An inequality can be written in two different ways depending on the desired result. In both cases, the inequality is used to represent the desired result of Mario earning no more than or more than $500.
If Mario wants to earn no more than $500:
I ≤ 500
If Mario wants to earn more than $500:
I > 500
An inequality can be written in two different ways depending on the desired result. In the first case, Mario wants to earn no more than $500. This can be written as I ≤ 500, which means "I is less than or equal to 500". The symbol ≤ indicates that the maximum value for I is 500. In the second case, Mario wants to earn more than $500. This can be written as I > 500, which means "I is greater than 500". The symbol > indicates that the minimum value for I is 500. In both cases, the inequality is used to represent the desired result of Mario earning no more than or more than $500.
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Given the equation d over 13 equals 15, solve for d.
195
196
2
28
Answer:
195
Step-by-step explanation:
Since: d / 13 = 15, we need to do the inverse which is multiplication:
15 x 13 = 195
Hot milk is poured into a cold ceramic bowl. Which of the following most likely happens?
Answer:
When hot milk is poured into a cold ceramic bowl, heat moves from the milk to the bowl.
PLEASE HELP, needed ASAP. THANK YOU!!!
Question A
a. Perpendicular Lines Theorem
b. Exterior Intersection Theorem
c. Radius Tangent Theorem
d. Tangent Radius Theorem
Question B
a. The tangent line (or segment, or ray) is perpendicular to the radius of the circle at the point of tangency.
b. If two chords intersect inside a circle, the products of the measures of the segments of the chords are equal.
c. If two secants, a secant and a tangent, or two tangents intersect in the exterior of a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs.
d. If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.
Question C
- What is the measure of ∠PRS
At the point of tangency, the tangent line (or segment, or ray) is perpendicular to the circle's radius.
What is meant by tangent line?In geometry, the straight line that "just touches" the curve at a particular position is known as the tangent line to a plane curve at that location. According to Leibniz, it is the path connecting two points on a curve that are infinitely close to one another.
A tangent line is a simple straight line that only touches a function once. (See atop.) The instantaneous rate of change of the function at that specific position is shown by the tangent line. The derivative of the function at a location on the function is equal to the slope of the tangent line at that point (See below.)
Therefore, the correct answer is option a. The tangent line (or segment, or ray) is perpendicular to the radius of the circle at the point of tangency.
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Is 3x³ a polynomial?
Yes, 3x^3 is a polynomial. It is a third-degree polynomial, which is a monomial.
A polynomial is a mathematical expression that can be written as the sum or difference of one or more terms, where each term is a constant multiplied by one or more variables raised to a non-negative integer power.
A monomial is a polynomial with only one term. It is of the form ax^n, where a is a constant and n is a non-negative integer. In this case, the constant is 3 and the variable is x raised to the power of 3.
The degree of a polynomial is the highest power of the variable in the polynomial.
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Can you help me with this question pls
If one side of a square notebook measures 20 cm, what is the area of the front cover of the notebook?
40 centimeters squared
Answer:
Area of square = side x side = 20 x 20 = 400 cm²
Cheers.
What is the remainder when x⁴ x³ 2x² X 1 is divided by x 1?
The remainder is 2 when x⁴ + x³ - 2x² + x + 1 is divided by x - 1.
The given polynomial is x⁴ + x³ - 2x² + x + 1.
The given divisor is x - 1
First we choose a term to multiply with the first term of the divisor such that we get the first term of the polynomial.
(x)(x^3) = x^4
Thus, we multiply the divisor (x - 1) by x^3 which gives x^4 - x^2.
Now we subtract this from the polynomial which gives 2x^3 - 2x^2 + x + 1.
Next we multiply the divisor by 2x^2 which gives 2x^3 - 2x^2. Again we subtract the same from the remaining polynomial 2x^3 - 2x^2 + x + 1 and get x + 1.
Repeating the same we multiply the divisor by 1 which gives x - 1. Subtracting the same from the remaining polynomial x + 1 we get the remainder 2.
