Use the given points of line a and line b to determine whether the lines intersect, are parallel, or coincide.Line a: (1,5) and (4,14) line b: (-2,5) and (6,-27)

The solution by substituting 15 for b in the Original equation. The answer is true.

The steps needed to solve the equation b + 6 = 21 are:

Subtract 6 from both sides of the equation: b + 6 - 6 = 21 - 6, which simplifies to b = 15.

Check the solution by substituting 15 for b in the original equation: 15 + 6 = 21, which is true.

Therefore, the correct steps to solve the equation are:

Subtract 6 from both sides of the equation. The answer is b = 15

the solution by substituting 15 for b in the original equation. The answer is true.

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Answer:

Not a triangle.

Criteria for it to be a triangle:

3 = A

6 = B

2 = C

A + B > C

B + C > A

A + C > B

What this says, is that if you add any two sides of the triangle, it needs to be bigger than the one you left out.

3 + 6 > 2 This one works

6 + 2 > 3 This one works

3 + 2 > 6 This one doesn't work because 5 is less than 6

Since the last one didn't work, it's not a triangle.

Answer:

Could you please question correctly??

Step-by-step explanation:

Total Students:450

Oranges:250

Apples:280

Dislike:40

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Answer

i dont see the question sorry

Therefore , the solution to the given problem of function comes out to be slant asymptotes are y = x -4.

Numbers and their variants, equations & related structures, and geometry and their regions and potential applications are all mathematical topics. The link between a group of input, each of which generates a related output, is referred to as a "function." A function is a relationship between outputs and inputs where each input results in a single, distinct output. Each procedure has a domain and a city / municipality, which are frequently referred to as a scope. Functions are usually represented by the letter f. (x). The input is X. On activity, one-to-one activities, many-to-one activities, throughout operations, as well as on functions are the four main categories of supplied functions.

Here,

There are no limitations on the type of rational function, therefore it is feasible to construct one with each of the three asymptotes.

This is depicted in the attached graph, along with the graph of the rational function it represents. These are the asymptotes of the function.

Vertical asymptotes are x = -4,

horizontal asymptotes are y = 0 and

slant asymptotes are y = x -4.

Additional remarks

We employ an exponential function in our example function. Although it can be expressed as a polynomial of infinite degree, that is not often regarded as a polynomial. The proportion of polynomials is how most authors describe a rational function.

Therefore , the solution to the given problem of function comes out to be slant asymptotes are y = x -4.

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Answer:

57

Step-by-step explanation:

this is the boybfiend

Answer:

There is 5% of the juice left.

Step-by-step explanation:

We know that originally, the container had 80 oz of orange juice, this is 100% in our case.

Then we can write a relation:

80 oz = 100%

Now there are 4 ounces left, in the same way as before, we can write this as:

4 oz = X%

We want to find X%

First, let's write our equations:

4 oz = X%

80 oz = 100%

We can take the quotient between these two equations to get:

(4oz/80oz) = (X%/100%)

We need to solve this for X%, then we get:

(4oz/80oz)*100% = X% = 5%

This means that 4 oz is 5% of the initial volume of the juice container.

Then we can conclude that there is 5% of the juice left.

Answer:

B. -15

Step-by-step explanation:

Took the test, this question was correct when you choose -15.

Answer:

b

Step-by-step explanation:

Cooper ran 286 miles in 21 weeks.

After answering the presented question, we can conclude that This is equation true for all values of a and (11n+3), so we can conclude that the value of "a" is simply 30.8 divided by (11n+3): a = 30.8/(11n+3)

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

We are given that the factored form of 30.8n+8.4 is a(11n+3).

To find the value of a, we can expand the product a(11n+3) and equate it to the given expression 30.8n+8.4.

Expanding a(11n+3), we get:

a(11n+3) = 11an + 3a

Equating this to 30.8n+8.4, we have:

11an + 3a = 30.8n + 8.4

We can factor out an "a" from the left-hand side:

a(11n + 3) = 30.8n + 8.4

Now we can see that this is the same as the given factored form, so we can equate the two expressions:

a(11n + 3) = a(11n + 3)

This is true for all values of a and (11n+3), so we can conclude that the value of "a" is simply 30.8 divided by (11n+3):

a = 30.8/(11n+3)

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Answer:

-7 = x +6

Step-by-step explanation:

Answer:

Step-by-step explanation:si

Think of the letter as four vectors starting from the center and pointing outward. label the four vectors starting from the top left and proceeding clockwise as outward does point in or out of the page and the point inward of the page.

