Y is inversely proportional to the square of x. if y = 5 when x = 3, then what is y when x is 7?

The first derivatives for the given functions are:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For  \(y = 100200x + 7x,\) the first derivative is dy/dx = 100207.

For \(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

To find the first derivative for each of the given functions, we'll use the power rule, constant rule, and chain rule as needed.

For the function\(y = 3x^2 + 5x + 10:\)

Taking the derivative term by term:

\(d/dx (3x^2) = 6x\)

d/dx (5x) = 5

d/dx (10) = 0

Therefore, the first derivative is:

dy/dx = 6x + 5

For the function y = 100200x + 7x:

Taking the derivative term by term:

d/dx (100200x) = 100200

d/dx (7x) = 7

Therefore, the first derivative is:

dy/dx = 100200 + 7 = 100207

For the function \(y = ln(9x^4):\)

Using the chain rule, the derivative of ln(u) is du/dx divided by u:

dy/dx = (1/u) \(\times\) du/dx

Let's differentiate the function using the chain rule:

\(u = 9x^4\)

\(du/dx = d/dx (9x^4) = 36x^3\)

Now, substitute the values back into the derivative formula:

\(dy/dx = (1/u) \times du/dx = (1/(9x^4)) \times (36x^3) = 36x^3 / (9x^4) = 4/x\)

Therefore, the first derivative is:

dy/dx = 4/x

To summarize:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For y = 100200x + 7x, the first derivative is dy/dx = 100207.

For\(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

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We need to find the probability that you are randomly assigned a General Practitioner or a doctor under the age of 45.

In order to find this probability, we need to find the number of doctors that are General Practitioner or under under the age of 45. Then, divide that number by he total of 17.

We know that 7 doctors are General Practitioners. And 2 of them are also under the age of 45.

Therefore, since ther are 4 doctors that are under the age of 45, there are 2 additional doctors, besided those 2 that follow in both categories, there are under the age of 45.

Summarizing, the number of doctors that are General Practitioner or a doctor under the age of 45 is:

Notice that this result can also be obtained by the formula:

where A is the set of General Practitioners, B is the set of doctors under the age of 45, and the symbol |...| represents the number of elements in that set:

Therefore, the required probability is:

Answer

Answer:

x(x²+x+1)

Step-by-step explanation:

im not surewhat answer u want but take note this is FACTORIZATION

Answer:

45º

Step-by-step explanation:

Since we know the relatiionship of a 45-45-90 degree triangle, we can go two ways. Either we can use this to find CA and get the tangent of (6/6) or we can go straight to it. The hypotenuse in a 45-45-90 is always 6√2 and we know it is a right triangle so we can confirm this. So, measure of angle B is 45º.

M a t h w a y will help you my friend!

I was struggling with math and using it got me get back on track :)

The set of vectors that form an

orthonormal basis

for R² is B. {[1,0]ᵀ,[0,1]ᵀ}.

To determine which of the sets of vectors form an orthonormal basis for R², we need to check if the vectors are orthogonal and have a length of 1. For set A, we can calculate the dot product of the two vectors and see that it is not equal to zero, so they are not orthogonal. For set C, the dot product of the two vectors is also not equal to zero, so they are not orthogonal. For set D, we can calculate the length of the vectors and see that they are not equal to 1, so they do not have a length of 1. Therefore, the only set of vectors that form an orthonormal basis for R² is set B, which consists of the standard basis

vectors

{[1,0]ᵀ,[0,1]ᵀ}.

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Linear functions are functions that have uniform and constant rates.

(a) Ordered pairs

The ordered pair is given as (-9,-4) and (-3,-16).

The slope (m) is calculated as:

\(m = \frac{y_2 -y_1}{x_2 -x_1}\)

So, we have:

\(m = \frac{-16 --4}{-3--9}\)

\(m = \frac{-12}{6}\)

\(m = -2\)

Hence, the slope (m) is 2

(b) The rate of y = -7x + 1

The function is given as \(y = -7x + 1\)

A linear function is represented as:

\(y = mx + b\)

Where m represents the slope/rate

By comparison

\(m = -7\)

Hence, the rate (m) is -7

(c) The y-intercept of a linear function

The y-intercept of a linear function is where the x-value is 0

From the table,

y = 6 when x = 0

Hence, the y-intercept (b) is 6

(d) Rate of a linear function

From the table, we have the following ordered pairs

(2,18) and (0,6).

The slope (m) is calculated as:

\(m = \frac{y_2 -y_1}{x_2 -x_1}\)

So, we have:

\(m = \frac{6 -18}{0-2}\)

\(m = \frac{-12}{-2}\)

\(m = 6\)

Hence, the slope (m) is 6

(e) Equation of a linear function

From the table, we have the following ordered pairs

(0,-5) and (-3,4).

