What is the y-intercept of the following equation?
- 3y + x = 18
(12 points)

9514 1404 393

Answer:

  (c)  5x and 3x, and 4 and 1

Step-by-step explanation:

Like terms have the same variable(s) to the same power(s).

The terms of this expression are ...

The like terms are {5x, -3x}, which have the x-variable to the first power, and {4, -1}, which have no variable.

a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:

\(x' = Ax\)

where x is a vector and A is a square matrix.

b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.

If all eigenvalues have negative real parts, the system is stable.

If at least one eigenvalue has a zero real part, the system is neutrally stable.

If at least one eigenvalue has a positive real part, the system is unstable.

c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation

\(det(A - \lambda I) = 0\),

where λ is the eigenvalue and I is the identity matrix.

By solving this equation, we obtain the eigenvalues.

Substituting each eigenvalue into the equation

\((A - \lambda I)v = 0\),

where v is the eigenvector, we can solve for the eigenvectors.

d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:

\(A = PDP^{(-1)}\)

where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.

To show that this relationship is valid, we can compute \(PDP^{(-1)}\) and verify that it equals A.

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The dot plot that displays the data distribution is the dot plot on the lower left corner of the options with

Two dots at 0

One dot at 2

Two dots at 3

Four dots each at 4, 5, and 6

One dot at 7

A dot plot is a graphical presentation of data, on a number line, with the number of points of dot representing the frequency of data at each value on the number line.

The data can be presented as follows;

2, 6, 4, 3, 0, 3, 4, 6, 5, 0, 4, 5, 7, 5, 6, 4, 5, 6

The above data can be arranged in increasing order as follows; 0, 0, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7
Therefore, the frequencies of 0s is two, the frequencies of 4s, 5s and 6s are four each, and the frequency of 7 is one, which corresponds to the third graph or the graph in the bottom left corner of the figure.

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(i)  \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = -1

(iii) h(0) = 1/7

The value of λ must be 7, for h(x) to be continuous at x = 0.

The given function is,

h(x) = 1/7, when x = 0

      = 1 - 2 cos 2x, when x < π/2

      = 1 + 2 cos 2x, when x > π/2

      = x cos x/sin λx, when x < 0

Now,

(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^-}{2}}\) (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^+}{2}}\) (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1

(iii) h(0) = 1/7

Since the function is continuous at x = 0, so

\(\lim_{x \to 0}\) h(x) = h(0)

\(\lim_{x \to 0}\) x cos x/sin λx = 1/7

\(\lim_{x \to 0}\) cos x.\(\lim_{x \to 0}\) 1/λ(sinλx/λx) = 1/7

1/λ = 1/7

λ = 7

Hence the value of λ must be 7.

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Answer:

the answer is essentially d

In the provided text is a questionnaire or form related to a research tool for assessing a campaign in the community.

The first question asks whether the campaign pursues its aims, with the options of answering "YES" or "NO." The respondent is then instructed to elaborate on their answer.

A questionnaire is a research tool   used to collect data by presenting a series of questions to respondents,typically in a written format.

Questionnaires are an important research tool as they allow researchers to gather   large amounts of data from a large number of participants in   a standardized and efficient manner.

They provide a structured approach to collecting information,allowing for easy analysis and comparison   of responses.

Questionnaires can be used in various   research settings and are particularly useful for collecting quantitative data,measuring attitudes, opinions, behaviors, and gathering demographic information.

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The Equivalent ratio to 8/2 is 4/1, 24/6, 32/8 and 48/12.

We have,

Cylinder and prism.

Here we have to find the equivalent ratio to 8/2.

First simplifying the given ratio as

8/2

= (4 x 2)/2

= 4 /1

Now, some more ratios equivalent to 8/2.

