To solve for the positive number when the sum of 5 and three times the number is subtracted from the square of the number to yield zero, set up and solve the quadratic equation x^2 - 3x - 5 = 0 using the quadratic formula.
Explanation:The student has asked for help in finding a positive number when the sum of 5 and three times the number is subtracted from the square of the number, and the result is 0. This involves setting up a quadratic equation and solving for the number.
Let's denote this positive number as 'x'. According to the problem statement, the equation can be written as:
x2 - (5 + 3x) = 0.
We can then expand and simplify this equation:
x2 - 5 - 3x = 0
And, rearrange it into standard quadratic form:
x2 - 3x - 5 = 0
Next, we can either factorize this equation, if possible, or use the quadratic formula to find the value of 'x' that satisfies the equation. Since this equation does not factor neatly, we use the quadratic formula:
x = ∛2 - 4ac) / 2a
In this case, a = 1, b = -3, and c = -5. Plugging these into the quadratic formula, we find the two possible solutions for x. Only the positive solution is relevant since the problem states that the number is positive.
Choose the equation of a line in standard form that satisfies the given conditions. perpendicular to 4x + y = 8 through (4, 3) A. x − 4y = −8 B. x + 4y = 16 C. 4x − y = 11 D. 4x + y = 19
Express Express 0.45 as a percent
To change 0.45 to a percent, we can move the decimal point 2 places to the right and add the percent sign.
If we move the decimal 2 places to the right, we will end up with 45 and then we will add the percent sign and it will become 45%
Therefore, 0.45 to a percent is 45%
If f(x) = 2x - 8 and g(x) = square root of x - 5, what is (f ^ g)(30).
The output of the function (f ^ g)(30) in this context refers to first calculating the output of the g function given x = 30, then substituting this output into the f function. With g(30) = sqrt(x - 5) and f(x) = 2x - 8, we find that (f ^ g)(30) = 2.
Explanation:To find (f ^ g)(30), we first need to find the output of the g function when x = 30 and then substitute this output into the f function. This is also known as the composition of functions.
First, let's find the output of the g function when x = 30. Given that g(x) = sqrt(x - 5), for x = 30, g(30) = sqrt(30 - 5) = sqrt(25) = 5.
Next, we substitute this output into the f function. Given that f(x) = 2x - 8, when x = 5, f(5) = 2(5) - 8 = 10 - 8 = 2.
Therefore, (f ^ g)(30) = 2.
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To find the value of [tex](f ^ g)(30)[/tex], substitute 30 into both f(x) and g(x) to find f(30) and g(30). Then substitute g(30) into f(x) to find the final value.
Explanation:In this mathematics question, you're asked to find the value of [tex](f ^ g)(30)[/tex]where [tex]f(x) = 2x - 8[/tex]and g(x) = square root of x - 5. To calculate (f ^ g)(x), we first need to find the value x in both functions f and g. So, let's find f(30) and g(30) first.
Firstly, substitute x = 30 into f(x). So, [tex]f(30) = 2*30 - 8 = 52[/tex]. Now, substitute x = 30 into g(x). So, g(30) = square root of (30 - 5) = square root of 25 = 5.
Now, f ^ g(30) means we substitute the output of g(30) = 5 into f(x) which gives us [tex]f(5) = 2*5 - 8 = 2.[/tex]
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A right cylinder has a radius r of 19.4 cm and a height h of 48.3 cm. what is the volume of the cylinder in m3
If the mean waiting time for the next arrival is 12 minutes, what is the median waiting time? 8.3 minutes 12 minutes 9.1 minutes 7.2 minutes
Since the mean waiting time is 12 minutes, the median waiting time would also be 12 minutes.
Here's how we can find the median waiting time:
Since the mean waiting time is 12 minutes, it means that if you were to add up all the waiting times of different arrivals and divide by the number of arrivals, you would get 12 minutes.
Now, for the median waiting time, we're looking for the value that falls exactly in the middle of all the waiting times.
If the distribution is symmetrical, which is often the case with waiting times, the mean and median will be the same.
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what is the solution to...
[tex]|x| +19 \leqslant 3[/tex]
(4k^4 + 2 - 3k) + (5k^4 + k - 8)
If f(3) = 11 and f '(x) ≥ 2 for 3 ≤ x ≤ 8, how small can f(8) possibly be?