Thus, the quotient is x^3 + 2x^2 + 1.
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8-3 study guide and intervention special right triangles
Properties of Special right angled triangle,
a) If the leg of a 45°-45°-90° right triangle is x units, then the length of hypotenuse is x√2 units.
b) If a 30°-60°-90° right triangle the hypotenuse is twice the shorter leg, then longer leg is √3 times the shorter leg.
We have to discuss properties of special Right Triangles :
a) Properties of 45°-45°-90° Triangles : The sides of a 45°-45°-90° right triangle have a special relationship.
Example 1: If the leg of a 45°-45°-90° right triangle is x units, show that the hypotenuse is x√2 units.
Using the Pythagorean Theorem with
a = b = x, then c² = a² + b²
=> c² = x² + x²
=> c² = 2x²
=> c = √2x²
=> c = x√2
Thus, hypotenuse is x√2 units.
b) The sides of a 30°-60°-90° right triangle also have a special relationship.
Example 1: In a 30°-60°-90° right triangle the hypotenuse is twice the shorter leg. Show that the longer leg is √3 times the shorter leg.
∆MNQ is a 30°-60°-90° right triangle, and the length of the hypotenuse MN is two times the length of the shorter side NQ. Use the Pythagorean Theorem, c² = a²+ b²
let length of shorter side of ∆MNQ, NQ= x units, so, length of hypotenuse,MN = 2x
=> MN² = NQ² + MQ²
=> MQ² = MN² - NQ²
=> MQ² = (2x)² - x²
=> MQ² = 4x² - x² = 3x²
=> MQ = √3x²
=> MQ = √3 x = √3 NQ
So, longer side of right angled triangle is √3 times the short side.
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Complete question:
8-3 study guide and intervention special right triangles
a) Properties of 45°-45°-90° Triangles
b) Properties of 30°-60°-90° Triangles
Jayden and Brooklynn have daily chores they must complete. They also have extra chores
they can earn money for. Jayden earns $6 an hour for raking leaves in the yard. Brooklynn
earns $9 for making everyone's beds and an additional $1.50 an hour for helping with the
laundry.
Write the equation/expression that represents the amount of money that Jayden can earn
Write the equation/expression that represents the amount of money that Brooklyn can earn
Write the equation you would use to find how many hours each need to work in order to earn the same amount of money
After how many hours do they each need to work in order to have earned the same amount of money
Answer:
ayden earns $6 an hour for raking leaves in the yard, so the equation representing the amount of money he can earn is:
Earnings = 6 * (Number of hours worked)Brooklynn earns $9 for making everyone's beds and an additional $1.50 an hour for helping with the laundry, so the equation representing the amount of money she can earn is:
Earnings = 9 + (1.5 * (Number of hours worked))To find how many hours each need to work in order to earn the same amount of money, we can set the two equations equal to each other and solve for the number of hours worked.
6(Number of hours worked) = 9 + (1.5 * (Number of hours worked))Solving this equation gives us: Number of hours worked = 9/4 = 2.25 hoursSo after 2.25 hours, they each need to work in order to have earned the same amount of money.
Step-by-step explanation:
Jayden's equation: 6x
Brooklynn's equation: 9x + 1.5y
Equation to find how many hours each need to work: 6x = 9x + 1.5y
After 12 hours, they each need to work in order to have earned the same amount of money.
november 16, 2001, was a friday. if each of the years 2004, 2008, and 2012 had 366 days, and the remaining years from 2001 through 2014 had 365 days, what day of the week was november 16, 2014 ?
Sunday is the week was November 16, 2014
We see that there is a 13-year span from November 16, 2001, to November 6, 2014. If each year were 365 days, the total number of days in this 13-year span would be 365 x 13 = 4,745 days.
However, since 3 of the years during this span, each has 1 extra day, the actual number of days in this span is 4,745 + 3 = 4,748 days.