1. 8/2 x 3/3 = 24/ 6

2. 8/2 x 4/4 = 32/8

3. 8/2 x 6/6= 48/12

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Answer:

4x+7=3x+7

Step-by-step explanation:

-3(2x-5)=15-6x is infinite solution

top left is x=-3

top right is x=5 5x

Answer:

Area of annulus is 40.85cm² to 2d.p

Step-by-step explanation:

Area of shaded part=Area of bigger circle -Area of smaler circle

Area of annulus= πR²- πr²= π(R²-r²)

A=3.142(7²-6²)

A=3.142(49-36)

A=3.142×13

A=40.846cm²

A=40.85cm² to 2d.p

Answer:100

Step-by-step explanation:

40+40 =80 +20=100

Answer:

34 and 17 feet.

Step-by-step explanation:

We have that the volume is given by:

V = x * x * y = (x ^ 2) * y

The surface area of the tank would be: x ^ 2 + x * y + x * y + x * y + x * y

SA = x ^ 2 + 4 * x * y

we know that the volume is 19652, replacing it would remain:

 19652 = (x ^ 2) * y, we solve for y:

y = 19652 / (x ^ 2)

replacing in SA we are left with:

SA = x ^ 2 + 4 * x * 19652 / (x ^ 2)

SA = x ^ 2 + 70608 / x

we derive and equal 0:

SA´ (x) = 2 * x - 70608 / (x ^ 2) = 0

2 * x = 70608 / (x ^ 2)

x ^ 3 = 39304

x = 34

for and would be:

y = 19652 / (34 ^ 2) = 17

dimensions are 34 and 17 feet.

Solution:

√y - ⁴√y - 6 = 0

(⁴√y)² - ⁴√y - 6 = 0

u² - u - 6 = 0

u = 3 and u = -2

⁴√y = 3

y = 81

⁴√y = -2

y ∈ R

Answer: y = 81

Best of Luck!

Answer:

The value of y is 81.

Step-by-step explanation:

See the steps below :

\( \sqrt{y} - \sqrt[4]{y} - 6 = 0\)

\( {y}^{ \frac{1}{2} } - {y}^{ \frac{1}{4} } - 6 = 0\)

\(let \: {y}^{ \frac{1}{4} } = x\)

\( {x}^{2} - x - 6 = 0\)

\((x + 2)(x - 3) = 0\)

\(x = - 2\)

\( {y}^{ \frac{1}{4} } = - 2\)

\( log( {y}^{ \frac{1}{4} } ) = log( - 2) \: (rejected)\)

\(x = 3\)

\( {y}^{ \frac{1}{4} } = 3\)

\( log( {y}^{ \frac{1}{4} } ) = log(3) \)

\( \frac{1}{4} log(y) = log(3) \)

\( log(y) = 4 log(3) \)

\( log(y) = log( {3}^{4} ) \)

\( log(y) = log(81) \)

\(y = 81\)

Answer:

-3,694

I am not sure what in the world the rest means, so I am very sorry. I just subtracted some stuff. I have no clue if that helped...

The difference between ¼ of 5.00 and 37/½% of 1.50 is 0.6875 because 1/4 of 5.00 is 1.25 and 37.5% of 1.50 is 0.5625.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have:

\(\rm \dfrac{1}{4} \ \ of \ 5.00\)

\(\rm = \dfrac{1}{4}\times 5.00\)

= 1.25

\(\rm 37 \dfrac{1}{2} \% \ of \ 1.50\)

= 37.5% of 1.50

= 0.5625

Difference between the numbers:

= 1.25 - 0.5625

= 0.6875

Thus, the difference between ¼ of 5.00 and 37/½% of 1.50 is 0.6875 because 1/4 of 5.00 is 1.25 and 37.5% of 1.50 is 0.5625.

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Answer: The correct option is the third one; y=10(0.13)^x

Answer:

$375 375

Step-by-step explanation:

1250 x 7.5% =93.75

93.75 x 4 =

Answer:

A weak positive correlation or A

Step-by-step explanation:

Answer: a

Step-by-step explanation: right on edge

Answer:

D) 6

Step-by-step explanation:

Given: 6x-3>21

Fill in 6: 6(6)-3>21

Multiply: 36-3>21

Conclusion: 33>21

The point at (60, 55) represents an item with an original price of $60 that is now being sold at a sale price of $55.

