What is an equation of the line that passes through the points (-4, -1)and (3, -8)
Put your answer in fully reduced form.

Domain and Range of the given rational functions are:Given rational function f(x) = 3/(x-1)The denominator of f(x) cannot be zero.x ≠ 1 Therefore the domain of f(x) is {x | x ≠ 1}

The range of f(x) is all real numbers except zero.Given rational function f(x) = (2x)/(x-4)The denominator of f(x) cannot be zero.x ≠ 4 Therefore the domain of f(x) is {x | x ≠ 4}The range of f(x) is all real numbers except zero.Given rational function f(x) = (x+3)/(5x-5)The denominator of f(x) cannot be zero.5x - 5 ≠ 0x ≠ 1 Therefore the domain of f(x) is {x | x ≠ 1}The range of f(x) is all real numbers except 1/5.Given rational function f(x) = (2+x)/(2x)The denominator of f(x) cannot be zero.x ≠ 0 Therefore the domain of f(x) is {x | x ≠ 0}The range of f(x) is all real numbers except zero.Given rational function f(x) = (x^2+4x+3)/(x^2-9)For the denominator of f(x) to exist,x ≠ 3, -3

Therefore the domain of f(x) is {x | x ≠ 3, x ≠ -3}The range of f(x) is all real numbers except 1, -1. Function Domain Rangef(x) = 3/(x-1) {x | x ≠ 1} All real numbers except zerof(x) = (2x)/(x-4) {x | x ≠ 4} All real numbers except zerof(x) = (x+3)/(5x-5) {x | x ≠ 1} All real numbers except 1/5f(x) = (2+x)/(2x) {x | x ≠ 0} All real numbers except zerof(x) = (x^2+4x+3)/(x^2-9) {x | x ≠ 3, x ≠ -3} All real numbers except 1, -1

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The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

The given sequence is -4, 16, -64, 256,...

If we observe the sequence it is a geometric sequence

aₙ=a.rⁿ⁻¹

a is the first term and r is the common ratio

From the sequence the first term is -4 and common ratio is -4

aₙ=(-4).(-4)ⁿ⁻¹

Plug in the value n as 8

a₈=(-4).(-4)⁷

The value of minus four power seven is minus sixteen thousand three hundred eighty four

a₈=(-4)(-16384)

When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six

a₈= 65536

Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

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The inequality to represent the last statement that was made by Mai will be t <= 2.

It should be noted that an equation simply means the relationship that can be used to show the relationship among the variables.

It should be noted that the last statement made by Mai is that I think triathlon athletes generally train for no more than 2 hours a day.

Therefore, the inequality to represent this will be t <= 2.

where t = number of hours trained.

This implies that t is less than or equal to 2 hours

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Mai said, "I'm not sure the graph is right. For example, the point is in the shaded region, but it's not realistic for an athlete to swim for 10 hours and bike for 3 hours in a training session! I think triathlon athletes generally train for no more than 2 hours a day."

Write an inequality to represent Mai's last statement.

Answer:

b-15=16

31

Step-by-step explanation:

Because if your sister is 16 and your brother is that age minus 15 that is her sister's age which means      his age (variable); minus how much older: equals her age

a)

i. The probability of choosing a red marble is 10/18 or approximately 0.5556.

ii. The probability of the outcome of the die being less than 3, given that a red marble is chosen, is 3/10 or 0.3.

iii. The probability of choosing a red or green marble is 6/18 or approximately 0.3333.

b)

i. The probability of both marbles being red, with replacement, is (3/18) * (3/18) = 1/36 or approximately 0.0278.

ii. The probability of both marbles being red, without replacement, is (3/18) * (2/17) = 1/51 or approximately 0.0196.

a)

i. To find the probability of choosing a red marble, we consider the total number of red marbles (6) divided by the total number of marbles (18), which gives us 10/18 or approximately 0.5556.

ii. Given that a red marble is chosen, we only need to consider the marbles in urn A. The probability of getting a red marble from urn A is 3/10 or 0.3.

iii. To find the probability of choosing a red or green marble, we consider the total number of red and green marbles (6) divided by the total number of marbles (18), which gives us 6/18 or approximately 0.3333.

b)

i. With replacement means that after each marble is drawn, it is put back into the urn. Therefore, the probability of both marbles being red is calculated by multiplying the probability of selecting a red marble (3/18) for the first draw by the probability of selecting a red marble (3/18) again for the second draw. This gives us a probability of 1/36 or approximately 0.0278.

ii. Without replacement means that after each marble is drawn, it is not put back into the urn. In this case, the probability of both marbles being red is calculated by multiplying the probability of selecting a red marble (3/18) for the first draw by the probability of selecting another red marble (2/17) from the reduced number of marbles in the urn. This gives us a probability of 1/51 or approximately 0.0196.

