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3 years ago

Y=1/2x-1

Mathematics

1 answer:

Alinara [238K]3 years ago

8 0

Answer:

Find where the expression

1/2x−1 is undefined.

x=1/2

Consider the rational function

R(x)=ax^n/bx^m where n is the degree of the numerator and m is the degree of the denominator.

1. If n<m, then the x-axis, y=0, is the horizontal asymptote.

2. If n=m, then the horizontal asymptote is the line y = ab.

3. If n>m, then there is no horizontal asymptote (there is an oblique asymptote).

Find n and m.n=0m=1

Since n<m, the x-axis, y=0, is the horizontal asymptote.y=0

There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.

No Oblique Asymptotes

This is the set of all asymptotes.

Vertical Asymptotes:

x=1/2

Horizontal Asymptotes:

y=0

No Oblique Asymptotes

Subtract 2x from both sides of the equation.

y=4−2x

Rewrite in slope-intercept form.

The slope-intercept form is

y=mx+b, where m is the slope and b is the y-intercept.

y=mx+b

Reorder 4 and −2x.

y=−2x+4

Use the slope-intercept form to find the slope and y-intercept.

Find the values of m and b using the form

y=mx+b.

m= - 2b=4

The slope of the line is the value of m, and the y-intercept is the value of b.

Slope: −2

y-intercept: (0,4)

Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y

values.

Find the x-intercept.

x-intercept(s):

(2,0)

Find the y-intercept.

y-intercept(s):

(0,4)

Create a table of the x and y values.

x y

0 4

2 0

Graph the line using the slope and the y-intercept, or the points.

Slope: −2

y-intercept:

(0,4)

Step-by-step explanation:

Hope it is helpful...

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Answer:

reflection across BC
the image of a vertex will coincide with its corresponding vertex
SSS: AB≅GB, AC≅GC, BC≅BC.

Step-by-step explanation:

We want to identify a rigid transformation that maps congruent triangles to one-another, to explain the coincidence of corresponding parts, and to identify the theorems that show congruence.

Triangles GBC and ABC share side BC. Whatever rigid transformation we use will leave segment BC invariant. Translation and rotation do not do that. The only possible transformation that will leave BC invariant is <em>reflection across line BC</em>.

In part 3, we show ∆GBC ≅ ∆ABC. That means vertices A and G are corresponding vertices. When we map the congruent figures onto each other, <em>corresponding parts are coincident</em>. That is, vertex G' (the image of vertex G) will coincide with vertex A.

The markings on the figure show the corresponding parts to be ...

side AB and side GB
side AC and side GC
angle ABC and angle GBC
angle BAC and angle BGC

And the reflexive property of congruence tells us BC corresponds to itself:

side BC and side BC

There are four available congruence theorems applicable to triangles that are not right triangles

SSS -- three pairs of corresponding sides
SAS -- two corresponding sides and the angle between
ASA -- two corresponding angles and the side between
AAS -- two corresponding angles and the side not between

We don't know which of these are in your notes, but we do know that all of them can be used. AAS can be used with two different sides. SAS can be used with two different angles.

SSS

Corresponding sides are listed above. Here, we list them again:

AB and GB; AC and GC; BC and BC

SAS

One use is with AB, BC, and angle ABC corresponding to GB, BC, and angle GBC.

Another use is with BA, AC, and angle BAC corresponding to BG, GC, and angle BGC.

ASA

Angles CAB and CBA, side AB corresponding to angles CGB and CBG, side GB.

AAS

One use is with angles CBA and CAB, side CB corresponding to angles CBG and CGB, side CB.

Another use is with angles CBA and CAB, side CA corresponding to angles CBG and CGB, side CG.

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2 years ago

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Mamont248 [21]

Answer:

x = ± ∜175 = ± 3.6371

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

x^4-(175)=0

Step by step solution :

STEP

Trying to factor as a Difference of Squares:

1.1 Factoring: x4-175

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 175 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Polynomial Roots Calculator :

1.2 Find roots (zeroes) of : F(x) = x4-175

Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers. The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 1 and the Trailing Constant is -175.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1 ,5 ,7 ,25 ,35 ,175

Let us test ....

P Q P/Q F(P/Q) Divisor

-1 1 -1.00 -174.00

-5 1 -5.00 450.00

-7 1 -7.00 2226.00

-25 1 -25.00 390450.00

-35 1 -35.00 1500450.00

-175 1 -175.00 937890450.00

1 1 1.00 -174.00

5 1 5.00 450.00

7 1 7.00 2226.00

25 1 25.00 390450.00

35 1 35.00 1500450.00

175 1 175.00 937890450.00

Polynomial Roots Calculator found no rational roots

Equation at the end of step

x4 - 175 = 0

STEP

Solving a Single Variable Equation:

2.1 Solve : x4-175 = 0

Add 175 to both sides of the equation :

x4 = 175

x = ∜ 175

The equation has two real solutions

These solutions are x = ± ∜175 = ± 3.6371

Two solutions were found :

x = ± ∜175 = ± 3.6371

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