The triangle theorems will be:
Side-Side-Side (SSS) Congruence Theorem:Side-Angle-Side (SAS) Congruence Theorem:Angle-Side-Angle (ASA) Congruence Theorem:Hypotenuse-Leg (HL) Congruence Theorem:Angle-Angle-Side (AAS) Congruence TheoremHow to explain the theoremSide-Side-Side (SSS) Congruence Theorem: If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
Side-Angle-Side (SAS) Congruence Theorem: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
Angle-Side-Angle (ASA) Congruence Theorem: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
Angle-Angle-Side (AAS) Congruence Theorem: If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.
Hypotenuse-Leg (HL) Congruence Theorem: If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the two triangles are congruent.
Learn more about theorem on
https://brainly.com/question/17335144
#SPJ1
According to these three facts, which statements are true? Circle D has center (2, 3) and radius 7. Circle F is a translation of circle D, 2 units right. Circle F is a dilation of circle D with a scale factor of 4. Select each correct answer. Responses Circle F and circle D are similar. Circle , F, and circle , D, are similar. The radius of circle F is 28. The radius of circle , F, is 28. The center of circle F is (0, 3). The center of circle , F, is , begin ordered pair 0 comma 3 end ordered pair,. Circle F and circle D are congruent. Circle , F, and circle , D, are congruent
Answer:
The answer to your problem is:
The radius of circle F is 28.
Circle F and circle D are similar.
Step-by-step explanation:
How to find the radius:
A = π × [tex]r^{2}[/tex]
But the radius of a circle from diameter. If you can recall the diameter d, the radius is r = d / 2.
By looking at our facts we can actually see ( if we use the comparing method ) that the circles, F & D are very much similar.
Thus the answer to your problem is:
The radius of circle F is 28.
Circle F and circle D are similar.
George says his bicycle has a mass of 15 grams. If he takes the front wheel off what could be the mass?
If George's bicycle has a mass of 15 grams, then it is highly unlikely that he has stated the correct mass, as 15 grams is an extremely low mass for a bicycle.
If George`s bicycle weighs 15 grams, what would be the resulting weight of it if he removes the front wheel?Determine if the givens mass of 15 grams is reasonable for a bicycle.A typical bicycle weighs anywhere from 7 to 15 kilograms. It is highly unlikely that a bicycle would weigh only 15 grams, as this is much lighter than the lightest bicycle ever made.
Therefore, it is reasonable to assume that George made a mistake and meant to say 15 kilograms instead of grams.
Calculate the mass of the bicycle without the front wheel.Assuming the mass of the bicycle is 15 kilograms, removing the front wheel will decrease the mass slightly, but not by a significant amount.
The front wheel typically accounts for around 1-2 kilograms of the total mass of the bicycle, so removing it would leave a mass of approximately 14 kilograms.
However, assuming he made a mistake and meant to say 15 kilograms, then the mass of the bicycle without the front wheel would be approximately 14 kilograms.
Learn more about mass
brainly.com/question/19694949
#SPJ11
data from the bureau of labor statistics reports that the typical manufacturing worker in wisconsin in 1997 earned a weekly salary of $424.20. suppose you wanted to see if this were true just in the far southeastern portion of the state. you obtain a sample of tax returns for manufacturing workers in racine and kenosha for the year 1997. your sample consists of 54 workers and has a mean weekly salary of $432.69 with a standard deviation of $33.90 at a 90% confidence level test the claim that manufacturing workers in racine and kenosha had the same salary as workers across the state. what will be your critical value?
The critical value for this hypothesis test is 1.676.
To test the claim that manufacturing workers in Racine and Kenosha had the same salary as workers across the state, we can conduct a hypothesis test with the following null and alternative hypotheses:
Null hypothesis: The mean weekly salary of manufacturing workers in Racine and Kenosha is equal to $424.20.Alternative hypothesis: The mean weekly salary of manufacturing workers in Racine and Kenosha is different from $424.20.We can use a t-test for the sample mean to test this hypothesis. At a 90% confidence level, we have a significance level of alpha = 0.10. Since this is a two-tailed test (we are testing for a difference in either direction), we will split the significance level evenly between the two tails, so alpha/2 = 0.05.