Since 4,748/7 = 678 R2, we know that there were 678 weeks and 2 days from Friday, November 16, 2001, until November 16, 2014. The remainder of 2 tells us that November 16, 2014, was 2 days after Friday, so it was Sunday.
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Write a formula representing the following function. Use the lower case letter k as the proportionality constant. The number of animal species, N, of a certain body length, L, is inversely proportional to the square of L.?
The formula that can be used to represent this function is N*L^2 = k
The number of animal species, N, is inversely proportional to the square of the body length, L. Therefore, the formula representing the function would be:
N = k/L^2
Where k is the proportionality constant. It represents the relationship between N and L^2, and it is a constant value.
The above formula can also be written as
N*L^2 = k
It means that the product of N and L^2 is constant.
It can be derived by assuming that there is some proportionality constant k such that N=k/L^2 and then testing this relationship against data on animal species and body lengths.
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What is logarithmic function example?
The inverse of an exponential function is a logarithmic function.
A logarithm is a measurement of the amount that a fixed number (the base) must be increased in order to create a particular number.
Basically,
if y=ax
So, logₐ(y) = x
The base of the logarithm in this instance is a. The following two bases are frequently employed: base-10 and Base-e
'e' is a mathematical constant having a value of around 2.718.
If the base is "e," we use a specific expression: ln(x)
Fundamentally,
ln(x)=loge(x)
Here, e is the base.
Base-10 will be used if no base is provided, as in the formula
log(x)=log10(x)
Here 10 is the base
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A man walks 6 miles at 4 miles per hour. At what speed would he need to travel during the next 2 1/2 hours to have an average speed of 6 miles per hour during the complete trip?
In order to have an average speed of 6 miles per hour over the entirety of the trip, the man would need to travel 15 miles in the next 2 1/2 hours. This means that he would need to travel at a speed of 6 miles per hour for the remainder of the trip.
PLEASE HELP I NEED ANSWER AND STEPS TO THIS QUESTION
The triangle ABC is equal to DEF because they possess the same sides.
What are congruent angles about?If all three sides and all three angles of two triangles are equal, then two triangles are said to be congruent.
The triangles are congruent if two sides and the included angle of one triangle match the corresponding sides and angle of another triangle.
Side-Side-Side, or SSS, is a type of triangle congruence rule that states that two triangles are congruent if their three sides are equal to their respective three sides of another triangle.
In this case, triangle ABC is equal to triangle DEF.
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The sides of a quadrilateral are in the ratio 2:3:5:8. The difference between the shortest side and the longest side is 7.5 cm. Work out the perimeter of the quadrilateral.
Answer:
Step-by-step explanation:
To answer this problem, we may use the information provided about the quadrilateral's side ratio and the difference between the smallest and longest sides.
To begin, we may utilize the difference in length between the shortest and longest sides (7.5 cm) to establish a baseline for one of the sides. We may infer that the shortest side is 7.5 cm and the longest side is (7.5 cm + 7.5 cm) = 15 cm since the difference between the shortest and longest sides is 7.5 cm.
We can calculate the length of the other three sides using the side ratio:
3/2 x 7.5 cm = 11.25 cm is the length of the second shortest side.5/2 x 7.5 cm = 18.75 cm is the length of the second longest side.30 cm is the length of the third longest side (8/2 x 7.5 cm).We sum together all the sides to find the quadrilateral's perimeter:
Perimeter = 67.5 cm = 7.5 cm + 11.25 cm + 18.75 cm + 30 cm
As a result, the quadrilateral's perimeter is 67.5 cm.
What number is 10 more than 80?
The answer of 10 more than 80 is 90.
The answer of 10 more than 80 is 90 which can be derived using simple mathematical calculations.
To find 10 more than 80, you can add 10 to the original number 80.
10 + 80 = 90
It's a simple arithmetic operation where you add a specific number, in this case 10, to the original number.
An arithmetic operation is a mathematical process that combines two or more numbers to produce a new number. The most basic arithmetic operations are addition, subtraction, multiplication, and division.