The slope (m) is calculated as:

\(m = \frac{y_2 -y_1}{x_2 -x_1}\)

So, we have:

\(m = \frac{4 --5}{-3-0}\)

\(m = \frac{9}{-3}\)

\(m = -3\)

The equation is then calculated as:

\(y = m(x - x_1) + y_1\)

So, we have:

\(y = -3(x - 0) -5\)

\(y = -3x -5\)

Hence, the linear equation is \(y = -3x -5\)

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Answer: It's 64

Hope this helps!

The relationship between attending the 5:00 a.m. training session and subsequent improved game performance is an example of a correlation.

In daily speech, the term "correlation" designates an association of some kind. We could claim to have observed a connection between wheezy episodes and foggy days.

Specifically, it is a positive correlation because attending the 5:00 a.m. session is associated with an increase in game performance. It is important to note that correlation does not necessarily imply causation, and further research would be needed to determine if attending the 5:00 a.m. session directly causes improved game performance or if there are other factors at play.

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Answer:

x= 10, x=1

Step-by-step explanation:

(x-1)(x-10)=0

then solve for x

Answer:

\(f(-1)=-11\\f(0)=16\\f(2)=22\)

Step-by-step explanation:

\(\displaystyle f(-1)=3(-1)-8=-3-8=-11\\f(0)=3(0)+16=16\\f(2)=3(2)+16=6+16=22\)

Given:

Consider the given polynomial is:

\(x^3+4x^2+16x+64\)

To find:

The complete factorization of the given polynomial.

Solution:

We have,

\(x^3+4x^2+16x+64\)

Using grouping method, we get

\(=(x^3+4x^2)+(16x+64)\)

\(=x^2(x+4)+16(x+4)\)

\(=(x+4)(x^2+16)\)

\(=(x+4)(x+4i)(x-4i)\)         \([\because x^2+y^2=(x+iy)(x-iy)]\)

Therefore, the correct option is C.

Answer:

680x + 170

Step-by-step explanation:

calculate the product

4\(x\) x170 +170=

680x+ 170

If the numbers cannot be repeated, there can be 5040 possible codes. The probability to select the correct code in first try will be 1/5040. If the digits can be repeated then there can be 10000 possible combinations.

The code can be of digits between 0 to 9. Hence we have a choice of 10 digits

If the number cannot be repeated then the first digit of the code can be selected in

10 ways.

Similarly the second, third and fourth can be selected in 9, 8, and 7 ways.

Hence the code can be formed in

10 X 9 X 8 X 7 ways

= 5040ways

Now out of these 5040 codes, there can be only one code.

The probability to select it in first try i

1/5040

If the digits can be repeated, then we can use 10 digits for every specific number. Hence there can be

10 X 10 X 10 X 10 ways

= 10000 codes.

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Answer:

16.

Step-by-step explanation:

7×4= 28

since this is a ratio you so the same to the other side

4×4=16

These statements and proofs in mathematics are

a.  If a is a divisor of b, then it can also be a divisor of the expression (17b174 – 29b15! + 9006).

b. The sum of three odd numbers and two even numbers is always even.

c. The expression En 2p + 1 is always even when n is odd and always odd when n is even.

d. If a is not divisible by 4, then a is odd.

e. If a ≡ b (mod n), then a and b have the same remainder when divided by n.

f. If x? + 17x5 + 4x3 > x6 + 11x4 + 2x2, then x > 0.

a. To prove that if a | b, then a | (17b174 – 29b15! + 9006), we can use the fact that if a | b, then a | (k * b) for any integer k. In this case, we have a = 1 and b = (17b174 – 29b15! + 9006).

Therefore, a | (17b174 – 29b15! + 9006).

b. To prove that the sum of 3 odd numbers and 2 even numbers is odd, we can consider the parity of the numbers.

Let's say we have three odd numbers represented by 2k + 1, and two even numbers represented by 2m.

The sum can be written as (2k + 1) + (2k + 1) + (2k + 1) + 2m + 2m. Simplifying this expression, we get 6k + 2 + 4m. Notice that this expression can be further simplified to 2(3k + 1 + 2m), which is an even number.

Therefore, the sum of 3 odd numbers and 2 even numbers is even.

c. To prove that En 2p + 1 is always even when n is odd and always odd when n is even, we can consider the parity of the terms.

When n is odd, let's say n = 2k + 1, the expression becomes E(2k + 1)(2p + 1). Expanding this expression, we get E(4kp + 2k + 2p + 1).

Notice that this expression can be further simplified to 2(2kp + k + p) + 1, which is an odd number.

When n is even, let's say n = 2k, the expression becomes E(2k)(2p + 1). Expanding this expression, we get E(4kp). This expression is divisible by 2 and can be written as 2(2kp), which is an even number.

d. To prove that if a is not divisible by 4, then a is odd, we can consider the possible remainders of a when divided by 4.

If a is not divisible by 4, then the possible remainders are 1, 2, or 3. We can rule out the possibility of a being 2 or 3, as those are even numbers.