We need to calculate the critical value of the t-distribution with n-1 degrees of freedom, where n is the sample size. In this case, n = 54, so the degrees of freedom is 53. We can use a t-distribution table or a calculator to find the critical value. For a two-tailed test with alpha/2 = 0.05 and 53 degrees of freedom, the critical value is approximately 1.676.
Therefore, the critical value for this hypothesis test is 1.676.
Learn more about hypothesis test
https://brainly.com/question/30588452
#SPJ4
The value of lim a^x-x^a/x^x-a^a is
lim (1 - a^(1-a)) / (ln(a)) as x -> a This is the value of the given limit.
To find the value of the given limit, which can be represented as lim (a^x - x^a) / (x^x - a^a) as x approaches 'a', you can apply L'Hôpital's Rule, which states that if the limit of the ratio of the derivatives of two functions exists, then the limit of the original functions is equal to that limit.
First, differentiate the numerator and denominator with respect to x:
Numerator: d(a^x - x^a) / dx = a^x * ln(a) - a * x^(a-1)
Denominator: d(x^x - a^a) / dx = x^x * ln(x)
Now, we can find the limit of the ratio of the derivatives as x approaches 'a':
lim (a^x * ln(a) - a * x^(a-1)) / (x^x * ln(x)) as x -> a
After substituting 'a' for 'x' in the limit:
lim (a^a * ln(a) - a * a^(a-1)) / (a^a * ln(a)) as x -> a
Now, cancel out the common term a^a * ln(a):
lim (1 - a^(1-a)) / (ln(a)) as x -> a
To learn more about derivatives click here
brainly.com/question/25324584
#SPJ11
5u–u+3u=14
help! me please
Answer:
u = 2
Step-by-step explanation:
In the expression πr² + πrℓ, what
part of the expression is π?
a constant
a coefficient
a variable
a term
In the expression πr² + πrℓ, the part of the expression that is π is a constant.
A constant is a value that does not change in an expression, and in this case π represents a fixed value of approximately 3.14159. It is not a coefficient, which is a numerical factor that multiplies a variable, nor a variable or term, which represent varying quantities in an expression.
The monomial -3xy2z(-2x2yz) has degree of:
The degree of the monomial expression -3xy²z(-2x²yz) is derived to be equal to 8.
What is a monomialA monomial is a type of algebraic expression that consists of only one term. It is an expression in which the variables and their exponents are multiplied together, with no addition or subtraction involved. The degree of a monomial is the sum of the exponents of its variables.
Given the monomial:
-3xy²z(-2x²yz)
We can simplify it by multiplying the coefficients and adding the exponents of the variables:
-3(-2)x^(2+1) y^(2+1) z^(1+1)
= 6x³y³ z²
Therefore, the degree of the given monomial expression is: 3 + 3 + 2 = 8.
Read more about monomial here:https://brainly.com/question/4521414
#SPJ1
The roof of a building is in the shape of a hyperbola, y^2-x^2=38, where x and y are in meters. Determine the height of the outside. The distance between the center of the hyperbola and the walls is 3m.
a) -29. 1
b) 47. 3
c) 35. 2
d) 6. 9
The height of the outside is given as 17.44 meters
How to solveThe equation of hyperbola is :
[tex]y^2 - x^2 = 38[/tex]
=>[tex]y^2/38 - x^2/38 = 1[/tex]
(of the form [tex]y^2/a^2 - x^2/b^2 = 1[/tex] and transverse axis is y-axis.)
Here, [tex]a^2 = b^2 = 38[/tex]
[tex]c^2 = a^2 + b^2 = 38+38 = 76[/tex]
( a is the distance of vertices from the center and c is the distance of foci from the center.)
Distance between walls = 2 a = [tex]2*\sqrt(38) = 12.33[/tex] meters at the center
and = [tex]2c = 2*\sqrt(76) = 17.44[/tex] meters at the end when the line joining
end points of the wall on one side is through the foci point.