Addition: It is the process of combining two or more numbers to find their sum. For example, 2 + 3 = 5 is an addition operation.
Subtraction: It is the process of finding the difference between two numbers. For example, 5 - 3 = 2 is a subtraction operation.
Multiplication: It is the process of finding the product of two or more numbers. For example, 3 x 4 = 12 is a multiplication operation.
Division: It is the process of finding the quotient of two numbers. For example, 12 ÷ 3 = 4 is a division operation.
Therefore, The answer of 10 more than 80 is 90.
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Which representation shows a nonproportional relationship between x and y?
A graph that does not show a straight line shows a non-proportional relationship between x and y.
A graph that does not show a straight line, but instead shows a curve, would represent a non-proportional relationship between x and y. A non-linear or curved graph indicates that the relationship between the two variables is not a constant ratio or proportionate relationship. The slope of a line that represents a non-proportional relationship will change depending on the x-value.
A non-proportional relationship exists between two variables when the ratio of their values does not stay constant. In other words, the relationship is not directly proportional. In mathematical terms, this means that the slope of a graph of the relationship is not constant, and the graph will not be a straight line. Instead, it will be a curved line. A non-proportional relationship is also known as a non-linear relationship.
For example, the relationship between the time it takes to run a certain distance and the distance run is non-proportional. If it takes you 10 minutes to run 1 mile, it will not necessarily take you 20 minutes to run 2 miles. The time it takes to run a certain distance increases at a faster rate than the distance run.
In a non-proportional relationship, there is no constant of proportionality. For example, y = 2x doesn't have a constant of proportionality because the ratio of y to x changes as x increases, and the slope of the line is not constant.
Therefore, A graph that does not show a straight line shows a non-proportional relationship between x and y.
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Mr. White is renting a large truck for one week and a few additional days d. He does not have to pay a per mile fee. Evaluate the expression 295+90d to find how much he will pay for a 10-day rental.
Answer:
I believe the answer is 1195 dollars
Step-by-step explanation:
Pls answer quick as possible !
Answer: The 4th option
Step-by-step explanation:
On the first day, a tourist hiked 9 miles to the east from the camp. On the second day, the tourist hiked a few miles to the north. On the third day, the tourist returned to camp by straight way. If the tourist hiked a total of 90 miles, how many miles did the tourist hike on the third day?
On the third day of the camp miles hiked by the tourist as per given data is equal to 41 miles .
As given in the question,
On the first day,
Miles hiked by tourist is 9 miles to the east from camp.
Let x miles be hiked by tourist on the second day to the north.
let h miles be hiked by tourist on third day
Total distance travelled = 90 miles
It represent the right angled triangle
'h' represents the hypotenuse.
By Pythagoras theorem,
h² = x² + 9² ___(1)
x + h + 9 = 90
h = 81 - x __(2)
Substitute the value h from (2) in (1) we get,
( 81 - x )² = x² + 9²
⇒ 6561 - 162x + x² = x² + 9²
⇒ 162x = 6480
⇒ x = 40
⇒ h = 41 miles
Therefore, on the third day of the camp miles hiked by tourist is equal to 41 miles.
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math again... help..??
Answer: 20
Step-by-step explanation:
5x - 7 + 3x + 27 = 180
8x = 180 - 20
8x = 160
x = 20
Answer:
x = 20°
Step-by-step explanation:
5x - 7 + 3x + 27 = 180° (Linear pair)
8x + 20° = 180°
8x = 160°
x = 20°
Cheers and mark as brainliest if possible
raj inteded to run a certain distance on saturday he ran an entire distance and then half of the way back to the starting point what percentage did he run on saturday did he actully run on saturday?
The percentage he run on Saturday is 150%
How to determine the distance Raj run on Saturday?A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation
Let the d represent the entire distance Raj run on Saturday.