Given the derivative f '(x) ≥ 2, the function f(x) increases by at least 2 units for every increase in 'x' from 3 to 8. Therefore, the smallest possible value of f(8) is reached when the increase is exactly 2 per 'x', giving us a result of 21.
Explanation:
The question is about calculus, specifically related to the concept of derivatives and their role in function interval analysis. Given the information that f(3) = 11 and f '(x) ≥ 2 for 3 ≤ x ≤ 8, we are asked to find the smallest possible value of f(8).
The derivative, f '(x), represents the rate of change of the function f(x). It is mentioned that f '(x) ≥ 2, which means that the function f(x) is increasing at a rate not less than 2 units per increase in 'x' from 3 to 8.
This suggests that the smallest possible value of f(8) could be achieved by assuming that f(x) increases exactly by 2 units for every increase in 'x'. So, from x = 3 to x = 8 is a change of 5 units in 'x'. Multiply this by the rate of change 2 to obtain the total change in f(x), which is 5 * 2 = 10. Added to the initial value f(3) = 11, we get the smallest possible value for f(8) is 11 + 10 = 21.
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solve for x z= 19+2 (x+y)
A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of .) 452.16 cm3 840.54 cm3 1,055.04 cm3 1,456.96 cm3 NextReset
The polar coordinates of a point are given. find the rectangular coordinates of this point.(5, 3pi/4
Tangerine trees yield 50 pounds of fruit per acre and grapefruit trees yield 75 pounds of fruit per acre. John's orchard produced a maximum total of 1,500 pounds of fruit. Is it possible for John to have 25 acres of tangerine trees and 15 acres of grapefruit trees?
No, because 50(25) + 75(15) ≠ 1500 No, because (50 + 75)(20 + 15) ≠ 1500 Yes, because 50(25) + 75(15) ≥ 1500 Yes, because 50 + 75 + 25 + 15 ≤ 1500
Two people started from the same point at the same time and traveled in opposite directions. One traveled at 60 mph and the other at 50 mph. How long will it take before the two people are 440 miles apart?
HELP FAST ILL MAKE BRAINIEST Mr. McClellan compared the weights (in pounds) of pairs of elk antlers dropped at Mount St Helens NVM and Rocky Mountain NP. He tabulated them in the following colored data tables. Purple: Weight of elk antler pairs at Mount St Helens NVM: {34, 34, 30, 30, 30, 28, 28, 26} Red: Weight of elk antler pairs at Rocky Mountain NP: {40, 38, 36, 36, 36, 36, 34, 32}
(a) Create a line plot for each data set.
(b) Calculate the following for each set of data: a. Purple Mean: b. Red Mean: c. Purple Median: d. Red Median: e. Purple MAD: f. Red MAD:
(c) Calculate the means-to-MAD ratio for the two areas of collection. (
d) What inference can be made about the areas in regard to weight of dropped elk antlers? Explain. Answer:
MAD tells us how far, on average, all values are from the middle. So, in the example weight of elk antler pairs at Mount St Helens NVM are, on average, 2 away from the middle. On the other hand, weight of elk antler pairs at Rocky Mountain NP are, on average, 1.5 away from the middle. So, we can assure that elk antler pairs at Rocky Mountain NP weighs more than elk antler pairs at Mount St Helens NVM.
The numbers of rooms for 15 homes recently sold were: 8, 8, 8, 5, 9, 8, 7, 6, 6, 7, 7, 7, 7, 9, 9. what is the sample standard deviation?
Hence, the sample standard deviation is:
1.1832
Step-by-step explanation:The data is given by:
8, 8, 8, 5, 9, 8, 7, 6, 6, 7, 7, 7, 7, 9, 9.
The mean of these data points is given by:
[tex]Mean(x')=\dfrac{8+8+8+5+9+8+7+6+6+7+7+7+7+9+9}{15}\\\\i.e.\\\\Mean(x')=\dfrac{111}{15}\\\\i.e.\\\\Mean(x')=7.4[/tex]
Now,
x x-x' (x-x')²
8 8-7.4=0.6 0.36
8 8-7.4=0.6 0.36
8 8-7.4=0.6 0.36
5 5-7.4= -2.4 5.76
9 9-7.4=1.6 2.56
8 8-7.4=0.6 0.36
7 7-7.4= -0.4 0.16
6 6-7.4= -1.4 1.96
6 6-7.4= -1.4 1.96
7 7-7.4= -0.4 0.16
7 7-7.4= -0.4 0.16
7 7-7.4= -0.4 0.16
7 7-7.4= -0.4 0.16
9 9-7.4=1.6 2.56
9 9-7.4=1.6 2.56
∑(x-x')²=19.69
Now the variance of the sample population is given by:
[tex]Variance=\dfrac{\sum (x-x')^2}{n-1}[/tex]
where n is the number of data points.