Read more about Distance here:
https://brainly.com/question/2854969
#SPJ1
3x − 15y = 11 in slope intercept form
Answer:
To convert the equation 3x - 15y = 11 into slope-intercept form, we need to solve for y.
First, we'll subtract 3x from both sides:
-15y = -3x + 11
Next, we'll divide both sides by -15:
y = (3/15)x - (11/15)
Simplifying the fraction:
y = (1/5)x - (11/15)
This is the slope-intercept form, where the slope is 1/5 and the y-intercept is -11/15.
in right triangle abc, mzb + m2c. let sinb = r and cos b = s. what is sinc-cosc?
The value of the trigonometric expression sin c - cos c is: s - r
How to solve Trigonometric Ratios?The three most common trigonometric ratios are:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
We are given that:
sinb = r and cos b = s
Thus, from the diagram attached, we can see that:
sin B = rh/h = r
cos B = sh/h = s
Thus, using trigonometric ratios, we can equally say that:
cos C = rh/h = r
sin C = sh/h = s
Thus:
sin c - cos c = s - r
Read more about Trigonometric Ratios at: https://brainly.com/question/13276558
#SPJ4
Evaluate the integral (Use symbolic notation and fractions where needed. Use C for the arbitrary constant. Absorb into C as much as possible.) 3 V x2 +8514 dx = Shule) 32+2). 10/8+) 6 + + *(x+8) corec
To evaluate the integral ∫(3/(√(x² + 8514))) dx, we can use the substitution u = x² + 8514 and du/dx = 2x, which gives us:
∫(3/(√(x² + 8514))) dx = (3/2)∫(1/√u) du
= (3/2) * 2√u + C
= 3√(x² + 8514) + C
Note that we absorbed the arbitrary constant into C as much as possible.
It seems that your question contains some typos and unclear expressions. However, I can help you evaluate a definite integral that includes fractions and an arbitrary constant.
Consider the integral:
∫(3√(x² + 8514) dx)
To solve this integral, let's perform a substitution:
u = x² + 8514
du = 2x dx
Now, we can rewrite the integral as:
(3/2) ∫(√u du)
Now, we can integrate:
(3/2) ∫(u^(1/2) du) = (3/2) * (2/3) * u^(3/2) + C
Now, substitute u back with the original expression:
(3/2) * (2/3) * (x² + 8514)^(3/2) + C = (x² + 8514)^(3/2) + C
So, the evaluated integral is:
(x^2 + 8514)^(3/2) + C
Where C is the arbitrary constant.
Visit here to learn more about integral brainly.com/question/18125359
#SPJ11
Let (x) = -x^4 -8x^3 +6x - 2. Find the open intervals on which is concave up (down). Then determine the x-coordinates of all inflection points a f.
The x-coordinates of all inflection points a f of the function[tex]f(x) = -x^4 - 8x^3 + 6x - 2[/tex]are (-4, f(-4)) and (0, f(0)).
To find the intervals of concavity and the inflection points of the function[tex]f(x) = -x^4 - 8x^3 + 6x - 2,[/tex] we need to find the second derivative and analyze its sign.
First, we find the first derivative:
[tex]f'(x) = -4x^3 - 24x^2 + 6[/tex]
Then, we find the second derivative:
[tex]f''(x) = -12x^2 - 48x[/tex]
To determine the intervals of concavity, we need to find where f''(x) is positive or negative.
[tex]f''(x) = -12x^2 - 48x = -12x(x + 4)[/tex]
f''(x) is negative for x < -4 and x > 0, and positive for -4 < x < 0.
Therefore, the function f(x) is concave down on the intervals (-∞, -4) and (0, ∞), and concave up on the interval (-4, 0).
To find the inflection points, we need to find where the concavity changes. This occurs at x = -4 and x = 0.
At x = -4, the function changes from concave down to concave up. Therefore, (-4, f(-4)) is an inflection point.
