by dy/dx, we'll be assuming that "y" is encapsulating a function, a function in terms of "x".
\(x^y\cdot y^x=1\implies \stackrel{\textit{\large product rule}}{\stackrel{\textit{chain rule}}{yx^{y-1}(1)}\cdot y^x+x^y\cdot \stackrel{\textit{chain rule}}{xy^{x-1}\cdot \frac{dy}{dx}}}~~ = ~~0 \\\\\\ y^{1+x}x^{y-1}+x^{y+1}y^{x-1}\cdot \cfrac{dy}{dx}=0\implies \cfrac{dy}{dx}=\cfrac{-y^{1+x}x^{y-1}}{x^{y+1}y^{x-1}} \\\\\\ \cfrac{dy}{dx}=-~~ y^{(1+x)-(x-1)}~~x^{(y-1)-(y+1)} \\\\\\ \cfrac{dy}{dx}=-~~ y^2x^{-2}\implies \cfrac{dy}{dx}=\cfrac{-y^2}{x^2}\)
The graph shows the square root parent function.
-5
5
5
Which statement best describes the function?
OA. The function is negative when x > 0.
OB. The function is negative when x<0 and also when x > 0.
OC. The function is negative when x < 0.
D. The function is never negative.
The function is never negative.
option D is the correct answer.
What is a negative function?A negative function is a function in which the resulting y value is negative.
Also, a negative function is a function that has y values that are less than zero for any x values. In other words, a negative function has a negative sign in front of its output.
From the given graph, the x and y values started from 0 and increases into the positive direction, so we can conclude that the function can never be negative.
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When the scale factor is 1, what is the ratio of the side length of the side opposite ∠A and the length of the hypotenuse?
when the scale factor is 1, we have:
(side length of side opposite ∠A) / (length of hypotenuse) = sin A
When the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse remains the same as in the original triangle. In a right triangle, the side opposite ∠A is referred to as the "opposite" side, and the hypotenuse is the longest side.
The ratio of the side length of the side opposite ∠A to the length of the hypotenuse is commonly known as the sine of angle A (sin A). So, when the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse is equal to sin A.
In mathematical terms, when the scale factor is 1, we have:
(side length of side opposite ∠A) / (length of hypotenuse) = sin A
It's important to note that this ratio holds true for any right triangle, regardless of its size or dimensions, as long as the angle A remains the same.
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Brainliest to whoever gets this correct.
Which of the functions below could have created this graph?
Answer:
see below
Step-by-step explanation:
The general left-to-right downward slant tells you the function is odd degree with a negative leading coefficient. Only one answer choice matches: choice C.
__
Additionally, the "touch" of the x-axis at x=0 tells you x^2 is one of the factors of the function. The two sign changes are consistent with 2 (or 0) positive real roots. If signs of odd-degree terms are reversed, then the one sign change tells you there is one negative real root.
Which of these inequalities means that
18 is greater than three times a number?
Let's write this verbal phrase as an inequality.
First of all, let the number be n.
"three times n" can be written like so:-
\(\pmb{3n}\)
Now, 18 is greater than 3n:-
\(\pmb{18 > 3n}\)
Which means 3n is less than 18:-
\(\bigstar{\boxed{\pmb{3n < 18}}}\)
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I'll comment and/or edit my answer :)
true/false.
____1.When the non-Standard unit used is small few unit's are
needed to fill a container when the non-standard the non-standard units used is bigger more units are needed to fill the container.
____2.Objects with shape can have the same volume.
____3. To find the volume of rectangular prism multiply the length,width and height.
_____4. Volume is measured in square unit's.
_____5. the amount of space inside an object is called the volume of the object.
____6. The volume of a rectangular prism is equal to the product of its length, width, and height V = 1xwxh cubic units.
____7. Standard units give a consistant and accurate measure of a container.
____8. Non-Standard units cannot be used to measure volume.
____9. Volume is measured in cubic units, such as cubic centimeters.
1. It is false that when non-Standard unit used is small few unit's are
needed .
2. Objects with different shapes can have the same volume. True
3. Length, width and height and multiplied to find volume of a rectangular prism. True
4. It is false that volume is measured in square unit.
5. It is true that Volume is a measure of the amount of space inside an object.
6. The formula for volume of a rectangular prism is V = l × w × h. True
7. It is true that Standard units give a consistent and accurate measure of a container.
8. It is false that Non-Standard units cannot be used to measure volume.
9. Volume is measured in cubic units. True
What is volume of an object?Volume can be defined as the amount of space inside and object. the object can be in different form such as cone, rectangular prism, cylinder and many other shapes. Even though shapes are different, It is possible for different shapes or objects to have the same volume when measure.