In physics, vectors are often used to describe the motion and forces acting on objects. However, vectors can also be used to represent other things, such as points in space or even letters of the alphabet.

When we think of a letter as four vectors starting from the center and pointing outward, we can imagine each vector as an arrow that extends from the center of the letter to its edge. If we label the four vectors starting from the top left and proceeding clockwise as "A," "B," "C," and "D," we can determine whether the letter points in or out of the page by analyzing the direction of each vector.

In mathematical terms, we can represent each vector as a set of coordinates (x, y) that describe its direction and magnitude. We can then use cross products and dot products to determine the orientation of the letter in three-dimensional space.

These operations involve multiplying vectors together and analyzing the resulting scalar values, which tell us whether the vectors are parallel or perpendicular to each other.

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The triangles are similar and

Yes , ΔPSQ ≅ ΔRST because ∠S ≅ ∠S and PS / RS = QS / TS . Thus the triangles are similar by the SAS theorem

Given data ,

Let the first triangle be ΔPSQ

Let the second triangle be ΔRST

Now , the corresponding sides are

PS / RS = QS / TS

where the corresponding sides of similar triangles are in the same ratio

And , the common angle to both the triangles is m∠S

So , ∠S ≅ ∠S and PS / RS = QS / TS

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

Hence , the triangles are similar

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Answer:

Formula for Geometric Mean is given by,. ⇒ Geometric ... Thanks!!!! 6 21 __ = __ х 31.5 a. X = 4 b. X = 9 C. X = 110.25.

The quotient for the division of given decimal numbers is 62.

Given that, 142.6 divided by 2.3.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Here, 142.6 divided by 2.3 \(=\frac{142.6}{2.3}\)

\(=62\)

Therefore, the quotient for the division of given decimal numbers is 62.

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The required angle is 24.5°.

Given is a right triangle with perpendicular side 16 and the base = 35 we need to find an acute angle in it,

To find the acute angle in a right triangle given the lengths of the perpendicular side and the base, you can use the tangent function.

The tangent of an angle is defined as the ratio of the length of the perpendicular side to the length of the base side.

In this case, the perpendicular side is 16 and the base is 35.

Let's denote the acute angle as θ.

Using the tangent function, we can set up the equation:

tan(θ) = perpendicular side / base

tan(θ) = 16 / 35

To find the value of θ, we can take the inverse tangent of both sides:

θ = tan⁻¹(16 / 35)

θ = 24.5°

Hence the required angle is 24.5°.

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Answer:

C. 4

Step-by-step explanation:

Use the slope formula:

\(m=\frac{y2}{x2} -\frac{y1}{x1}\)

m = the slope.

Substitute the values into the formula:

\(\frac{9}{3} -\frac{-7}{-1} =\frac{?}{?}\)

Solve:

\(\frac{9}{3} -\frac{-7}{-1} =\frac{16}{4}\)

Simplify 16/4:

\(\frac{16/4}{4/4} =\frac{4}{1}=4\)

The correct statement regarding the translation in this problem is given as follows:

A. The graph of f(x) is shifted three units down from the graph of g(x).

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

In the context of this problem, we have that 3 is subtracted on the definition of the function, hence it is translated down 3 units.

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Answer:

Degree of polynomial → 4

Step-by-step explanation:

Conjugate roots theorem states that if a polynomial has a root (a + ib), then (a - ib) will be the other root.

In this question it has been given that a polynomial function has the zeros (roots) as x = \(\sqrt{3}\), 4i and -2.

Therefore, the given polynomial will have four roots, \(\sqrt{3}\), 4i, -4i and -2.

Function will be f(x) = (x - \(\sqrt{3}\))(x + 4i)(x - 4i)(x + 2)

Degree of the polynomial → 4

The tangent line to the graph of f(x) = 2e²ˣ-5 at the point (2, 1/e) is given by y=2e⁴+1-2e⁵/e

Two or more expressions with an Equal sign is called as Equation.

The equation of the tangent line to the graph of f(x) = e²ˣ-5

To find the Equation of a tangent to any curve you must first find the derivative of the function.

y = e²ˣ-5

y'=2e²ˣ

sub x=2 into derivative function

y'(2)=2e⁴

so we have found that the tangent line is y=2e⁴+c

now we have to sub in the point and solve for c:

1/e=2e⁴+c

c=1/e-2e⁴

c=1-2e⁵/e

c=0 when x is 2.