If he ran an entire distance and then half of the way back to the starting point. We can write:
Percentage ran on Saturday = (d + 1/2(d))/(d) × 100%
Percentage ran on Saturday = 1.5d/d × 100%
Percentage ran on Saturday = 1.5 × 100%
Percentage ran on Saturday = 150%
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20y−25x=140 and y+5/4x=-5
The solution of the given equations are; x = -10.5 and y = 8.25
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We are given that the system of equation are;
20y−25x=140
y+5/4x=-5
Therefore, solving the equations;
y = -5/4x -5
Substitute;
20y−25x=140
20(-5/4x -5)−25x = 140
-25 - 100 - 25x = 140
-125 - 25x = 140
-25x = 140 + 125
x = -10.5
Then y = -5/4x -5
y = 8.25
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A hockey player ran a simulation twice to estimate the proportion of wins to expect using a new game strategy. Each time, the simulation ran a trial of 1,000 games. The first simulation returned 590 wins, and the second simulation returned 640 wins. Construct and interpret 95% confidence intervals for the outcomes of each simulation.
The confidence interval from the first simulation is (0.560, 0.620), and the confidence interval from the second simulation is (0.610, 0.670). For the first trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.560 and 0.620. For the second trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.610 and 0.670.
The confidence interval from the first simulation is (0.564, 0.616), and the confidence interval from the second simulation is (0.615, 0.665). For the first trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.564 and 0.616. For the second trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.615 and 0.665.
The confidence interval from the first simulation is (0.564, 0.616), and the confidence interval from the second simulation is (0.615, 0.665). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.564 and 0.616. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.615 and 0.665.
The confidence interval from the first simulation is (0.560, 0.620), and the confidence interval from the second simulation is (0.610, 0.670). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.560 and 0.620. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.610 and 0.670.
The 95% confidence intervals, along with their interpretations, are described by the following option:
The confidence interval from the first simulation is (0.560, 0.620), and the confidence interval from the second simulation is (0.610, 0.670). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.560 and 0.620. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.610 and 0.670.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.
The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
For the first simulation, the parameters are given as follows:
[tex]n = 1000, \pi = \frac{590}{1000} = 0.59[/tex]
Hence the lower bound of the interval is of:
[tex]0.59 - 1.96\sqrt{\frac{0.59(0.41)}{1000}} = 0.56[/tex]
The upper bound is of:
[tex]0.59 + 1.96\sqrt{\frac{0.59(0.41)}{1000}} = 62[/tex]
For the second simulation, the parameters are given as follows:
[tex]n = 1000, \pi = \frac{640}{1000} = 0.64[/tex]
Hence the lower bound of the interval is of:
[tex]0.64 - 1.96\sqrt{\frac{0.64(0.36)}{1000}} = 0.61[/tex]
The upper bound is of:
[tex]0.64 + 1.96\sqrt{\frac{0.64(0.36)}{1000}} = 0.67[/tex]
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4. What is the solution to 4(q + 56.5) = 30q- 112?
To find the solution to the equation 4(q + 56.5) = 30q - 112, we can start by isolating the variable on one side of the equation.
First, we'll distribute the 4 on the left side:
4q + 4(56.5) = 30q - 112
4q + 226 = 30q - 112
Now we'll subtract 4q from both sides:
226 = 26q - 112
Next, we'll add 112 to both sides:
338 = 26q
Finally, we'll divide both sides by 26 to find the value of q:
q = 13
So the solution to the equation 4(q + 56.5) = 30q - 112 is q = 13.
Answer:
q=13
Step-by-step explanation:
Adjacent angles (select ALL that apply)
1.have a common angle.
2. have a common side.
3. have a common vertex.
4. are equal.
The adjacent angles share, option 2: a common side and option 3: a common vertex.
What are adjacent angels?
Angles that do not overlap but share a common vertex and arm (side) are said to be adjacent angles. Adjacent angles are ones that are consistently positioned next to one another and are generated when two rays intersect at a shared terminal.
Adjacent angles are placed side by side to each other.
They do not overlap each other.
Adjacent angles are drawn from a common point known as a vertex.
