Which point would be a solution to the system of linear inequalities shown below

The direct variation equation for x and y is y = k x.

The required value of y is 18 when the value of x is 12.

The definition of direct variation is the relationship between two variables when one is a fixed multiple of the other.

Given that,

Y directly varies as x.

And the value of y is 12 when value of x is 8.

According to given condition,

y directly varies as x, let y is k times multiple of x.

Implies that,

y = k . x          (1)

Substitute, x = 8 and y = 12 in equation (1),

12 = k × 8

k = 12 / 8

k = 3 / 2

To find the value of y when x = 12,

Substitute values k = 3/2 and x = 12 in equation (1),

y = 3/2 × 12

y = 18

The value of y is 18 when the value of x is 12.

To know more about Direct variation on:

https://brainly.com/question/14254277

#SPJ1

Answer:

1)  See attachment.

2a)  Initial Amount = 3600.
      Growth/Decay factor = ³/₂.

2b)  Growth function.

\(\textsf{3)}\;\;\; f(x)=1*2^x\)

4)  69 lions.

Step-by-step explanation:

General form of an exponential function

\(\boxed{y=ab^x}\)

where:

If b > 1 then it is an increasing function.

If 0 < b < 1 then it is a decreasing function.

Given function:

\(f(x)=\left(\dfrac{1}{2}\right)^x\)

Complete the table of ordered pairs by substituting the values of x into the given function:

\(\begin{array}{|c|c|}\cline{1-2}x&y\\\cline{1-2}-3&8\\\cline{1-2}-2&4\\\cline{1-2}-1&2\\\cline{1-2}0&1\\\cline{1-2}1&0.5\\ \cline{1-2}\end{array}\)

Plot the ordered pairs on the given coordinate plane (see attached graph) and draw a curve through them.

This exponential function has a horizonal asymptote at y = 0.  

As the value of x approaches infinity, the function gets closer and closer to y = 0 (x-axis) but doesn't actually touch it.

Given exponential function:

\(f(x)=3600\left(\dfrac{3}{2}\right)^x\)

Part 2a

To find the initial amount "a" and growth/decay factor "b", simply compare the given function with the general exponential function.  

Therefore:

Part 2b

As  b = ³/₂ and ³/₂ > 1, this is a growth function (increasing).

"a" is the initial value (y-intercept) of an exponential function.

The y-intercept of a function is the y-value when x = 0.  

Therefore, from inspection of the given table, the y-intercept of the given function is 1.

Therefore, a = 1.

"b" is the base (growth/decay factor) of an exponential function.

To find the base (growth/decay factor) of the given function, divide a value of y by its preceding value of y:

\(\implies b=\dfrac{4}{2}=\dfrac{2}{1}=\dfrac{1}{\frac{1}{2}}=...=2\)

Therefore, b = 2.

So the exponential function for the given table is:

\(f(x)=\boxed{1}*\boxed{2}\;^x\)

If the population of lions started at 80, then the initial value "a" of the exponential function is 80.

If the population has been decreasing by 3.5% per year, then the population each year is 96.5% of the previous year since:

Therefore, the base "b" of the exponential function is 0.965 (in decimal form).

Substitute the found values of a and b into the exponential function formula to create an exponential function for the given scenario:

\(\boxed{f(t)=80(0.965)^t}\)

where:

To find how many lions will there be in four years, substitute t = 4 into the found exponential equation:

\(\implies f(4)=80(0.965)^4=69.37440005\)

Therefore, there will be 69 lions in four years.

Answer:

\(\frac{4}{5}\)

Step-by-step explanation:

If you have completed \(5\) questions, you still have \(25-5=20\) more questions to answer. We need to find what fraction \(20\) is of \(25\), if that makes sense. A fraction is simply a part over a whole. In this case, the part is \(20\) and the whole is \(25\). Therefore, the fraction we are looking for is \(\frac{20}{25}\), which simplifies to \(\frac{4}{5}\). Hope this helps!

Answer:

4\5

Step-by-step explanation:

25-5

20\25

4\5

hope this helps!

