Find the absolute value of the jacobian, ∣∣∂(x,y)∂(s,t)∣∣, for the change of variables given by x=s+5t,y=3s+8t

Step 1

Find the slope of the given line

Let

[tex]A(-4,4)\ B(4,-2)[/tex]

we know that

the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{-2-4}{4+4}[/tex]

[tex]m=\frac{-6}{8}[/tex]

[tex]m=-\frac{3}{4}[/tex]

Step 2

Find the slope of the line perpendicular to the given line

we know that

if two lines are perpendicular

then

the product of their slopes is equal to minus one

so

[tex]m1*m2=-1[/tex]

we have

[tex]m1=-\frac{3}{4}[/tex] ------> slope of the given line

Find the value of m2

[tex]m2=-1/m1[/tex]

substitute

[tex]m2=-1/(-3/4)[/tex]

[tex]m2=\frac{4}{3}[/tex]

Step 3

Find the equation of the line

we know that

the equation of the line into point-slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{4}{3}[/tex]

x-intercept is equal to [tex]6[/tex] --------> is the point [tex](6,0)[/tex]

substitute in the formula

[tex]y-0=\frac{4}{3}(x-6)[/tex]

[tex]y=\frac{4}{3}x-8[/tex]

therefore

the answer is the option

[tex]y=\frac{4}{3}x-8[/tex]

The largest number which divides 149 and 101 , leaving remainder of 5 : 48

The division operation is one of the basic arithmetic operations

Common signs used are [tex] \large {\boxed {:}}} [/tex] or [tex] \large {\boxed {\slash}} [/tex]

The division is written by placing the numerator above the denominator with a horizontal line between them or use a slash with the numerator's position and the denominator is parallel

The division is actually an iterative subtraction operation (as many as the number of divisors)

Division is the opposite of multiplying

The general form of division can be stated by:

[tex] \large {\boxed {\bold {divident:divisor=quotient+remainder}} [/tex]

example:

7: 3 = 2 + 1

Division operation statement:

"7 divided by 3 equals 2 remainder 1"

A number have many factors

A common factor is a factor of two / more numbers.

Greatest common factor (GCF or HCF = Highest Common Factor) is the largest of the common factors

The largest number which divides 149 and 101 leaving remainder of 5

Division operation:

We find the value of x which is the GCF of the numbers 144 and 96

149 - 5 = 144

101 - 5 = 96

We look for GCF from factors of 144 and 96

GCF of 144 and 96 is 48

Or we can use prime factors:

144: 2⁴ X 3²

96: 2⁵ X 3

GCF = 2⁴ X 3 = 48

Highest common factor

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The GCF of any two even numbers

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Keywords : Greatest common factor , division, prime factors

Answer:

Option A is correct that is [tex]360^{\circ}[/tex]

Step-by-step explanation:

We have been given a triangle  we need to tell which one of these is a triangle below to map onto itself.

[tex]360^{\circ}[/tex] rotation is the complete rotation which eventually leads to the same figure which is given.

Option A is correct that is [tex]360^{\circ}[/tex] that will cause the triangle below to map onto itself.

Answer:

C

Step-by-step explanation:

k is the slope of the line

The equation of the line is y = kx. Therefore, the special thing about k is that it is the slope of the line.

Using a slope intercept equation,

y = kx + b

where

Therefore, the y-intercept of the line y = kx is zero.

What is special about k is that it is the slope of the line y = kx.

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Answer:

Option: B is the correct answer.

The equation of the new function g(x) on flipping the function f(x) over the x-axis is:

[tex]g(x)=-2^x[/tex]

Step-by-step explanation:

We are given a graph of the exponential function f(x) which is represented by:

[tex]f(x)=2^x[/tex]

We know that when a graph of a function is reflected or flipped over the x-axis then the the change that take place to the function is that f(x) is transformed to -f(x).

( Since on flipping the function over the x-axis the positive value of the function get changed to negative and the negative value of the function is changed to positive)

Hence, the equation for the new function is:

[tex]g(x)=-f(x)\\\\g(x)=-2^x[/tex]

Answer:

Heres the correct answer. Hope this helps anyone who needs it!!!

Step-by-step explanation:

The polynomial function is one that involves only non-negative number powers of x, unlike a polynomial, cubic, or quartic function, and further calculation can be defined as follows:

Given:

[tex]\bold{f(x)=x^4-3x^3-23x^2+75x-50}[/tex]

To find:

Solution:

[tex]\to \bold{f(x)=x^4-3x^3-23x^2+75x-50}[/tex]

Let [tex]\bold{x=2}[/tex]

[tex]\to \bold{f(2)=2^4-3(2)^3-23(2)^2+75(2)-50}\\\\\to \bold{f(2)=16-3(8)-23(4)+75(2)-50}\\\\\to \bold{f(2)=16-24-92+150-50}\\\\\to \bold{f(2)=166-166}\\\\\to \bold{f(2)=0}\\\\[/tex]

So the factor is [tex]\bold{(x-2)}[/tex].

[tex]\to \bold{(x-5)(x-2)(x-1)(x+5)}\\\\[/tex]

Therefore, the final answer is "[tex]\bold{ f(x)=(x-5)(x-2)(x-1)(x+5)}\\\\[/tex]".

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First let us calculate for the z score using the formula:

z = (x – u) / s

where x = 8, u is the mean = 12.7 years, s is the standard deviation

z = (8 – 12.7) / 2.5

z = -1.88

From the standard probability tables, the p value at z = -1.88 is:

P = 0.0301 = 3.01%

Answer:

D) 8²

Step-by-step explanation:

Evaluate each of the choices and see which one is equal to 64.