The adjacent angles are on the same side and are not opposite to each other.
The image for a pair of adjacent angles is given.
Adjacent angles do not share a common angle and are not equal.
Therefore, adjacent angles have a common side and a common vertex.
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Line A is perpendicular to Line B.
If the slope of Line A is -4,
what is the slope of Line B?
[?]
Answer: The slope of Line B is 1/-4 = -1/4.
Step-by-step explanation:
When two lines are perpendicular to each other, the product of their slopes is -1. If the slope of Line A is -4, the slope of Line B must be 1/-4 = -1/4 in order for the two lines to be perpendicular.
Hannah needs to buy apples and on box of cereal at the grocery store. At Giant Eagle, a box of cereal costs $2.89 and apples cost $1.29 per pound. At Shop & Save, the apples are $1.05 per pound and a box of
cereal is $3.37. How many pounds of apples can Hannah buy for the cost for her purchase to be the same from both stores?
a. Choose a variable and explain what it represents
b. Write and solve the equation
c. Explain your answer using a complete sentence.
There are 2 pounds of apples Hannah buy for the cost for her purchase to be the same from both stores.
What is an expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math. An expression that includes variables, constants, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, etc.). Terms combine to form expressions. The addition, subtraction, multiplication, and division mathematical operations are used to create mathematical expressions. For instance, "4 added to 2" will be expressed as 2+4 in mathematics.Given that;
At Giant Eagle, a box of cereal costs $2.89 and apples cost $1.29 per pound.
And, At Shop & Save, the apples are $1.05 per pound and a box of
cereal is $3.37.
Now,
Let number of pounds of apples can Hannah buy for the cost for her purchase to be the same from both stores = x
So, We can formulate;
For, At Giant Eagle, a box of cereal costs $2.89 and apples cost $1.29 per pound.
The total cost is,
⇒ $2.89 + $1.29x
And, For Shop & Save, the apples are $1.05 per pound and a box of
cereal is $3.37.
Total cost is,
⇒ $3.37 + $1.05x
Now, We can equate both the equation to find the number of pounds of apple to buy.
⇒ $3.37 + $1.05x = $2.89 + $1.29x
⇒ 3.37 + 1.05x = 2.89 + 1.29x
⇒ 3.37 - 2.89 = 1.29x - 1.05x
⇒ 0.48 = 0.24x
⇒ x = 0.48 / 0.24
⇒ x = 2
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Refer to the figure to complete the following problem.
Given: A RST is circumscribed about circle A. What is the measure of angle S?
0.5 arc XQ minus arc XPQ
0.5 (arc XPQ- arc XQ)
angle R + angle T
Answer:
B) 0.5 (Arc XPQ-Arc XQ)
What is the derivative of x² log x?
The derivative of x² log x is 2x log x + x/ ln(10).
The derivative of a function f(x) is usually represented by d/dx (f(x)) (or) df/dx (or) Df(x) (or) f'(x). Let us see what a derivative technically means. Consider a curve of function f(x) and let two points on it be (x, f(x)) and ((x + h), f(x + h)). Then the slope of the secant line through these points is given by [f(x + h) - f(x)]/(x + h - x) = [f(x + h) - f(x) / h. See the figure below and observe that when the distance between two points is closely equal to 0 (i.e., as h approaches 0), the second point overlaps the original point and the secant line becomes the tangent line. In calculus, the slope of the tangent line is referred to as the derivative of the function.
The derivative of a function at a point is the slope of the tangent drawn to that curve at that point.
It also represents the instantaneous rate of change at a point on the function.
The velocity of a particle is found by finding the derivative of the displacement function.
The derivatives are used to optimize (maximize/minimize) a function.
They are also used to find the intervals where the function is increasing/decreasing as well as the intervals where the function is concave up/down.
Given equation: y = x² log x
Differentiating this equation with respect to x, we get
dy/dx = 2x log x + x/ ln(10)
Thus, the derivative of x² log x is 2x log x + x/ ln(10).
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