ounces of trail mix. The hikers only ate 5.26 ounces of the trail mix. How much trail mix was left?
A square picture with a side length of 4 inches needs to be enlarged. The final area needs to be 81 square inches.
Which equation can be used to solve for x, the increase in side length of the square in inches?
x2 + 4x – 81 = 0
x2 + 4x – 65 = 0
x2 + 8x – 65 = 0
x2 + 8x – 81 = 0
Answer:
[tex]x^2+8x-65=0[/tex]
Step-by-step explanation:
Side length of square = 4 inches
Let x be the increase in length
So, New length = x+4
Area of square = [tex]Side^2[/tex]
Area of enlarged square = [tex](x+4)^2[/tex]
Using identity : [tex](a+b)^2=a^2+b^2+2ab[/tex]
Area of enlarged square = [tex]x^2+16+8x[/tex]
We are given that The final area needs to be 81 square inches.
So, [tex]x^2+16+8x=81[/tex]
[tex]x^2+16+8x-81=0[/tex]
[tex]x^2+8x-65=0[/tex]
So, Option C is true
Hence equation can be used to solve for x, the increase in side length of the square in inches is [tex]x^2+8x-65=0[/tex]
Convert 5.6 liters to milliliter
5,600 ml
560 ml
0.056 ml
0.0056
Convert the measurement as indicated.
26ft= _ yd _ ft
The value of y is inversely proportional to the value of x. When y=40, x=5. What is the value of y when x=8
Answer: 64
Step-by-step explanation:
i put it into math-way
53 ℃ below zero degrees
Please help quick !!
If the parent function f(x) = (2x − 3)3 is transformed to g(x) = (-2x + 3)3, which type of transformation occurs?
A motorboat takes 3 hours to travel 108 km going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
If p is a positive integer,then p(p+1)(p-1) is always divisible by?
I am not quite sure what the choices are, but the answer to that problem is:
If p is a positive integer, then p(p+1)(p-1) is always divisible by “an even number”.
The explanation to this is that whatever number you input to that equation, the answer will always be an even number. This is due to the expression p(p+1)(p-1) which always result in a even product.
For example if p=3, then (p+1)(p-1) becomes (4)(2) giving you a even number.
And if for example if p=2, then (p+1)(p-1) becomes (3)(1) which gives an odd product, but we still have to multiply this with p therefore 2*3 = 6 which is even product. The outcome is always even number.
Answer: From the choices, select the even number
Final answer:
If p is a positive integer, p(p+1)(p-1) is always divisible by 3.
Explanation:
If p is a positive integer, then p(p+1)(p-1) is always divisible by 3.
This can be proven by applying the property of divisibility by 3. According to this property, a number is divisible by 3 if and only if the sum of its digits is divisible by 3.
In the expression p(p+1)(p-1), the three terms p, (p+1), and (p-1) represent three consecutive numbers. Since the sum of the digits of any consecutive numbers is always divisible by 3, the expression is always divisible by 3.
Explain why we need more than one digit to express certain quantities
When Sharon began shopping this morning, she had $40.00. She purchased five paperback books and had lunch. The books were all the same price, and lunch cost $3.25. She now has $7.00 left over. What was the price of each of the books? A. $5.95 B. $6.60 C. $7.35 D. $8.75