Score-based generative modeling through SDEs is an active area of research, and there are many variations and extensions of the method that are being developed to improve its performance and scalability.

In this method, the goal is to learn a set of SDEs that can generate samples that are similar to the true data distribution. The SDEs are typically specified as a system of coupled differential equations that describe the evolution of the system over time. The parameters of the SDEs are learned by maximizing the likelihood of the data under the model, which can be achieved by minimizing a loss function that is derived from the score function.

One advantage of this approach is that it can be used to model complex, high-dimensional data distributions, such as images or videos, that are difficult to model using traditional parametric methods. Another advantage is that it can handle missing data or irregularly sampled data, which can be common in many real-world datasets.

To know more about differential equation,

https://brainly.com/question/14620493

#SPJ11

The inverse equation of the equation is: A =T2/3

The equation is given as:

T = A3/2

To calculate the inverse equation, we start by multiplying both sides of the equation by 2

T2 = A3

Next, we divide both sides of the equation by 3

A =T2/3

The equation cannot be further simplified

Hence, the inverse of the equation is: A =T2/3

Read more about change of subject at:

https://brainly.com/question/790938

The  value of A in terms of T is \(A=\frac{2}{3}T\)

The given equation is,

                       \(T=\frac{3}{2}A\)

We have to find value of A in terms of T.

                      \(T=\frac{3}{2}A\\\\A=T\div \frac{3}{2}\\ \\A=T*\frac{2}{3}\\ \\A=\frac{2}{3}T\)

Thus, the  value of A in terms of T is \(A=\frac{2}{3}T\)

Learn more about the Inverse equation here:

https://brainly.com/question/13998680

Abby climbed above her original starting position of a height of 18 feet .

According to the graph Abby's climb begins at 4 feet in 0 minute and ends at 0 feet in 22 minutes. However, Abby reaches her highest point at 22 feet in 8 minutes .

Starting point of Abby's climb = 4 feet in 0 minute

End point of Abby's climb = 0 feet in 22 minutes

Highest point of Abby's climb = 22 feet in 8 minutes

Abby climbed above her original starting position = highest point - starting point

Abby climbed above her original starting position = 22 feet - 4 feet

Abby climbed above her original starting position = 18 feet .

To know more about height click here :

https://brainly.com/question/27944398

#SPJ4

Answer:

18 days

Step-by-step explanation:

3days to consume 1/2 apple

3days/ 1/2 apple or

6 days to consume 1 apple

So 6 days for 1 apple + another 6 days for another apple + one more six days for another apple = 18 days for 3 apples

Answer:

18

Step-by-step explanation:

I set up a proportion

1/2 apple/3 days

3 apples/ x

I cross multiplied after that

Answer:

they look similar but one of them is upside down.

The existence of a set to which every singleton belongs leads to a contradiction.

Suppose there exists a set A such that every singleton {x} belongs to A. Then, using A, we can construct a set B = {{x} | x ∉ x}, which contains all sets that are not elements of themselves.

This leads to a contradiction, since if B belongs to itself, then B must not belong to itself. And if B does not belong to itself, then B must belong to itself. Hence, there cannot exist a set to which every singleton belongs. This result is known as Russell's paradox.

To know more about singleton click on below link:

https://brainly.com/question/21850798#

#SPJ11

(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

To know more about nonzero vector refer here:

https://brainly.com/question/32673773#

#SPJ11

The solution of the given system is \(x1 = 0, x2 = 1, x3 = 3, and x4 = -3/8.\)

a. The augmented matrix of the given linear system is given as;

\([1 2 3 4 13][2 -1 1 0 8][3 -2 1 2 13]\)

The required linear system can be solved using the Gaussian elimination method.