Measurement of volume can be through standard measurement and non standard measurements such as a cup of rice. However, for consistency and the sake of accuracy, it is advisable to always use standard measurements of volume where possible to avoid error that may occur in non standard measurement. The acceptable and recognized unit of volume is cubic meter (\(m^3\)).
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5
Enter the correct answer in the box.
Solve the quadratic equation by completing the square.
2x² + 12x = 66
Fill in the values of a and b to complete the solutions.
x=a-√b
x=a+√b
The values of a and b are a = -3 and b = 42. The solutions for x can be written as:
x = -3 - √42
x = -3 + √42
To solve the quadratic equation 2x² + 12x = 66 by completing the square, we need to follow these steps:
Step 1: Move the constant term to the right side:
2x² + 12x - 66 = 0
Step 2: Divide the equation by the leading coefficient (2):
x² + 6x - 33 = 0
Step 3: To complete the square, we take half of the coefficient of x, square it, and add it to both sides of the equation:
x² + 6x + (6/2)² = 33 + (6/2)²
x² + 6x + 9 = 33 + 9
x² + 6x + 9 = 42
Step 4: Rewrite the left side as a perfect square:
(x + 3)² = 42
Step 5: Take the square root of both sides:
√(x + 3)² = ±√42
x + 3 = ±√42
Step 6: Solve for x:
x = -3 ± √42.
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Hey certain medicine is giving in an amount proportional to a patient’s body weight suppose a patient weighing 132 pounds equal 143 mg of medicine what is the amount of medicine required by the patient waiting 156 pounds
if the medicine is proportional to the pateints body weight,
lets say x= the amount of medicine required by the person who weights 156 lbs
x=(156*143)/132=169
the person who weights 156 lbs needs 169 mg of medicine
Find the area of the figure pictured below.
15 yd
10 yd
17 yd
5 yd
A
First find the area of the square, then the triangle.
15 times 17 = 255 sq. yd
Triangle:
(5 times 5)/2 = 12.5 sq. yd
Your answer is 267.5 sq. yd
Hope this helps.
Help please this is pre calculus
Answer:
5pi/12
105 degrees
Step-by-step explanation:
I can help with the first 2 too many answers in one will get my answer deleted
7pi/12 x 180/pi
7x15=105
Hopes this helps please mark brainliest
5/8 entre 6 personas
Based on the information we can infer that 5/8 between 6 people is equal to 15/24.
How to divide 5/8 between 6 people?To calculate the part that corresponds to each person, divide the fraction 5/8 by the number of people, which in this case is 6. To simplify the fraction, you can reduce the numerator and denominator by dividing both by their maximum common factor, which is 3.
5 ÷ 3 = 1 and 2 remainder8 ÷ 3 = 2 and 2 remainder
So the fraction can be simplified to 1 2/8, which can also be expressed as 1 1/4 or 5/4 in its most simplified form. This means that each person would receive 5/4 of the original share, and since there are 6 people in total, you can multiply 5/4 by 6 to get the total share that corresponds to all 6 people:
(5/4) x 6 = 30/4 = 15/2 = 15/24
So each person would receive 15/24 of the original amount.
Note: Here is the question in English:
5/8 divided in 6 people
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Order cube root of eighty-eight, twenty-eight ninths, square root of nineteen from greatest to least.
cube root of eighty-eight, twenty-eight ninths, square root of nineteen
twenty-eight ninths, square root of nineteen, cube root of eighty-eight
twenty-eight ninths, cube root of eighty-eight, square root of nineteen
cube root of eighty-eight, square root of nineteen, twenty-eight ninths
Answer:
(a) twenty-eight ninths, square root of nineteen, cube root of eighty-eight
Step-by-step explanation:
When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.
OrderThe attachment shows the ordering, least to greatest, to be ...
\(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)
__
Additional comment
We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.
One way to do the comparison is to convert these to values that need to have the same root:
√19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)
∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)
The roots will have the same ordering as 19³ and 88².
Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...
19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859
88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744
Then the ordering is ...