At x = 0, the function changes from concave up to concave down. Therefore, (0, f(0)) is also an inflection point.
Thus, the inflection points of f(x) are (-4, f(-4)) and (0, f(0)).
To know more about intervals of concavity refer here:
https://brainly.com/question/29121586
#SPJ11
Paula works part time ABC Nursery. She makes $5 per hour watering plants and $10 per hour sweeping the nursery. Paula is a full-time student so she cannot work more than 12 hours each week but must make at least $60 per week.
Part A: Write the system of inequalities that models this scenario.
Part B: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set.
The system of inequalities that models this scenario are:
x + y ≤ 12 (she is unable to work more than 12 hours each week)5x + 10y ≥ 60 (she need to make at least $60 per week)What is the system of inequalities?Part A: Based on the question, we take x be the number of hours that Paula spends watering plants and also we take y be the number of hours she spends sweeping the nursery. Hence system of inequalities equation will be:
x + y ≤ 12 (she is unable to work more than 12 hours each week)
5x + 10y ≥ 60 (she need to make about $60 per week)
Learn more about system of inequalities from
https://brainly.com/question/9290436
#SPJ1
The value in dollars, v (x), of a certain truck after x years is represented
The truck would have lost 36% of its initial value.
How we get the initial value?The value in dollars, v(x), of a certain truck after x years can be represented by a mathematical function or equation. In the absence of a specific equation, it is difficult to provide an answer.
However, I can provide an example of a possible equation that represents the depreciation of a truck's value over time.
Let's assume that the truck loses 20% of its value every year. If the initial value of the truck is V0 dollars, then the value of the truck after x years, Vx, can be represented by the following equation:
Vx = [tex]V0(0.8)^x[/tex]
In this equation, the term [tex](0.8)^x[/tex] represents the percentage of the truck's value that remains after x years of depreciation. For example, after one year, the truck's value would be V1 = [tex]V0(0.8)^1[/tex] = 0.8V0,
which means that the truck would have lost 20% of its initial value. After two years, the truck's value would be V2 = V0[tex](0.8)^2[/tex]= 0.64V0,
Learn more about Initial value
brainly.com/question/8223651
#SPJ11
What is the area of a regular hexagon with side length of 12. 7 and apothem length of 11?
PLEASE HELP!
The area of the regular hexagon with a side length of 12.7 and apothem length of 11 is approximately 416.61 square units.
To find the area of a regular hexagon, you can use the formula , where A is the [tex]A =\frac{3\sqrt{3} }{2} (s^{2} )[/tex]area, s is the length of one side, and √3 is the square root of 3.
However, since the apothem length is given, you can also use the formula , where ap is the apothem length and p is the perimeter of the hexagon.
First, let's find the perimeter of the hexagon. Since a hexagon has six sides, the perimeter will be 6 x 12.7 = 76.2.
Next, we can use the apothem length of 11 and the side length of 12.7 to find the length of the radius of the circle inscribed in the hexagon. This is because the apothem is the distance from the center of the hexagon to the midpoint of any side, and the radius is the distance from the center to any vertex.
Using the Pythagorean theorem, we can find the radius:
[tex]r^2 = ap^2 + (\frac{s}{2} )^{2}[/tex]
[tex]r^2 = 11^2 + (\frac{12.2}{7} )^{2}[/tex]
[tex]r^2 = 121 + 40.1225[/tex]
[tex]r^2 = 161.1225[/tex]
[tex]r = \sqrt{161.1225}[/tex]
[tex]r = 12.69[/tex]
Now that we know the radius, we can use the formula for the area of a regular polygon in terms of the radius: A = (1/2) x r x ap x n, where n is the number of sides (which is 6 for a hexagon).
Plugging in the values we have:
[tex]A = \frac{1}{2} (12.69)(11)(6)[/tex]
[tex]A = 416.61[/tex]
Therefore, the area of the regular hexagon with a side length of 12.7 and apothem length of 11 is approximately 416.61 square units.