There are many tools we can use to find the information of the relation which was used to form the graph.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.

If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

We are given that;

The point at (60, 55)

Now,

This means that customers who enter the special discount code can save $5 on this particular item.

In general, the point (x, y) on the graph represents an item with an original price of x dollars that is being sold at a sale price of y dollars. The graph is showing how the sale price of items changes as the original price increases.

Therefore, by the graph the answer will be $60 and $55.

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Answer:

B

Step-by-step explanation:

30

Step-by-step explanation:

did it

Answer:

exact form: x=20/9

decimal Form: x=2.222...

Step-by-step explanation:

The value of x in 1st equation is x ≤ 3 i.e.  x ∈ (-infinity,3] and the value of x in 2nd equation is x > 18 i.e.  x ∈ (18,infinity)

Given two equations  1)6x-10<8 and 2) \(\frac{x}{3}\)+6 > 12

Solving the above equations

1) 6x-10≤8

⇒6x ≤ 18

⇒X≤ 3

⇒x ≤ 3 i.e.  x ∈ (-infinity,3]

2)\(\frac{x}{3}\)+6 > 12

⇒\(\frac{x}{3}\) > 6

⇒x>18

⇒ x > 18 i.e.  x ∈ (18,infinity)

Therefore,The value of x in 1st equation is x ≤ 3 i.e.  x ∈ (-infinity,3] and the value of x in 2nd equation is x > 18 i.e.  x ∈ (18,infinity)

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Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

Ten rugby balls are randomly selected from the production line to see if their shape is correct. Over time, the company has found that 89.4% of all their rugby balls have the correct shape. If exactly 6 of the 10 have the right shape, should the company stop the production line?

1)Yes as the probability of six having the correct shape is not unusual

2)NO. as the probability of six having the correct shape is unusual

3)Yes as the probability of six having the correct shape is unusual

4) No. as the probability of six having the correct shape is not unusual

Solution:

If exactly 6 of the 10 have the right shape, it means that the probability of success for the sample is

6/10 = 0.6

Expressing the probability in terms if percentage, it becomes

0.6 × 100 = 60%

Over time, the company has found that 89.4% of all their rugby balls have the correct shape. It means that the probability of success for the population is 89.4%

Comparing both probabilities, the probability of only 6 having the right shape is unusual. Therefore, the correct option is

3)Yes as the probability of six having the correct shape is unusual

Answer:5.666666667

Step-by-step explanation:

Answer:

400 litres

Step-by-step explanation:

To determine the amount that will be on the account after 4 years you have to apply the given exponential function that models the amount of money on the account with respect to the time.

Where

a represents the initial amount

r represents the interest rate expressed as a decimal value

t is the time period in years

The initial amount on the account is a= $600

The time period is t= 4 years

The interest rate is r=5%, divide it by 100 to express it as a decimal value:

Using this information, you can calculate the final amount:

After 4 years there will be $732.84 on the account. The correct option is B.

Answer:

Y = -½x + 3/2

Y = -3x + 5

Y = 1/4x - 3¼

Step-by-step explanation:

Parallel implies they have the same gradient

Perpendicular implies the gradient is a negative reciprocal of the other.

The coordinates of point B are (-3, 17).

The given equation is M = I₁ + I₂ = 31 + 32.

Now let's substitute in our given values:

(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)

We will now set up two equations to solve for our two unknowns, x₂ and y₂:

Equation 1: (-5 + x₂) / 2 = -4

Multiply both sides by 2:

-5 + x₂ = -8

Add 5 to both sides:

x₂ = -3

This gives us the x-coordinate of point B.

Equation 2: (-5 + 2 + y₂) / 2 = 7

Simplify:

(-3 + y₂) / 2 = 7

Multiply both sides by 2:

-3 + y₂ = 14

Add 3 to both sides:

y₂ = 17

This gives us the y-coordinate of point B.

Therefore, the coordinates of point B are (-3, 17).

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