The elementary row operations applied on the matrix to find its echelon form are given as;

\(R2-2R1 - > R2R3-3R1 - > R3[1 2 3 4 13][0 -5 -5 -8 -18][0 -8 -8 -10 -26]\)

Again applying the elementary row operations on the above matrix to find its reduced row echelon form, we get;

\(2R2-R3 - > R3 -1R2+2R1 - > R1 -2R3+3R1 - > R1[-1 0 0 2 3][0 1 1.6 2.4 3.6][0 0 0 0 0]\)

Thus, the solution of the given system is \(x1 = 3-2x4, x2 = 3.6-1.6x3-2.4x4, x3\) is free and x4 is also free.

b. The augmented matrix of the given linear system is given as;

\([1 1 -1 -1 1][2 5 -7 -5 -2][2 -1 1 3 4][5 2 -4 2 6]T\)

he required linear system can be solved using the Gaussian elimination method.

The elementary row operations applied on the matrix to find its echelon form are given as;

\(R2-2R1 - > R2R3-2R1 - > R3R4-5R1 - > R4[1 1 -1 -1 1][0 3 -5 3 0][0 -3 2 5 2][0 -3 1 7 1]\)

Again applying the elementary row operations on the above matrix to find its reduced row echelon form, we get;

\(R2/3 - > R2R3+R2 - > R3R4+R2 - > R4[1 1 -1 -1 1][0 1 -5/3 1 0][0 0 -1/3 8/3 2][0 0 -8/3 10/3 1]R4/(-8/3) - > R4R3+8/3R4 - > R3 -R2+5/3R3 - > R2R1+R3 - > R1[1 0 0 0 0][0 1 0 0 1][0 0 1 0 3][0 0 0 1 -3/8]\)

Thus, the solution of the given system is \(x1 = 0, x2 = 1, x3 = 3, and x4 = -3/8.\)

Know more about augmented matrix here:

https://brainly.com/question/12994814

#SPJ11

Account A: Decreasing at 8 % per year

Account B: Decreasing at 10.00 % per year

Account B shows the greater percentage change

Exponential function, in mathematics, a relation of the form y = \(a^x\), with the independent variable x ranging over the entire real number line as the exponent of a positive number a.

Given:

f(x) = 9628(0.92)ˣ

A)The general formula for an exponential function is

y = a\(b^x\), where b = the base of the exponential function.

if b < 1, we have an exponential decay function.

So, ƒ(x) decreases as x increases.

Thus, Account A is decreasing each year.

B) Now, the formula for an exponential decay function as:

y = a(1 – b)ˣ, where

1 – b = the decay factor

If we compare the two formulas, we find

0.92 = 1 - b

b = 1 - 0.92 = 0.08

b = 8 %

The account is decreasing at an annual rate of 8 %.

The account is decreasing at an annual rate of 10.00 %.

Account B recorded a greater percentage change in the amount of money over the previous year.

Learn more about Exponential Function here:

https://brainly.com/question/14355665

#SPJ1

The translation would be:

A(1,2) = > A(-1, -2)

B(5,1) = > B(3,-3)

C(5,4) = > (3, 0)

Number 3

the triangle R'S'T' is a translation of the vector <3,2>

Number 4

J(4,5) with the translation ( x + 6, y -3)

J(4 + 6, 5 - 3)

J(10, 2)

The answer would be J(10,2)

As angle OAB =40-degree, angle AOB is 100 degrees according to the properties of circle and triangle.

Some Properties of circle are distance from center of the circle to each point on the circumstances are equal. hence, OA=OB

Diameter is twice of radius.

The triangle having two equal side length is called isosceles triangle. In the figure, triangle OAB is an isosceles as OA=OB=radius

According to the criteria of isosceles triangle angle OAB =OBA =40°

hence, angle AOB= 180 degrees - (40°+40°) [angle sum of triangle =180°]

                  angle AOB= 100 degrees.