To know more about "Hexagon" refer here:
https://brainly.com/question/29762907#
#SPJ11
two cards are drawn from a deck of 52 playing cards. the first card is not replace before the 2nd card is drawn. what is the probabilty of drawing a king and another king?
A. 3/676
B. 1/221
C. 1/169
D. 2/169
Answer:
1/221.
Step-by-step explanation:
Probability(first card is a King) = 4/52 = 1/13 (as there are 4 kings in the pack).
Now there are 51 cards left in the pack, 3 of which are Kings, so:
Probability(second card is a King) = 3/51 = 1/17.
These 2 events are independent so we multiply the probabilities:
Required probability =
1/13 * 1/17
= 1/221.
Write each of teh following expressions without using absolute value.
|y-x|, if y>x
The expression |y-x| without absolute value is simply: y-x
In mathematics, the absolute value refers to the magnitude or numerical value of a real number without considering its sign. It gives the distance of the number from zero on the number line. The absolute value of a number x is denoted by |x| and is defined as follows:
If x is positive or zero, then |x| = x.
If x is negative, then |x| = -x (the negative sign is removed).
Since y > x, the difference (y-x) will be positive. The absolute value of a positive number is the number itself. Therefore, the expression |y-x| without absolute value is simply: y-x
Learn more about absolute value here, https://brainly.com/question/24368848
#SPJ11
Can anyone tell me the coordinates of this graph?
Savannah recorded the average rainfall amount, in inches, for two cities over the course of 6 months. Show your work
City A: {2.5, 3, 6, 1.5, 4, 1}
City B: {4, 7, 3.5, 4, 3.5, 2}
What is the mean monthly rainfall amount for each city?
What is the mean absolute deviation (MAD) for each city? Round to the nearest tenth.
What is the median for each city?
Hello, I am Alyssa Ann Verrett.
Put the numbers in order:
City A: {2, 3.5, 4, 4, 5, 5.5}
City B: {3.5, 4, 5, 5.5, 6, 6}
a)
The mean monthly rainfall amount for city A: 4 in;
The mean monthly rainfall amount for city B: 5 in;
b)
The MAD monthly rainfall amount for city A: 0.8 in;
The MAD monthly rainfall amount for city B: 0.8 in;
c)
The median monthly rainfall amount for city A: 4 in;
The median monthly rainfall amount for city A: 5.25 in;
Step-by-step explanation:
a) The general definition of mean of a set X is:
mean = (x₁ + x₂ + x₃ + ... xₙ)/n
For City a:
mean = (4+3.5+5+5.5+4+2)/6 = 4
For City b:
mean = (5+6+3.5+5.5+4+6)/6 = 5
b) The general definition of mean absolute deviation of a set X is:
MAD = (|x₁-mean| + |x₂-mean| + |x₃-mean| + ... + |xₙ-mean|)/n
For City a:
MAD = ( |4-4| + |3.5-4| + |5-4| + |5.5-4| + |4-4| + |2-4| )/6 = (0 + 0.5 + 1 + 1.5 + 0 + 2)/6 = 5/6 =0.8
For City b:
MAD = ( |5-5| + |6-5| + |3.5-5| + |5.5-5| + |4-5| + |6-5| )/6 = (0 + 1 + 1.5 + 0.5 + 1 + 1)/6 = 5/6 = 0.8
c) The general definition of median depends on the quantity of elements in the set X and it represents the middlemost value of the set:
When the quantity is odd:
median= x₍ₙ₊₁₎/₂
When the quantity is even:
median= (xₙ/₂ + x ₙ₊₂/₂) /2
For City A:
median = 2, 3.5, 4, 4, 5, 5.5 = (4 + 4) / 2 = 4
For City B:
median = 3.5, 4, 5, 5.5, 6, 6 = (5 + 5.5) / 2 = 5.25
(1 bookmark
the produce manager at the local pig & whistle grocery store must determine how many pounds of
bananas to order weekly. based upon past experience, the demand for bananas is expected to be 100,
150, 200, or 250 pounds with the following probabilities: 100lbs 0.20; 150lbs 0.25, 200lbs 0.35, 250lbs 0.20.
the bananas cost the store $.45 per pound and are sold for $.085 per pound. any unsold bananas at the
end of each week are sold to a local zoo for $.30 per pound. use your knowledge of decision analysis to
model and solve this problem in order to recommend how many pounds of bananas the manager should
order each week
As per the probability, the expected demand for bananas per week is 182.5 pounds.
