Write an equation for a rational function with: vertical asymptotes at x = -4 and x = 4 x-intercepts at x = -6 and x = 5 horizontal asymptote at y = 8

The solution to a system of inequalities y ≥ x – 5 and y < –x + 4 is the region where these two inequalities intersect on the graph. This region is below the line y = -x + 4, and also above or on the line y = x - 5.

The subject of your concern lies in the field of Mathematics, more specifically, in the topic related to graphical representation of systems of inequalities. To find which graph represents the solution to the system of inequalities y ≥ x – 5 and y < –x + 4, you need to plot both inequalities on the same graph.

For the inequality y ≥ x – 5, plot a line with a slope of 1 and a y-intercept of -5. This line will slope upwards, to reflect that y is greater than or equal to x - 5. For the inequality y < –x + 4, plot a line with slope of -1 and a y-intercept of 4, which will slope downwards as y is lesser than -x + 4.

The region where both these inequalities intersect would be the solution to the system of inequalities. This region would be below the line y = -x + 4, but also above and on the line y = x - 5.

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A graph that represents the solution to the system of inequalities y ≥ x – 5 and y < –x + 4 is shown in the image below.

In Mathematics, there are several rules that are generally used for writing and interpreting an inequality or system of inequalities that are plotted on a graph and these include the following:

In this context, we can logically deduce that the graph of this linear inequality, y ≥ x – 5 would be a solid line and shaded above while the graph of this linear inequality, y < –x + 4 would be a dashed line and shaded below.

In conclusion, a possible solution is (2, 1).

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Missing Information

The question is incomplete. Hence, a general answer was provided.

If there was a piece of rope from the top of the building to Joel, how long would it be approx 222.01 feet. The angle of elevation from Joel to the top of the building is approx [tex]31.18 ^ \circ[/tex]

You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.

Similarly, there is angle of depression, when you look horizontal, then down, the angle between both positions is the angle of depression.

Remember that we assume that buildings are usually vertical to the ground. This means, there is 90° formation. The length of the rope can be taken as length of hypotenuse.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

Referring to the figure attached below, we get:
Length of the rope = Length of the line segment AC = |AC|

Using the fact that the triangle ABC is right angled triangle, we can use Pythagoras theorem.

We get the length of AC as:

[tex]|AC|^2 = |AB|^2 + |BC|^2\\|AC| = \sqrt{|AB|^2 + |BC|^2} \\\text{positive square root since length is non-negative quantity}\\\\|AC| = \sqrt{115^2 + 190^2} = \sqrt{51325} \approx 222.01 \: \rm ft[/tex]

Thus, if there was a piece of rope from the top of the building to Joel, how long would it be approx 222.01 feet.

The angle of elevation is calculated as:

[tex]\tan(\angle ABC) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}} = \dfrac{|AB|}{|BC|}\\\theta = tan^{-1}(\dfrac{115}{190}) \approx 31.18^\circ[/tex]

The angle of depression is actually equal to angle of depression because they are pair of alternate interior angles (made by traversing line AC between two parallel lines).

Thus, Margaret statement is false.

Therefore, we get the answers as:

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The factor of quadratic function 2x²-2x-40 is 2 (x-5) (x+4).

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

Given:

The quadratic function 2x²-2x-40.

To find the factors;

Take common term out,

2(x²-x-20)

= 2 (x²-5x + 4x -20)

= 2 {x (x-5) + 4(x -5)}

= 2 (x-5) (x+4)

Therefore, the factors are 2 (x-5) (x+4).

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Final answer:

The equation of the line in slope-intercept form, given the points (-2, 8) and (1, 2), is y = -2x + 4, which is option D.

Explanation:

The question asks for the equation of a line in slope-intercept form given two points on the line (-2, 8) and (1, 2). To find the equation, we first calculate the slope (m) which is the change in y-values divided by the change in x-values. Using the given points,

m = (2 - 8) / (1 - (-2))

= -6 / 3

= -2.

With the slope known, we use one point to solve for the y-intercept (b) in the equation,

y = mx + b.

Let's use the point (1, 2):

2 = (-2)(1) + b, which simplifies to,

2 = -2 + b, so,

b = 4. Therefore, the equation in slope-intercept form is y = -2x + 4, which corresponds to option D.