The equation of tangent to the line is y=2e⁴+(1-2e⁵)/e

Hence,  the equation of the tangent line to the graph of f(x) = 2e²ˣ-5 at the point (2, 1/e) is given by y=2e⁴+1-2e⁵/e

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From the resulting solution, the correct linear inequality graph is Graph C.

Given the inequality equation below:

2(2x-1)+7< 13 or -2x+5 ≤ -10.​

Simplify the expression

2(2x-1)+7< 13

Expand

4x - 2 + 7 < 13

4x + 5 < 13

4x < 13 - 5

4x < 8

x < 2

For the inequality -2x+5 ≤ -10.

-2x+5 ≤ -10

-2x  ≤ -15

x  ≥ 7.5

Hence the solution to the given system of inequalities are x < 2 and x  ≥ 7.5

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The set of prime numbers greater than 11 with the cardinality of 5 is {13, 17, 19, 23, 29}

From the question, we have the following parametes that can be used in our computation:

Set = prime numbers

Cardinality = 5

The cardinality implies that the number of elements in the set is 5

5 prime numbers greater than 11 are 13, 17, 19, 23, 29

Hence, the set is {13, 17, 19, 23, 29}

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Answer:

u = 8 ; v = 7

Step-by-step explanation:

5u = u + 32

5u - u = 32

4u = 32

4/4 u = 32/4

u = 8

v + 7 = 2v

2v - v = 7

v = 7

Answer:

Step-by-step explanation:

The general solution to the differential equation y'' + 2y = −18x^2e^(2x) by undetermined coefficients is y = (-9x^2)e^(2x).

The given differential equation is y'' + 2y = −18x^2e^(2x)

To solve this equation by undetermined coefficients, we first find the characteristic equation of the homogeneous equation, which is r^2 + 2 = 0.

The solutions to this equation are r = i and r = -i. Therefore the general solution to the homogeneous equation is yh(x) = c1 cos(x) + c2 sin(x)

Now, we use the method of undetermined coefficients to guess the form of the particular solution. Since the non-homogeneous term is −18x^2e^(2x), we guess that the particular solution is of the form

yp = (Ax^3 + Bx^2)e^(2x) + Cx^2e^(2x).

Substituting this into the differential equation, we get

y'' + 2y = (6Ax + 2B)e^(2x) + 2Cxe^(2x) = −18x^2e^(2x)

Equating the coefficients of the like terms, we get:

6A = 0, 2B = −18, and 2C = 0

Solving for A, B and C, we get A = 0, B = −9 and C = 0

Therefore, the general solution to the differential equation y'' + 2y = −18x^2e^(2x) by undetermined coefficients is y = (Ax^3 + Bx^2)e^(2x) + Cx^2e^(2x) = (-9x^2)e^(2x)

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An equation for the function graphed above include the following: g(x) = -1/4|x + 1| - 2.

By critically observing the graph of this absolute value function, we can reasonably infer and logically deduce that the parent absolute value function f(x) = |x| was vertically compressed by a factor of 1/4, reflected over the x-axis, followed by a vertical translation 2 units down, and then a horizontal translation to the left by 1 unit, in order to produce the transformed absolute value function as follows;

f(x) = |x|

y = A|x + B| + C

g(x) = -1/4|x + 1| - 2

In conclusion, the value of the variables A, B, and C are -1/4, 1, and 2 respectively.

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Answer:

E

Step-by-step explanation:

ab is sometimes rational

The relation that can not be supported by the evidence in the image is option B

Corresponding angles are those that are located on the same side of the transversal and in identical relative positions to the parallel lines. Angles that correspond to one another have the same measure.

Alternate interior angles are those that are located on the transverse and within the area between the parallel lines, respectively. Congruent alternate interior angles exist.

Alternate external angles are those that are outside of the space between the parallel lines and on the opposing sides of the transversal. Congruent external angles exist between the two.

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Answer:

log_{b} (5b) = 2.609

Given that:

log_{b} (3) = 1.099

log_{b} (5) = 1.609

Evaluating with that:

\(\sf log_b (5b) = log_b\left(5\right)+log_b\left(b\right)\)

            \(= \sf 1.609 + 1\)

             \(= \sf 2.609\)

Rule Used:

\(\rm \log _a\left(xy\right)=\log _a\left(x\right)+\log _a\left(y\right)\)