To model this problem, we can use decision analysis, which involves identifying the possible outcomes, assigning probabilities to each outcome, and calculating the expected value of each decision.
In this case, the possible outcomes are the demand for bananas, which can be 100, 150, 200, or 250 pounds per week. The probabilities of each demand level are given as 0.20, 0.25, 0.35, and 0.20, respectively.
Let X denote the demand for bananas in pounds. Then, the expected demand for bananas, denoted as E(X), can be calculated as follows:
E(X) = 100(0.20) + 150(0.25) + 200(0.35) + 250(0.20) = 182.5
To know more about probability here
https://brainly.com/question/11234923
#SPJ4
HELP PLEASE!! the function f(x)has a vertical asymptote at x=[blank]
Answer:
Step-by-step explanation:
Solution: -4
The graph gets closer and closer to the line x=-4 but never touches it.
Earth's distance from the sun is 1. 496 x 108 km. Saturn's distance from the sun is 1. 4246 x 10 km. How many times further from the sun is Saturn? Explain how you arrived at your answer.
Saturn is approximately 9.52 times further from the sun than Earth.
To find out how many times further from the sun Saturn is compared to Earth, we need to divide Saturn's distance from the sun by Earth's distance from the sun.
First, let's correct the distances given:
- Earth's distance from the sun: 1.496 x 10^8 km
- Saturn's distance from the sun: 1.4246 x 10^9 km (I assume you missed the exponent)
Now, let's calculate the ratio:
Ratio = (Saturn's distance) / (Earth's distance)
Ratio = (1.4246 x 10^9 km) / (1.496 x 10^8 km)
To make the calculation easier, let's factor out the common exponent (10^8):
Ratio = (1.4246 x 10) / (1.496)
Ratio ≈ 9.52
So, Saturn is approximately 9.52 times further from the sun than Earth.
To learn more about Saturn, refer below:
https://brainly.com/question/12181523
#SPJ11
Consider ABC.
What is the length of AC
A. 32units
B.48units
C.16units
D.24units
Write a function to describe the following scenario.
Jonathan is selling his old trading cards.
Each customer that buys gets the first
box they purchase for $10, and each
additional box for only $5.
y = [?]x + [?]
Answer:
y = 5x + 5
Step-by-step explanation:
If x is the number of boxes sold and y is the cost
The first box costs $10
Each additional box costs $5.
If the total number of boxes sold is x, then after selling the first box for $10, there will be x - 1 boxes left to be sold
The cost of x -1 boxes at $5 per box = 5(x - 1) = 5x - 5
Therefore for a total of x boxes sold the total cost, y in dollars is
y = 10 (for the first box) + 5x - 5 (for the remaining x - 1 boxes)
= 10 + 5x - 5
= 5 + 5x
which in standard form is written as
y = 5x + 5
We can verify our equation using specific numbers for x
For x = 1
y = 5 + 5(1) = 10 ; since only one box has been sold, the cost is fixed at $10
For x = 2 y = 5 + 5(2) = 5 + 10 = $15
This works out to since first box is sold at $10 and the second box at $5
Leave it to you to work out for other numbers
Calculate the bearing of U from T. U N 32° T
The bearing of U from T in the image is 32 degrees South by West of T
What is Bearing?In mathematics, bearings refer to the direction of an object or location in relation to two points. It is determined by the angle between the line joining them and that of the north.
Measured typically in degrees, it follows a cardinal system where 0° or 360° signifies North; East stands for 90°, South denotes at 180° while West represents 270°.