28/9 < 19³ < 88² ⇒ 28/9 < √19 < ∛88
Answer:
the ordering is
28/9 < 19³ < 88² ⇒ 28/9 < √19 < ∛88
Step-by-step explanation:
thank u if u help I’m in question 16 out of 35:(
Answer:
The answer is 20 because when you divide 56 by 2.8 you get 20
a fair die is rolled 100 times.the results are shown below
number:. 1. 2. 3. 4. 5. 6
no of times:. 12. 16. 25. 18. 15. 14
what is the probability of getting
1?
2?
3?
4?
5?
6?
1.) Probability of getting 1: 0.12 or 12%.
2.) Probability of getting 2: 0.16 or 16%.
3.) Probability of getting 3: 0.25 or 25%.
4.) Probability of getting 4: 0.18 or 18%.
5.) Probability of getting 5: 0.15 or 15%.
6.) Probability of getting 6: 0.14 or 14%.
To calculate the probability of getting a specific number on a fair die, we divide the number of times that number appears by the total number of rolls. In this case, the die was rolled 100 times, and the results are given as follows:
Number: 1 2 3 4 5 6
Times: 12 16 25 18 15 14
To find the probability of getting each number, we divide the corresponding number of times by the total number of rolls (100):
Probability of getting 1 = 12 / 100 = 0.12.
Probability of getting 2 = 16 / 100 = 0.16.
Probability of getting 3 = 25 / 100 = 0.25.
Probability of getting 4 = 18 / 100 = 0.18.
Probability of getting 5 = 15 / 100 = 0.15.
Probability of getting 6 = 14 / 100 = 0.14.
Therefore, the probabilities of getting each number on a fair die, based on the given results of 100 rolls, are approximately:
1: 0.12 or 12%,
2: 0.16 or 16%,
3: 0.25 or 25%,
4: 0.18 or 18%,
5: 0.15 or 15%,
6: 0.14 or 14%.
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Can somone please help me
Answer:
D
Is correct cus a straight line is 180
Practice interpreting two-variable linear inequalities.
On a coordinate plane, a dashed straight line with positive slope goes through (negative 1.5, 0) and (0, 3). Everything to the right of the line is shaded.
Which of the points are solutions to the inequality? Check all that apply.
(–3, 3)
(–2, –2)
(–1, 1)
(0, 1)
(2, 5)
Solutions to the inequality are point (-2 , -2), (0,1) and (2, 5)
What is inequality?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values.
Given,
A dashed straight line passes through (-1.5 , 0) and (0,3)
Equation of the line
y - y₁ = ((y₂ - y₁)/(x₂ - x₁)). (x - x₁)
y - 0 = ((3 - 0)/(0 - -1.5)). (x - -1.5)
y = 2x + 3
Shaded region is right side the dashed line,
Inequality becomes,
y < 2x + 3
For point (-3 , 3)
3 < 2(-3) + 3
3 < -6 + 3
3 > -3
(-3 , 3) is not a solution for inequality.
For point (-2 , -2)
-2 < 2(-2) + 3
-2 < -4 + 3
-2 < -1
(-2 , -2) is a solution for inequality.
For point (-1 , 1)
1 < 2(-1) + 3
1 < -2 + 3
1 = 1
(-1 , 1) is not a solution for inequality.
For point (0 , 1)
1 < 2(0) + 3
1 < 3
(0 , 1) is a solution for inequality.
For point (2 , 5)
5 < 2(2) + 3
5 < 4 + 3
5 < 7
(2 , 5) is a solution for inequality.
Hence, point (-2 , -2), (0,1) and (2, 5) are solutions to the inequality.
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Taryn mowed 9 yards and makes $112.50. How much does Taryn charge
to mow one yard?
The difference of seven times a number and four is eighty. Find the number.
Answer: 12
Step-by-step explanation:
difference = subtraction
and = addition
times = multiplication
Therefore,
7x - 4 = 80
7x = 84
x = 12
Given that -5 is a zero of the polynomial P(x) = x³ + 3x²-12x-10, find the other zeros.
Answer:
Below
Step-by-step explanation:
If -5 is one of the roots then that means (x+5) is one of the factors
divide (x+5) into x^3 + 3x^2 -12x -10
to get x^2-2x-2 which you can easily (using Quadratic Formula) find the roots 1 + sqrt 3 and 1 -sqrt 3
('roots' and 'zeroes' are the same thing)
A man gave 90000.00 to his two daughters Jane and Lydia, 75.00 was given to Lydia to pay her load. After sharing the money Lydia has twice as
much as Jane. How much did each received?