Here n= 15
Hence, n-1=14
Hence, we get:
[tex]Variance=\dfrac{19.6}{14}\\\\i.e.\\\\Variance=1.4[/tex]
We know that the standard deviation is the square root of the variance.
i.e.
[tex]Standard\ deviation=\sqrt{1.4}\\\\i.e.\\\\Standard\ deviation=1.1832[/tex]
in the sport competition France won more gold medals than Italy, who won more good medals than Korea. if the total number of gold medals won by the consecutive intergers whose sum is 36. find the number of gold medals won by each.
The price of a pair of jeans at a store increased by 25% to $40. Find the price of the pair of jeans before the increase
What is the formula for margin of error?
Answer:
ME=z×s/√n
Step-by-step explanation:
Basically the answer is C.
A cylindrical can of cat food has a diameter of 3.5 inches and a height of 1.25 inches. A second brand of cat food is packaged in a cylindrical can with a radius of 1.2 inches and a height of 1.25 inches. What is the difference between the volumes of the cans? Show your work.
List all integers between -15 and 25 that are congruent to 3 mod (11)
For his phone service, Jason pays a monthly fee of $19, and he pays an additional $0.05 per minute of use. The least he has been charged in a month is $75.10.
What are the possible numbers of minutes he has used his phone in a month?
Use m for the number of minutes, and solve your inequality for m.
helppppppppppppp stat
This is a priority! The equation of a parabola is 1/16 (y+3)^=x+4 what are the coordinates of the focus?
hey can you please help me posted picture of question
A collection of dimes and quarters worth $9.25. There are 46 coins in all. Find how many of each there are. How many dimes are there?
Fill in the blank 300mm =___m
Final answer:
To convert 300mm to meters, divide 300 by 1000 because there are 1000 mm in a meter, resulting in 0.3 meters.
Explanation:
To convert millimeters to meters, we use the conversion factor that 1000 mm equals 1 m. Therefore, to convert 300mm to meters, you divide 300 mm by 1000 because there are 1000 mm in a single meter. So, let's carry out the calculation:
300 mm ÷ 1000 = 0.3 m
Thus, 300 mm is equal to 0.3 meters.
The base of an isosceles triangle is 7 cm longer than the legs. Find the legs if the perimeter of the triangle is 43 cm.
Which of these points does not change its location when it is reflected across the y-axis? (2, 0) (0, 6) (3, 3) (–5, 5)
Answer:
-5,5
Step-by-step explanation:
Show that the vector field f(x,y,z)=⟨ycos(−2x),−2xsin(y),0⟩f(x,y,z)=⟨ycos(−2x),−2xsin(y),0⟩ is not a gradient vector field by computing its curl. how does this show what you intended?
Final answer:
To show that the given vector field is not a gradient vector field, we need to compute its curl. The curl is computed by taking the cross product of the gradient operator with the vector field. By computing the partial derivatives and simplifying, we find that the curl of the given vector field is not zero, which indicates that it is not a gradient vector field.
Explanation:
To show that the vector field is not a gradient vector field, we need to compute its curl. The given vector field is f(x,y,z) = <ycos(-2x), -2xsin(y), 0>. The curl of a vector field is defined as the cross product of the gradient operator with the vector field. In this case, the curl of f(x,y,z) is computed as:
curl(f) = ∇ × f = (∂f_z/∂y - ∂f_y/∂z)i + (∂f_x/∂z - ∂f_z/∂x)j + (∂f_y/∂x - ∂f_x/∂y)k
By computing the partial derivatives and simplifying, we find that:
∂f_z/∂y = 0∂f_y/∂z = 0∂f_x/∂z = 0∂f_z/∂x = 2ycos(-2x)∂f_y/∂x = 0∂f_x/∂y = -2sin(y)Substituting these values back into the curl formula, we get:
curl(f) = (2ycos(-2x))i + 0j + (-2sin(y))k
This shows that the curl of the vector field is not zero, which means the vector field is not a gradient vector field.
all real cube roots of 27