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Answer:

Kami sold 28 large figurines

Step-by-step explanation:

L = number of large figurines

S = number of small figurines

L+S = 70   since he sold 70 figurines

12L  = 8S  since the amount  of money  collected for the large figurines is equal to the amount of money for the small figurines

L+S = 70  

12L  = 8S

Divide by 8

12/8 L = S    

3/2 L = S

Substitute this into the first equation

L+S = 70

L + 3/2 L = 70

Get a common denominator

2/2 L + 3/2L = 70

5/2 L = 70

Multiply each side by 2/5

2/5 * 5/2 L = 70 * 2/5

L = 28

Kami sold 28 large figurines

Answer:

22

Step-by-step explanation:

Answer:

-11

Step-by-step explanation:

Add all the negative numbers.

Hope this helps!

Answer:

-11

Step-by-step explanation:

-3 + -1 = -4

-4 + -5 = -9

-9 + -2 = -11

§(*￣▽￣*)§

I tried and good luck xx

Answer:

To find the perimeter of a rectangle, add the lengths of the rectangle's four sides. If you have only the width and the height, then you can easily find all four sides (two sides are each equal to the height and the other two sides are equal to the width). Multiply both the height and width by two and add the results.

Answer:

The area is 18.83 meters². The perimeter is 17.76 meters.

Step-by-step explanation:

To find the area you need to multiply the width and the length. So you need to use the equation \(5.38*3.5\). That equals 18.83. That is the area.

To find the perimeter you need to add \(5.38+5.38+3.5+3.5\). You need to use this equation because there are 4 sides; 2 lengths and 2 widths. This adds up to 17.76

Answer: 68 seconds

Step-by-step explanation:

Answer: 68sec

Step-by-step explanation:

Answer:

Step-by-step explanation:

easy y is 120

Answer:

1020 students

Step-by-step explanation:

We have the equation y = 0.1x + 18

If we have a school of 120 staff members, we can just set y = 120 and solve for the predicted total number of students, x.

120 = 0.1x +18

0.1x = 102

x = 1020 students

Answer:

5.3

Step-by-step explanation:

For functions (a) to (f): (a), (b), (c), and (d) have x as O(g(x)), while (e) does not and (f) does because of their limit.

a) Yes, x is O(g(x)) where g(x) = x^2 because the limit of x/g(x) as x approaches infinity is a finite constant.

b) Yes, x is O(g(x)) where g(x) = x^3 because the limit of x/g(x) as x approaches infinity is a finite constant.

c) Yes, x is O(g(x)) where g(x) = x^2 + x^3 because the limit of x/g(x) as x approaches infinity is a finite constant.

d) Yes, x is O(g(x)) where g(x) = x^2 + x^4 because the limit of x/g(x) as x approaches infinity is a finite constant.

e) No, x is not O(g(x)) where g(x) = 3 because the limit of x/g(x) as x approaches infinity is not a finite constant.

f) Yes, x is O(g(x)) where g(x) = x^(3/2) because the limit of x/g(x) as x approaches infinity is a finite constant.

In each case, we determine whether x is O(g(x)) by taking the limit of x/g(x) as x approaches infinity. If the limit is a finite constant, then x is O(g(x)). If the limit is infinity or undefined, then x is not O(g(x)).

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patternpatternGreat!

The patteren is 1, 4, 9, 16,...

All these numbers are square numbers, which means

1 * 1 = 1

2 * 2 = 4

3 * 3 = 9

4 * 4 = 16

That means

1st term = 1^2

2nd term = 2^2

3rd term = 3^2

4th term = 4^2

so

nth term = n^2

The conjecture is

The pattern is 100%, 93%, 86%, ...........

Since 93% - 100% = -7%

Since 86% - 93% = -7%

Then this pattern is decreases by 7%

So it is an arithmetic sequence

Its rule is:

Where a is the first term

d is the constant difference

n is the position of the number

Since a = 100%

Since d = -7%

Let us substitute these values in the rule

Simplify it

an = 100% + (n)(-7%) + (-1)(-7%)

an = 100% + (-7n%) + (7%)

Add the like terms

an = (100% + 7%) - 7n%

an = 107% - 7n%

Let us check the rule

What is the 3rd term

n = 3

a3 = 107% - 7(3)%

a3 = 107% - 21%

a3 = 86% which is true

Answer:

x = -2 u got this

Step-by-step explanation:

-7x = 4x + 22

-11x = 22

x = -2

Easy bro

The process of simplify the equation is explained below.

The term equation is known as a mathematical statement that defines the equality between two expressions.

Here we have to define the process of simplifying the equation.

The first and foremost step is to remove parentheses and brackets by multiplying factors.

And then we have to use the exponent rule to remove grouping if the terms contain exponents.

Then we have to combine like terms by adding or subtracting coefficients.

Finally, we have to Combine the constants.