Thus, it can be seen that the bearing of U from T in the image is 32 degrees South by West of T
Read more about bearing here:
https://brainly.com/question/28782815
#SPJ1
Why are rectangles relatable to factors
Rectangles are relatable to factors because of their areas and perimeter equations
Why are rectangles relatable to factorsFrom the question, we have the following parameters that can be used in our computation:
Explaining why rectangles are relatable to factors
Rectangles are relatable to factors because of the following reasons
Perimeter = 2 * (Length + width)
Area = Length * width
This means that in calculating the areas and the perimeters of a rectangles, we make use of arithmetic expressions
These arithmetic expressions, when expanded form terms and factors of expression
Read more about rectangles at
https://brainly.com/question/25292087
#SPJ1
Find the derivative of the function f by using the rules of differentiation. f(x) = 7/x^3 – 2/x^2 – 1/x + 140
f’(x) =
Since the derivative of a constant is always 0, we can drop the last term:
f’(x) = -21/x^4 + 4/x^3 + 1/x^2
Using the rules of differentiation, we can find the derivative of f(x) by taking the derivative of each term separately. The power rule and the constant multiple rule will come in handy here.
f(x) = 7/x^3 – 2/x^2 – 1/x + 140
f’(x) = d/dx(7/x^3) – d/dx(2/x^2) – d/dx(1/x) + d/dx(140)
To find the derivative of 7/x^3, we can use the power rule, which states that the derivative of x^n is nx^(n-1).
f’(x) = -21/x^4 – (-4/x^3) – (-1/x^2) + 0
To find the derivative of -2/x^2, we can again use the power rule:
f’(x) = -21/x^4 + 4/x^3 – (-1/x^2) + 0
To find the derivative of -1/x, we use the power rule once more:
f’(x) = -21/x^4 + 4/x^3 + 1/x^2 + 0
And since the derivative of a constant is always 0, we can drop the last term:
f’(x) = -21/x^4 + 4/x^3 + 1/x^2
To learn more about power rule, refer below:
https://brainly.com/question/23418174
#SPJ11
Select the proper inverse operation to check the answer to 25
-13=12
12+13 = 25, therefor the answer is correct
Please help I need it ASAP, also needs to be rounded to the nearest 10th
The length of segment BC is given as follows:
BC = 47.2 km.
What is the law of cosines?The Law of Cosines is a trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is also known as the Cosine Rule.
The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation holds true:
c² = a² + b² - 2ab cos(C)
The parameters for this problem are given as follows:
a = 27.8, b = 24.7, C = 129.1
Hence the length of segment BC is given as follows:
(BC)² = 27.8² + 24.7² - 2 x 27.8 x 24.7 x cosine of 129.1 degrees
(BC)² = 2249.0497
[tex]BC = \sqrt{2249.0497}[/tex]
BC = 47.2 km.
More can be learned about the law of cosines at https://brainly.com/question/4372174
#SPJ1
A musician charges C (x) = 64x + 20,000 where x is the total - number of attendees at the concert. The venue charges $80 per ticket. After how many people buy tickets does the venue break even, and what is the value of the total tickets sold at that point?
The venue breaks even when 1,250 people buy tickets, and the total value of tickets sold at that point is $100,000.
To find the break-even point for the venue, we need to set the musician's charges (C(x) = 64x + 20,000) equal to the venue's earnings from ticket sales ($80 per ticket). Hence,
1. Set the musician's charges equal to the venue's earnings:
64x + 20,000 = 80x
2. Subtract 64x from both sides:
20,000 = 16x
3. Divide both sides by 16:
x = 1,250
At the break-even point, 1,250 people need to buy tickets. To find the value of the total tickets sold at this point:
1. Multiply the number of attendees (x) by the ticket price:
Total ticket sales = x * ticket price
2. Substitute the values:
Total ticket sales = 1,250 * $80
3. Calculate the total ticket sales:
Total ticket sales = $100,000
So, the breaks even point is 1,250 people buying tickets, and corresponding total value of tickets sold is $100,000.
Learn more about Break even:
https://brainly.com/question/21137380
#SPJ11