We get, AOB = 100 degrees

to know more about types of triangle visit:

https://brainly.com/question/2773823

#SPJ1

Answer: 46/100 or in its simplest form it would be 23/50

Step-by-step explanation:

Answer:

46/100

Step-by-step explanation:

It's just how you say the number.   forty six hundredths right,

Pls mark Brainliest

Answer:

9 x 3/9  is less than 9

Step-by-step explanation:

Answer:

No because when multiplyin a fraction your outcome is less than the orginal

number most likely

Step -by-step explanation:

Answer:

54

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Answer: 3x+6=9

3x=3

x=1

Step-by-step explanation:

Answer:

x = 1

Step-by-step explanation:

To solve this, we must first isolate the variable 'x':

3x + 6 = 9

      -6   -6

3x = 9 - 6

Combine like terms

3x = 3

Isolate 'x' fully

3x = 3

/3    /3

x = 1

Hope this helps :)

Answer:

The two ratios are not equivalent

Step-by-step explanation:

If two ratios a/b and a/c are the same and we cross multiply, the left side should equal the right side

In other words if a/b = c/d

a x d = b x c

So if 6/7 = 24/27,

6 x 27 = 7 x 24

6 x 27 = 162

7 x 24 = 168

Since 162 ≠ 168 the two ratios are not equal

The given sum can be simplified to Σ 3(k+2)2 -7k + 116 where k is an integer running from n2 to n+1-4k+1. To solve this, we can use the summation formula, Sn = (n/2)(a1 + an).

In this case, a1 = 3(n2+2)2 - 7n2 + 116, and an = 3(n+1-4k+1+2)2 - 7(n+1-4k+1) + 116.

Substituting these values into the summation formula gives us: Sn = (n/2)[3(n2+2)2 - 7n2 + 116 + 3(n+1-4k+1+2)2 - 7(n+1-4k+1) + 116]

We can simplify this further to obtain the result: Sn = 3n3+36n2-72n-24k2+128k+276

This is the result for the sum of the given expression. In order to justify each step, it is important to note that we used the summation formula, which can be derived from the definition of the sum. By substituting the values of the first and last terms of the sequence, we obtained the final result.

To know more about summation refer here:

https://brainly.com/question/30858408

#SPJ11

Answer:

The ratio of the circumference to the diameter is equal to pi

Step-by-step explanation:

For circles

C = pi d   ( The circumference is equal to  the diameter times pi)

Divide each side by d

C / d = pi   The ratio of the circumference to the diameter is equal to pi

Answer:

The ratio of the circumference to the diameter is equal to pi

180° rotation rule  (x, y) → (–x, –y)..

Triangle XYZ is rotated to create the image triangle X'Y'Z'. On a coordinate plane, 2 triangles are shown.

The first triangle has points X (-5, 3), Y (-2, 3), Z (2, 1).

The second triangle has points X prime (5, - 1), Y prime (5, - 4), Z prime

(3, - 4).

Here the sign of both coordinates has been changed but the magnitude remains same.

So, the rule is  (x, y) → (–x, –y)  which is for 180° rotation.

Hence, the  180° rotation rule  (x, y) → (–x, –y).

Learn more about Triangle at:

https://brainly.com/question/16304905

#SPJ4

To find the extraneous solutions of an equation, you need to solve a related equation that is obtained by reversing the operation that was applied to the original equation.

An equation is a statement that asserts the equality of two expressions. In an equation, the expressions on both sides of the equals sign (=) represent the same value, so they must be equivalent.

Extraneous solutions are solutions of an equation that are obtained when a mathematical operation (such as taking the square root or the logarithm) is applied to both sides of the equation and then the equation is solved for the variable, but the operation introduces new solutions that are not actually solutions of the original equation.

To learn more about Extraneous solutions visit:

https://brainly.com/question/28362830

#SPJ4

Answer:

The answer is b

Step-by-step explanation:

The distance traveled by the passenger train and the cattle train is equal to the total distance between them, which is 960 miles. Let x be the time (in hours) traveled by the passenger train and cattle train. Then, the equation that represents this situation is:

55x + 65x = 960

Simplifying the left-hand side of the equation, we get:

120x = 960

Dividing both sides by 120, we get:

x = 8

Therefore, the correct equation is:

B - 65x - 55x = 960

Answer: linear combo of terms involving x & y, with respective numbers determining their contribution to the expression

Answer:

1/5

Step-by-step explanation:

Answer: B. \(x^{2} - 16x + 64 = -21 + 64\)

Step-by-step explanation:

Answer:

reflection

transition left / right are the location of the vertex