Therefore, if a is not divisible by 4, the only possibility is that a has a remainder of 1 when divided by 4, which means a is odd.

e. To prove that if a ≡ b (mod n), then a and b have the same remainder when divided by n, we can use the definition of congruence. If a ≡ b (mod n), it means that a - b is divisible by n.

This can be written as a - b = kn for some integer k. When a and b are divided by n, they both have the same remainder k.

Therefore, a and b have the same remainder when divided by n.

f. To prove that if x? + 17x5 + 4x3 > x6 + 11x4 + 2x2, then x > 0, we can rearrange the terms and factorize. By moving all terms to one side, we get x6 - x? + 11x4 - 17x5 + 2x2 - 4x3 > 0.

We can notice that all terms are even-degree polynomials, which means they are non-negative for all real values of x.

Since the left-hand side is greater than zero, it implies that x must be greater than zero to satisfy the inequality. Therefore, x > 0.

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The required range of the given function g(x) = -1/2 |x-6| + 1 will be g(x) ≤ 1 or in internal notation form as (-∞, 1]. which is the correct answer would be an option (A).

The function is given in the question below as:

g(x) = -1/2 |x-6| + 1

We have to determine the range of the given function.

As per the given question, we have

⇒ g(x) = -1/2 |x-6| + 1

The range of an absolute function of the form:-

c|ax+b|+k is :f (x) ≤ k

In this case k = 1

⇒ g(x) ≤ 1

\(\mathrm{Range\:of\:}-\frac{1}{2}\left|x-6\right|+1:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\le \:1\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:1]\end{bmatrix}\)

Therefore, the required range of the given function will be g(x) ≤ 1 or in internal notation form as (-∞, 1].

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Answer:

Her average speed is 45 mph

Step-by-step explanation:

Let the average speed be x mph

Time taken complete the journey = distance/ average speed

Time = 300/x

Now , at 9 mph less, she could have only traveled 240 miles in same time

At 9 mph less, the average speed is x-9

so the time would be 240/x-9

since the time is same as before;

300/x = 240/x-9

Divide both sides by 60

5/x = 4/x-9

Cross multiply

5(x-9) = 4(x)

5x - 45 = 4x

5x -4x = 45

x = 45 mph

Answer:

false

Step-by-step explanation:

you have to multiply the 52 and 68, making the n1 = 5577, not 5575

Still 5 seconds.

(Assuming the Earth around that building is flat.

Answer:

x = 42

Step-by-step explanation:

x - 10 = 32

32 + 10 = 42

Answer: Angles ∠4 and∠2 are not alternate interior angles and neither are ∠1 and ∠5

Step-by-step explanation: Khan Academy

Joe made the mistake by guessing Angles ∠4 and∠2 are not alternate interior angles and neither are ∠1 and ∠5.

The correct option is (b).

The fundamental characteristics listed below make it simple to recognise parallel lines.

Given:

WE have to  prove that the sum of a triangle's interior angle measures is 180°

According to the figure <1 and <4 are the alternate interior angle and <2 and <5 are  alternate interior angle.

So, Joe made the mistake by guessing Angles ∠4 and∠2  and ∠1 and ∠5 are alternate interior angles.

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In 2019, the number of death due to measles is approximately 77000, the number of persons who developed pneumonia is 78, and percent decrease in number of measles between 2014-2015 is 15.25%.

From graph, we see that global number of measles cases are approximately 410000.

The 75% of these measles cases are from developing countries.

So, number of cases in developing countries = 0.75×410000 = 307500.

In US, the fatality rate is = 0.2% , whereas in developing countries the fatality rate is = 25%.

So, fatalities from the measles in developing countries is ;

⇒  25% of 307500 = 0.25 × 307500 = 76875, on rounding to nearest thousand ≈ 77000.

If there are 1296 people with measles in US in the year2019, and 6% of people contract pneumonia, then in U.S. the number of people that developed pneumonia in year 2019 is = 0.06 × 1296 = 77.76 ≈ 78.

The Number of cases in 2014 is approximately = 295000,

The Number of cases in 2015 is approximately = 250000,

So, the decrease in number of cases is = 45000,

The percentage relative change = (45000/295000) × 100 = 15.25%.

Therefore, the percent decline in number of cases is 15.25%.

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The given question is incomplete, the complete question is

The fatality rate for measles is 0.2% in the United States. However, in developing countries it is approximately 25%. According to the World Health Organization about 75% of measles cases occurred in developing countries in 2019. How many deaths from measles are likely to have resulted? Round your answer to the nearest thousand.

6% of people who contract measles also develop pneumonia. If there were 1,296 cases of the measles in the United States in 2019, how many people developed pneumonia? Round to the nearest whole person.

Approximately what percentage (relative change) did measles decline between 2014-2015?

Answer:

18

Step-by-step explanation:

54/18=3

72/18=4

90/18=5

Answer:

18

Step-by-step explanation:

GCF of 54, 72, 90 is:

54÷3= 18

72÷4= 18

90÷5= 18

The GCF of 54, 72, and 90 is 18.