Answer:

Given the system of equations, what is the value of the system determinant?  x + y = 8  

x - y = 10  

C. -2

Given the system of equations, what is the value of the y-determinant?

3x + y - 10 = 0

4x - y - 4 = 0

A. -28

Step-by-step explanation:

The determinant of the system is the determinant of the matrix formed with the coefficients of the system, usually, this matrix is called A.

[tex]A=\left[\begin{array}{cc}1&1\\1&-1\end{array}\right][/tex]

In the 2x2 matrix, the determinant is calculated by obtaining the difference between the diagonally down product and the diagonally up product.

[tex]det(A)=\left|\begin{array}{cc}1&1\\1&-1\end{array}\right|=(1)(-1)-(1)(1)=-1-1=-2[/tex]

The y-determinant is the determinant of the matrix [tex]A_y[/tex], this matrix is formed substituting in the matrix A the coefficients of y with the constant terms.

[tex]A_y=\left[\begin{array}{cc}3&10\\4&4\end{array}\right][/tex]

[tex]det(A_y)=\left|\begin{array}{cc}3&10\\4&4\end{array}\right|=(3)(4)-(4)(10)=12-40=-28[/tex]

To find the smallest possible ages for Jose and Robert, set up a system of equations based on the given information. Robert's age is X, and Jose's age is 3X. The sum of their ages is more than 40, so the smallest possible age for Robert is 11, and Jose would be three times that, which is 33.

To find the smallest possible ages for Jose and Robert, we need to set up a system of equations based on the given information.

Let's assume Robert's age is x. Since Jose is three times as old as Robert, his age would be 3x.

The sum of their ages is more than 40, so we can write the equation: x + 3x > 40.

Simplifying the equation: 4x > 40.

Dividing both sides of the equation by 4, we get x > 10.

Therefore, the smallest possible age for Robert is 11, and Jose would be three times that, which is 33.

Answer: the 3 one is the answer

Answer:

fourth degree trinomial

Step-by-step explanation:

Answer: its horizontal

Answer:

It's all below...

Step-by-step explanation:

Part 1.

quadratic poynomial function:   f(x)=x2−5x+6

linear binomial:   x−2

x−3x−2x2−5x+6x2−2x−−−−−−−−−−3x+6−3x+6−−−−−−−−0

Part 2.  

f(2)=22−5(2)+6=4−10+6=−6+6=0

Part 3.  

The remainder theorem says that if f(x) is divided by x-a, then f(a) will be the remainder. When we divided f(x) by x - 2 , we got a remainder of 0, which by the remainder theorem implies f(2) = 0.  That means x-2 is a factor of f(x).

see attached sketch with the coordinates the line passes

 the picture is upside down for some reason, rotate it 180 degrees

To simplify 2^4\*2^7, you add the exponents because the bases are the same, resulting in 2^11 which equals 2048.

When simplifying the expression 2^4\*2^7, we use the property of exponents that states when multiplying two exponential terms with the same base, you add the exponents. So, the simplified form of the expression would be 2^(4+7) which is 2^11. Since we are adding the exponents, this process is known as the sum of exponents and is a fundamental concept in the squaring of exponentials.

To calculate 2^11, you would multiply 2 by itself 11 times, but for the sake of simplicity, the answer is 2048.

The algebraic multiplicity of an eigenvalue equals the geometric multiplicity when the corresponding eigenspace is sufficiently spanned by independent vectors, usually implying that the matrix or linear transformation is diagonalizable.

In cases of linear algebra, the algebraic multiplicity of an eigenvalue equals the geometric multiplicity when the respective eigenvector space is completely spanned by independent vectors. Nevertheless, the algebraic multiplicity of an eigenvalue is always greater than or equal to the geometric multiplicity. The situation where algebraic multiplicity is equal to geometric multiplicity generally signifies that the linear transformation or matrix is diagonalizable.

To clarify, the algebraic multiplicity of an eigenvalue is the number of times it appears as a root of the characteristic polynomial, and the geometric multiplicity is the dimension of the corresponding eigenspace. When these two quantities are equal, it often leads to a simpler set of calculations in practical applications of linear algebra.

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