Jane received $30025 and Lydia received $60000. Let's assume the amount of money that Jane received as x; then Lydia's share of the money will be twice the share of Jane.
We are to find out the share of each person. Here is the solution in steps:Suppose Jane's share was x dollars, and Lydia's share was y dollars.
Given that the total amount given to the two daughters was $90000. Also, given that Lydia paid off her $75, hence she got $75 less than Jane.
Therefore, y = 2x - 75; this is because we are given that Lydia got twice the share of Jane, and also, she got $75 less than Jane. Hence, x + y = $90000, this is because the total sum of money shared is $90000.
Substituting y = 2x - 75 into x + y = $90000 gives x + (2x - 75) = $90000.
Simplifying, we have :3x = $90000 + 75 = $90075.
Dividing both sides by 3, we get:x = $30025. Hence, Jane's share is $30025 Lydia's share = 2x - 75 = 2($30025) - $75 = $60075 - $75 = $60000.
Therefore, Jane received $30025 and Lydia received $60000.
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A suspect of a crime is traveling on 26th Street toward Cherry Street. The diagram shows the locations of the suspect and a police officer. Your friend says that the officer should wait at point C to intercept the suspect because the officer will have the same distance to travel no matter which route the suspect takes. Is your friend correct? Explain.
AC is not equal to CE based on the angle bisector theorem. The answer is: C. NO, you cannot use the angle bisector theorem to determine that AC = CE.
What is the Angle Bisector Theorem?According to the angle bisector theorem, when a line segment divides an angle of a triangle, the line segment also divides the opposite side but does so in such a way that the two segments are proportional to the other two sides of the triangle. However, the two segments are not congruent to each other.
In the diagram given below that shows the suspect, the police officer, and the 26th Street toward Cherry Street, the angle bisector divides the side opposite to the angle divided into AC and CE. Thus, their length cannot be ascertain to be congruent to each other, however, based on the angle bisector theorem, we can only prove that their length is proportional to the other two sides of the triangle.
Therefore, we can conclude as saying:
C. NO, you cannot use the angle bisector theorem to determine that AC = CE.
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Tres hermanas reciben una herencia de modo que la segunda recibe estilo en línea 1 medio fin estilo de lo que recibe la primera y la tercera recibe estilo en línea 1 quinto fin estilo de lo que recibe la segunda. Si simbolizamos por a lo que recibe la primera hermana y el total de la herencia es $1.600.000, ¿qué ecuación es la que describe esta situación?
Answer:
X + 1/2X + 1/5(1/2X) = 1,600,000
Step-by-step explanation:
Si se plantea que en una herencia de $1,600,000, la primer hermana recibirá un monto de dinero indeterminado, mientras que la segunda recibirá un medio del valor que reciba la primera, y la segunda recibirá un quinto de lo que reciba la segunda, la ecuación que visualiza dicha situación es la siguiente:
X + 1/2X + 1/5(1/2X) = 1,600,000
X + 1/2X + 1/10X = 1,600,000
10X + 5X + X = 16,000,000
16X = 16,000,000
X = 16,000,000 / 16
X = 1,000,000
Así, la primer hermana recibirá $1,000,000, la segunda $500,000, y la tercera $100,000.
Find the critical value
χ2R
corresponding to a sample size of 5 and a confidence level of 99.0 percent
The critical value, given the sample size of 5 and the confidence level of 99. 0 percent would be 16. 812.
How to find the critical value ?The critical values for the chi-squared (χ^2) distribution depend on the degree of freedom and the level of significance.
The degree of freedom for a chi-squared distribution typically equals the sample size minus 1 so the degrees of freedom here is:
= 5 - 1
= 4
The level of significance would be:
= 1 - 99. 0 %
= 0. 01
The critical value of the sample would therefore be found on a chi -squared distribution table for df = 4 and α = 0.01 to be 16. 812.
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for a normal distribution where the mean is 50 and the standard deviation is 10, what percentage of the area is below a score of 31 and above a score of 69 g
The solution is, the required z-score is, 0.25.
What is Z-score?In statistics, the standard score is the number of standard deviations by which the value of a raw score is above or below the mean value of what is being observed or measured. Raw scores above the mean have positive standard scores, while those below the mean have negative standard scores.
here, we have,
Given that :
Mean score, μ = 69
Standard deviation, σ = 4
Score, x = 64
The standardized score, Zscore can be obtained using the formular :
Zscore = (x - μ) / σ
Zscore = (69 - 68) / 4
Zscore = 1 / 4
Zscore = 0.25
Hence, The solution is, the required z-score is, 0.25.