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The tax due for a single taxpayer by virtue of the tax rate for single filers; 22% as required in the task content is; 14,459.5.

It follows from the task content that the taxable income of the single taxpayer as discussed in the task content is; 65,725.

Since, the tax rate which is alloted to such individual single filers is; 22%.

It simply follows that the tax due on the individual can be determined as follows;

Tax due = 22% of 65, 725

= (22/100) × 65,725

= 14,459.5

Ultimately, the tax due for a single taxpayer by virtue of the tax rate for single filers; 22% as required in the task content is; 14,459.5.

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The missing values in the triangle are:

∠B = 90°

AB =  20.98

CB = 16.99

First, remember that the sum of the interior angles of any triangle is always equal to 180°, then we can write:

51 + 39 + ∠B = 180

∠B = 180 - 51 - 39 = 90

So we have a right triangle.

Now, to find the values of AB and CB, we can use trigonometric relations, we know that teh hypotenuse is 27 units, then we can use:

cos(51°) = CB/27

27*cos(51°) = CB = 16.99

And:

cos(39°) = AB/27

27*cos(39°) = AB = 20.98

These are the missing values.

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Answer:

370 hours.

Step-by-step explanation:

Divide $5,180/14 to get your answer of the hours she worked.

Answer:

370 hours is how many she worked

14×370= 5,180

hope this helps

The indicated maximum or minimum value of f is subject to the given constraint maximum is 125/27.

An instance of a constraint is the fact that there are only such a lot of hours in a day to perform things. Embarrassed reserve or reticence; awkwardness. One that restricts, limits, or regulates; a take a look at.

A constraint is something that limits or controls what you can do. Their decision to abandon the trip was made due to monetary constraints. Water shortages in the location can be the primary constraint on development.  Synonyms: restriction, issue, lessen, rein greater Synonyms of constraint.

Constraints are used to limit the kind of records which can move right into a desk. This guarantees the accuracy and reliability of the facts inside the table. If there's any violation between the constraint and the facts motion, the motion is aborted. Constraints can be column stage or desk level.

From &22 = x²y 2

2

Given 2²+7+2=5

= <**,4),2=>

By Logange's multijet

(2643805 = 12'aresta

Mithaling by by and

and y

x²²* = P ←

: +(1,2,2) = $

= 125

279

The maximum value is 12r

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The median exceeds the mean by more. The histogram is skewed to the right, which shows that lower values are dragging down the mean.

The median of the histogram on the right is higher than the mean. This is evident from the histogram's form, which is tilted to the right. This shows that the lower values tend to drag the mean down. The median is greater than the mean. The right-handed skewness of the histogram indicates that the mean is being pulled down by lesser values and However, because it is the centre number and is only impacted by the higher and lower values equally, the median is unaffected by the lower values. Because of this, the mean in this histogram is less than the median.

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The general solution in both vector and scalar form is as follows:

Vector form:

\(\[\mathbf{x} = c_1\mathbf{v}_1e^{\lambda_1t} + c_2\mathbf{v}_2e^{\lambda_2t}\]\)

Scalar form:

\(\[\begin{aligned}x &= c_1v_{11}e^{\lambda_1t} + c_2v_{21}e^{\lambda_2t} \\y &= c_1v_{12}e^{\lambda_1t} + c_2v_{22}e^{\lambda_2t}\end{aligned}\]\)

What are eigenvalues?

Eigenvalues are a concept in linear algebra that are used to analyze the properties of linear transformations or matrices. In simple terms, eigenvalues represent the scaling factors by which a vector is stretched or compressed when it is transformed by a linear transformation or multiplied by a matrix.

To find the general solution for the given system of differential equations:

\(\[\begin{aligned}x' &= -6x + 5y \\y' &= -5x - 4y\end{aligned}\]\)

We can rewrite the system in matrix form as follows:

\(\[\mathbf{x'} = \begin{bmatrix} -6 & 5 \\ -5 & -4 \end{bmatrix} \mathbf{x}\]\)

where \($\mathbf{x} = \begin{bmatrix} x \\ y \end{bmatrix}$.\)

To find the general solution, we need to find the eigenvalues and eigenvectors of the coefficient matrix\($\begin{bmatrix} -6 & 5 \\ -5 & -4 \end{bmatrix}$.\)

The characteristic equation is given by:

\(\[\det(\mathbf{A} - \lambda \mathbf{I}) = 0\]\)

where \($\mathbf{A}$\) is the coefficient matrix,\($\lambda$\)is the eigenvalue, and \($\mathbf{I}$\)is the identity matrix.