_____

It helps if appropriate mathematical symbols are used.

The exponent form of the given multiplication 5x5x5x5x5x5 is 5⁶.

Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied. Since 2 is the "base" and 5 is the "exponent,"

it can be represented as 2x2x2x2=25 for the number 32. This phrase should be understood as "two to the fifth power."

The given expression is 5x5x5x5x5x5. The exponent form of the number will be written below,

E = 5x5x5x5x5x5

E = 5⁶

Therefore, the exponent form of the given multiplication 5x5x5x5x5x5 is 5⁶.

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Answer: 9 hours

Step-by-step explanation:

Given proportion : [tex]\frac{\text{180 Kilometers}}{\text{3 hours}}=\frac{\text{540 Kilometers }}{x}[/tex]

To find the value of x , we need to multiply 3x hours and divide 180 Kilometers on both the sides, we get

[tex]\text{x}=3\times\frac{540}{180}\text{hours}\\\\\Rightarrow\ x=3\times3\\\\\Rightarrow\ x=9\text{ hours} [/tex]

Hence, the value of x = 9 hours.

Answer:

y = [tex]\frac{-3x}{4}[/tex] + [tex]\frac{1}{4}[/tex].

Step-by-step explanation:

Given : Graph of slope [tex]\frac{-3}{4}[/tex] and passes through the point (–5, 4).

To find : Which is the equation of the line.

Solution : we have given that point ( -5 ,4)

By equation of line ([tex]y-y_{1}) = m (x -x_{1})[/tex]

y - 4 =  [tex]\frac{-3}{4}[/tex]( x +5).

y - 4 =  [tex]\frac{-3x}{4}[/tex] +[tex]\frac{-15}{4}[/tex].

On adding 4  both sides we get,

y = [tex]\frac{-3x}{4}[/tex] + [tex]\frac{-15}{4}+4[/tex].

y = [tex]\frac{-3x}{4}[/tex] + [tex]\frac{-15 +16}{4}[/tex].

y = [tex]\frac{-3x}{4}[/tex] + [tex]\frac{1}{4}[/tex].

Therefore, y = [tex]\frac{-3x}{4}[/tex] + [tex]\frac{1}{4}[/tex].

Answer:

the answer is 3

Step-by-step explanation:

just got it right on iready

The company which  has the least expensive cartridge is:

                       LMN office company.

LMN Office Company sells 20 printer cartridges for $240.

This means that the cost of 1 printer cartridge is:  $ 240/20=$ 12

Also, . XYZ Supplies has a box of printer cartridges for $150.

The box contains 12 cartridges.

This means that the cost of 12 cartridge is: $ 150

Hence, cost of 1 printer cartridge is: $ 150/12=$ 12.5

Hence, the company which has the least expensive cartridge is:

            LMN Office Company.

( Since, 12 < 12.5  )

Jase's chickens laid more eggs.

From the information given, Jase farm has 9 chickens and each laid 3 eggs, therefore the total eggs laid will be:

= 9 × 3

= 27 eggs.

On the other hand, Ednas farm has chickens which lay a total of 23 eggs. Therefore, since 27 eggs are more than 23 eggs, Jase's chickens laid more eggs.

In conclusion, Jase's chickens laid more eggs.

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Final answer:

There is a family of normal probability distributions, each representing different populations or sets of data with varying mean and standard deviation values.

Explanation:

Yes, there is a family of normal probability distributions. The normal distribution is a continuous probability distribution that can take on different forms depending on the mean and standard deviation. The family of normal distributions is characterized by different mean and standard deviation values, which result in different shapes of the distribution curve.

For example, the standard normal distribution has a mean of 0 and a standard deviation of 1, and its curve is symmetrical around the mean. Other normal distributions may have different means and standard deviations, resulting in curves that are shifted or stretched.

Each normal distribution in the family represents a different population or set of data, and knowing the specific mean and standard deviation allows us to calculate probabilities and make statistical inferences.

To express the number of miles driven, y, in terms of the number of hours driven, t, we first find the speed and then use it to formulate the equation of the line as y = 60t. However, to accurately represent the entire trip, we must include the initial 100 miles driven in 2 hours, leading to y = 60t - 20 as the final equation.

To write an equation that gives the number of miles driven, y, in terms of the number of hours driven, t, we can use the relationship between distance and travel time. Given that after two hours you had gone 100 miles and after 8 hours, you reached your destination, which is 460 miles away, we establish two points on our distance-time graph: (2, 100) and (8, 460).

Using the two points, we can find the slope of the line, which represents the speed:
Slope (speed) = (change in distance) / (change in time) = (460 - 100) miles / (8 - 2) hours = 360 miles / 6 hours = 60 miles/hour.

We can now express the equation of the line as y = mx + b, where m is the slope and b is the y-intercept. The y-intercept represents the distance at time zero, which for most driving scenarios we assume to be 0 miles. Thus, the equation becomes y = 60t. However, this equation would not accurately represent the entire trip since it doesn't account for the initial 100 miles driven in the first 2 hours.

To adjust for that, we'll introduce an offset for the initial 100 miles traveled in the first 2 hours. The y-intercept would be 100 miles less than if we had started from 0 miles at 0 hours. The corrected equation for the entire trip would be of the form y = 60t + b, where b = y - 60t and y are the miles covered in the initial 2 hours, which is 100 miles. Substituting the values, we get b = 100 - 60 x 2 which equals -20.

The final equation, accounting for the first 2 hours of travel, would therefore be: y = 60t - 20.