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PLEASE HELP ASAP! THE CORRECT ANSWER WILL RECEIVE BRAINLIEST!
How does the variable of Data Set A compare to the variability of Data Set B?
Data Set A: 14, 15, 19, 29, 44
Data Set B: 9, 20, 25, 30, 38
Select from the drop-down menus to correctly complete the statements.
Data Set A has {Choose...} Data Set B because the range of Data Set A is {Choose...}
the range of Data Set B.
{Choose...} 1: A. Less variability than | B. The same variability as | C. Greater variability than
{Choose...} 2: A: Less than | B: Equal to | C: Greater than
The density of ethanol is around 0.8g/mL. What is the mass of 20mL of ethanol?
Answer: 0.7893g//mL
If 20 mL of ethanol (density =0.7893g//mL) is mixed with 40mL water (density = 0.9971g//mL)
Step-by-step explanation:
Un viajero ha recorrido la tercera parte de su trayecto y sabe que si cubre 65 km más completa la mitad del recorrido. Determine la distancia recorrida.
The travelled distance of the traveller is equal to 195 kilometers.
How to find the travelled distance by a traveller
According to the statement of the problem, a traveller already walked a third part of his trail and if he travels the half of his trail, then the half of his trail shall be covered. Mathematically, the travelled distance shall be described by following expression:
x = d / 3
x + 65 = d / 2
Where:
d - Travelled distance, in kilometers.x - Initial travelled distance, in kilometers.Now we proceed to determine the travelled distance:
d / 3 + 65 = d / 2
d / 2 - d / 3 = 65
3 · d - d = 390
2 · d = 390
d = 195
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Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. common ratio; growth multiplier) was around 1.9. In 1983, about 1600 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2003?
Question 5(Multiple Choice Worth 2 points)
(Sample Spaces MC)
Julia had a bag filled with gumballs. There were 2 watermelon, 3 lemon-lime, and 5 grape gumballs. What is the correct sample space for the gumballs in her bag?
A) Sample space = watermelon, watermelon, lemon-lime, lemon-lime, lemon-lime, grape, grape, grape, grape, grape
B) Sample space = watermelon, lemon-lime, grape
C) Sample space = 2, 3, 5
D) Sample space = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
The sample space is (a) watermelon, watermelon, lemon-lime, lemon-lime, lemon-lime, grape gumballs, grape gumballs, grape gumballs, grape gumballs, grape gumballs
How to determine the sample spaceFrom the question, we have the following parameters that can be used in our computation:
2 watermelon, 3 lemon-lime, and 5 grape gumballs
Rewrite the items according to their frequencies
So, we have the following representation
watermelon, watermelon, lemon-lime, lemon-lime, lemon-lime, grape gumballs, grape gumballs, grape gumballs, grape gumballs, grape gumballs
The above represents the sample space
Hence, the sample space is (a)
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Two airplanes leave an airport at the same time and travel in opposite directions. One plane travels 60km\h slower than the other. If the two planes are 7304 kilometers apart after 4 hours, what is the rate of each plane?
Answer:
4 V + 4 (V - 60) = D where D is distance apart after 4 hrs
8 V - 240 = 7304
V = 943 km/hr
and V2 = 943 - 60 = 883 km/hr where second plane is 60 km/hr slower
ead the situations below and determine which relationship is not functional.
Situation 1: a cell phone bill to the amount of minutes used
Situation 2: the perimeter of a square to the length of one of the sides of a square
Situation 3: the total amount of money charged monthly on credit cards to the number of credit cards owned
Situation
does not represent a function.
This is because
.
There can be multiple outputs (monthly charges) for a given input (number of credit cards), violating the definition of a function. hence, Situation 3 does not represent a function.
Situation 3: the total amount of money charged monthly on credit cards to the number of credit cards owned does not represent a function.
In a function, each input (or x-value) should have a unique output (or y-value). However, in this situation, the total amount of money charged monthly on credit cards depends on the number of credit cards owned. It is possible to have different credit card numbers but still have the same total amount of money charged monthly.
For example, two people could own different numbers of credit cards but have the same monthly charges.
As a result, the definition of a function can be violated by having many outputs (monthly charges) for a single input (number of credit cards).
Because of this, case 3 does not represent a function.
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