Substituting the values, we have:

\(\[\begin{aligned}\det \begin{pmatrix} -6-\lambda & 5 \\ -5 & -4-\lambda \end{pmatrix} &= 0 \\(-6-\lambda)(-4-\lambda) - (5)(-5) &= 0 \\\lambda^2 + 10\lambda + 6 &= 0\end{aligned}\]\)

Solving this quadratic equation, we find the eigenvalues \(\lambda_1$ and $\lambda_2$.\left \{ {{y=2} \atop {x=2}} \right.\)

Once we have the eigenvalues, we can find the corresponding eigenvectors\($\mathbf{v}_1$ and $\mathbf{v}_2$\) by solving the equation:

\(\[(\mathbf{A}-\lambda\mathbf{I})\mathbf{v} = 0\]\)

Substituting the eigenvalues, we solve for the eigenvectors.

Let's denote the eigenvalues as \(\lambda_1$ and $\lambda_2$,\) and the corresponding eigenvectors as \(\mathbf{v}_1$ and $\mathbf{v}_2$.\)

Once we have the eigenvalues and eigenvectors, we can express the general solution in both vector and scalar form as follows:

Vector form:

\(\[\mathbf{x} = c_1\mathbf{v}_1e^{\lambda_1t} + c_2\mathbf{v}_2e^{\lambda_2t}\]\)

Scalar form:

\(\[\begin{aligned}x &= c_1v_{11}e^{\lambda_1t} + c_2v_{21}e^{\lambda_2t} \\y &= c_1v_{12}e^{\lambda_1t} + c_2v_{22}e^{\lambda_2t}\end{aligned}\]\)

wherec_1 andc_2 are arbitrary constants\(, $v_{ij}$\) that represent the \(i$-th\)component of the jth eigenvector and \($e^{\lambda_it}$\) represent the exponential term with the eigenvalue.

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Answer:

Answer  for the first question is D

Step-by-step explanation:

^^^^^

Using the simplex method, the maximum value of Z=5A+4B is found to be 19.2 when A=3.6 and B=1.2. The calculations can be confirmed by using any software that solves linear programming problems.

To solve the given linear programming problem using the simplex method, we start by converting the problem into standard form. We introduce slack variables to convert the inequalities into equations.The initial tableau is as follows:

      | A | B | S1 | S2 | S3 | S4 |   RHS

------------------------------------------

 Z    | -5 | -4 | 0  | 0  | 0  | 0  |    0

------------------------------------------

 S1   |  6 |  4 | 1  | 0  | 0  | 0  |   24

 S2   |  1 |  2 | 0  | 1  | 0  | 0  |    6

 S3   | -1 |  1 | 0  | 0  | 1  | 0  |    1

 S4   |  0 |  1 | 0  | 0  | 0  | 1  |    2

We perform the simplex iterations until the optimal solution is reached. After applying the simplex method, the final tableau is obtained as follows:

      |  A  |  B  |  S1  |  S2  |  S3  |  S4  |   RHS

------------------------------------------------------

 Z    |  0  | 1.8 | 0.2  | -1   | -0.4 |  0.4 | 19.2

------------------------------------------------------

 S1   |  0  |  0  |  0   | 1.5  | -1   |  1   |  3

 S2   |  1  |  0  | -0.5 |  0.5 |  0.5 | -0.5 | 1.5

 A    |  1  |  0  | 0.5  | -0.5 | -0.5 |  0.5 |  0.5

 S4   |  0  |  0  |  1   | -1   | -1   |  1   |  1

From the final tableau, we can see that the maximum value of Z is 19.2 when A=3.6 and B=1.2. This solution satisfies all the constraints of the problem. The calculations can be verified using any software that solves linear programming problems, which should yield the same optimal solution.

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Answer:

227222685 i cant tell if u want me to multiply them all or solve for X

Step-by-step explanation:

The answer is 227,222,685

y = x + 1

y = 2x +8

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be 0 or 1 for each of its variables. In this case, the degree of variable y is 1 and the degree of variable x is 1.

The standred form is Ax + By = C. So y = 2x + 8 and y = x + 1 is a linear equation because the degree of a linear equation must be 0 or 1 for each of its variables.

The measure of angle CKB (m ∠CKB) is 144°

From the question, we are to determine the measure of angle CKB (m ∠CKB)

First, we will determine the value of x

From the given information,

m ∠KAE = 3x

m ∠KCD = 2x

In the diagram,

m ∠KCD = m ∠AKE (Alternate angles)

∴ m ∠AKE = 2x

Also,

m ∠KAE + m ∠AKE + m ∠AEK = 180° (Sum of angles in a triangle)

3x + 2x + 90° = 180°

5x = 180° - 90°

5x = 90°

x = 90°/5

x = 18°

But,

m ∠CKB = 180° - m ∠AKE (Sum of angles on a line segment)

m ∠CKB = 180° - 2x

m ∠CKB = 180° - 2(18°)

m ∠CKB = 180° - 36°

m ∠CKB = 144°

Hence, the measure of angle CKB (m ∠CKB) is 144°

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